| diff -ru src/src/basemath/base1.c b/src/basemath/base1.c |
| --- src/src/basemath/base1.c 2013-05-06 16:01:56.000000000 +0200 |
| +++ b/src/basemath/base1.c 2013-05-06 16:49:09.042406927 +0200 |
| @@ -1675,40 +1675,42 @@ |
| ZX_is_better(GEN y, GEN x, GEN *dx) |
| { |
| GEN d = ZX_disc(y); |
| - long cmp = absi_cmp(d, *dx); |
| + int cmp; |
| + if (!*dx) *dx = ZX_disc(x); |
| + cmp = absi_cmp(d, *dx); |
| if (cmp < 0) { *dx = d; return 1; } |
| if (cmp == 0) return cmp_abs_ZX(y, x) < 0; |
| return 0; |
| } |
| |
| -static GEN polred_aux(nfbasic_t *T, GEN *pro, long flag); |
| +static void polredbest_aux(nfbasic_t *T, GEN *pro, GEN *px, GEN *pdx, GEN *pa); |
| /* Seek a simpler, polynomial pol defining the same number field as |
| * x (assumed to be monic at this point) */ |
| static GEN |
| nfpolred(nfbasic_t *T, GEN *pro) |
| { |
| - GEN x = T->x, dx = T->dx, a, z, rev, pow, dpow; |
| + GEN x = T->x, dx, b, rev, pow, dpow; |
| long i, n = degpol(x), v = varn(x); |
| |
| if (n == 1) { |
| T->x = deg1pol_shallow(gen_1, gen_m1, v); |
| *pro = NULL; return pol_1(v); |
| } |
| - z = polred_aux(T, pro, nf_ORIG | nf_RED); |
| - if (typ(z) != t_VEC || !ZX_is_better(gel(z,1),x,&dx)) |
| - return NULL; /* no improvement */ |
| - |
| - rev = QXQ_reverse(gel(z,2), x); |
| - x = gel(z,1); if (DEBUGLEVEL>1) err_printf("xbest = %Ps\n",x); |
| + polredbest_aux(T, pro, &x, &dx, &b); |
| + if (x == T->x) return NULL; /* no improvement */ |
| + if (DEBUGLEVEL>1) err_printf("xbest = %Ps\n",x); |
| |
| /* update T */ |
| + rev = QXQ_reverse(b, T->x); |
| pow = QXQ_powers(rev, n-1, x); |
| pow = Q_remove_denom(pow, &dpow); |
| - a = T->bas; |
| - for (i=2; i<=n; i++) gel(a,i) = QX_ZXQV_eval(gel(a,i), pow, dpow); |
| + for (i=2; i<=n; i++) gel(T->bas,i) = QX_ZXQV_eval(gel(T->bas,i), pow, dpow); |
| (void)Z_issquareall(diviiexact(dx,T->dK), &(T->index)); |
| - T->basden = get_bas_den(a); |
| - T->dx = dx; T->x = x; *pro = NULL; return rev; |
| + T->basden = get_bas_den(T->bas); |
| + T->dx = dx; |
| + T->x = x; |
| + *pro = NULL; /* reset */ |
| + return rev; |
| } |
| |
| /* let bas a t_VEC of QX giving a Z-basis of O_K. Return the index of the |
| @@ -1776,7 +1778,7 @@ |
| x = Q_primpart(x); |
| RgX_check_ZX(x, "nfinit"); |
| if (!ZX_is_irred(x)) pari_err(redpoler, "nfinit"); |
| - if (flag & nf_RED || !gequal1(gel(x,lg(x)-1))) |
| + if (flag & nf_RED || !equali1(gel(x,lg(x)-1))) |
| x = ZX_Q_normalize(x, &(T->lead)); |
| nfmaxord(&S, x, flag, fa); |
| index = S.index; |
| @@ -1822,26 +1824,32 @@ |
| nfinitall(GEN x, long flag, long prec) |
| { |
| const pari_sp av = avma; |
| - GEN nf; |
| + GEN nf, lead; |
| nfbasic_t T; |
| |
| nfbasic_init(x, flag, NULL, &T); |
| nfbasic_add_disc(&T); /* more expensive after set_LLL_basis */ |
| - if (T.lead != gen_1 && !(flag & nf_RED)) |
| + lead = T.lead; |
| + if (lead != gen_1 && !(flag & nf_RED)) |
| { |
| pari_warn(warner,"non-monic polynomial. Result of the form [nf,c]"); |
| flag |= nf_RED | nf_ORIG; |
| } |
| if (flag & nf_RED) |
| { |
| - GEN ro, rev = nfpolred(&T, &ro); |
| + GEN ro, rev; |
| + /* lie to polred: more efficient to update *after* modreverse, than to |
| + * unscale in the polred subsystem */ |
