Datasets:

h4iku

/

coconut_c2005

like 1

*F = RgX_to_FpX(*F, p);

*F = FpX_normalize(RgX_to_FpX(*F, p), p);

factmod_init(GEN *F, GEN p){ long d; if (typ(*F)!=t_POL || typ(p)!=t_INT) err(typeer,"factmod"); *F = RgX_to_FpX(*F, p); d = degpol(*F); if (d < 0) err(zeropoler,"factmod"); return d;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/0653bf4e80ffba66b9dad8b9b9bf38de88f14841/polarit1.c/clean/src/basemath/polarit1.c

autvec_TH(int pk, GEN z, GEN v, GEN C)

autvec_TH(long pk, GEN z, GEN v, GEN C)

autvec_TH(int pk, GEN z, GEN v, GEN C){ int i, lv = lg(v); GEN s = polun[varn(C)]; for (i=1; i<lv; i++) { long y = v[i]; if (y) s = RgXQ_mul(s, RgXQ_u_pow(aut(pk,z, y), y, C), C); } return s;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/b03001ef86c74799b6280212f7a40aee0823ed89/aprcl.c/clean/src/modules/aprcl.c

int i, lv = lg(v);

long i, lv = lg(v);

autvec_TH(int pk, GEN z, GEN v, GEN C){ int i, lv = lg(v); GEN s = polun[varn(C)]; for (i=1; i<lv; i++) { long y = v[i]; if (y) s = RgXQ_mul(s, RgXQ_u_pow(aut(pk,z, y), y, C), C); } return s;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/b03001ef86c74799b6280212f7a40aee0823ed89/aprcl.c/clean/src/modules/aprcl.c

rtems_libio_fcntl_flags(unsigned32 fcntl_flags)

unsigned32 rtems_libio_fcntl_flags( unsigned32 fcntl_flags )

rtems_libio_fcntl_flags(unsigned32 fcntl_flags){ unsigned32 flags = 0; unsigned32 access_modes; /* * Access mode is a small integer */ access_modes = fcntl_flags & O_ACCMODE; fcntl_flags &= ~O_ACCMODE; flags = rtems_assoc_local_by_remote(access_modes_assoc, access_modes); /* * Everything else is single bits */ flags |= rtems_assoc_local_by_remote_bitfield(status_flags_assoc, fcntl_flags); return flags;}

10355 /local/tlutelli/issta_data/temp/c/2005_temp/2005/10355/07a3253de2c3f9bc2d96a351680ec72548dadd2d/libio.c/clean/c/src/lib/libc/libio.c

unsigned32 flags = 0; unsigned32 access_modes;

unsigned32 flags = 0; unsigned32 access_modes;

rtems_libio_fcntl_flags(unsigned32 fcntl_flags){ unsigned32 flags = 0; unsigned32 access_modes; /* * Access mode is a small integer */ access_modes = fcntl_flags & O_ACCMODE; fcntl_flags &= ~O_ACCMODE; flags = rtems_assoc_local_by_remote(access_modes_assoc, access_modes); /* * Everything else is single bits */ flags |= rtems_assoc_local_by_remote_bitfield(status_flags_assoc, fcntl_flags); return flags;}

10355 /local/tlutelli/issta_data/temp/c/2005_temp/2005/10355/07a3253de2c3f9bc2d96a351680ec72548dadd2d/libio.c/clean/c/src/lib/libc/libio.c

/* * Access mode is a small integer */ access_modes = fcntl_flags & O_ACCMODE; fcntl_flags &= ~O_ACCMODE; flags = rtems_assoc_local_by_remote(access_modes_assoc, access_modes);

/* * Access mode is a small integer */ access_modes = fcntl_flags & O_ACCMODE; fcntl_flags &= ~O_ACCMODE; flags = rtems_assoc_local_by_remote( access_modes_assoc, access_modes );

rtems_libio_fcntl_flags(unsigned32 fcntl_flags){ unsigned32 flags = 0; unsigned32 access_modes; /* * Access mode is a small integer */ access_modes = fcntl_flags & O_ACCMODE; fcntl_flags &= ~O_ACCMODE; flags = rtems_assoc_local_by_remote(access_modes_assoc, access_modes); /* * Everything else is single bits */ flags |= rtems_assoc_local_by_remote_bitfield(status_flags_assoc, fcntl_flags); return flags;}

10355 /local/tlutelli/issta_data/temp/c/2005_temp/2005/10355/07a3253de2c3f9bc2d96a351680ec72548dadd2d/libio.c/clean/c/src/lib/libc/libio.c

/* * Everything else is single bits */

/* * Everything else is single bits */

rtems_libio_fcntl_flags(unsigned32 fcntl_flags){ unsigned32 flags = 0; unsigned32 access_modes; /* * Access mode is a small integer */ access_modes = fcntl_flags & O_ACCMODE; fcntl_flags &= ~O_ACCMODE; flags = rtems_assoc_local_by_remote(access_modes_assoc, access_modes); /* * Everything else is single bits */ flags |= rtems_assoc_local_by_remote_bitfield(status_flags_assoc, fcntl_flags); return flags;}

10355 /local/tlutelli/issta_data/temp/c/2005_temp/2005/10355/07a3253de2c3f9bc2d96a351680ec72548dadd2d/libio.c/clean/c/src/lib/libc/libio.c

flags |= rtems_assoc_local_by_remote_bitfield(status_flags_assoc, fcntl_flags); return flags;

flags |= rtems_assoc_local_by_remote_bitfield(status_flags_assoc, fcntl_flags); return flags;

rtems_libio_fcntl_flags(unsigned32 fcntl_flags){ unsigned32 flags = 0; unsigned32 access_modes; /* * Access mode is a small integer */ access_modes = fcntl_flags & O_ACCMODE; fcntl_flags &= ~O_ACCMODE; flags = rtems_assoc_local_by_remote(access_modes_assoc, access_modes); /* * Everything else is single bits */ flags |= rtems_assoc_local_by_remote_bitfield(status_flags_assoc, fcntl_flags); return flags;}

10355 /local/tlutelli/issta_data/temp/c/2005_temp/2005/10355/07a3253de2c3f9bc2d96a351680ec72548dadd2d/libio.c/clean/c/src/lib/libc/libio.c

rtems_libio_allocate(void)

rtems_libio_t *rtems_libio_allocate( void )

rtems_libio_allocate(void){ rtems_libio_t *iop; rtems_status_code rc; rtems_semaphore_obtain(rtems_libio_semaphore, RTEMS_WAIT, RTEMS_NO_TIMEOUT); for (iop = rtems_libio_iops; iop <= rtems_libio_last_iop; iop++) if ((iop->flags & LIBIO_FLAGS_OPEN) == 0) { /* * Got one; create a semaphore for it */ rc = rtems_semaphore_create( RTEMS_LIBIO_IOP_SEM(iop - rtems_libio_iops), 1, RTEMS_BINARY_SEMAPHORE | RTEMS_INHERIT_PRIORITY | RTEMS_PRIORITY, RTEMS_NO_PRIORITY, &iop->sem ); if (rc != RTEMS_SUCCESSFUL) goto failed; iop->flags = LIBIO_FLAGS_OPEN; goto done; } failed: iop = 0; done: rtems_semaphore_release(rtems_libio_semaphore); return iop;}

10355 /local/tlutelli/issta_data/temp/c/2005_temp/2005/10355/07a3253de2c3f9bc2d96a351680ec72548dadd2d/libio.c/clean/c/src/lib/libc/libio.c

rtems_libio_t *iop; rtems_status_code rc;

rtems_libio_t *iop; rtems_status_code rc; rtems_semaphore_obtain( rtems_libio_semaphore, RTEMS_WAIT, RTEMS_NO_TIMEOUT ); for (iop = rtems_libio_iops; iop <= rtems_libio_last_iop; iop++) if ((iop->flags & LIBIO_FLAGS_OPEN) == 0) { /* * Got an IOP -- create a semaphore for it. */ rc = rtems_semaphore_create( RTEMS_LIBIO_IOP_SEM(iop - rtems_libio_iops), 1, RTEMS_BINARY_SEMAPHORE | RTEMS_INHERIT_PRIORITY | RTEMS_PRIORITY, RTEMS_NO_PRIORITY, &iop->sem ); if ( rc != RTEMS_SUCCESSFUL ) goto failed;

rtems_libio_allocate(void){ rtems_libio_t *iop; rtems_status_code rc; rtems_semaphore_obtain(rtems_libio_semaphore, RTEMS_WAIT, RTEMS_NO_TIMEOUT); for (iop = rtems_libio_iops; iop <= rtems_libio_last_iop; iop++) if ((iop->flags & LIBIO_FLAGS_OPEN) == 0) { /* * Got one; create a semaphore for it */ rc = rtems_semaphore_create( RTEMS_LIBIO_IOP_SEM(iop - rtems_libio_iops), 1, RTEMS_BINARY_SEMAPHORE | RTEMS_INHERIT_PRIORITY | RTEMS_PRIORITY, RTEMS_NO_PRIORITY, &iop->sem ); if (rc != RTEMS_SUCCESSFUL) goto failed; iop->flags = LIBIO_FLAGS_OPEN; goto done; } failed: iop = 0; done: rtems_semaphore_release(rtems_libio_semaphore); return iop;}

10355 /local/tlutelli/issta_data/temp/c/2005_temp/2005/10355/07a3253de2c3f9bc2d96a351680ec72548dadd2d/libio.c/clean/c/src/lib/libc/libio.c

rtems_semaphore_obtain(rtems_libio_semaphore, RTEMS_WAIT, RTEMS_NO_TIMEOUT); for (iop = rtems_libio_iops; iop <= rtems_libio_last_iop; iop++) if ((iop->flags & LIBIO_FLAGS_OPEN) == 0) { /* * Got one; create a semaphore for it */ rc = rtems_semaphore_create( RTEMS_LIBIO_IOP_SEM(iop - rtems_libio_iops), 1, RTEMS_BINARY_SEMAPHORE | RTEMS_INHERIT_PRIORITY | RTEMS_PRIORITY, RTEMS_NO_PRIORITY, &iop->sem ); if (rc != RTEMS_SUCCESSFUL) goto failed; iop->flags = LIBIO_FLAGS_OPEN; goto done; }

iop->flags = LIBIO_FLAGS_OPEN; goto done; }

rtems_libio_allocate(void){ rtems_libio_t *iop; rtems_status_code rc; rtems_semaphore_obtain(rtems_libio_semaphore, RTEMS_WAIT, RTEMS_NO_TIMEOUT); for (iop = rtems_libio_iops; iop <= rtems_libio_last_iop; iop++) if ((iop->flags & LIBIO_FLAGS_OPEN) == 0) { /* * Got one; create a semaphore for it */ rc = rtems_semaphore_create( RTEMS_LIBIO_IOP_SEM(iop - rtems_libio_iops), 1, RTEMS_BINARY_SEMAPHORE | RTEMS_INHERIT_PRIORITY | RTEMS_PRIORITY, RTEMS_NO_PRIORITY, &iop->sem ); if (rc != RTEMS_SUCCESSFUL) goto failed; iop->flags = LIBIO_FLAGS_OPEN; goto done; } failed: iop = 0; done: rtems_semaphore_release(rtems_libio_semaphore); return iop;}

10355 /local/tlutelli/issta_data/temp/c/2005_temp/2005/10355/07a3253de2c3f9bc2d96a351680ec72548dadd2d/libio.c/clean/c/src/lib/libc/libio.c

iop = 0;

iop = 0;

rtems_libio_allocate(void){ rtems_libio_t *iop; rtems_status_code rc; rtems_semaphore_obtain(rtems_libio_semaphore, RTEMS_WAIT, RTEMS_NO_TIMEOUT); for (iop = rtems_libio_iops; iop <= rtems_libio_last_iop; iop++) if ((iop->flags & LIBIO_FLAGS_OPEN) == 0) { /* * Got one; create a semaphore for it */ rc = rtems_semaphore_create( RTEMS_LIBIO_IOP_SEM(iop - rtems_libio_iops), 1, RTEMS_BINARY_SEMAPHORE | RTEMS_INHERIT_PRIORITY | RTEMS_PRIORITY, RTEMS_NO_PRIORITY, &iop->sem ); if (rc != RTEMS_SUCCESSFUL) goto failed; iop->flags = LIBIO_FLAGS_OPEN; goto done; } failed: iop = 0; done: rtems_semaphore_release(rtems_libio_semaphore); return iop;}

