path: root/sci-mathematics/pari/files/pari-2.5.4-polred.patch

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