| + T.lead = gen_1; |
| + rev = nfpolred(&T, &ro); |
| nf = nfbasic_to_nf(&T, ro, prec); |
| if (flag & nf_ORIG) |
| { |
| if (!rev) rev = pol_x(varn(T.x)); /* no improvement */ |
| - if (T.lead != gen_1) rev = RgX_Rg_div(rev, T.lead); |
| + if (lead != gen_1) rev = RgX_Rg_div(rev, lead); |
| nf = mkvec2(nf, mkpolmod(rev, T.x)); |
| } |
| + T.lead = lead; /* restore */ |
| } else { |
| GEN ro; set_LLL_basis(&T, &ro, 0.99); |
| nf = nfbasic_to_nf(&T, ro, prec); |
| @@ -1948,7 +1956,7 @@ |
| get_polchar(CG_data *d, GEN x) |
| { return get_pol(d, RgM_RgC_mul(d->ZKembed,x)); } |
| |
| -/* return a defining polynomial for Q(w_i) */ |
| +/* return a defining polynomial for Q(w_k) */ |
| static GEN |
| get_polmin_w(CG_data *d, long k) |
| { |
| @@ -1956,6 +1964,22 @@ |
| if (g) (void)ZX_gcd_all(g, ZX_deriv(g), &g); |
| return g; |
| } |
| +/* return a defining polynomial for Q(w_k+w_l) */ |
| +static GEN |
| +get_polmin_add2(CG_data *d, long k, long l) |
| +{ |
| + GEN g = get_pol(d, RgV_add(gel(d->ZKembed,k), gel(d->ZKembed,l))); |
| + if (g) (void)ZX_gcd_all(g, ZX_deriv(g), &g); |
| + return g; |
| +} |
| +/* return a defining polynomial for Q(w_k-w_l) */ |
| +static GEN |
| +get_polmin_sub2(CG_data *d, long k, long l) |
| +{ |
| + GEN g = get_pol(d, RgV_sub(gel(d->ZKembed,k), gel(d->ZKembed,l))); |
| + if (g) (void)ZX_gcd_all(g, ZX_deriv(g), &g); |
| + return g; |
| +} |
| |
| /* does x generate the correct field ? */ |
| static GEN |
| @@ -2044,13 +2068,67 @@ |
| d->v = varn(T->x); |
| d->r1= T->r1; return prec; |
| } |
| +static void |
| +update(GEN *pai, GEN *pch, nfbasic_t *T, long orig) |
| +{ |
| + GEN ch = *pch, ai = *pai; |
| + if (!ch) |
| + { /* accuracy too low, compute algebraically */ |
| + ch = ZXQ_charpoly(ai, T->x, varn(T->x)); |
| + (void)ZX_gcd_all(ch, ZX_deriv(ch), &ch); |
| + } |
| + if (ZX_canon_neg(ch) && orig) ai = RgX_neg(ai); |
| + if (DEBUGLEVEL>3) err_printf("polred: generator %Ps\n", ch); |
| + if (T->lead != gen_1 && orig) ai = RgX_unscale(ai, ginv(T->lead)); |
| + *pch = ch; *pai = ai; |
| +} |
| +static GEN |
| +findmindisc(GEN y, GEN *pa) |
| +{ |
| + GEN a = *pa, x = gel(y,1), b = gel(a,1), dx = NULL; |
| + long i, l = lg(y); |
| + for (i = 2; i < l; i++) |
| + { |
| + GEN yi = gel(y,i); |
| + if (ZX_is_better(yi,x,&dx)) { x = yi; b = gel(a,i); } |
| + } |
| + *pa = b; return x; |
| +} |
| +/* filter [y,b] from polred_aux: keep a single polynomial of degree n in y |
| + * [ the best wrt discriminant ordering ], but keep all non-primitive |
| + * polynomials */ |
| +static void |
| +filter(GEN y, GEN b, long n) |
| +{ |
| + GEN x, a, dx; |
| + long i, k = 1, l = lg(y); |
| + a = x = dx = NULL; |
| + for (i = 1; i < l; i++) |
| + { |
| + GEN yi = gel(y,i), ai = gel(b,i); |
| + if (degpol(yi) == n) |
| + { |
| + if (dx && !ZX_is_better(yi,x,&dx)) continue; |
| + if (!dx) dx = ZX_disc(yi); |
| + x = yi; a = ai; continue; |
| + } |
| + gel(y,k) = yi; |
| + gel(b,k) = ai; k++; |
| + } |
| + if (dx) |
| + { |
| + gel(y,k) = x; |
| + gel(b,k) = a; k++; |
| + } |
| + setlg(y, k); |
| + setlg(b, k); |
| +} |
| + |
| static GEN |
| -polred_aux(nfbasic_t *T, GEN *pro, long flag) |