10355 /local/tlutelli/issta_data/temp/c/2005_temp/2005/10355/07a3253de2c3f9bc2d96a351680ec72548dadd2d/libio.c/clean/c/src/lib/libc/libio.c

rtems_semaphore_release(rtems_libio_semaphore); return iop;

rtems_semaphore_release( rtems_libio_semaphore ); return iop;

rtems_libio_allocate(void){ rtems_libio_t *iop; rtems_status_code rc; rtems_semaphore_obtain(rtems_libio_semaphore, RTEMS_WAIT, RTEMS_NO_TIMEOUT); for (iop = rtems_libio_iops; iop <= rtems_libio_last_iop; iop++) if ((iop->flags & LIBIO_FLAGS_OPEN) == 0) { /* * Got one; create a semaphore for it */ rc = rtems_semaphore_create( RTEMS_LIBIO_IOP_SEM(iop - rtems_libio_iops), 1, RTEMS_BINARY_SEMAPHORE | RTEMS_INHERIT_PRIORITY | RTEMS_PRIORITY, RTEMS_NO_PRIORITY, &iop->sem ); if (rc != RTEMS_SUCCESSFUL) goto failed; iop->flags = LIBIO_FLAGS_OPEN; goto done; } failed: iop = 0; done: rtems_semaphore_release(rtems_libio_semaphore); return iop;}

10355 /local/tlutelli/issta_data/temp/c/2005_temp/2005/10355/07a3253de2c3f9bc2d96a351680ec72548dadd2d/libio.c/clean/c/src/lib/libc/libio.c

rtems_libio_free(rtems_libio_t *iop)

void rtems_libio_free( rtems_libio_t *iop )

rtems_libio_free(rtems_libio_t *iop){ rtems_semaphore_obtain(rtems_libio_semaphore, RTEMS_WAIT, RTEMS_NO_TIMEOUT); if (iop->sem) rtems_semaphore_delete(iop->sem); (void) memset(iop, 0, sizeof(*iop)); rtems_semaphore_release(rtems_libio_semaphore);}

10355 /local/tlutelli/issta_data/temp/c/2005_temp/2005/10355/07a3253de2c3f9bc2d96a351680ec72548dadd2d/libio.c/clean/c/src/lib/libc/libio.c

rtems_semaphore_obtain(rtems_libio_semaphore, RTEMS_WAIT, RTEMS_NO_TIMEOUT);

rtems_semaphore_obtain( rtems_libio_semaphore, RTEMS_WAIT, RTEMS_NO_TIMEOUT );

rtems_libio_free(rtems_libio_t *iop){ rtems_semaphore_obtain(rtems_libio_semaphore, RTEMS_WAIT, RTEMS_NO_TIMEOUT); if (iop->sem) rtems_semaphore_delete(iop->sem); (void) memset(iop, 0, sizeof(*iop)); rtems_semaphore_release(rtems_libio_semaphore);}

10355 /local/tlutelli/issta_data/temp/c/2005_temp/2005/10355/07a3253de2c3f9bc2d96a351680ec72548dadd2d/libio.c/clean/c/src/lib/libc/libio.c

if (iop->sem) rtems_semaphore_delete(iop->sem); (void) memset(iop, 0, sizeof(*iop));

if (iop->sem) rtems_semaphore_delete(iop->sem);

rtems_libio_free(rtems_libio_t *iop){ rtems_semaphore_obtain(rtems_libio_semaphore, RTEMS_WAIT, RTEMS_NO_TIMEOUT); if (iop->sem) rtems_semaphore_delete(iop->sem); (void) memset(iop, 0, sizeof(*iop)); rtems_semaphore_release(rtems_libio_semaphore);}

10355 /local/tlutelli/issta_data/temp/c/2005_temp/2005/10355/07a3253de2c3f9bc2d96a351680ec72548dadd2d/libio.c/clean/c/src/lib/libc/libio.c

rtems_semaphore_release(rtems_libio_semaphore);

(void) memset(iop, 0, sizeof(*iop)); rtems_semaphore_release( rtems_libio_semaphore );

rtems_libio_free(rtems_libio_t *iop){ rtems_semaphore_obtain(rtems_libio_semaphore, RTEMS_WAIT, RTEMS_NO_TIMEOUT); if (iop->sem) rtems_semaphore_delete(iop->sem); (void) memset(iop, 0, sizeof(*iop)); rtems_semaphore_release(rtems_libio_semaphore);}

10355 /local/tlutelli/issta_data/temp/c/2005_temp/2005/10355/07a3253de2c3f9bc2d96a351680ec72548dadd2d/libio.c/clean/c/src/lib/libc/libio.c

return (*fp)(fd);

status = (*fp)(fd); rtems_libio_free(iop); return status;

__rtems_close( int fd ) { rtems_status_code rc; rtems_driver_name_t *np; rtems_libio_t *iop; rtems_libio_open_close_args_t args; if (rtems_file_descriptor_type(fd)) { int (*fp)(int fd); fp = handlers[rtems_file_descriptor_type_index(fd)].close; if (fp == NULL) { errno = EBADF; return -1; } return (*fp)(fd); } iop = rtems_libio_iop(fd); rtems_libio_check_fd(fd); np = iop->driver; args.iop = iop; args.flags = 0; args.mode = 0; rc = rtems_io_close(np->major, np->minor, (void *) &args); if (rc != RTEMS_SUCCESSFUL) return rtems_libio_errno(rc); return 0;}

10355 /local/tlutelli/issta_data/temp/c/2005_temp/2005/10355/78d87bd3f3ffbf31c8e3893e1054a3d47a9ee992/libio.c/buggy/cpukit/libcsupport/src/libio.c

rtems_libio_free(iop);

__rtems_close( int fd ) { rtems_status_code rc; rtems_driver_name_t *np; rtems_libio_t *iop; rtems_libio_open_close_args_t args; if (rtems_file_descriptor_type(fd)) { int (*fp)(int fd); fp = handlers[rtems_file_descriptor_type_index(fd)].close; if (fp == NULL) { errno = EBADF; return -1; } return (*fp)(fd); } iop = rtems_libio_iop(fd); rtems_libio_check_fd(fd); np = iop->driver; args.iop = iop; args.flags = 0; args.mode = 0; rc = rtems_io_close(np->major, np->minor, (void *) &args); if (rc != RTEMS_SUCCESSFUL) return rtems_libio_errno(rc); return 0;}

10355 /local/tlutelli/issta_data/temp/c/2005_temp/2005/10355/78d87bd3f3ffbf31c8e3893e1054a3d47a9ee992/libio.c/buggy/cpukit/libcsupport/src/libio.c

rtems_panic_in_progress++; /* disable task switches */ _Thread_Disable_dispatch();

if (rtems_panic_in_progress++) _Thread_Disable_dispatch(); /* disable task switches */

static int rtems_verror( unsigned32 error_flag, const char *printf_format, va_list arglist){ int local_errno = 0; int chars_written = 0; rtems_status_code status; if (error_flag & RTEMS_ERROR_PANIC) { rtems_panic_in_progress++; /* disable task switches */ _Thread_Disable_dispatch(); /* don't aggravate things */ if (rtems_panic_in_progress > 2) return 0; } (void) fflush(stdout); /* in case stdout/stderr same */ status = error_flag & ~RTEMS_ERROR_MASK; if (error_flag & RTEMS_ERROR_ERRNO) /* include errno? */ local_errno = errno; if (_System_state_Is_multiprocessing) fprintf(stderr, "[%d] ", _Configuration_MP_table->node); if (rtems_progname && *rtems_progname) chars_written += fprintf(stderr, "%s: ", rtems_progname); chars_written += vfprintf(stderr, printf_format, arglist); if (status) chars_written += fprintf(stderr, " (status: %s)", rtems_status_text(status)); if (local_errno) { if ((local_errno > 0) && *strerror(local_errno)) chars_written += fprintf(stderr, " (errno: %s)", strerror(local_errno)); else chars_written += fprintf(stderr, " (unknown errno=%d)", local_errno); } chars_written += fprintf(stderr, "\n"); (void) fflush(stderr); if (error_flag & (RTEMS_ERROR_PANIC | RTEMS_ERROR_ABORT)) { if (error_flag & RTEMS_ERROR_PANIC) { rtems_error(0, "fatal error, exiting"); _exit(local_errno); } else { rtems_error(0, "fatal error, aborting"); abort(); } } return chars_written;}

10355 /local/tlutelli/issta_data/temp/c/2005_temp/2005/10355/85734b3c8f00abe81af80bd0a7e00874d6635104/error.c/buggy/c/src/libmisc/error/error.c

struct iovec iov[16]; apr_size_t nvec, nbytes;

struct iovec iov[4]; apr_size_t nbytes;

static void serialize_data(serf_bucket_t *bucket){ request_context_t *ctx = bucket->data; serf_bucket_t *new_bucket; const char *new_data; struct iovec iov[16]; apr_size_t nvec, nbytes; /* Serialize the request-line and headers into one mother string, * and wrap a bucket around it. */ iov[0].iov_base = (char*)ctx->method; iov[0].iov_len = strlen(ctx->method); iov[1].iov_base = " "; iov[1].iov_len = sizeof(" ") - 1; iov[2].iov_base = (char*)ctx->uri; iov[2].iov_len = strlen(ctx->uri); iov[3].iov_base = " HTTP/1.1\r\n"; iov[3].iov_len = sizeof(" HTTP/1.1\r\n") - 1; nvec = 4; if (bucket->metadata) { apr_hash_index_t *hi; apr_pool_t *p; const void *hash_ptr; apr_hash_t *hash; /* Okay, we might have headers. */ serf_bucket_get_metadata(bucket, SERF_REQUEST_HEADERS, 0, &hash_ptr); if (hash_ptr) { hash = (apr_hash_t*)hash_ptr; /* Check to see if we have enough free IO vecs to handle this. */ if ((apr_hash_count(hash) * 3) > 16 - nvec) { /* XXX: Handle me. */ abort(); } p = serf_bucket_allocator_get_pool(bucket->allocator); for (hi = apr_hash_first(p, hash); hi; hi = apr_hash_next(hi)) { const void *key; void *val; apr_ssize_t key_len; apr_hash_this(hi, &key, &key_len, &val); iov[nvec].iov_base = (char*)key; iov[nvec++].iov_len = key_len; iov[nvec].iov_base = ": "; iov[nvec++].iov_len = sizeof(": ") - 1; iov[nvec].iov_base = val; iov[nvec++].iov_len = strlen((char*)val); iov[nvec].iov_base = "\r\n"; iov[nvec++].iov_len = sizeof("\r\n") - 1; } } } iov[nvec].iov_base = "\r\n"; iov[nvec++].iov_len = sizeof("\r\n") - 1; /* ### pool allocation! */ new_data = apr_pstrcatv(serf_bucket_allocator_get_pool(bucket->allocator), iov, nvec, &nbytes); /* Create a new bucket for this string. A free function isn't needed * since the string is residing in a pool. */ new_bucket = SERF_BUCKET_SIMPLE_STRING_LEN(new_data, nbytes, bucket->allocator); /* Build up the new bucket structure. * * Note that self needs to become an aggregate bucket so that a * pointer to self still represents the "right" data. */ serf_bucket_aggregate_become(bucket); /* Insert the two buckets. */ serf_bucket_aggregate_append(bucket, new_bucket); if (ctx->body != NULL) { serf_bucket_aggregate_append(bucket, ctx->body); } /* Our private context is no longer needed, and is not referred to by * any existing bucket. Toss it. */ serf_bucket_mem_free(bucket->allocator, ctx);}

