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Diff for /OpenXM_contrib2/asir2000/lib/sp between version 1.3 and 1.13

version 1.3, 2000/03/10 09:22:39 version 1.13, 2004/04/13 07:43:20
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 /* $OpenXM: OpenXM_contrib2/asir2000/lib/sp,v 1.2 2000/03/10 07:12:06 noro Exp $ */  /*
    * Copyright (c) 1994-2000 FUJITSU LABORATORIES LIMITED
    * All rights reserved.
    *
    * FUJITSU LABORATORIES LIMITED ("FLL") hereby grants you a limited,
    * non-exclusive and royalty-free license to use, copy, modify and
    * redistribute, solely for non-commercial and non-profit purposes, the
    * computer program, "Risa/Asir" ("SOFTWARE"), subject to the terms and
    * conditions of this Agreement. For the avoidance of doubt, you acquire
    * only a limited right to use the SOFTWARE hereunder, and FLL or any
    * third party developer retains all rights, including but not limited to
    * copyrights, in and to the SOFTWARE.
    *
    * (1) FLL does not grant you a license in any way for commercial
    * purposes. You may use the SOFTWARE only for non-commercial and
    * non-profit purposes only, such as academic, research and internal
    * business use.
    * (2) The SOFTWARE is protected by the Copyright Law of Japan and
    * international copyright treaties. If you make copies of the SOFTWARE,
    * with or without modification, as permitted hereunder, you shall affix
    * to all such copies of the SOFTWARE the above copyright notice.
    * (3) An explicit reference to this SOFTWARE and its copyright owner
    * shall be made on your publication or presentation in any form of the
    * results obtained by use of the SOFTWARE.
    * (4) In the event that you modify the SOFTWARE, you shall notify FLL by
    * e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification
    * for such modification or the source code of the modified part of the
    * SOFTWARE.
    *
    * THE SOFTWARE IS PROVIDED AS IS WITHOUT ANY WARRANTY OF ANY KIND. FLL
    * MAKES ABSOLUTELY NO WARRANTIES, EXPRESSED, IMPLIED OR STATUTORY, AND
    * EXPRESSLY DISCLAIMS ANY IMPLIED WARRANTY OF MERCHANTABILITY, FITNESS
    * FOR A PARTICULAR PURPOSE OR NONINFRINGEMENT OF THIRD PARTIES'
    * RIGHTS. NO FLL DEALER, AGENT, EMPLOYEES IS AUTHORIZED TO MAKE ANY
    * MODIFICATIONS, EXTENSIONS, OR ADDITIONS TO THIS WARRANTY.
    * UNDER NO CIRCUMSTANCES AND UNDER NO LEGAL THEORY, TORT, CONTRACT,
    * OR OTHERWISE, SHALL FLL BE LIABLE TO YOU OR ANY OTHER PERSON FOR ANY
    * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, PUNITIVE OR CONSEQUENTIAL
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    * ARISING OUT OF OR RELATING TO THE SOFTWARE OR THIS AGREEMENT, DAMAGES
    * FOR LOSS OF GOODWILL, WORK STOPPAGE, OR LOSS OF DATA, OR FOR ANY
    * DAMAGES, EVEN IF FLL SHALL HAVE BEEN INFORMED OF THE POSSIBILITY OF
    * SUCH DAMAGES, OR FOR ANY CLAIM BY ANY OTHER PARTY. EVEN IF A PART
    * OF THE SOFTWARE HAS BEEN DEVELOPED BY A THIRD PARTY, THE THIRD PARTY
    * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE,
    * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE.
    *
    * $OpenXM: OpenXM_contrib2/asir2000/lib/sp,v 1.12 2004/01/07 08:23:11 noro Exp $
   */
 /*  /*
         sp : functions related to algebraic number fields          sp : functions related to algebraic number fields
   
         Revision History:          Revision History:
   
         2000/03/10    noro    fixed several bugs          2001/10/12    noro    if USE_PARI_FACTOR is nonzero, pari factor is called
           2000/03/10    noro    fixed several bugs around gathering algebraic numbers
         1999/08/24    noro    modified for 1999 release version          1999/08/24    noro    modified for 1999 release version
 */  */
   
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 extern ASCENT,GCDTIME,UFTIME,RESTIME,SQTIME,PRINT$  extern ASCENT,GCDTIME,UFTIME,RESTIME,SQTIME,PRINT$
 extern Ord$  extern Ord$
   extern USE_PARI_FACTOR$
   
   /* gen_sp can handle non-monic poly */
   
   def gen_sp(P)
   {
           P = ptozp(P);
           V = var(P);
           D = deg(P,V);
           LC = coef(P,D,V);
           F = LC^(D-1)*subst(P,V,V/LC);
           /* F must be monic */
           L = sp(F);
           return cons(map(subst,car(L),V,LC*V),cdr(L));
   }
   
 def sp(P)  def sp(P)
 {  {
         RESTIME=UFTIME=GCDTIME=SQTIME=0;          RESTIME=UFTIME=GCDTIME=SQTIME=0;
Line 40  def sp(P)
Line 104  def sp(P)
         }          }
 }  }
   