| +polred_aux(nfbasic_t *T, GEN *pro, long orig) |
| { |
| GEN b, y, x = T->x; |
| - long i, v = varn(x), l = lg(T->bas); |
| - const long orig = flag & nf_ORIG; |
| - const long nfred = flag & nf_RED; |
| + long maxi, i, j, k, v = varn(x), n = lg(T->bas)-1; |
| nffp_t F; |
| CG_data d; |
| |
| @@ -2058,27 +2136,41 @@ |
| *pro = F.ro; |
| d.ZKembed = F.M; |
| |
| - y = cgetg(l, t_VEC); |
| - b = cgetg(l, t_COL); |
| + /* n + 2 sum_{1 <= i <= n} n-i = n + n(n-1) = n*n */ |
| + y = cgetg(n*n + 1, t_VEC); |
| + b = cgetg(n*n + 1, t_COL); |
| + /* i = 1 */ |
| gel(y,1) = deg1pol_shallow(gen_1, gen_m1, v); |
| gel(b,1) = gen_1; |
| - for (i = 2; i < l; i++) |
| + for (i = k = 2; i <= n; i++) |
| { |
| - GEN ch, ai = gel(T->bas,i); |
| + GEN ch, ai; |
| + ai = gel(T->bas,i); |
| ch = get_polmin_w(&d, i); |
| - /* if accuracy too low, compute algebraically */ |
| - if (!ch) |
| + update(&ai, &ch, T, orig); |
| + gel(y,k) = ch; |
| + gel(b,k) = ai; k++; |
| + } |
| + k = i; |
| + maxi = minss(n, 3); |
| + for (i = 1; i <= maxi; i++) |
| + for (j = i+1; j <= n; j++) |
| { |
| - ch = ZXQ_charpoly(ai, x, v); |
| - (void)ZX_gcd_all(ch, ZX_deriv(ch), &ch); |
| + GEN ch, ai; |
| + ai = gadd(gel(T->bas,i), gel(T->bas,j)); |
| + ch = get_polmin_add2(&d, i, j); |
| + update(&ai, &ch, T, orig); |
| + gel(y,k) = ch; |
| + gel(b,k) = ai; k++; |
| + |
| + ai = gsub(gel(T->bas,i), gel(T->bas,j)); |
| + ch = get_polmin_sub2(&d, i, j); |
| + update(&ai, &ch, T, orig); |
| + gel(y,k) = ch; |
| + gel(b,k) = ai; k++; |
| } |
| - if (ZX_canon_neg(ch) && orig) ai = RgX_neg(ai); |
| - if (nfred && degpol(ch) == l-1) return mkvec2(ch, ai); |
| - if (DEBUGLEVEL>3) err_printf("polred: generator %Ps\n", ch); |
| - if (T->lead != gen_1 && orig) ai = RgX_unscale(ai, ginv(T->lead)); |
| - gel(y,i) = ch; |
| - gel(b,i) = ai; |
| - } |
| + setlg(y, k); |
| + setlg(b, k); filter(y, b, n); |
| if (!orig) return gen_sort_uniq(y, (void*)cmpii, &gen_cmp_RgX); |
| (void)sort_factor_pol(mkmat2(y, b), cmpii); |
| settyp(y, t_COL); return mkmat2(b, y); |
| @@ -2089,10 +2181,58 @@ |
| { |
| pari_sp av = avma; |
| GEN ro; |
| - nfbasic_t T; nfbasic_init(x, flag & (nf_PARTIALFACT|nf_RED), fa, &T); |
| + nfbasic_t T; nfbasic_init(x, flag & nf_PARTIALFACT, fa, &T); |
| return gerepilecopy(av, polred_aux(&T, &ro, flag & nf_ORIG)); |
| } |
| |
| +/* finds "best" polynomial in polred_aux list, defaulting to T->x if none of |
| + * them is primitive. *px is the ZX, characteristic polynomial of *pb, *pdx |
| + * its discriminant. |
| + * Set *pro = polroots(T->x) [ NOT *px ], in case caller needs it. */ |
| +static void |
| +polredbest_aux(nfbasic_t *T, GEN *pro, GEN *px, GEN *pdx, GEN *pb) |
| +{ |
| + GEN a, v, y, x = T->x, b = pol_x(varn(x)); /* default values */ |
| + long i, l, n = degpol(x); |
| + v = polred_aux(T, pro, nf_ORIG); |
| + *pdx = T->dx; |
| + y = gel(v,2); |
| + a = gel(v,1); l = lg(a); |
| + for (i=1; i<l; i++) |
| + { |
| + GEN yi = gel(y,i); |
| + pari_sp av = avma; |
| + if (degpol(yi) == n && ZX_is_better(yi,x,pdx)) { x = yi; b = gel(a,i); } |
| + else avma = av; |
| + } |
| + *px = x; |
| + *pb = b; |
| +} |
| +GEN |
| +polredbest(GEN x, long flag) |