1874 /local/tlutelli/issta_data/temp/c/2005_temp/2005/1874/2ca954891a4128162d15a2813f1ade79299fdbf4/request_buckets.c/buggy/buckets/request_buckets.c

nvec = 4; if (bucket->metadata) { apr_hash_index_t *hi; apr_pool_t *p; const void *hash_ptr; apr_hash_t *hash; /* Okay, we might have headers. */ serf_bucket_get_metadata(bucket, SERF_REQUEST_HEADERS, 0, &hash_ptr); if (hash_ptr) { hash = (apr_hash_t*)hash_ptr; /* Check to see if we have enough free IO vecs to handle this. */ if ((apr_hash_count(hash) * 3) > 16 - nvec) { /* XXX: Handle me. */ abort(); } p = serf_bucket_allocator_get_pool(bucket->allocator); for (hi = apr_hash_first(p, hash); hi; hi = apr_hash_next(hi)) { const void *key; void *val; apr_ssize_t key_len; apr_hash_this(hi, &key, &key_len, &val); iov[nvec].iov_base = (char*)key; iov[nvec++].iov_len = key_len; iov[nvec].iov_base = ": "; iov[nvec++].iov_len = sizeof(": ") - 1; iov[nvec].iov_base = val; iov[nvec++].iov_len = strlen((char*)val); iov[nvec].iov_base = "\r\n"; iov[nvec++].iov_len = sizeof("\r\n") - 1; } } } iov[nvec].iov_base = "\r\n"; iov[nvec++].iov_len = sizeof("\r\n") - 1;

static void serialize_data(serf_bucket_t *bucket){ request_context_t *ctx = bucket->data; serf_bucket_t *new_bucket; const char *new_data; struct iovec iov[16]; apr_size_t nvec, nbytes; /* Serialize the request-line and headers into one mother string, * and wrap a bucket around it. */ iov[0].iov_base = (char*)ctx->method; iov[0].iov_len = strlen(ctx->method); iov[1].iov_base = " "; iov[1].iov_len = sizeof(" ") - 1; iov[2].iov_base = (char*)ctx->uri; iov[2].iov_len = strlen(ctx->uri); iov[3].iov_base = " HTTP/1.1\r\n"; iov[3].iov_len = sizeof(" HTTP/1.1\r\n") - 1; nvec = 4; if (bucket->metadata) { apr_hash_index_t *hi; apr_pool_t *p; const void *hash_ptr; apr_hash_t *hash; /* Okay, we might have headers. */ serf_bucket_get_metadata(bucket, SERF_REQUEST_HEADERS, 0, &hash_ptr); if (hash_ptr) { hash = (apr_hash_t*)hash_ptr; /* Check to see if we have enough free IO vecs to handle this. */ if ((apr_hash_count(hash) * 3) > 16 - nvec) { /* XXX: Handle me. */ abort(); } p = serf_bucket_allocator_get_pool(bucket->allocator); for (hi = apr_hash_first(p, hash); hi; hi = apr_hash_next(hi)) { const void *key; void *val; apr_ssize_t key_len; apr_hash_this(hi, &key, &key_len, &val); iov[nvec].iov_base = (char*)key; iov[nvec++].iov_len = key_len; iov[nvec].iov_base = ": "; iov[nvec++].iov_len = sizeof(": ") - 1; iov[nvec].iov_base = val; iov[nvec++].iov_len = strlen((char*)val); iov[nvec].iov_base = "\r\n"; iov[nvec++].iov_len = sizeof("\r\n") - 1; } } } iov[nvec].iov_base = "\r\n"; iov[nvec++].iov_len = sizeof("\r\n") - 1; /* ### pool allocation! */ new_data = apr_pstrcatv(serf_bucket_allocator_get_pool(bucket->allocator), iov, nvec, &nbytes); /* Create a new bucket for this string. A free function isn't needed * since the string is residing in a pool. */ new_bucket = SERF_BUCKET_SIMPLE_STRING_LEN(new_data, nbytes, bucket->allocator); /* Build up the new bucket structure. * * Note that self needs to become an aggregate bucket so that a * pointer to self still represents the "right" data. */ serf_bucket_aggregate_become(bucket); /* Insert the two buckets. */ serf_bucket_aggregate_append(bucket, new_bucket); if (ctx->body != NULL) { serf_bucket_aggregate_append(bucket, ctx->body); } /* Our private context is no longer needed, and is not referred to by * any existing bucket. Toss it. */ serf_bucket_mem_free(bucket->allocator, ctx);}

1874 /local/tlutelli/issta_data/temp/c/2005_temp/2005/1874/2ca954891a4128162d15a2813f1ade79299fdbf4/request_buckets.c/buggy/buckets/request_buckets.c

iov, nvec, &nbytes);

iov, 4, &nbytes);

static void serialize_data(serf_bucket_t *bucket){ request_context_t *ctx = bucket->data; serf_bucket_t *new_bucket; const char *new_data; struct iovec iov[16]; apr_size_t nvec, nbytes; /* Serialize the request-line and headers into one mother string, * and wrap a bucket around it. */ iov[0].iov_base = (char*)ctx->method; iov[0].iov_len = strlen(ctx->method); iov[1].iov_base = " "; iov[1].iov_len = sizeof(" ") - 1; iov[2].iov_base = (char*)ctx->uri; iov[2].iov_len = strlen(ctx->uri); iov[3].iov_base = " HTTP/1.1\r\n"; iov[3].iov_len = sizeof(" HTTP/1.1\r\n") - 1; nvec = 4; if (bucket->metadata) { apr_hash_index_t *hi; apr_pool_t *p; const void *hash_ptr; apr_hash_t *hash; /* Okay, we might have headers. */ serf_bucket_get_metadata(bucket, SERF_REQUEST_HEADERS, 0, &hash_ptr); if (hash_ptr) { hash = (apr_hash_t*)hash_ptr; /* Check to see if we have enough free IO vecs to handle this. */ if ((apr_hash_count(hash) * 3) > 16 - nvec) { /* XXX: Handle me. */ abort(); } p = serf_bucket_allocator_get_pool(bucket->allocator); for (hi = apr_hash_first(p, hash); hi; hi = apr_hash_next(hi)) { const void *key; void *val; apr_ssize_t key_len; apr_hash_this(hi, &key, &key_len, &val); iov[nvec].iov_base = (char*)key; iov[nvec++].iov_len = key_len; iov[nvec].iov_base = ": "; iov[nvec++].iov_len = sizeof(": ") - 1; iov[nvec].iov_base = val; iov[nvec++].iov_len = strlen((char*)val); iov[nvec].iov_base = "\r\n"; iov[nvec++].iov_len = sizeof("\r\n") - 1; } } } iov[nvec].iov_base = "\r\n"; iov[nvec++].iov_len = sizeof("\r\n") - 1; /* ### pool allocation! */ new_data = apr_pstrcatv(serf_bucket_allocator_get_pool(bucket->allocator), iov, nvec, &nbytes); /* Create a new bucket for this string. A free function isn't needed * since the string is residing in a pool. */ new_bucket = SERF_BUCKET_SIMPLE_STRING_LEN(new_data, nbytes, bucket->allocator); /* Build up the new bucket structure. * * Note that self needs to become an aggregate bucket so that a * pointer to self still represents the "right" data. */ serf_bucket_aggregate_become(bucket); /* Insert the two buckets. */ serf_bucket_aggregate_append(bucket, new_bucket); if (ctx->body != NULL) { serf_bucket_aggregate_append(bucket, ctx->body); } /* Our private context is no longer needed, and is not referred to by * any existing bucket. Toss it. */ serf_bucket_mem_free(bucket->allocator, ctx);}

1874 /local/tlutelli/issta_data/temp/c/2005_temp/2005/1874/2ca954891a4128162d15a2813f1ade79299fdbf4/request_buckets.c/buggy/buckets/request_buckets.c

serf_bucket_aggregate_append(bucket, ctx->headers);

static void serialize_data(serf_bucket_t *bucket){ request_context_t *ctx = bucket->data; serf_bucket_t *new_bucket; const char *new_data; struct iovec iov[16]; apr_size_t nvec, nbytes; /* Serialize the request-line and headers into one mother string, * and wrap a bucket around it. */ iov[0].iov_base = (char*)ctx->method; iov[0].iov_len = strlen(ctx->method); iov[1].iov_base = " "; iov[1].iov_len = sizeof(" ") - 1; iov[2].iov_base = (char*)ctx->uri; iov[2].iov_len = strlen(ctx->uri); iov[3].iov_base = " HTTP/1.1\r\n"; iov[3].iov_len = sizeof(" HTTP/1.1\r\n") - 1; nvec = 4; if (bucket->metadata) { apr_hash_index_t *hi; apr_pool_t *p; const void *hash_ptr; apr_hash_t *hash; /* Okay, we might have headers. */ serf_bucket_get_metadata(bucket, SERF_REQUEST_HEADERS, 0, &hash_ptr); if (hash_ptr) { hash = (apr_hash_t*)hash_ptr; /* Check to see if we have enough free IO vecs to handle this. */ if ((apr_hash_count(hash) * 3) > 16 - nvec) { /* XXX: Handle me. */ abort(); } p = serf_bucket_allocator_get_pool(bucket->allocator); for (hi = apr_hash_first(p, hash); hi; hi = apr_hash_next(hi)) { const void *key; void *val; apr_ssize_t key_len; apr_hash_this(hi, &key, &key_len, &val); iov[nvec].iov_base = (char*)key; iov[nvec++].iov_len = key_len; iov[nvec].iov_base = ": "; iov[nvec++].iov_len = sizeof(": ") - 1; iov[nvec].iov_base = val; iov[nvec++].iov_len = strlen((char*)val); iov[nvec].iov_base = "\r\n"; iov[nvec++].iov_len = sizeof("\r\n") - 1; } } } iov[nvec].iov_base = "\r\n"; iov[nvec++].iov_len = sizeof("\r\n") - 1; /* ### pool allocation! */ new_data = apr_pstrcatv(serf_bucket_allocator_get_pool(bucket->allocator), iov, nvec, &nbytes); /* Create a new bucket for this string. A free function isn't needed * since the string is residing in a pool. */ new_bucket = SERF_BUCKET_SIMPLE_STRING_LEN(new_data, nbytes, bucket->allocator); /* Build up the new bucket structure. * * Note that self needs to become an aggregate bucket so that a * pointer to self still represents the "right" data. */ serf_bucket_aggregate_become(bucket); /* Insert the two buckets. */ serf_bucket_aggregate_append(bucket, new_bucket); if (ctx->body != NULL) { serf_bucket_aggregate_append(bucket, ctx->body); } /* Our private context is no longer needed, and is not referred to by * any existing bucket. Toss it. */ serf_bucket_mem_free(bucket->allocator, ctx);}

1874 /local/tlutelli/issta_data/temp/c/2005_temp/2005/1874/2ca954891a4128162d15a2813f1ade79299fdbf4/request_buckets.c/buggy/buckets/request_buckets.c

/* This should never happen */ if ( bd_count == 16 ) { printk(("TX ERROR:Too many mbufs in the packet!!!\n")) printk(("Must coalesce!\n")) }