   /*
           Input:
                   F=F(x,a1,...,an)
                   DL = [[an,dn(an,...,a1)],...,[a2,d2(a2,a1)],[a1,d1(a1)]]
                   'ai' denotes a root of di(t).
           Output:
                   irreducible factorization of F over Q(a1,...,an)
                   [[F1(x,a1,...,an),e1],...,[Fk(x,a1,...,an),ek]]
                   'ej' denotes the multiplicity of Fj.
   */
   
   def af_noalg(F,DL)
   {
           DL = reverse(DL);
           N = length(DL);
           Tab = newvect(N);
           /* Tab = [[a1,r1],...]; ri is a root of di(t,r(i-1),...,r1). */
           AL = [];
           for ( I = 0; I < N; I++ ) {
                   T = DL[I];
                   for ( J = 0, DP = T[1]; J < I; J++ )
                           DP = subst(DP,Tab[J][0],Tab[J][1]);
                   B = newalg(DP);
                   Tab[I] = [T[0],B];
                   F = subst(F,T[0],B);
                   AL = cons(B,AL);
           }
           FL = af(F,AL);
           for ( T = FL, R = []; T != []; T = cdr(T) )
                   R = cons([conv_noalg(T[0][0],Tab),T[0][1]],R);
           return reverse(R);
   }
   
   /*
           Input:
                   F=F(x) univariate polynomial over the rationals
           Output:
                   [FL,DL]
                   DL = [[an,dn(an,...,a1)],...,[a2,d2(a2,a1)],[a1,d1(a1)]]
                   'ai' denotes a root of di(t).
                   FL = [F1,F2,...]
                   irreducible factors of F over Q(a1,...,an)
   */
   
   def sp_noalg(F)
   {
           L = sp(F);
           FL = map(algptorat,L[0]);
           for ( T = L[1], DL = []; T != []; T = cdr(T) )
                   DL = cons([algtorat(T[0][0]),T[0][1]],DL);
           return [FL,reverse(DL)];
   }
   
   def conv_noalg(F,Tab)
   {
           N = size(Tab)[0];
           F = algptorat(F);
           for ( I = N-1; I >= 0; I-- )
                   F = subst(F,algtorat(Tab[I][1]),Tab[I][0]);
           return F;
   }
   
 def aflist(L,AL)  def aflist(L,AL)
 {  {
         for ( DC = []; L != []; L = cdr(L) ) {          for ( DC = []; L != []; L = cdr(L) ) {
Line 482  def simpcoef(P) {
Line 608  def simpcoef(P) {
 }  }
   
 def ufctrhint_heuristic(P,HINT,PP,SHIFT) {  def ufctrhint_heuristic(P,HINT,PP,SHIFT) {
           if ( USE_PARI_FACTOR )
                   return pari_ufctr(P);
           else
                   return asir_ufctrhint_heuristic(P,HINT,PP,SHIFT);
   }
   
   def pari_ufctr(P) {
           F = pari(factor,P);
           S = size(F);
           for ( I = S[0]-1, R = []; I >= 0; I-- )
                   R = cons(vtol(F[I]),R);
           return cons([1,1],R);
   }
   
   def asir_ufctrhint_heuristic(P,HINT,PP,SHIFT) {
         V = var(P); D = deg(P,V);          V = var(P); D = deg(P,V);
         if ( D == HINT )          if ( D == HINT )
                 return [[P,1]];                  return [[P,1]];
Line 662  def norm_ch_lag(V,VM,P,P0) {
Line 803  def norm_ch_lag(V,VM,P,P0) {
   
 def cr_gcda(P1,P2)  def cr_gcda(P1,P2)
 {  {
         if ( !(V = var(P1)) || !var(P2) )          if ( !P1 )
                   return P2;
           if ( !P2 )
                   return P1;
           if ( !var(P1) || !var(P2) )
                 return 1;                  return 1;
           V = var(P1);
         EXT = union_sort(getalgtreep(P1),getalgtreep(P2));          EXT = union_sort(getalgtreep(P1),getalgtreep(P2));
         if ( EXT == [] )          if ( EXT == [] )
                 return gcd(P1,P2);                  return gcd(P1,P2);
Line 1200  def resfctr(F,L,V,N)
Line 1346  def resfctr(F,L,V,N)
         N = ptozp(N);          N = ptozp(N);
         V0 = var(N);          V0 = var(N);
         DN = diff(N,V0);          DN = diff(N,V0);
           LC = coef(N,deg(N,V0),V0);
           LCD = coef(DN,deg(DN,V0),V0);
         for ( I = 0, J = 2, Len = deg(N,V0)+1; I < 5; J++ ) {          for ( I = 0, J = 2, Len = deg(N,V0)+1; I < 5; J++ ) {
                 M = prime(J);                  M = prime(J);
                   if ( !(LC%M) || !(LCD%M))
                           continue;
                 G = gcd(N,DN,M);                  G = gcd(N,DN,M);
                 if ( !deg(G,V0) ) {                  if ( !deg(G,V0) ) {
                         I++;                          I++;
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