| +{ |
| + pari_sp av = avma; |
| + GEN dx, ro, b; |
| + long fl; |
| + nfbasic_t T; |
| + switch(flag) |
| + { |
| + default: pari_err(talker, "invalid flag in polredbest()"); |
| + case 0: fl = nf_PARTIALFACT; break; |
| + case 1: fl = nf_PARTIALFACT|nf_ORIG; break; |
| + } |
| + nfbasic_init(x, fl, NULL, &T); |
| + polredbest_aux(&T, &ro, &x, &dx, &b); |
| + if (flag) |
| + { |
| + if (x == T.x) |
| + b = pol_x(varn(x)); /* no improvement */ |
| + else |
| + b = QXQ_reverse(b, T.x); |
| + x = mkvec2(x, mkpolmod(b,x)); |
| + } |
| + return gerepilecopy(av, x); |
| +} |
| /* FIXME: backward compatibility */ |
| GEN |
| polred0(GEN x, long flag, GEN fa) |
| @@ -2273,22 +2413,6 @@ |
| return bound; |
| } |
| |
| -static GEN |
| -findmindisc(GEN y, GEN *pa) |
| -{ |
| - GEN a = *pa, x = gel(y,1), b = gel(a,1), dx; |
| - long i, l = lg(y); |
| - |
| - if (l == 2) { *pa = b; return x; } |
| - dx = ZX_disc(x); |
| - for (i = 2; i < l; i++) |
| - { |
| - GEN yi = gel(y,i); |
| - if (ZX_is_better(yi,x,&dx)) { x = yi; b = gel(a,i); } |
| - } |
| - *pa = b; return x; |
| -} |
| - |
| /* z "small" minimal polynomial of Mod(a,x), deg z = deg x */ |
| static GEN |
| store(GEN x, GEN z, GEN a, nfbasic_t *T, long flag, GEN u) |
| @@ -2355,7 +2479,7 @@ |
| GEN y, a, u; |
| nfbasic_t T; |
| |
| - nfbasic_init(x, flag & (nf_PARTIALFACT|nf_RED), NULL, &T); |
| + nfbasic_init(x, flag & nf_PARTIALFACT, NULL, &T); |
| x = T.x; vx = varn(x); |
| |
| if (degpol(x) == 1) |
| diff -ru src/src/functions/number_fields/polredabs b/src/functions/number_fields/polredabs |
| --- src/src/functions/number_fields/polredabs 2013-05-06 16:01:57.000000000 +0200 |
| +++ b/src/functions/number_fields/polredabs 2013-05-06 16:47:04.542393431 +0200 |
| @@ -17,8 +17,8 @@ |
| \misctitle{Warning} This routine uses an exponential-time algorithm to |
| enumerate all potential generators, and may be exceedingly slow when the |
| number field has many subfields, hence a lot of elements of small $T_2$-norm. |
| - E.g. do not try it on the compositum of many quadratic fields; in that case, |
| - use \tet{polred} instead. |
| + The function \tet{polredbest} is in general much faster (it runs in |
| + polynomial time), and tends to return polynomials with smaller discriminants. |
| |
| The binary digits of $\fl$ mean |
| |
| @@ -38,6 +38,15 @@ |
| (has at most one large prime factor not in the \kbd{addprimes} table), the |
| result is the same. |
| |
| + \bprog |
| + ? T = x^16 - 136*x^14 + 6476*x^12 - 141912*x^10 + 1513334*x^8 - 7453176*x^6 + 13950764*x^4 - 5596840*x^2 + 46225 |
| + ? T1 = polredabs(T); T2 = polredbest(T); |
| + ? [ norml2(polroots(T1)), norml2(polroots(T2)) ] |
| + %3 = [88.0000000, 120.000000] |
| + ? [ sizedigit(poldisc(T1)), sizedigit(poldisc(T2)) ] |
| + %4 = [75, 67] |
| + @eprog |
| + |
| Variant: Instead of the above hardcoded numerical flags, one should use an |
| or-ed combination of |
| |
| diff -ruN src/src/functions/number_fields/polredbest b/src/functions/number_fields/polredbest |
| --- src/src/functions/number_fields/polredbest 1970-01-01 01:00:00.000000000 +0100 |
| +++ b/src/functions/number_fields/polredbest 2013-01-31 14:49:05.547513332 +0100 |
