is a computer algebra system designed for fast computations in number theory (factorizations, algebraic number theory, elliptic curves...), but also contains a large number of other mathematical functions.
| alglin1.c (pari-2.13.0) | : | alglin1.c (pari-2.13.1) |
|---|
| | |
| skipping to change at line 2890 | | skipping to change at line 2890 |
|---|
| } | | } |
| /* N.B. Our delta/lambda are SQUARES of those in the paper | | /* N.B. Our delta/lambda are SQUARES of those in the paper |
| * log(delta lambda) / log p, where lambda is 3+sqrt(5) / 2, | | * log(delta lambda) / log p, where lambda is 3+sqrt(5) / 2, |
| * whose log is < 1, hence + 1 (to cater for rounding errors) */ | | * whose log is < 1, hence + 1 (to cater for rounding errors) */ |
| m = (long)ceil((dbllog2(delta)*M_LN2 + 1) / log((double)p)); | | m = (long)ceil((dbllog2(delta)*M_LN2 + 1) / log((double)p)); |
| res = ZlM_gauss_ratlift(a, b, p, m, C); | | res = ZlM_gauss_ratlift(a, b, p, m, C); |
| if (iscol) return gerepilecopy(av, gel(res, 1)); | | if (iscol) return gerepilecopy(av, gel(res, 1)); |
| return gerepileupto(av, res); | | return gerepileupto(av, res); |
| } | | } |
| | |
|
| | /* #C = n, C[z[i]] = K[i], complete by 0s */ |
| static GEN | | static GEN |
|
| RgC_inflate(GEN K, GEN v, long n) | | RgC_inflate(GEN K, GEN z, long n) |
| { | | { |
| GEN c = zerocol(n); | | GEN c = zerocol(n); |
| long j, l = lg(K); | | long j, l = lg(K); |
|
| for (j = 1; j < l; j++) gel(c, v[j]) = gel(K, j); | | for (j = 1; j < l; j++) gel(c, z[j]) = gel(K, j); |
| return c; | | return c; |
| } | | } |
|
| | /* in place: C[i] *= cB / v[i] */ |
| | static void |
| | QC_normalize(GEN C, GEN v, GEN cB) |
| | { |
| | long l = lg(C), i; |
| | for (i = 1; i < l; i++) |
| | { |
| | GEN c = cB, k = gel(C,i), d = gel(v,i); |
| | if (d) |
| | { |
| | if (isintzero(d)) { gel(C,i) = gen_0; continue; } |
| | c = div_content(c, d); |
| | } |
| | gel(C,i) = c? gmul(k,c): k; |
| | } |
| | } |
| | |
| /* same as above, M rational; if flag = 1, call indexrank and return 1 sol */ | | /* same as above, M rational; if flag = 1, call indexrank and return 1 sol */ |
| GEN | | GEN |
| QM_gauss_i(GEN M, GEN B, long flag) | | QM_gauss_i(GEN M, GEN B, long flag) |
| { | | { |
| pari_sp av = avma; | | pari_sp av = avma; |
|
| long i, l = lg(M); | | long i, l, n; |
| | int col = typ(B) == t_COL; |
| GEN K, cB, N = cgetg_copy(M, &l), v = cgetg(l, t_VEC), z2 = NULL; | | GEN K, cB, N = cgetg_copy(M, &l), v = cgetg(l, t_VEC), z2 = NULL; |
|
| | |
| for (i = 1; i < l; i++) | | for (i = 1; i < l; i++) |
| gel(N,i) = Q_primitive_part(gel(M,i), &gel(v,i)); | | gel(N,i) = Q_primitive_part(gel(M,i), &gel(v,i)); |
| if (flag) | | if (flag) |
| { | | { |
| GEN z = ZM_indexrank(N), z1 = gel(z,1); | | GEN z = ZM_indexrank(N), z1 = gel(z,1); |
| z2 = gel(z,2); | | z2 = gel(z,2); |
| N = shallowmatextract(N, z1, z2); | | N = shallowmatextract(N, z1, z2); |
|
| B = typ(B) == t_MAT? rowpermute(B,z1): vecpermute(B,z1); | | B = col? vecpermute(B,z1): rowpermute(B,z1); |
| if (lg(z2) == l) z2 = NULL; else { v = vecpermute(v, z2); l = lg(v); } | | if (lg(z2) == l) z2 = NULL; else v = vecpermute(v, z2); |
| } | | } |
| B = Q_primitive_part(B, &cB); | | B = Q_primitive_part(B, &cB); |
| K = ZM_gauss(N, B); if (!K) return gc_NULL(av); | | K = ZM_gauss(N, B); if (!K) return gc_NULL(av); |
|
| for (i = 1; i < l; i++) | | n = l - 1; |
| | if (col) |
| { | | { |
|
| GEN c, k = gel(K,i), d = gel(v,i); | | QC_normalize(K, v, cB); |
| if (d) | | if (z2) K = RgC_inflate(K, z2, n); |
| { | | |
| if (isintzero(d)) | | |
| { | | |
| if (gequal0(k)) continue; | | |
| return NULL; | | |
| } | | |
| d = inv_content(d); | | |
| } | | |
| c = mul_content(cB, d); | | |
| if (c) gel(K,i) = gmul(gel(K,i), c); | | |
| } | | } |
|
| if (z2) | | else |
| { | | { |
|
| long n = lg(M)-1; | | long lK = lg(K); |
| if (typ(B) == t_COL) K = RgC_inflate(K, z2, n); | | for (i = 1; i < lK; i++) |
| else | | |
| { | | { |
|
| l = lg(B); | | QC_normalize(gel(K,i), v, cB); |
| for (i = 1; i < l; i++) gel(B,i) = RgC_inflate(gel(B,i), z2, n); | | if (z2) gel(K,i) = RgC_inflate(gel(K,i), z2, n); |
| } | | } |
| } | | } |
| return gerepilecopy(av, K); | | return gerepilecopy(av, K); |
| } | | } |
| GEN | | GEN |
| QM_gauss(GEN M, GEN B) { return QM_gauss_i(M, B, 0); } | | QM_gauss(GEN M, GEN B) { return QM_gauss_i(M, B, 0); } |
| | |
| static GEN | | static GEN |
| ZM_inv_slice(GEN A, GEN P, GEN *mod) | | ZM_inv_slice(GEN A, GEN P, GEN *mod) |
| { | | { |
| | | |
| End of changes. 12 change blocks. |
|---|
| 24 lines changed or deleted | | 34 lines changed or added |
|---|
"Fossies" - the Fresh Open Source Software Archive 