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Diff for /OpenXM_contrib2/asir2000/lib/sp between version 1.1 and 1.8

version 1.1, 1999/12/03 07:39:11 version 1.8, 2000/08/22 05:04:23
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 /* $OpenXM: OpenXM/src/asir99/lib/sp,v 1.1.1.1 1999/11/10 08:12:30 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
    * DAMAGES OF ANY CHARACTER, INCLUDING, WITHOUT LIMITATION, DAMAGES
    * 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 1.7 2000/08/21 08:31:43 noro Exp $
   */
 /*  /*
         sp : functions related to algebraic number fields          sp : functions related to algebraic number fields
   
         Revision History:          Revision History:
   
         99/08/24    noro    modified for 1999 release version          2000/03/10    noro    fixed several bugs around gathering algebraic numbers
           1999/08/24    noro    modified for 1999 release version
 */  */
   
 #include "defs.h"  #include "defs.h"
Line 39  def sp(P)
Line 88  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 84  def flatmf(L) {
Line 195  def flatmf(L) {
 def af(P,AL)  def af(P,AL)
 {  {
         RESTIME=UFTIME=GCDTIME=SQTIME=0;          RESTIME=UFTIME=GCDTIME=SQTIME=0;
         S = reverse(asq(P,AL));          S = reverse(asq(P));
         for ( L = []; S != []; S = cdr(S) ) {          for ( L = []; S != []; S = cdr(S) ) {
                 FM = car(S); F = FM[0]; M = FM[1];                  FM = car(S); F = FM[0]; M = FM[1];
                 G = af_sp(F,AL,1);                  G = af_sp(F,AL,1);
Line 124  def af_spmain(P,AL,INIT,HINT,PP,SHIFT)
Line 235  def af_spmain(P,AL,INIT,HINT,PP,SHIFT)
         N = simpcoef(sp_norm(A0,V,subst(P,V,V-INIT*A0),AL));          N = simpcoef(sp_norm(A0,V,subst(P,V,V-INIT*A0),AL));
         RESTIME+=time()[0]-TTT;          RESTIME+=time()[0]-TTT;
         TTT = time()[0];          TTT = time()[0];
         DCSQ = sortfs(asq(N,AL));          DCSQ = sortfs(asq(N));
         SQTIME+=time()[0]-TTT;          SQTIME+=time()[0]-TTT;
         for ( G = P, A = V+INIT*A0, DCR = []; DCSQ != []; DCSQ = cdr(DCSQ) ) {          for ( G = P, A = V+INIT*A0, DCR = []; DCSQ != []; DCSQ = cdr(DCSQ) ) {
                 C = TT(DCSQ); D = TS(DCSQ);                  C = TT(DCSQ); D = TS(DCSQ);
Line 142  def af_spmain(P,AL,INIT,HINT,PP,SHIFT)
Line 253  def af_spmain(P,AL,INIT,HINT,PP,SHIFT)
                         else {                          else {
                                 S = subst(car(DCT),V,A);                                  S = subst(car(DCT),V,A);
                                 if ( pra(G,S,AL) )                                  if ( pra(G,S,AL) )
                                         U = cr_gcda(S,G,AL);                                          U = cr_gcda(S,G);
                                 else                                  else
                                         U = S;                                          U = S;
                         }                          }
Line 270  def getalgp(P) {
Line 381  def getalgp(P) {
         else {          else {
                 for ( V = var(P), I = deg(P,V), T = []; I >= 0; I-- )                  for ( V = var(P), I = deg(P,V), T = []; I >= 0; I-- )
                         if ( C = coef(P,I) )                          if ( C = coef(P,I) )
                                 T = union(T,getalgp(C));                                  T = union_sort(T,getalgp(C));
                 return T;                  return T;
         }          }
 }  }
   