| @@ -0,0 +1,21 @@ |
| +Function: polredbest |
| +Section: number_fields |
| +C-Name: polredbest |
| +Prototype: GD0,L, |
| +Help: polredbest(T,{flag=0}): reduction of the polynomial T (gives minimal |
| + polynomials only). If flag=1, gives also elements. |
| +Doc: finds a polynomial with reasonably |
| + small coefficients defining the same number field as $T$. |
| + All $T$ accepted by \tet{nfinit} are also allowed here (e.g. non-monic |
| + polynomials, \kbd{nf}, \kbd{bnf}, \kbd{[T,Z\_K\_basis]}). Contrary to |
| + \tet{polredabs}, this routine runs in polynomial time, but it offers no |
| + guarantee as to the minimality of its result. |
| + |
| + If $\fl = 1$: outputs a two-component row vector $[P,a]$, where $P$ is the |
| + default output and \kbd{Mod(a, P)} is a root of the original $T$. |
| + \bprog |
| + ? polredbest(x^4 + 8, 1) |
| + %1 = [x^4 + 2, Mod(x^3, x^4 + 2)] |
| + ? charpoly(%[2]) |
| + %2 = x^4 + 8 |
| + @eprog |
| diff -ruN src/src/headers/paridecl.h b/src/headers/paridecl.h |
| --- src/src/headers/paridecl.h 2012-09-25 23:10:47.000000000 +0200 |
| +++ b/src/headers/paridecl.h 2013-01-31 14:49:05.557525771 +0100 |
| @@ -889,6 +889,7 @@ |
| GEN polredabs0(GEN x, long flag); |
| GEN polredabs2(GEN x); |
| GEN polredabsall(GEN x, long flun); |
| +GEN polredbest(GEN x, long flag); |
| GEN smallpolred(GEN x); |
| GEN smallpolred2(GEN x); |
| GEN tschirnhaus(GEN x); |
| diff -ru src/src/test/32/compat b/src/test/32/compat |
| --- src/src/test/32/compat 2013-05-06 16:01:57.000000000 +0200 |
| +++ b/src/test/32/compat 2013-05-06 16:47:04.542393431 +0200 |
| @@ -787,13 +787,9 @@ |
| ? factoreddiscf(p,fa) |
| 136866601 |
| ? factoredpolred(p,fa) |
| -[x - 1, x^5 - 2*x^4 - 62*x^3 + 85*x^2 + 818*x + 1, x^5 - 2*x^4 - 53*x^3 - 46 |
| -*x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52 |
| -*x^3 - 197*x^2 - 273*x - 127] |
| +[x - 1, x^5 - 80*x^3 - 223*x^2 + 800*x + 2671] |
| ? factoredpolred2(p,fa) |
| -[x - 1, x^5 - 2*x^4 - 62*x^3 + 85*x^2 + 818*x + 1, x^5 - 2*x^4 - 53*x^3 - 46 |
| -*x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52 |
| -*x^3 - 197*x^2 - 273*x - 127] |
| +[x - 1, x^5 - 80*x^3 - 223*x^2 + 800*x + 2671] |
| ? factornf(x^3+x^2-2*x-1,t^3+t^2-2*t-1) |
| |
| [x + mod(-t, t^3 + t^2 - 2*t - 1) 1] |
| @@ -904,7 +900,7 @@ |
| ? gcd(12345678,87654321) |
| 9 |
| ? getheap() |
| -[208, 45748] |
| +[208, 45584] |
| ? getrand() |
| Vecsmall([1220248512, -582244995, 485580680, -1643185972, -2103930341, -9694 |
| 07356, 336208700, 1439513079, -1910826353, -2042699820, 222745475, 183991374 |
| @@ -2014,7 +2010,7 @@ |
| ? orderell(tcurve,[1,2]) |
| 6 |
| ? ordred(x^3-12*x+45*x-1) |
| -[x - 1, x^3 - 363*x - 2663, x^3 + 33*x - 1] |
| +[x - 1, x^3 + 33*x - 1] |
| ? padicprec(padicno,127) |
| 5 |
| ? pascal(8) |
| @@ -2093,15 +2089,16 @@ |
| ? polint([0,2,3],[0,4,9],5) |
| 25 |
| ? polred(x^5-2*x^4-4*x^3-96*x^2-352*x-568) |
| -[x - 1, x^5 - x^4 - 6*x^3 + 6*x^2 + 13*x - 5, x^5 - x^4 + 2*x^3 - 4*x^2 + x |
| -- 1, x^5 - x^4 + 4*x^3 - 2*x^2 + x - 1, x^5 + 4*x^3 - 4*x^2 + 8*x - 8] |
| +[x - 1, x^5 - x^4 + 2*x^3 - 4*x^2 + x - 1] |
| ? polred2(x^4-28*x^3-458*x^2+9156*x-25321) |
| |
| [1 x - 1] |