void send_packet( struct ifnet *ifp, struct mbuf *m){ i596_tbd *pPrev = I596_NULL; i596_tbd *pRemainingTbdList; i596_tbd *pTbd; struct mbuf *n, *input_m = m; uti596_softc_ *sc = ifp->if_softc; struct mbuf *l = NULL; unsigned int length = 0; rtems_status_code status; int bd_count = 0; rtems_event_set events; /* * For all mbufs in the chain, * fill a transmit buffer descriptor for each */ pTbd = (i596_tbd*) word_swap ((unsigned long)sc->pTxCmd->pTbd); do { if (m->m_len) { /* * Fill in the buffer descriptor */ length += m->m_len; pTbd->data = (char *) word_swap ((unsigned long) mtod (m, void *)); pTbd->size = m->m_len; pPrev = pTbd; pTbd = (i596_tbd *) word_swap ((unsigned long) pTbd->next); l = m; m = m->m_next; } else { /* * Just toss empty mbufs */ MFREE (m, n); m = n; if (l != NULL) l->m_next = m; } } while( m != NULL && ++bd_count < 16 ); /* This should never happen */ if ( bd_count == 16 ) { printk(("TX ERROR:Too many mbufs in the packet!!!\n")) printk(("Must coalesce!\n")) } if ( length < UTI_596_ETH_MIN_SIZE ) { pTbd->data = (char *) word_swap ((unsigned long) sc->zeroes); /* add padding to pTbd */ pTbd->size = UTI_596_ETH_MIN_SIZE - length; /* zeroes have no effect on the CRC */ } else /* Don't use pTbd in the send routine */ pTbd = pPrev; /* Disconnect the packet from the list of Tbd's */ pRemainingTbdList = (i596_tbd *) word_swap ((unsigned long)pTbd->next); pTbd->next = I596_NULL; pTbd->size |= UTI_596_END_OF_FRAME; sc->rawsndcnt++; #ifdef DBG_SEND printk(("send_packet: sending packet\n")) #endif /* Sending Zero length packet: shouldn't happen */ if (pTbd->size <= 0) return; #ifdef DBG_PACKETS printk (("\nsend_packet: Transmitter adds packet\n")) print_hdr ( sc->pTxCmd->pTbd->data ); /* print the first part */ print_pkt ( sc->pTxCmd->pTbd->next->data ); /* print the first part */ print_echo (sc->pTxCmd->pTbd->data); #endif /* add the command to the output command queue */ uti596_addCmd ( (i596_cmd *) sc->pTxCmd ); /* sleep until the command has been processed or Timeout encountered. */ status= rtems_bsdnet_event_receive (INTERRUPT_EVENT, RTEMS_WAIT|RTEMS_EVENT_ANY, RTEMS_NO_TIMEOUT, &events); if ( status != RTEMS_SUCCESSFUL ) { printk(("Could not sleep %s\n", rtems_status_text(status))) } #ifdef DBG_SEND printk(("send_packet: RAW - wake\n")) #endif sc->txInterrupts++; if ( sc->pTxCmd -> cmd.status & STAT_OK ) { sc->stats.tx_packets++; } else { printk(("*** send_packet: Driver Error 0x%x\n", sc->pTxCmd -> cmd.status )) sc->stats.tx_errors++; if ( sc->pTxCmd->cmd.status & 0x0020 ) sc->stats.tx_retries_exceeded++; if (!(sc->pTxCmd->cmd.status & 0x0040)) sc->stats.tx_heartbeat_errors++; if ( sc->pTxCmd->cmd.status & 0x0400 ) sc->stats.tx_carrier_errors++; if ( sc->pTxCmd->cmd.status & 0x0800 ) sc->stats.collisions++; if ( sc->pTxCmd->cmd.status & 0x1000 ) sc->stats.tx_aborted_errors++; } /* end if stat_ok */ /* * Restore the transmitted buffer descriptor chain. */ pTbd -> next = (i596_tbd *) word_swap ((unsigned long)pRemainingTbdList); /* * Free the mbufs used by the sender. */ m = input_m; while ( m != NULL ) { MFREE(m,n); m = n; }}

10355 /local/tlutelli/issta_data/temp/c/2005_temp/2005/10355/8ef38186faea3d9b5e6f0f1242f668cb7e7a3d52/network.c/buggy/c/src/lib/libbsp/m68k/mvme167/network/network.c

if ( !status )

if ( status != 0 )

int sem_unlink( const char *name){ int status; register POSIX_Semaphore_Control *the_semaphore; Objects_Id the_semaphore_id; Objects_Locations location; status = _POSIX_Semaphore_Name_to_id( name, &the_semaphore_id ); if ( !status ) set_errno_and_return_minus_one( status ); the_semaphore = _POSIX_Semaphore_Get( &the_semaphore_id, &location ); switch ( location ) { case OBJECTS_ERROR: set_errno_and_return_minus_one( EINVAL ); case OBJECTS_REMOTE: _Thread_Dispatch(); return POSIX_MP_NOT_IMPLEMENTED(); set_errno_and_return_minus_one( EINVAL ); case OBJECTS_LOCAL:#if defined(RTEMS_MULTIPROCESSING) if ( the_semaphore->process_shared == PTHREAD_PROCESS_SHARED ) { _Objects_MP_Close( &_POSIX_Semaphore_Information, the_semaphore->Object.id ); }#endif the_semaphore->linked = FALSE; _POSIX_Semaphore_Delete( the_semaphore ); _Thread_Enable_dispatch(); return 0; } return POSIX_BOTTOM_REACHED();}

10355 /local/tlutelli/issta_data/temp/c/2005_temp/2005/10355/17879f4750a2bc0d556c8cd1d0f6715b127d681a/semunlink.c/buggy/c/src/exec/posix/src/semunlink.c

_POSIX_Semaphore_Namespace_remove( the_semaphore );

int sem_unlink( const char *name){ int status; register POSIX_Semaphore_Control *the_semaphore; Objects_Id the_semaphore_id; Objects_Locations location; status = _POSIX_Semaphore_Name_to_id( name, &the_semaphore_id ); if ( !status ) set_errno_and_return_minus_one( status ); the_semaphore = _POSIX_Semaphore_Get( &the_semaphore_id, &location ); switch ( location ) { case OBJECTS_ERROR: set_errno_and_return_minus_one( EINVAL ); case OBJECTS_REMOTE: _Thread_Dispatch(); return POSIX_MP_NOT_IMPLEMENTED(); set_errno_and_return_minus_one( EINVAL ); case OBJECTS_LOCAL:#if defined(RTEMS_MULTIPROCESSING) if ( the_semaphore->process_shared == PTHREAD_PROCESS_SHARED ) { _Objects_MP_Close( &_POSIX_Semaphore_Information, the_semaphore->Object.id ); }#endif the_semaphore->linked = FALSE; _POSIX_Semaphore_Delete( the_semaphore ); _Thread_Enable_dispatch(); return 0; } return POSIX_BOTTOM_REACHED();}

10355 /local/tlutelli/issta_data/temp/c/2005_temp/2005/10355/17879f4750a2bc0d556c8cd1d0f6715b127d681a/semunlink.c/buggy/c/src/exec/posix/src/semunlink.c

long av,tetpil,k,st;

ulong av = avma; long k,st;

thueinit(GEN poly, long flag, long prec){ GEN thueres,ALH,csts,c0; long av,tetpil,k,st; double d,dr; av=avma; uftot=0; if (checktnf(poly)) { uftot=(GEN)poly[2]; poly=(GEN)poly[1]; } else if (typ(poly)!=t_POL) err(notpoler,"thueinit"); if (degpol(poly)<=2) err(talker,"invalid polynomial in thue (need deg>2)"); if (!gisirreducible(poly)) err(redpoler,"thueinit"); st=sturm(poly); if (st) { dr=(double)((st+lgef(poly)-5)>>1); d=(double)degpol(poly); d=d*(d-1)*(d-2); /* Try to guess the precision by approximating Baker's bound. * Note that the guess is most of the time pretty generous, * ie 10 to 30 decimal digits above what is *really* necessary. * Note that the limiting step is the reduction. See paper. */ Prec=3 + (long)((5.83 + (dr+4)*5 + log(fact(dr+3)) + (dr+3)*log(dr+2) + (dr+3)*log(d) + log(log(2*d*(dr+2))) + (dr+1)) / 10.); ConstPrec=4; if (Prec<prec) Prec = prec; if (!checktnf(poly)) inithue(poly,flag); thueres=cgetg(8,t_VEC); thueres[1]=(long)poly; thueres[2]=(long)uftot; thueres[3]=(long)roo; Compute_Fund_Units(gmael(uftot,8,5)); ALH=cgetg(r+1,t_COL); for (k=1; k<=r; k++) ALH[k]=(long)Logarithmic_Height(k); thueres[4]=(long)ALH; thueres[5]=(long)MatFU; T_A_Matrices(); thueres[6]=(long)A; csts=cgetg(7,t_VEC); csts[1]=(long)c1; csts[2]=(long)c2; csts[3]=(long)halpha; csts[4]=(long)x0; csts[5]=(long)eps3; csts[6]=(long)stoi(Prec); thueres[7]=(long)csts; tetpil=avma; return gerepile(av,tetpil,gcopy(thueres)); } thueres=cgetg(3,t_VEC); c0=gun; Prec=4; roo=roots(poly,Prec); for (k=1; k<lg(roo); k++) c0=gmul(c0, gimag((GEN)roo[k])); c0=ginv(gabs(c0,Prec)); thueres[1]=(long)poly; thueres[2]=(long)c0; tetpil=avma; return gerepile(av,tetpil,gcopy(thueres));}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/7168973a923818508c45aa17d871c53e9225fad1/thue.c/buggy/src/modules/thue.c

av=avma; uftot=0;

uftot = NULL;

thueinit(GEN poly, long flag, long prec){ GEN thueres,ALH,csts,c0; long av,tetpil,k,st; double d,dr; av=avma; uftot=0; if (checktnf(poly)) { uftot=(GEN)poly[2]; poly=(GEN)poly[1]; } else if (typ(poly)!=t_POL) err(notpoler,"thueinit"); if (degpol(poly)<=2) err(talker,"invalid polynomial in thue (need deg>2)"); if (!gisirreducible(poly)) err(redpoler,"thueinit"); st=sturm(poly); if (st) { dr=(double)((st+lgef(poly)-5)>>1); d=(double)degpol(poly); d=d*(d-1)*(d-2); /* Try to guess the precision by approximating Baker's bound. * Note that the guess is most of the time pretty generous, * ie 10 to 30 decimal digits above what is *really* necessary. * Note that the limiting step is the reduction. See paper. */ Prec=3 + (long)((5.83 + (dr+4)*5 + log(fact(dr+3)) + (dr+3)*log(dr+2) + (dr+3)*log(d) + log(log(2*d*(dr+2))) + (dr+1)) / 10.); ConstPrec=4; if (Prec<prec) Prec = prec; if (!checktnf(poly)) inithue(poly,flag); thueres=cgetg(8,t_VEC); thueres[1]=(long)poly; thueres[2]=(long)uftot; thueres[3]=(long)roo; Compute_Fund_Units(gmael(uftot,8,5)); ALH=cgetg(r+1,t_COL); for (k=1; k<=r; k++) ALH[k]=(long)Logarithmic_Height(k); thueres[4]=(long)ALH; thueres[5]=(long)MatFU; T_A_Matrices(); thueres[6]=(long)A; csts=cgetg(7,t_VEC); csts[1]=(long)c1; csts[2]=(long)c2; csts[3]=(long)halpha; csts[4]=(long)x0; csts[5]=(long)eps3; csts[6]=(long)stoi(Prec); thueres[7]=(long)csts; tetpil=avma; return gerepile(av,tetpil,gcopy(thueres)); } thueres=cgetg(3,t_VEC); c0=gun; Prec=4; roo=roots(poly,Prec); for (k=1; k<lg(roo); k++) c0=gmul(c0, gimag((GEN)roo[k])); c0=ginv(gabs(c0,Prec)); thueres[1]=(long)poly; thueres[2]=(long)c0; tetpil=avma; return gerepile(av,tetpil,gcopy(thueres));}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/7168973a923818508c45aa17d871c53e9225fad1/thue.c/buggy/src/modules/thue.c

thueres[7]=(long)csts; tetpil=avma; return gerepile(av,tetpil,gcopy(thueres));

thueres[7]=(long)csts; return gerepilecopy(av,thueres);

thueinit(GEN poly, long flag, long prec){ GEN thueres,ALH,csts,c0; long av,tetpil,k,st; double d,dr; av=avma; uftot=0; if (checktnf(poly)) { uftot=(GEN)poly[2]; poly=(GEN)poly[1]; } else if (typ(poly)!=t_POL) err(notpoler,"thueinit"); if (degpol(poly)<=2) err(talker,"invalid polynomial in thue (need deg>2)"); if (!gisirreducible(poly)) err(redpoler,"thueinit"); st=sturm(poly); if (st) { dr=(double)((st+lgef(poly)-5)>>1); d=(double)degpol(poly); d=d*(d-1)*(d-2); /* Try to guess the precision by approximating Baker's bound. * Note that the guess is most of the time pretty generous, * ie 10 to 30 decimal digits above what is *really* necessary. * Note that the limiting step is the reduction. See paper. */ Prec=3 + (long)((5.83 + (dr+4)*5 + log(fact(dr+3)) + (dr+3)*log(dr+2) + (dr+3)*log(d) + log(log(2*d*(dr+2))) + (dr+1)) / 10.); ConstPrec=4; if (Prec<prec) Prec = prec; if (!checktnf(poly)) inithue(poly,flag); thueres=cgetg(8,t_VEC); thueres[1]=(long)poly; thueres[2]=(long)uftot; thueres[3]=(long)roo; Compute_Fund_Units(gmael(uftot,8,5)); ALH=cgetg(r+1,t_COL); for (k=1; k<=r; k++) ALH[k]=(long)Logarithmic_Height(k); thueres[4]=(long)ALH; thueres[5]=(long)MatFU; T_A_Matrices(); thueres[6]=(long)A; csts=cgetg(7,t_VEC); csts[1]=(long)c1; csts[2]=(long)c2; csts[3]=(long)halpha; csts[4]=(long)x0; csts[5]=(long)eps3; csts[6]=(long)stoi(Prec); thueres[7]=(long)csts; tetpil=avma; return gerepile(av,tetpil,gcopy(thueres)); } thueres=cgetg(3,t_VEC); c0=gun; Prec=4; roo=roots(poly,Prec); for (k=1; k<lg(roo); k++) c0=gmul(c0, gimag((GEN)roo[k])); c0=ginv(gabs(c0,Prec)); thueres[1]=(long)poly; thueres[2]=(long)c0; tetpil=avma; return gerepile(av,tetpil,gcopy(thueres));}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/7168973a923818508c45aa17d871c53e9225fad1/thue.c/buggy/src/modules/thue.c