 def union(A,B)  def getalgtreep(P) {
 {          if ( type(P) <= 1 )
         for ( T = B; T != []; T = cdr(T) )                  return getalgtree(P);
                 A = union1(A,car(T));          else {
         return A;                  for ( V = var(P), I = deg(P,V), T = []; I >= 0; I-- )
                           if ( C = coef(P,I) )
                                   T = union_sort(T,getalgtreep(C));
                   return T;
           }
 }  }
   
 def union1(A,E)  /* C = union of A and B; A and B is sorted. C should also be sorted. */
   
   def union_sort(A,B)
 {  {
         if ( A == [] )          if ( A == [] )
                 return [E];                  return B;
         else if ( car(A) == E )          else if ( B == [] )
                 return A;                  return A;
         else          else {
                 return cons(car(A),union1(cdr(A),E));                  A0 = car(A);
                   B0 = car(B);
                   if ( A0 == B0 )
                           return cons(A0,union_sort(cdr(A),cdr(B)));
                   else if ( A0 > B0 )
                           return cons(A0,union_sort(cdr(A),B));
                   else
                           return cons(B0,union_sort(A,cdr(B)));
           }
 }  }
   
 def invalgp(A)  def invalgp(A)
Line 359  def sortfs(L)
Line 484  def sortfs(L)
   
 def pdiva(P1,P2)  def pdiva(P1,P2)
 {  {
         A = union(getalgp(P1),getalgp(P2));          A = union_sort(getalgp(P1),getalgp(P2));
         P1 = algptorat(P1); P2 = algptorat(P2);          P1 = algptorat(P1); P2 = algptorat(P2);
         return simpalg(rattoalgp(sdiv(P1*LCOEF(P2)^(DEG(P1)-DEG(P2)+1),P2),A));          return simpalg(rattoalgp(sdiv(P1*LCOEF(P2)^(DEG(P1)-DEG(P2)+1),P2),A));
 }  }
Line 371  def pqra(P1,P2)
Line 496  def pqra(P1,P2)
         else if ( (type(P1) != POLY) || (deg(P1,var(P1)) < deg(P2,var(P1))) )          else if ( (type(P1) != POLY) || (deg(P1,var(P1)) < deg(P2,var(P1))) )
                 return [0,P1];                  return [0,P1];
         else {          else {
                 A = union(getalgp(P1),getalgp(P2));                  A = union_sort(getalgp(P1),getalgp(P2));
                 P1 = algptorat(P1); P2 = algptorat(P2);                  P1 = algptorat(P1); P2 = algptorat(P2);
                 L = sqr(P1*LCOEF(P2)^(DEG(P1)-DEG(P2)+1),P2);                  L = sqr(P1*LCOEF(P2)^(DEG(P1)-DEG(P2)+1),P2);
                 return [simpalg(rattoalgp(L[0],A)),simpalg(rattoalgp(L[1],A))];                  return [simpalg(rattoalgp(L[0],A)),simpalg(rattoalgp(L[1],A))];
Line 410  def sort_alg(VL)
Line 535  def sort_alg(VL)
         return L;          return L;
 }  }
   