| |
| -[1/115*x^2 - 14/115*x - 327/115 x^2 - 10] |
| +[1/115*x^2 - 14/115*x - 212/115 x^2 - 2*x - 9] |
| + |
| +[-1/115*x^2 + 14/115*x + 442/115 x^2 - 2*x - 9] |
| |
| -[2/897*x^3 - 14/299*x^2 - 1171/897*x + 9569/897 x^4 - 32*x^2 + 6] |
| +[1/115*x^2 - 14/115*x - 327/115 x^2 - 10] |
| |
| [1/4485*x^3 - 7/1495*x^2 - 1034/4485*x + 7924/4485 x^4 - 8*x^2 + 6] |
| |
| @@ -2454,13 +2451,21 @@ |
| ? smallinitell([0,0,0,-17,0]) |
| [0, 0, 0, -17, 0, 0, -34, 0, -289, 816, 0, 314432, 1728] |
| ? smallpolred(x^4+576) |
| -[x - 1, x^2 - x + 1, x^2 + 1, x^4 - x^2 + 1] |
| +[x - 1, x^2 - 3*x + 3, x^2 - 2*x + 2, x^2 - x + 1, x^2 + 1, x^4 - x^2 + 1] |
| ? smallpolred2(x^4+576) |
| |
| [1 x - 1] |
| |
| +[-1/192*x^3 - 1/8*x + 3/2 x^2 - 3*x + 3] |
| + |
| +[1/24*x^2 + 1 x^2 - 2*x + 2] |
| + |
| +[-1/24*x^2 + 1 x^2 - 2*x + 2] |
| + |
| [-1/192*x^3 - 1/8*x + 1/2 x^2 - x + 1] |
| |
| +[1/192*x^3 + 1/8*x + 1/2 x^2 - x + 1] |
| + |
| [1/24*x^2 x^2 + 1] |
| |
| [1/192*x^3 + 1/48*x^2 - 1/8*x x^4 - x^2 + 1] |
| @@ -2650,6 +2655,6 @@ |
| ? getstack() |
| 104 |
| ? getheap() |
| -[599, 110982] |
| +[599, 110954] |
| ? print("Total time spent: ",gettime); |
| -Total time spent: 236 |
| +Total time spent: 140 |
| diff -ru src/src/test/32/nfields b/src/test/32/nfields |
| --- src/src/test/32/nfields 2013-05-06 16:01:57.000000000 +0200 |
| +++ b/src/test/32/nfields 2013-05-06 16:47:04.542393431 +0200 |
| @@ -926,45 +926,50 @@ |
| ? polgalois(x^6-3*x^2-1) |
| [12, 1, 1, "A_4(6) = [2^2]3"] |
| ? polred(x^5-2*x^4-4*x^3-96*x^2-352*x-568) |
| -[x - 1, x^5 - x^4 - 6*x^3 + 6*x^2 + 13*x - 5, x^5 - x^4 + 2*x^3 - 4*x^2 + x |
| -- 1, x^5 - x^4 + 4*x^3 - 2*x^2 + x - 1, x^5 + 4*x^3 - 4*x^2 + 8*x - 8] |
| +[x - 1, x^5 - x^4 + 2*x^3 - 4*x^2 + x - 1] |
| ? polred(x^4-28*x^3-458*x^2+9156*x-25321,3) |
| |
| [1 x - 1] |
| |
| -[1/115*x^2 - 14/115*x - 327/115 x^2 - 10] |
| +[1/115*x^2 - 14/115*x - 212/115 x^2 - 2*x - 9] |
| + |
| +[-1/115*x^2 + 14/115*x + 442/115 x^2 - 2*x - 9] |
| |
| -[2/897*x^3 - 14/299*x^2 - 1171/897*x + 9569/897 x^4 - 32*x^2 + 6] |
| +[1/115*x^2 - 14/115*x - 327/115 x^2 - 10] |
| |
| [1/4485*x^3 - 7/1495*x^2 - 1034/4485*x + 7924/4485 x^4 - 8*x^2 + 6] |
| |
| ? polred(x^4+576,1) |
| -[x - 1, x^2 - x + 1, x^2 + 1, x^4 - x^2 + 1] |
| +[x - 1, x^2 - 3*x + 3, x^2 - 2*x + 2, x^2 - x + 1, x^2 + 1, x^4 - x^2 + 1] |
| ? polred(x^4+576,3) |
| |
| [1 x - 1] |
| |
| +[-1/192*x^3 - 1/8*x + 3/2 x^2 - 3*x + 3] |
| + |
| +[1/24*x^2 + 1 x^2 - 2*x + 2] |
| + |
| +[-1/24*x^2 + 1 x^2 - 2*x + 2] |
| + |
| [-1/192*x^3 - 1/8*x + 1/2 x^2 - x + 1] |
| |
| +[1/192*x^3 + 1/8*x + 1/2 x^2 - x + 1] |
| + |
| [1/24*x^2 x^2 + 1] |
| |
| [1/192*x^3 + 1/48*x^2 - 1/8*x x^4 - x^2 + 1] |
| |
| ? polred(p2,0,fa) |
| -[x - 1, x^5 - 2*x^4 - 62*x^3 + 85*x^2 + 818*x + 1, x^5 - 2*x^4 - 53*x^3 - 46 |
| -*x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52 |
| -*x^3 - 197*x^2 - 273*x - 127] |
| +[x - 1, x^5 - 80*x^3 - 223*x^2 + 800*x + 2671] |
| ? polred(p2,1,fa) |
| -[x - 1, x^5 - 2*x^4 - 62*x^3 + 85*x^2 + 818*x + 1, x^5 - 2*x^4 - 53*x^3 - 46 |
| -*x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52 |
| -*x^3 - 197*x^2 - 273*x - 127] |
| +[x - 1, x^5 - 80*x^3 - 223*x^2 + 800*x + 2671] |
| ? polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568) |
| x^5 - x^4 + 2*x^3 - 4*x^2 + x - 1 |
| ? polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568,1) |
| [x^5 - x^4 + 2*x^3 - 4*x^2 + x - 1, Mod(2*x^4 - x^3 + 3*x^2 - 3*x - 1, x^5 - |
| x^4 + 2*x^3 - 4*x^2 + x - 1)] |
| ? polredord(x^3-12*x+45*x-1) |
| -[x - 1, x^3 - 363*x - 2663, x^3 + 33*x - 1] |
| +[x - 1, x^3 + 33*x - 1] |
| ? polsubcyclo(31,5) |
| x^5 + x^4 - 12*x^3 - 21*x^2 + x + 5 |
| ? setrand(1);poltschirnhaus(x^5-x-1) |
| @@ -1028,6 +1033,6 @@ |
| ? sizebyte(%) |
| 152 |
| ? getheap |
| -[175, 113027] |
| +[175, 112999] |
| ? print("Total time spent: ",gettime); |
| -Total time spent: 116 |
| +Total time spent: 76 |
| diff -ru src/src/test/64/compat b/src/test/64/compat |
| --- src/src/test/64/compat 2013-05-06 16:01:58.000000000 +0200 |
| +++ b/src/test/64/compat 2013-05-06 16:47:04.542393431 +0200 |
| @@ -789,13 +789,9 @@ |
| ? factoreddiscf(p,fa) |
| 136866601 |
| ? factoredpolred(p,fa) |
| -[x - 1, x^5 - 2*x^4 - 62*x^3 + 85*x^2 + 818*x + 1, x^5 - 2*x^4 - 53*x^3 - 46 |
| -*x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52 |
| -*x^3 - 197*x^2 - 273*x - 127] |
| +[x - 1, x^5 - 80*x^3 - 223*x^2 + 800*x + 2671] |
| ? factoredpolred2(p,fa) |
| -[x - 1, x^5 - 2*x^4 - 62*x^3 + 85*x^2 + 818*x + 1, x^5 - 2*x^4 - 53*x^3 - 46 |
| -*x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52 |
| -*x^3 - 197*x^2 - 273*x - 127] |
| +[x - 1, x^5 - 80*x^3 - 223*x^2 + 800*x + 2671] |
| ? factornf(x^3+x^2-2*x-1,t^3+t^2-2*t-1) |
| |
| [x + mod(-t, t^3 + t^2 - 2*t - 1) 1] |
| @@ -906,7 +902,7 @@ |
| ? gcd(12345678,87654321) |
| 9 |
| ? getheap() |
| -[208, 44472] |
| +[208, 44308] |
| ? getrand() |
| Vecsmall([-696235626332558091, -7363039021536514678, -3123062006620239999, - |
| 2510915082749224356, -5278885121447018503, 8033304491650294704, 333461878925 |
| @@ -2014,7 +2010,7 @@ |
| ? orderell(tcurve,[1,2]) |
| 6 |
| ? ordred(x^3-12*x+45*x-1) |
| -[x - 1, x^3 - 363*x - 2663, x^3 + 33*x - 1] |
| +[x - 1, x^3 + 33*x - 1] |
| ? padicprec(padicno,127) |
| 5 |
| ? pascal(8) |
| @@ -2093,15 +2089,16 @@ |
| ? polint([0,2,3],[0,4,9],5) |
| 25 |
| ? polred(x^5-2*x^4-4*x^3-96*x^2-352*x-568) |
| -[x - 1, x^5 - x^4 - 6*x^3 + 6*x^2 + 13*x - 5, x^5 - x^4 + 2*x^3 - 4*x^2 + x |
| -- 1, x^5 - x^4 + 4*x^3 - 2*x^2 + x - 1, x^5 + 4*x^3 - 4*x^2 + 8*x - 8] |
| +[x - 1, x^5 - x^4 + 2*x^3 - 4*x^2 + x - 1] |
| ? polred2(x^4-28*x^3-458*x^2+9156*x-25321) |
| |
| [1 x - 1] |
| |
| -[1/115*x^2 - 14/115*x - 327/115 x^2 - 10] |
| +[1/115*x^2 - 14/115*x - 212/115 x^2 - 2*x - 9] |
| + |
| +[-1/115*x^2 + 14/115*x + 442/115 x^2 - 2*x - 9] |
| |
| -[2/897*x^3 - 14/299*x^2 - 1171/897*x + 9569/897 x^4 - 32*x^2 + 6] |
| +[1/115*x^2 - 14/115*x - 327/115 x^2 - 10] |
| |
| [1/4485*x^3 - 7/1495*x^2 - 1034/4485*x + 7924/4485 x^4 - 8*x^2 + 6] |
| |
| @@ -2454,13 +2451,21 @@ |
| ? smallinitell([0,0,0,-17,0]) |
| [0, 0, 0, -17, 0, 0, -34, 0, -289, 816, 0, 314432, 1728] |
| ? smallpolred(x^4+576) |
| -[x - 1, x^2 - x + 1, x^2 + 1, x^4 - x^2 + 1] |
| +[x - 1, x^2 - 3*x + 3, x^2 - 2*x + 2, x^2 - x + 1, x^2 + 1, x^4 - x^2 + 1] |
| ? smallpolred2(x^4+576) |
| |
| [1 x - 1] |
| |