tetpil=avma; return gerepile(av,tetpil,gcopy(thueres));

return gerepilecopy(av,thueres);

thueinit(GEN poly, long flag, long prec){ GEN thueres,ALH,csts,c0; long av,tetpil,k,st; double d,dr; av=avma; uftot=0; if (checktnf(poly)) { uftot=(GEN)poly[2]; poly=(GEN)poly[1]; } else if (typ(poly)!=t_POL) err(notpoler,"thueinit"); if (degpol(poly)<=2) err(talker,"invalid polynomial in thue (need deg>2)"); if (!gisirreducible(poly)) err(redpoler,"thueinit"); st=sturm(poly); if (st) { dr=(double)((st+lgef(poly)-5)>>1); d=(double)degpol(poly); d=d*(d-1)*(d-2); /* Try to guess the precision by approximating Baker's bound. * Note that the guess is most of the time pretty generous, * ie 10 to 30 decimal digits above what is *really* necessary. * Note that the limiting step is the reduction. See paper. */ Prec=3 + (long)((5.83 + (dr+4)*5 + log(fact(dr+3)) + (dr+3)*log(dr+2) + (dr+3)*log(d) + log(log(2*d*(dr+2))) + (dr+1)) / 10.); ConstPrec=4; if (Prec<prec) Prec = prec; if (!checktnf(poly)) inithue(poly,flag); thueres=cgetg(8,t_VEC); thueres[1]=(long)poly; thueres[2]=(long)uftot; thueres[3]=(long)roo; Compute_Fund_Units(gmael(uftot,8,5)); ALH=cgetg(r+1,t_COL); for (k=1; k<=r; k++) ALH[k]=(long)Logarithmic_Height(k); thueres[4]=(long)ALH; thueres[5]=(long)MatFU; T_A_Matrices(); thueres[6]=(long)A; csts=cgetg(7,t_VEC); csts[1]=(long)c1; csts[2]=(long)c2; csts[3]=(long)halpha; csts[4]=(long)x0; csts[5]=(long)eps3; csts[6]=(long)stoi(Prec); thueres[7]=(long)csts; tetpil=avma; return gerepile(av,tetpil,gcopy(thueres)); } thueres=cgetg(3,t_VEC); c0=gun; Prec=4; roo=roots(poly,Prec); for (k=1; k<lg(roo); k++) c0=gmul(c0, gimag((GEN)roo[k])); c0=ginv(gabs(c0,Prec)); thueres[1]=(long)poly; thueres[2]=(long)c0; tetpil=avma; return gerepile(av,tetpil,gcopy(thueres));}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/7168973a923818508c45aa17d871c53e9225fad1/thue.c/buggy/src/modules/thue.c

unsigned8 b[NUM_FIELDS];

uint8_t b[NUM_FIELDS];

command_port(FTPD_SessionInfo_t *info, char const *args){ enum { NUM_FIELDS = 6 }; unsigned int a[NUM_FIELDS]; int n; close_data_socket(info); n = sscanf(args, "%u,%u,%u,%u,%u,%u", a+0, a+1, a+2, a+3, a+4, a+5); if(NUM_FIELDS == n) { int i; unsigned8 b[NUM_FIELDS]; for(i = 0; i < NUM_FIELDS; ++i) { if(a[i] > 255) break; b[i] = (unsigned8)a[i]; } if(i == NUM_FIELDS) { /* Note: while it contradicts with RFC959, we don't allow PORT command * to specify IP address different than those of the originating client * for the sake of safety. */ unsigned32 const *ip = (unsigned32 *)b; if(*ip == info->def_addr.sin_addr.s_addr) { info->data_addr.sin_addr.s_addr = *ip; info->data_addr.sin_port = *(unsigned16 *)(b + 4); info->data_addr.sin_family = AF_INET; memset(info->data_addr.sin_zero, 0, sizeof(info->data_addr.sin_zero)); info->use_default = 0; send_reply(info, 200, "PORT command successful."); return; /* success */ } else { send_reply(info, 425, "Address doesn't match peer's IP."); return; } } } send_reply(info, 501, "Syntax error.");}

10355 /local/tlutelli/issta_data/temp/c/2005_temp/2005/10355/5146462f04bebbed0de4200c934bf5472c5a5427/ftpd.c/buggy/cpukit/ftpd/ftpd.c

b[i] = (unsigned8)a[i];

b[i] = (uint8_t)a[i];

command_port(FTPD_SessionInfo_t *info, char const *args){ enum { NUM_FIELDS = 6 }; unsigned int a[NUM_FIELDS]; int n; close_data_socket(info); n = sscanf(args, "%u,%u,%u,%u,%u,%u", a+0, a+1, a+2, a+3, a+4, a+5); if(NUM_FIELDS == n) { int i; unsigned8 b[NUM_FIELDS]; for(i = 0; i < NUM_FIELDS; ++i) { if(a[i] > 255) break; b[i] = (unsigned8)a[i]; } if(i == NUM_FIELDS) { /* Note: while it contradicts with RFC959, we don't allow PORT command * to specify IP address different than those of the originating client * for the sake of safety. */ unsigned32 const *ip = (unsigned32 *)b; if(*ip == info->def_addr.sin_addr.s_addr) { info->data_addr.sin_addr.s_addr = *ip; info->data_addr.sin_port = *(unsigned16 *)(b + 4); info->data_addr.sin_family = AF_INET; memset(info->data_addr.sin_zero, 0, sizeof(info->data_addr.sin_zero)); info->use_default = 0; send_reply(info, 200, "PORT command successful."); return; /* success */ } else { send_reply(info, 425, "Address doesn't match peer's IP."); return; } } } send_reply(info, 501, "Syntax error.");}

10355 /local/tlutelli/issta_data/temp/c/2005_temp/2005/10355/5146462f04bebbed0de4200c934bf5472c5a5427/ftpd.c/buggy/cpukit/ftpd/ftpd.c

unsigned32 const *ip = (unsigned32 *)b;

uint32_t const *ip = (uint32_t *)b;

command_port(FTPD_SessionInfo_t *info, char const *args){ enum { NUM_FIELDS = 6 }; unsigned int a[NUM_FIELDS]; int n; close_data_socket(info); n = sscanf(args, "%u,%u,%u,%u,%u,%u", a+0, a+1, a+2, a+3, a+4, a+5); if(NUM_FIELDS == n) { int i; unsigned8 b[NUM_FIELDS]; for(i = 0; i < NUM_FIELDS; ++i) { if(a[i] > 255) break; b[i] = (unsigned8)a[i]; } if(i == NUM_FIELDS) { /* Note: while it contradicts with RFC959, we don't allow PORT command * to specify IP address different than those of the originating client * for the sake of safety. */ unsigned32 const *ip = (unsigned32 *)b; if(*ip == info->def_addr.sin_addr.s_addr) { info->data_addr.sin_addr.s_addr = *ip; info->data_addr.sin_port = *(unsigned16 *)(b + 4); info->data_addr.sin_family = AF_INET; memset(info->data_addr.sin_zero, 0, sizeof(info->data_addr.sin_zero)); info->use_default = 0; send_reply(info, 200, "PORT command successful."); return; /* success */ } else { send_reply(info, 425, "Address doesn't match peer's IP."); return; } } } send_reply(info, 501, "Syntax error.");}

10355 /local/tlutelli/issta_data/temp/c/2005_temp/2005/10355/5146462f04bebbed0de4200c934bf5472c5a5427/ftpd.c/buggy/cpukit/ftpd/ftpd.c

info->data_addr.sin_port = *(unsigned16 *)(b + 4);

info->data_addr.sin_port = *(uint16_t *)(b + 4);

command_port(FTPD_SessionInfo_t *info, char const *args){ enum { NUM_FIELDS = 6 }; unsigned int a[NUM_FIELDS]; int n; close_data_socket(info); n = sscanf(args, "%u,%u,%u,%u,%u,%u", a+0, a+1, a+2, a+3, a+4, a+5); if(NUM_FIELDS == n) { int i; unsigned8 b[NUM_FIELDS]; for(i = 0; i < NUM_FIELDS; ++i) { if(a[i] > 255) break; b[i] = (unsigned8)a[i]; } if(i == NUM_FIELDS) { /* Note: while it contradicts with RFC959, we don't allow PORT command * to specify IP address different than those of the originating client * for the sake of safety. */ unsigned32 const *ip = (unsigned32 *)b; if(*ip == info->def_addr.sin_addr.s_addr) { info->data_addr.sin_addr.s_addr = *ip; info->data_addr.sin_port = *(unsigned16 *)(b + 4); info->data_addr.sin_family = AF_INET; memset(info->data_addr.sin_zero, 0, sizeof(info->data_addr.sin_zero)); info->use_default = 0; send_reply(info, 200, "PORT command successful."); return; /* success */ } else { send_reply(info, 425, "Address doesn't match peer's IP."); return; } } } send_reply(info, 501, "Syntax error.");}

10355 /local/tlutelli/issta_data/temp/c/2005_temp/2005/10355/5146462f04bebbed0de4200c934bf5472c5a5427/ftpd.c/buggy/cpukit/ftpd/ftpd.c

if (!signe(x)) { y=cgetr(3); y[1]=x[1]; y[2]=0; return y; }

if (!signe(x)) return realzero_bit(expo(x));

mpsin(GEN x){ long mod8,av,tetpil; GEN y,p1; if (typ(x)!=t_REAL) err(typeer,"mpsin"); if (!signe(x)) { y=cgetr(3); y[1]=x[1]; y[2]=0; return y; } av=avma; p1=mpsc1(x,&mod8); tetpil=avma; switch(mod8) { case 0: case 6: y=mpaut(p1); break; case 1: case 5: y=addsr(1,p1); break; case 2: case 4: y=mpaut(p1); setsigne(y,-signe(y)); break; default: /* case 3: case 7: */ y=subsr(-1,p1); break; } return gerepile(av,tetpil,y);}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/1558baf8c3b715dd704e6dddf2c7f1f51dc47e84/trans1.c/buggy/src/basemath/trans1.c

/* ### not true. we only want to read IF we have sent some data */

static apr_status_t update_pollset(serf_connection_t *conn){ serf_context_t *ctx = conn->ctx; apr_status_t status; apr_pollfd_t desc = { 0 }; if (conn->address) { /* Remove the socket from the poll set. */ desc.desc_type = APR_POLL_SOCKET; desc.desc.s = conn->skt; } else { /* XXX This clearly ain't right. */ desc.desc_type = APR_POLL_FILE; desc.desc.f = conn->write_baton; } status = apr_pollset_remove(ctx->pollset, &desc); if (status && !APR_STATUS_IS_NOTFOUND(status)) return status; /* Now put it back in with the correct read/write values. */ desc.reqevents = 0; if (conn->requests) { /* If there are any outstanding events, then we want to read. */ desc.reqevents |= APR_POLLIN; /* If the connection has unwritten data, or there are any requests * that still have buckets to write out, then we want to write. */ if (conn->unwritten_len) desc.reqevents |= APR_POLLOUT; else { serf_request_t *request = conn->requests; while (request != NULL && request->req_bkt == NULL) request = request->next; if (request != NULL) desc.reqevents |= APR_POLLOUT; } } desc.client_data = conn; /* Note: even if we don't want to read/write this socket, we still * want to poll it for hangups and errors. */ return apr_pollset_add(ctx->pollset, &desc);}