 def asq(P,AL)  def asq(P)
 {  {
         P = simpalg(P);          P = simpalg(P);
         if ( type(P) == NUM )          if ( type(P) == NUM )
Line 423  def asq(P,AL)
Line 548  def asq(P,AL)
                         if ( type(F) == NUM )                          if ( type(F) == NUM )
                                 break;                                  break;
                         F1 = diff(F,V);                          F1 = diff(F,V);
                         GCD = cr_gcda(F,F1,AL);                          GCD = cr_gcda(F,F1);
                         FLAT = pdiva(F,GCD);                          FLAT = pdiva(F,GCD);
                         if ( type(GCD) == NUM ) {                          if ( type(GCD) == NUM ) {
                                 A[I] = F; B[I] = 1;                                  A[I] = F; B[I] = 1;
Line 479  def ufctrhint_heuristic(P,HINT,PP,SHIFT) {
Line 604  def ufctrhint_heuristic(P,HINT,PP,SHIFT) {
                 G = igcd(G,DT=deg(T,V));                  G = igcd(G,DT=deg(T,V));
         if ( G == 1 ) {          if ( G == 1 ) {
                 if ( K*deg(PPP,V) != deg(P,V) )                  if ( K*deg(PPP,V) != deg(P,V) )
                         PPP = cr_gcda(PPP,P,AL);                          PPP = cr_gcda(PPP,P);
                 return ufctrhint2(P,HINT,PPP,AL);                  return ufctrhint2(P,HINT,PPP,AL);
         } else {          } else {
                 for ( S = 0, T = P; T; T -= coef(T,DT)*V^DT ) {                  for ( S = 0, T = P; T; T -= coef(T,DT)*V^DT ) {
Line 489  def ufctrhint_heuristic(P,HINT,PP,SHIFT) {
Line 614  def ufctrhint_heuristic(P,HINT,PP,SHIFT) {
                 L = fctr(S);                  L = fctr(S);
                 for ( DC = [car(L)], L = cdr(L); L != []; L = cdr(L) ) {                  for ( DC = [car(L)], L = cdr(L); L != []; L = cdr(L) ) {
                         H = subst(car(car(L)),V,V^G);                          H = subst(car(car(L)),V,V^G);
                         HH = cr_gcda(PPP,H,AL);                          HH = cr_gcda(PPP,H);
                         T = ufctrhint2(H,HINT,HH,AL);                          T = ufctrhint2(H,HINT,HH,AL);
                         DC = append(DC,T);                          DC = append(DC,T);
                 }                  }
Line 645  def norm_ch_lag(V,VM,P,P0) {
Line 770  def norm_ch_lag(V,VM,P,P0) {
         return S;          return S;
 }  }
   
 def cr_gcda(P1,P2,EXT)  def cr_gcda(P1,P2)
 {  {
         if ( !(V = var(P1)) || !var(P2) )          if ( !(V = var(P1)) || !var(P2) )
                 return 1;                  return 1;
         AL = union(getalgp(P1),getalgp(P2));          EXT = union_sort(getalgtreep(P1),getalgtreep(P2));
         if ( AL == [] )          if ( EXT == [] )
                 return gcd(P1,P2);                  return gcd(P1,P2);
         T = newvect(length(EXT));  
         for ( TAL = AL; TAL != []; TAL = cdr(TAL) ) {  
                 A = getalg(car(TAL));  
                 for ( TA = A; TA != []; TA = cdr(TA) ) {  
                         B = car(TA);  
                         for ( TEXT = EXT, I = 0; TEXT != []; TEXT = cdr(TEXT), I++ )  
                                 if ( car(TEXT) == B )  
                                         T[I] = B;  
                 }  
         }  
         for ( I = length(EXT)-1, S = []; I >= 0; I-- )  
                 if ( T[I] )  
                         S = cons(T[I],S);  
         EXT = S;  
         NEXT = length(EXT);          NEXT = length(EXT);
         if ( deg(P1,V) < deg(P2,V) ) {          if ( deg(P1,V) < deg(P2,V) ) {
                 T = P1; P1 = P2; P2 = T;                  T = P1; P1 = P2; P2 = T;
Line 745  def member(E,L)
Line 856  def member(E,L)
                 if ( E == car(L) )                  if ( E == car(L) )
                         return 1;                          return 1;
         return 0;          return 0;
 }  
   
 def getallalg(A)  
 {  
         T = cdr(vars(defpoly(A)));  
         if ( T == [] )  
                 return [A];  
         else {  
                 for ( S = [A]; T != []; T = cdr(T) )  
                         S = union(S,getallalg(rattoalg(car(T))));  
                 return S;  
         }  
 }  }
   
 def discr(P) {  def discr(P) {
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