| +[-1/192*x^3 - 1/8*x + 3/2 x^2 - 3*x + 3] |
| + |
| +[1/24*x^2 + 1 x^2 - 2*x + 2] |
| + |
| +[-1/24*x^2 + 1 x^2 - 2*x + 2] |
| + |
| [-1/192*x^3 - 1/8*x + 1/2 x^2 - x + 1] |
| |
| +[1/192*x^3 + 1/8*x + 1/2 x^2 - x + 1] |
| + |
| [1/24*x^2 x^2 + 1] |
| |
| [1/192*x^3 + 1/48*x^2 - 1/8*x x^4 - x^2 + 1] |
| @@ -2649,6 +2654,6 @@ |
| ? getstack() |
| 200 |
| ? getheap() |
| -[599, 100048] |
| +[599, 100020] |
| ? print("Total time spent: ",gettime); |
| -Total time spent: 152 |
| +Total time spent: 180 |
| diff -ru src/src/test/64/nfields b/src/test/64/nfields |
| --- src/src/test/64/nfields 2013-05-06 16:01:58.000000000 +0200 |
| +++ b/src/test/64/nfields 2013-05-06 16:47:04.542393431 +0200 |
| @@ -928,45 +928,50 @@ |
| ? polgalois(x^6-3*x^2-1) |
| [12, 1, 1, "A_4(6) = [2^2]3"] |
| ? polred(x^5-2*x^4-4*x^3-96*x^2-352*x-568) |
| -[x - 1, x^5 - x^4 - 6*x^3 + 6*x^2 + 13*x - 5, x^5 - x^4 + 2*x^3 - 4*x^2 + x |
| -- 1, x^5 - x^4 + 4*x^3 - 2*x^2 + x - 1, x^5 + 4*x^3 - 4*x^2 + 8*x - 8] |
| +[x - 1, x^5 - x^4 + 2*x^3 - 4*x^2 + x - 1] |
| ? polred(x^4-28*x^3-458*x^2+9156*x-25321,3) |
| |
| [1 x - 1] |
| |
| -[1/115*x^2 - 14/115*x - 327/115 x^2 - 10] |
| +[1/115*x^2 - 14/115*x - 212/115 x^2 - 2*x - 9] |
| + |
| +[-1/115*x^2 + 14/115*x + 442/115 x^2 - 2*x - 9] |
| |
| -[2/897*x^3 - 14/299*x^2 - 1171/897*x + 9569/897 x^4 - 32*x^2 + 6] |
| +[1/115*x^2 - 14/115*x - 327/115 x^2 - 10] |
| |
| [1/4485*x^3 - 7/1495*x^2 - 1034/4485*x + 7924/4485 x^4 - 8*x^2 + 6] |
| |
| ? polred(x^4+576,1) |
| -[x - 1, x^2 - x + 1, x^2 + 1, x^4 - x^2 + 1] |
| +[x - 1, x^2 - 3*x + 3, x^2 - 2*x + 2, x^2 - x + 1, x^2 + 1, x^4 - x^2 + 1] |
| ? polred(x^4+576,3) |
| |
| [1 x - 1] |
| |
| +[-1/192*x^3 - 1/8*x + 3/2 x^2 - 3*x + 3] |
| + |
| +[1/24*x^2 + 1 x^2 - 2*x + 2] |
| + |
| +[-1/24*x^2 + 1 x^2 - 2*x + 2] |
| + |
| [-1/192*x^3 - 1/8*x + 1/2 x^2 - x + 1] |
| |
| +[1/192*x^3 + 1/8*x + 1/2 x^2 - x + 1] |
| + |
| [1/24*x^2 x^2 + 1] |
| |
| [1/192*x^3 + 1/48*x^2 - 1/8*x x^4 - x^2 + 1] |
| |
| ? polred(p2,0,fa) |
| -[x - 1, x^5 - 2*x^4 - 62*x^3 + 85*x^2 + 818*x + 1, x^5 - 2*x^4 - 53*x^3 - 46 |
| -*x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52 |
| -*x^3 - 197*x^2 - 273*x - 127] |
| +[x - 1, x^5 - 80*x^3 - 223*x^2 + 800*x + 2671] |
| ? polred(p2,1,fa) |
| -[x - 1, x^5 - 2*x^4 - 62*x^3 + 85*x^2 + 818*x + 1, x^5 - 2*x^4 - 53*x^3 - 46 |
| -*x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52 |
| -*x^3 - 197*x^2 - 273*x - 127] |
| +[x - 1, x^5 - 80*x^3 - 223*x^2 + 800*x + 2671] |
| ? polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568) |
| x^5 - x^4 + 2*x^3 - 4*x^2 + x - 1 |
| ? polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568,1) |
| [x^5 - x^4 + 2*x^3 - 4*x^2 + x - 1, Mod(2*x^4 - x^3 + 3*x^2 - 3*x - 1, x^5 - |
| x^4 + 2*x^3 - 4*x^2 + x - 1)] |
| ? polredord(x^3-12*x+45*x-1) |
| -[x - 1, x^3 - 363*x - 2663, x^3 + 33*x - 1] |
| +[x - 1, x^3 + 33*x - 1] |
| ? polsubcyclo(31,5) |
| x^5 + x^4 - 12*x^3 - 21*x^2 + x + 5 |
| ? setrand(1);poltschirnhaus(x^5-x-1) |
| @@ -1030,6 +1035,6 @@ |
| ? sizebyte(%) |
| 288 |
| ? getheap |
| -[175, 102929] |
| +[175, 102901] |
| ? print("Total time spent: ",gettime); |
| -Total time spent: 84 |
| +Total time spent: 110 |