1874 /local/tlutelli/issta_data/temp/c/2005_temp/2005/1874/e06b259bd43d48160ae3d1a29dcb0efa1cd91318/context.c/clean/context.c

testx(GEN bnfz, GEN bnf, GEN X, GEN module, GEN subgroup, GEN vecMsup, GEN vecWB, long g, GEN U)

testx(GEN bnfz, GEN bnr, GEN X, GEN subgroup, GEN vecMsup, GEN vecWB, long g, GEN U)

testx(GEN bnfz, GEN bnf, GEN X, GEN module, GEN subgroup, GEN vecMsup, GEN vecWB, long g, GEN U){ long i,l,lX; GEN be,polrelbe,p1,nf; if (gcmp0(X)) return NULL; lX = lg(X); for (i=dv+1; i<lX; i++) if (gcmp0((GEN)X[i])) return NULL; l = lg(vecMsup); for (i=1; i<l; i++) if (gcmp0(FpV_red(gmul((GEN)vecMsup[i],X), gell))) return NULL; be = gun; for (i=1; i<lX; i++) be = gmul(be, powgi((GEN)vecWB[i], (GEN)X[i])); if (DEBUGLEVEL>1) fprintferr("reducing beta = %Z\n",be); be = reducebeta(bnfz, be); if (DEBUGLEVEL>1) fprintferr("beta reduced = %Z\n",be); nf = (GEN)bnf[7]; polrelbe = computepolrelbeta((GEN)nf[1],be,g,U); p1 = unifpol(nf,polrelbe,0); l = lg(p1); /* lift to Q rational coeffs */ for (i=2; i<l; i++) if (isnfscalar((GEN)p1[i])) polrelbe[i] = mael(p1,i,1); p1 = denom(gtovec(p1)); polrelbe = rescale_pol(polrelbe,p1); if (DEBUGLEVEL>1) fprintferr("polrelbe = %Z\n",polrelbe); p1 = rnfconductor(bnf,polrelbe,0); if (!gegal((GEN)p1[1],module) || !gegal((GEN)p1[3],subgroup)) return NULL; return polrelbe;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/04840f96d7636290da57d0fd208561141349b8c5/kummer.c/buggy/src/modules/kummer.c

be = gun; for (i=1; i<lX; i++) be = gmul(be, powgi((GEN)vecWB[i], (GEN)X[i]));

be = factorback(vecWB, X);

testx(GEN bnfz, GEN bnf, GEN X, GEN module, GEN subgroup, GEN vecMsup, GEN vecWB, long g, GEN U){ long i,l,lX; GEN be,polrelbe,p1,nf; if (gcmp0(X)) return NULL; lX = lg(X); for (i=dv+1; i<lX; i++) if (gcmp0((GEN)X[i])) return NULL; l = lg(vecMsup); for (i=1; i<l; i++) if (gcmp0(FpV_red(gmul((GEN)vecMsup[i],X), gell))) return NULL; be = gun; for (i=1; i<lX; i++) be = gmul(be, powgi((GEN)vecWB[i], (GEN)X[i])); if (DEBUGLEVEL>1) fprintferr("reducing beta = %Z\n",be); be = reducebeta(bnfz, be); if (DEBUGLEVEL>1) fprintferr("beta reduced = %Z\n",be); nf = (GEN)bnf[7]; polrelbe = computepolrelbeta((GEN)nf[1],be,g,U); p1 = unifpol(nf,polrelbe,0); l = lg(p1); /* lift to Q rational coeffs */ for (i=2; i<l; i++) if (isnfscalar((GEN)p1[i])) polrelbe[i] = mael(p1,i,1); p1 = denom(gtovec(p1)); polrelbe = rescale_pol(polrelbe,p1); if (DEBUGLEVEL>1) fprintferr("polrelbe = %Z\n",polrelbe); p1 = rnfconductor(bnf,polrelbe,0); if (!gegal((GEN)p1[1],module) || !gegal((GEN)p1[3],subgroup)) return NULL; return polrelbe;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/04840f96d7636290da57d0fd208561141349b8c5/kummer.c/buggy/src/modules/kummer.c

nf = (GEN)bnf[7];

nf = checknf(bnr);

testx(GEN bnfz, GEN bnf, GEN X, GEN module, GEN subgroup, GEN vecMsup, GEN vecWB, long g, GEN U){ long i,l,lX; GEN be,polrelbe,p1,nf; if (gcmp0(X)) return NULL; lX = lg(X); for (i=dv+1; i<lX; i++) if (gcmp0((GEN)X[i])) return NULL; l = lg(vecMsup); for (i=1; i<l; i++) if (gcmp0(FpV_red(gmul((GEN)vecMsup[i],X), gell))) return NULL; be = gun; for (i=1; i<lX; i++) be = gmul(be, powgi((GEN)vecWB[i], (GEN)X[i])); if (DEBUGLEVEL>1) fprintferr("reducing beta = %Z\n",be); be = reducebeta(bnfz, be); if (DEBUGLEVEL>1) fprintferr("beta reduced = %Z\n",be); nf = (GEN)bnf[7]; polrelbe = computepolrelbeta((GEN)nf[1],be,g,U); p1 = unifpol(nf,polrelbe,0); l = lg(p1); /* lift to Q rational coeffs */ for (i=2; i<l; i++) if (isnfscalar((GEN)p1[i])) polrelbe[i] = mael(p1,i,1); p1 = denom(gtovec(p1)); polrelbe = rescale_pol(polrelbe,p1); if (DEBUGLEVEL>1) fprintferr("polrelbe = %Z\n",polrelbe); p1 = rnfconductor(bnf,polrelbe,0); if (!gegal((GEN)p1[1],module) || !gegal((GEN)p1[3],subgroup)) return NULL; return polrelbe;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/04840f96d7636290da57d0fd208561141349b8c5/kummer.c/buggy/src/modules/kummer.c

p1 = rnfconductor(bnf,polrelbe,0); if (!gegal((GEN)p1[1],module) || !gegal((GEN)p1[3],subgroup)) return NULL;

p1 = rnfnormgroup(bnr,polrelbe); if (!gegal(p1,subgroup)) return NULL;

testx(GEN bnfz, GEN bnf, GEN X, GEN module, GEN subgroup, GEN vecMsup, GEN vecWB, long g, GEN U){ long i,l,lX; GEN be,polrelbe,p1,nf; if (gcmp0(X)) return NULL; lX = lg(X); for (i=dv+1; i<lX; i++) if (gcmp0((GEN)X[i])) return NULL; l = lg(vecMsup); for (i=1; i<l; i++) if (gcmp0(FpV_red(gmul((GEN)vecMsup[i],X), gell))) return NULL; be = gun; for (i=1; i<lX; i++) be = gmul(be, powgi((GEN)vecWB[i], (GEN)X[i])); if (DEBUGLEVEL>1) fprintferr("reducing beta = %Z\n",be); be = reducebeta(bnfz, be); if (DEBUGLEVEL>1) fprintferr("beta reduced = %Z\n",be); nf = (GEN)bnf[7]; polrelbe = computepolrelbeta((GEN)nf[1],be,g,U); p1 = unifpol(nf,polrelbe,0); l = lg(p1); /* lift to Q rational coeffs */ for (i=2; i<l; i++) if (isnfscalar((GEN)p1[i])) polrelbe[i] = mael(p1,i,1); p1 = denom(gtovec(p1)); polrelbe = rescale_pol(polrelbe,p1); if (DEBUGLEVEL>1) fprintferr("polrelbe = %Z\n",polrelbe); p1 = rnfconductor(bnf,polrelbe,0); if (!gegal((GEN)p1[1],module) || !gegal((GEN)p1[3],subgroup)) return NULL; return polrelbe;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/04840f96d7636290da57d0fd208561141349b8c5/kummer.c/buggy/src/modules/kummer.c

const int pk = _pk(p,k), L = lg(tabaall)-1, lz = pk - L;

const int pk = u_pow(p,k), L = lg(tabaall)-1, lz = pk - L;

extendtabs(GEN N, int p, int k){ const int pk = _pk(p,k), L = lg(tabaall)-1, lz = pk - L; const ulong ltab = (NBITSN/kglob)+2; if (lz <= 0) { if (tabcyc[pk]==0) filltabs(N,p,k,ltab); return; } extend((GEN*)&tabaall, lz); extend((GEN*)&tabtall, lz); extend((GEN*)&tabcyc, lz); extend(&tabefin, lz); extend(&tabE, lz); extend(&tabTH, lz); extend(&tabeta, lz); extend(&sgt, lz); extend(&ctsgt, lz); filltabs(N,p,k, ltab);}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/8ac2292b2e02fd23dcdd96371571717ef1011e3f/aprcl.c/clean/src/modules/aprcl.c

extend(&tabefin, lz);

extendtabs(GEN N, int p, int k){ const int pk = _pk(p,k), L = lg(tabaall)-1, lz = pk - L; const ulong ltab = (NBITSN/kglob)+2; if (lz <= 0) { if (tabcyc[pk]==0) filltabs(N,p,k,ltab); return; } extend((GEN*)&tabaall, lz); extend((GEN*)&tabtall, lz); extend((GEN*)&tabcyc, lz); extend(&tabefin, lz); extend(&tabE, lz); extend(&tabTH, lz); extend(&tabeta, lz); extend(&sgt, lz); extend(&ctsgt, lz); filltabs(N,p,k, ltab);}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/8ac2292b2e02fd23dcdd96371571717ef1011e3f/aprcl.c/clean/src/modules/aprcl.c

pushtmatrix((SDL_svg_context *)closure);

pushtmatrix(c); c->minx = HUGE; c->miny = HUGE; c->maxx = -HUGE; c->maxy = -HUGE;

static svg_status_t _SDL_SVG_BeginElement (void *closure){ dprintf("svg_BeginElement\n"); pushtmatrix((SDL_svg_context *)closure); return SVG_STATUS_SUCCESS;}

1561 /local/tlutelli/issta_data/temp/c/2005_temp/2005/1561/2ffd9ca885a57849f9fbafa985ba5ebc76eb8d74/SDL_svg.c/buggy/SDL_svg.c

_extremes(c, x1, y1); _extremes(c, x2, y2); _extremes(c, x3, y3);

_SDL_SVG_CurveTo (void *closure, double x1, double y1, double x2, double y2, double x3, double y3){SDL_svg_context *c=closure;IPoint p1,p2,p3; dprintf("svg_CurveTo (x1=%5.5f, y1=%5.5f, x2=%5.5f, y2=%5.5f, x3=%5.5f, y3=%5.5f)\n", x1,y1,x2,y2,x3,y3); if(!c->path || !c->numpoints) return SVG_STATUS_INVALID_CALL; p1 = FixCoords(c, (IPoint) {x1, y1}); p2 = FixCoords(c, (IPoint) {x2, y2}); p3 = FixCoords(c, (IPoint) {x3, y3}); _AddIPoint(c, (IPoint) {p1.x, p1.y}, TAG_CONTROL3); _AddIPoint(c, (IPoint) {p2.x, p2.y}, TAG_CONTROL3); _AddIPoint(c, (IPoint) {p3.x, p3.y}, TAG_ONPATH); c->at = (IPoint) {x3, y3}; return SVG_STATUS_SUCCESS;}

1561 /local/tlutelli/issta_data/temp/c/2005_temp/2005/1561/2ffd9ca885a57849f9fbafa985ba5ebc76eb8d74/SDL_svg.c/buggy/SDL_svg.c

_extremes(c, x, y);

_SDL_SVG_LineTo (void *closure, double x, double y){SDL_svg_context *c=closure; dprintf("svg_LineTo (x=%5.5f, y=%5.5f)\n",x,y); _AddIPoint(c, FixCoords(c, (IPoint) {x, y}), TAG_ONPATH); c->at = (IPoint) {x, y}; return SVG_STATUS_SUCCESS;}

1561 /local/tlutelli/issta_data/temp/c/2005_temp/2005/1561/2ffd9ca885a57849f9fbafa985ba5ebc76eb8d74/SDL_svg.c/buggy/SDL_svg.c

_extremes(c, x, y);

_SDL_SVG_MoveTo (void *closure, double x, double y){SDL_svg_context *c=closure; dprintf("svg_MoveTo (x=%5.5f, y=%5.5f)\n",x,y); if(c->numpoints && needs_path_stop(c)) _AddPathStop(c, 0); _AddIPoint(c, FixCoords(c, (IPoint) {x, y}), TAG_ONPATH); c->at = (IPoint) {x, y}; return SVG_STATUS_SUCCESS;}

