+++ /dev/null
-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
projects / gentoo.git / commitdiff