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Diff for /OpenXM_contrib2/asir2000/lib/sp between version 1.3 and 1.7

version 1.3, 2000/03/10 09:22:39 version 1.7, 2000/08/21 08:31:43
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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@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
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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 1.6 2000/04/20 02:30:35 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          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
 */  */
   
Line 38  def sp(P)
Line 86  def sp(P)
                         L = aflist(append(H,append([X-A,R],cdr(T))),AL);                          L = aflist(append(H,append([X-A,R],cdr(T))),AL);
                 }                  }
         }          }
   }
   
   /*
           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)
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