1561 /local/tlutelli/issta_data/temp/c/2005_temp/2005/1561/2ffd9ca885a57849f9fbafa985ba5ebc76eb8d74/SDL_svg.c/buggy/SDL_svg.c

_extremes(c, x1, y1); _extremes(c, x2, y2);

_SDL_SVG_QuadraticCurveTo (void *closure, double x1, double y1, double x2, double y2){SDL_svg_context *c=closure;IPoint p1,p2; dprintf("svg_QuadraticCurveTo (x1=%5.5f, y1=%5.5f, x2=%5.5f, y2=%5.5f)\n", x1,y1,x2,y2); if(!c->path || !c->numpoints) return SVG_STATUS_INVALID_CALL; p1 = FixCoords(c, (IPoint) {x1, y1}); p2 = FixCoords(c, (IPoint) {x2, y2}); _AddIPoint(c, (IPoint) {p1.x, p1.y}, TAG_CONTROL2); _AddIPoint(c, (IPoint) {p2.x, p2.y}, TAG_ONPATH); c->at = (IPoint) {x2, y2}; return SVG_STATUS_SUCCESS;}

1561 /local/tlutelli/issta_data/temp/c/2005_temp/2005/1561/2ffd9ca885a57849f9fbafa985ba5ebc76eb8d74/SDL_svg.c/buggy/SDL_svg.c

_extremes(c, x1, y1); _extremes(c, x2, y2);

_SDL_SVG_RenderRect (void *closure, svg_length_t *x_len, svg_length_t *y_len, svg_length_t *width_len, svg_length_t *height_len, svg_length_t *rx_len, svg_length_t *ry_len){SDL_svg_context *c=closure;float x1,y1;float x2,y2; dprintf("svg_RenderRect\n"); x1 = x_len->value; y1 = y_len->value; x2 = x1 + width_len->value; y2 = y1 + height_len->value; _AddIPoint(c, FixCoords(c, (IPoint) {x1, y1}), TAG_ONPATH); _AddIPoint(c, FixCoords(c, (IPoint) {x2, y1}), TAG_ONPATH); _AddIPoint(c, FixCoords(c, (IPoint) {x2, y2}), TAG_ONPATH); _AddIPoint(c, FixCoords(c, (IPoint) {x1, y2}), TAG_ONPATH); _SDL_SVG_RenderPath(closure); return SVG_STATUS_SUCCESS;}

1561 /local/tlutelli/issta_data/temp/c/2005_temp/2005/1561/2ffd9ca885a57849f9fbafa985ba5ebc76eb8d74/SDL_svg.c/buggy/SDL_svg.c

dst.e = in->c * in->f - in->d * in->e; dst.f = in->b * in->e - in->a * in->f;

dst.e = (in->c * in->f - in->d * in->e)/det; dst.f = (in->b * in->e - in->a * in->f)/det;

svg_matrix_t svg_matrix_invert(svg_matrix_t *in){float det;svg_matrix_t dst; det = in->a * in->d - in->b * in->c; if(det == 0.0) return (svg_matrix_t) {1.0, 0.0, 0.0, 1.0, 0.0, 0.0}; dst.a = in->d/det; dst.b = -in->b/det; dst.c = -in->c/det; dst.d = in->a/det; dst.e = in->c * in->f - in->d * in->e; dst.f = in->b * in->e - in->a * in->f; return dst;}

1561 /local/tlutelli/issta_data/temp/c/2005_temp/2005/1561/5859f1732411637af272c589b6e2947495542a8c/matrix.c/buggy/matrix.c

the_object = _Objects_Get( information, id, OBJECTS_SEARCH_LOCAL_NODE );

the_object = _Objects_Get( information, id, &ignored_location );

Objects_Name_or_id_lookup_errors _Objects_Id_to_name ( Objects_Id id, Objects_Name *name){ unsigned32 the_api; unsigned32 the_class; Objects_Information *information; Objects_Control *the_object = (Objects_Control *) 0; if ( !name ) return OBJECTS_INVALID_NAME; the_api = _Objects_Get_API( id ); if ( the_api && the_api > OBJECTS_APIS_LAST ) return OBJECTS_INVALID_ID; the_class = _Objects_Get_class( id ); information = _Objects_Information_table[ the_api ][ the_class ]; if ( !information ) return OBJECTS_INVALID_ID; if ( information->is_string ) return OBJECTS_INVALID_ID; the_object = _Objects_Get( information, id, OBJECTS_SEARCH_LOCAL_NODE ); if (!the_object) return OBJECTS_INVALID_ID; *name = the_object->name; return OBJECTS_NAME_OR_ID_LOOKUP_SUCCESSFUL;}

10355 /local/tlutelli/issta_data/temp/c/2005_temp/2005/10355/b2b143f402b30c7bbe4ee98c58221b0cc78a1e9e/objectidtoname.c/clean/cpukit/score/src/objectidtoname.c

if (precision(p1)) return 1;

if (precision(p1)) res = 1;

use_maximal_pivot(GEN x){ long tx,i,j, lx = lg(x), ly = lg(x[1]); GEN p1; for (i=1; i<lx; i++) for (j=1; j<ly; j++) { p1 = gmael(x,i,j); tx = typ(p1); if (!is_scalar_t(tx)) return 0; if (precision(p1)) return 1; } return 0;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/40e574294e7e78bc748e3af5f0b3a447ab2c9e5f/alglin1.c/buggy/src/basemath/alglin1.c

return 0;

return res;

use_maximal_pivot(GEN x){ long tx,i,j, lx = lg(x), ly = lg(x[1]); GEN p1; for (i=1; i<lx; i++) for (j=1; j<ly; j++) { p1 = gmael(x,i,j); tx = typ(p1); if (!is_scalar_t(tx)) return 0; if (precision(p1)) return 1; } return 0;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/40e574294e7e78bc748e3af5f0b3a447ab2c9e5f/alglin1.c/buggy/src/basemath/alglin1.c

tmppool);

request->respool);

static apr_status_t read_from_connection(serf_connection_t *conn){ apr_status_t status; apr_pool_t *tmppool; /* Whatever is coming in on the socket corresponds to the first request * on our chain. */ serf_request_t *request = conn->requests; /* assert: request != NULL */ if ((status = apr_pool_create(&tmppool, request->respool)) != APR_SUCCESS) goto error; /* Invoke response handlers until we have no more work. */ while (1) { apr_pool_clear(tmppool); /* If the request doesn't have a response bucket, then call the * acceptor to get one created. */ if (request->resp_bkt == NULL) { request->resp_bkt = (*request->acceptor)(request, conn->skt, request->acceptor_baton, tmppool); apr_pool_clear(tmppool); } status = (*request->handler)(request->resp_bkt, request->handler_baton, tmppool); if (!APR_STATUS_IS_EOF(status)) { /* Whether success, or an error, there is no more to do unless * this request has been completed. */ goto error; } /* The request has been fully-delivered, and the response has * been fully-read. Remove it from our queue and loop to read * another response. */ conn->requests = request->next; /* The bucket is no longer needed, nor is the request's pool. */ serf_bucket_destroy(request->resp_bkt); apr_pool_destroy(request->respool); request = conn->requests; /* If we just ran out of requests, then update the pollset. We * don't want to read from this socket any more. We are definitely * done with this loop, too. */ if (request == NULL) { status = update_pollset(conn); goto error; } } error: apr_pool_destroy(tmppool); return status;}

1874 /local/tlutelli/issta_data/temp/c/2005_temp/2005/1874/c88ac5bbf7089fbf6690293c86593aaffc529c9c/context.c/buggy/context.c

unsigned32 erc32_sonic_read_register(

uint32_t erc32_sonic_read_register(

unsigned32 erc32_sonic_read_register( void *base, unsigned32 regno){ volatile unsigned32 *p = base; unsigned32 value; value = p[regno];#if (SONIC_DEBUG & SONIC_DEBUG_PRINT_REGISTERS) printf( "%p Read 0x%04x from %s (0x%02x)\n", &p[regno], value, SONIC_Reg_name[regno], regno ); fflush( stdout );#endif return 0x0ffff & value;}

10355 /local/tlutelli/issta_data/temp/c/2005_temp/2005/10355/1be1e913564b73bf50ce1aa58c003e564ddae83a/erc32sonic.c/buggy/c/src/lib/libbsp/sparc/erc32/erc32sonic/erc32sonic.c

unsigned32 regno

uint32_t regno

unsigned32 erc32_sonic_read_register( void *base, unsigned32 regno){ volatile unsigned32 *p = base; unsigned32 value; value = p[regno];#if (SONIC_DEBUG & SONIC_DEBUG_PRINT_REGISTERS) printf( "%p Read 0x%04x from %s (0x%02x)\n", &p[regno], value, SONIC_Reg_name[regno], regno ); fflush( stdout );#endif return 0x0ffff & value;}

10355 /local/tlutelli/issta_data/temp/c/2005_temp/2005/10355/1be1e913564b73bf50ce1aa58c003e564ddae83a/erc32sonic.c/buggy/c/src/lib/libbsp/sparc/erc32/erc32sonic/erc32sonic.c

volatile unsigned32 *p = base; unsigned32 value;

volatile uint32_t *p = base; uint32_t value;

unsigned32 erc32_sonic_read_register( void *base, unsigned32 regno){ volatile unsigned32 *p = base; unsigned32 value; value = p[regno];#if (SONIC_DEBUG & SONIC_DEBUG_PRINT_REGISTERS) printf( "%p Read 0x%04x from %s (0x%02x)\n", &p[regno], value, SONIC_Reg_name[regno], regno ); fflush( stdout );#endif return 0x0ffff & value;}

10355 /local/tlutelli/issta_data/temp/c/2005_temp/2005/10355/1be1e913564b73bf50ce1aa58c003e564ddae83a/erc32sonic.c/buggy/c/src/lib/libbsp/sparc/erc32/erc32sonic/erc32sonic.c

rtems_unsigned32 task_count = 0;

uint32_t task_count = 0;

void test1(){ boolean auto_extend; rtems_status_code result; rtems_unsigned32 task_count = 0; Objects_Information *the_information; char c1 = 'a'; char c2 = 'a'; char c3 = '0'; char c4 = '0'; printf( "\n TEST1 : auto-extend disabled.\n" ); /* * This is a major hack and only recommended for a test. Doing this * saves having another test. */ the_information = _Objects_Information_table[OBJECTS_CLASSIC_API][OBJECTS_RTEMS_TASKS]; auto_extend = the_information->auto_extend; the_information->auto_extend = FALSE; while (task_count < MAX_TASKS) { rtems_name name; printf(" TEST1 : creating task '%c%c%c%c', ", c1, c2, c3, c4); name = rtems_build_name(c1, c2, c3, c4); result = rtems_task_create(name, 10, RTEMS_MINIMUM_STACK_SIZE, RTEMS_DEFAULT_ATTRIBUTES, RTEMS_LOCAL, &task_id[task_count]); if (status_code_bad(result)) break; printf("number = %3i, id = %08x, starting, ", task_count, task_id[task_count]); fflush(stdout); result = rtems_task_start(task_id[task_count], test_task, (rtems_task_argument) task_count); if (status_code_bad(result)) break; /* * Update the name. */ NEXT_TASK_NAME(c1, c2, c3, c4); task_count++; } if (task_count >= MAX_TASKS) printf( "\nMAX_TASKS too small for work-space size, please make larger !!\n\n" ); if (task_count != (TASK_ALLOCATION_SIZE - 1)) { printf( " FAIL1 : the number of tasks does not equal the expected size -\n" " task created = %i, required number = %i\n", task_count, TASK_ALLOCATION_SIZE); exit( 1 ); } destory_all_tasks("TEST1"); the_information->auto_extend = auto_extend; printf( " TEST1 : completed\n" );}

10355 /local/tlutelli/issta_data/temp/c/2005_temp/2005/10355/4c84d7b760ceb1e140c1cfc0fa64289ca4d243ed/test1.c/clean/testsuites/samples/unlimited/test1.c

puts("");

void stat_a_file( const char *file){ int status; struct stat statbuf; assert( file ); printf( "stat( %s ) returned ", file ); fflush( stdout ); status = stat( file, &statbuf ); if ( status == -1 ) { printf( ": %s\n", strerror( errno ) ); } else { dump_statbuf( &statbuf ); }}

10355 /local/tlutelli/issta_data/temp/c/2005_temp/2005/10355/78edd4446b55fa9a1df5270736585b2b6d135028/test.c/clean/c/src/tests/psxtests/psxfile01/test.c

long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf;

long ell, i, j, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, vnf; long l, lSp, lSml2, lSl2, lW;

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp;

GEN polnf,bnf,nf,bnfz,nfz,bid,ideal,cycgen,gell,p1,p2,wk,U,vselmer; GEN clgp,fununits,torsunit,Tc,Tv,P; GEN Q,idealz,gothf,factgothf; GEN M,K,y,vecMsup,vecW,vecWA,vecWB,vecB,vecC; GEN u,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp,listprSp;

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

/* step 7 */

/* step 7 */

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

/* step 1 of alg 5.3.5. */

/* step 1 of alg 5.3.5. */

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */

compositum_red(&COMPO, polnf, cyclo(ell,vnf)); /* step 2 */

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

degKz = degpol(R); m = degKz/degK; d = (ell-1)/m;

degKz = degpol(COMPO.R); m = degKz / degK; d = (ell-1) / m;

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

/* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */

/* step 3 */

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

bnfz = bnfinit0(R,1,NULL,prec);

/* could factor disc(R) using th. 2.1.6. */ bnfz = bnfinit0(COMPO.R,1,NULL,prec); cycgen = check_and_build_cycgen(bnfz);

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

tau = get_tau(&_tau, nfz, U);

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

cycgen = check_and_build_cycgen(bnfz);

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

/* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell);

/* compute the u_j (see remark 5.2.15.) */ u = cgetg(l,t_VEC); for (j=1; j<=rc; j++) u[j] = zero; for ( ; j< l; j++) u[j] = lmpinvmod((GEN)cyc[j], gell);

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

/* step 4 */

/* compute action of tau */ U = gadd(gpowgs(COMPO.q, g), gmul(COMPO.k, COMPO.p)); U = poleval(COMPO.rev, U); tau = get_tau(&_tau, nfz, U); /* step 4 */

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc);

p1 = tauofideal(nfz, (GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,u,gell,rc);

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB;

p2 = vecB;

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

p3 = tauofvec(p3, tau);

p2 = tauofvec(p2, tau);

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2;

vecC[i] = (long)famat_mul((GEN)vecC[i], famat_factorback(p2, (GEN)T[i])); }

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

/* step 5 */

/* step 5 */

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

/* step 6 */

/* step 6 */

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */

/* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 8\n"); p1 = RXQ_powers(lift_intern(COMPO.p), COMPO.R, degK-1); p1 = vecpol_to_mat(p1, degKz); T.invexpoteta1 = invmat(p1); /* left inverse */

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

{ /* l | N(ideal) */

{ /* ell | N(ideal) */

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

/* step 9 */

/* step 9 */

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

/* step 10 and step 11 */

/* step 10, 11 */

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

/* step 12 */

/* step 12 */

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc);

GEN e, a, ap; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,u,gell,rc);

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT);

p2 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p2; ap = cgetg(1, t_MAT);

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau);

ap = famat_mul(ap, famat_pow(p2, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p2 = tauofelt(p2, tau);

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

vecalphap[j] = (long)p2; } /* step 13 */

vecalphap[j] = (long)ap; } /* step 13 */

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

/* step 14, 15, and 17 */

/* step 14, 15, and 17 */

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

GEN QtP = gmul(gtrans_i(Q),matP);

GEN QtP = gmul(gtrans_i(Q), matP);

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

/* step 16 */

/* step 16 */

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */

/* step 18 & ff */

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

y = cgetg(dK,t_VECSMALL); do

dK = lg(K)-1; y = cgetg(dK+1,t_VECSMALL); while (dK)

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

/* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do

y[i] = 1; /* y = [0,...,0,1] */ do { /* cf. algo 5.3.18 */ GEN be, res, X = FpV_red(gmul_mati_smallvec(K, y), gell); if (ok_congruence(X,gell,lW,vecMsup))

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); } DECREASE:

be = compute_beta(X, vecWB, gell, bnfz); res = compute_polrel(&T, be, g, ell); if (DEBUGLEVEL>1) fprintferr("polrel(beta) = %Z\n", res); if (gegal(subgroup, rnfnormgroup(bnr, res))) return gerepilecopy(av, res); /* DONE */ } } while (increment_y(y, dK, ell));

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

while (dK); avma = av; return gzero;

avma = av; return gzero; /* FAIL */

rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, *tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); /* step 7 */ if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); /* step 1 of alg 5.3.5. */ if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; /* step 2 */ if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ell*ell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* */ /* step reduction of R */ if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); /* step 3 */ /* one could factor disc(R) using th. 2.1.6. */ if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); /* computation of the uu(j) (see remark 5.2.15.) */ uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; /* step 4 */ if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((j*d)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 */ if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); /* famat */ Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); /* step 6 */ if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; /* step 7 done above */ /* step 8 */ if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); /* left inverse */ T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { /* l | N(ideal) */ GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } /* step 9 */ if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); /* step 10 and step 11 */ if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; /* step 12 */ if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } /* step 13 */ if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); /* step 14, 15, and 17 */ if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m * u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 */ if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } /* step 18 */ if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; /* step 19 */ for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); /* step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

int i;

subtask (rtems_task_argument arg){ int i; rtems_status_code sc; rtems_id sem = (rtems_id)arg; for (;;) { rtems_task_wake_after (ticksPerSecond * 2); sc = rtems_semaphore_release (sem); if (sc != RTEMS_SUCCESSFUL) printf ("%d: Can't release semaphore: %s\n", __LINE__, rtems_status_text (sc)); }}

10355 /local/tlutelli/issta_data/temp/c/2005_temp/2005/10355/bfded728ec4c912f666df94867c118a1004b0165/init.c/clean/c/src/tests/sptests/sp29/init.c

reducebeta(GEN bnfz, GEN be, long ell)

reducebeta(GEN bnfz, GEN be, GEN ell)

reducebeta(GEN bnfz, GEN be, long ell){ long j,ru, prec = nfgetprec(bnfz); GEN emb,z,u,matunit, nf = checknf(bnfz); matunit = gmulgs(greal((GEN)bnfz[3]), ell); /* log. embeddings of fu^ell */ for (;;) { z = get_arch_real(nf, be, &emb, prec); if (z) break; prec = (prec-1)<<1; if (DEBUGLEVEL) err(warnprec,"reducebeta",prec); nf = nfnewprec(nf,prec); } z = concatsp(matunit, z); u = lllintern(z, 100, 1, prec); if (u) { ru = lg(u); for (j=1; j < ru; j++) if (smodis(gcoeff(u,ru-1,j), ell)) break; /* prime to ell */ if (j < ru) { u = (GEN)u[j]; /* coords on (fu^ell, be) of a small generator */ ru--; setlg(u, ru); be = element_pow(nf, be, (GEN)u[ru]); be = fix_be(bnfz,be,u); } } return reducebetanaive(bnfz, be, NULL, ell);}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

matunit = gmulgs(greal((GEN)bnfz[3]), ell); /* log. embeddings of fu^ell */

if (DEBUGLEVEL>1) fprintferr("reducing beta = %Z\n",be); /* reduce mod Q^ell */ be = reduce_mod_Qell(nf, be, ell); /* reduce l-th root */ z = idealsqrtn(nf, be, ell, 0); z = ideallllred_elt(nf, z); be = element_div(nf, be, element_pow(nf, z, ell)); /* make be integral */ be = reduce_mod_Qell(nf, be, ell); if (DEBUGLEVEL>1) fprintferr("beta reduced via ell-th root = %Z\n",be); matunit = gmul(greal((GEN)bnfz[3]), ell); /* log. embeddings of fu^ell */

reducebeta(GEN bnfz, GEN be, long ell){ long j,ru, prec = nfgetprec(bnfz); GEN emb,z,u,matunit, nf = checknf(bnfz); matunit = gmulgs(greal((GEN)bnfz[3]), ell); /* log. embeddings of fu^ell */ for (;;) { z = get_arch_real(nf, be, &emb, prec); if (z) break; prec = (prec-1)<<1; if (DEBUGLEVEL) err(warnprec,"reducebeta",prec); nf = nfnewprec(nf,prec); } z = concatsp(matunit, z); u = lllintern(z, 100, 1, prec); if (u) { ru = lg(u); for (j=1; j < ru; j++) if (smodis(gcoeff(u,ru-1,j), ell)) break; /* prime to ell */ if (j < ru) { u = (GEN)u[j]; /* coords on (fu^ell, be) of a small generator */ ru--; setlg(u, ru); be = element_pow(nf, be, (GEN)u[ru]); be = fix_be(bnfz,be,u); } } return reducebetanaive(bnfz, be, NULL, ell);}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

if (smodis(gcoeff(u,ru-1,j), ell)) break; /* prime to ell */

if (!divise(gcoeff(u,ru-1,j), ell)) break; /* prime to ell */

reducebeta(GEN bnfz, GEN be, long ell){ long j,ru, prec = nfgetprec(bnfz); GEN emb,z,u,matunit, nf = checknf(bnfz); matunit = gmulgs(greal((GEN)bnfz[3]), ell); /* log. embeddings of fu^ell */ for (;;) { z = get_arch_real(nf, be, &emb, prec); if (z) break; prec = (prec-1)<<1; if (DEBUGLEVEL) err(warnprec,"reducebeta",prec); nf = nfnewprec(nf,prec); } z = concatsp(matunit, z); u = lllintern(z, 100, 1, prec); if (u) { ru = lg(u); for (j=1; j < ru; j++) if (smodis(gcoeff(u,ru-1,j), ell)) break; /* prime to ell */ if (j < ru) { u = (GEN)u[j]; /* coords on (fu^ell, be) of a small generator */ ru--; setlg(u, ru); be = element_pow(nf, be, (GEN)u[ru]); be = fix_be(bnfz,be,u); } } return reducebetanaive(bnfz, be, NULL, ell);}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

be = fix_be(bnfz,be,u);

be = fix_be(bnfz, be, gmul(ell,u));

reducebeta(GEN bnfz, GEN be, long ell){ long j,ru, prec = nfgetprec(bnfz); GEN emb,z,u,matunit, nf = checknf(bnfz); matunit = gmulgs(greal((GEN)bnfz[3]), ell); /* log. embeddings of fu^ell */ for (;;) { z = get_arch_real(nf, be, &emb, prec); if (z) break; prec = (prec-1)<<1; if (DEBUGLEVEL) err(warnprec,"reducebeta",prec); nf = nfnewprec(nf,prec); } z = concatsp(matunit, z); u = lllintern(z, 100, 1, prec); if (u) { ru = lg(u); for (j=1; j < ru; j++) if (smodis(gcoeff(u,ru-1,j), ell)) break; /* prime to ell */ if (j < ru) { u = (GEN)u[j]; /* coords on (fu^ell, be) of a small generator */ ru--; setlg(u, ru); be = element_pow(nf, be, (GEN)u[ru]); be = fix_be(bnfz,be,u); } } return reducebetanaive(bnfz, be, NULL, ell);}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c

if (DEBUGLEVEL>1) fprintferr("beta LLL-reduced mod units = %Z\n",be);

reducebeta(GEN bnfz, GEN be, long ell){ long j,ru, prec = nfgetprec(bnfz); GEN emb,z,u,matunit, nf = checknf(bnfz); matunit = gmulgs(greal((GEN)bnfz[3]), ell); /* log. embeddings of fu^ell */ for (;;) { z = get_arch_real(nf, be, &emb, prec); if (z) break; prec = (prec-1)<<1; if (DEBUGLEVEL) err(warnprec,"reducebeta",prec); nf = nfnewprec(nf,prec); } z = concatsp(matunit, z); u = lllintern(z, 100, 1, prec); if (u) { ru = lg(u); for (j=1; j < ru; j++) if (smodis(gcoeff(u,ru-1,j), ell)) break; /* prime to ell */ if (j < ru) { u = (GEN)u[j]; /* coords on (fu^ell, be) of a small generator */ ru--; setlg(u, ru); be = element_pow(nf, be, (GEN)u[ru]); be = fix_be(bnfz,be,u); } } return reducebetanaive(bnfz, be, NULL, ell);}

2195 /local/tlutelli/issta_data/temp/c/2005_temp/2005/2195/73929b165be3dc8f342788321bf5a06394a0cf3d/kummer.c/clean/src/modules/kummer.c