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Annotation of OpenXM_contrib2/asir2000/lib/bfct, Revision 1.3

1.2       noro        1: /*
                      2:  * Copyright (c) 1994-2000 FUJITSU LABORATORIES LIMITED
                      3:  * All rights reserved.
                      4:  *
                      5:  * FUJITSU LABORATORIES LIMITED ("FLL") hereby grants you a limited,
                      6:  * non-exclusive and royalty-free license to use, copy, modify and
                      7:  * redistribute, solely for non-commercial and non-profit purposes, the
                      8:  * computer program, "Risa/Asir" ("SOFTWARE"), subject to the terms and
                      9:  * conditions of this Agreement. For the avoidance of doubt, you acquire
                     10:  * only a limited right to use the SOFTWARE hereunder, and FLL or any
                     11:  * third party developer retains all rights, including but not limited to
                     12:  * copyrights, in and to the SOFTWARE.
                     13:  *
                     14:  * (1) FLL does not grant you a license in any way for commercial
                     15:  * purposes. You may use the SOFTWARE only for non-commercial and
                     16:  * non-profit purposes only, such as academic, research and internal
                     17:  * business use.
                     18:  * (2) The SOFTWARE is protected by the Copyright Law of Japan and
                     19:  * international copyright treaties. If you make copies of the SOFTWARE,
                     20:  * with or without modification, as permitted hereunder, you shall affix
                     21:  * to all such copies of the SOFTWARE the above copyright notice.
                     22:  * (3) An explicit reference to this SOFTWARE and its copyright owner
                     23:  * shall be made on your publication or presentation in any form of the
                     24:  * results obtained by use of the SOFTWARE.
                     25:  * (4) In the event that you modify the SOFTWARE, you shall notify FLL by
1.3     ! noro       26:  * e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification
1.2       noro       27:  * for such modification or the source code of the modified part of the
                     28:  * SOFTWARE.
                     29:  *
                     30:  * THE SOFTWARE IS PROVIDED AS IS WITHOUT ANY WARRANTY OF ANY KIND. FLL
                     31:  * MAKES ABSOLUTELY NO WARRANTIES, EXPRESSED, IMPLIED OR STATUTORY, AND
                     32:  * EXPRESSLY DISCLAIMS ANY IMPLIED WARRANTY OF MERCHANTABILITY, FITNESS
                     33:  * FOR A PARTICULAR PURPOSE OR NONINFRINGEMENT OF THIRD PARTIES'
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                     35:  * MODIFICATIONS, EXTENSIONS, OR ADDITIONS TO THIS WARRANTY.
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                     40:  * ARISING OUT OF OR RELATING TO THE SOFTWARE OR THIS AGREEMENT, DAMAGES
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                     43:  * SUCH DAMAGES, OR FOR ANY CLAIM BY ANY OTHER PARTY. EVEN IF A PART
                     44:  * OF THE SOFTWARE HAS BEEN DEVELOPED BY A THIRD PARTY, THE THIRD PARTY
                     45:  * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE,
                     46:  * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE.
                     47:  *
1.3     ! noro       48:  * $OpenXM: OpenXM_contrib2/asir2000/lib/bfct,v 1.2 2000/08/21 08:31:40 noro Exp $
1.2       noro       49: */
1.1       noro       50: /* requires 'primdec' */
                     51:
                     52: /* annihilating ideal of F^s ? */
                     53:
                     54: def ann(F)
                     55: {
                     56:        V = vars(F);
                     57:        W = append([y1,y2,t],V);
                     58:        N = length(V);
                     59:        B = [1-y1*y2,t-y1*F];
                     60:        for ( I = N-1, DV = []; I >= 0; I-- )
                     61:                DV = cons(strtov("d"+rtostr(V[I])),DV);
                     62:        DW = append([dy1,dy2,dt],DV);
                     63:        for ( I = 0; I < N; I++ ) {
                     64:                B = cons(DV[I]+y1*diff(F,V[I])*dt,B);
                     65:        }
                     66:        ctrl("do_weyl",1);
                     67:        dp_nelim(2);
                     68:        G0 = dp_gr_main(B,append(W,DW),0,0,6);
                     69:        G1 = [];
                     70:        for ( T = G0; T != []; T = cdr(T) ) {
                     71:                E = car(T); VL = vars(E);
                     72:                if ( !member(y1,VL) && !member(y2,VL) )
                     73:                        G1 = cons(E,G1);
                     74:        }
                     75:        G2 = map(subst,G1,dt,1);
                     76:        G3 = map(b_subst,G2,t);
                     77:        G4 = map(subst,G3,t,-1-s);
                     78:        ctrl("do_weyl",0);
                     79:        return G4;
                     80: }
                     81:
                     82: /* b-function of F ? */
                     83:
                     84: def bfct(F)
                     85: {
                     86:        G4 = ann(F);
                     87:
                     88:        ctrl("do_weyl",1);
                     89:        V = vars(F);
                     90:        N = length(V);
                     91:        for ( I = N-1, DV = []; I >= 0; I-- )
                     92:                DV = cons(strtov("d"+rtostr(V[I])),DV);
                     93:
                     94:        N1 = 2*(N+1);
                     95:
                     96:        M = newmat(N1+1,N1);
                     97:        for ( J = N+1; J < N1; J++ )
                     98:                M[0][J] = 1;
                     99:        for ( J = 0; J < N+1; J++ )
                    100:                M[1][J] = 1;
                    101: #if 0
                    102:        for ( I = 0; I < N+1; I++ )
                    103:                M[I+2][N-I] = -1;
                    104:        for ( I = 0; I < N; I++ )
                    105:                M[I+2+N+1][N1-1-I] = -1;
                    106: #elif 1
                    107:        for ( I = 0; I < N1-1; I++ )
                    108:                M[I+2][N1-I-1] = 1;
                    109: #else
                    110:        for ( I = 0; I < N1-1; I++ )
                    111:                M[I+2][I] = 1;
                    112: #endif
                    113:        V1 = cons(s,V); DV1 = cons(ds,DV);
                    114:        G5 = dp_gr_main(cons(F,G4),append(V1,DV1),0,0,M);
                    115:        for ( T = G5, G6 = []; T != []; T = cdr(T) ) {
                    116:                E = car(T);
                    117:                if ( intersection(vars(E),DV1) == [] )
                    118:                        G6 = cons(E,G6);
                    119:        }
                    120:        ctrl("do_weyl",0);
                    121:        G6_0 = remove_zero(map(z_subst,G6,V));
                    122:        F0 = flatmf(cdr(fctr(dp_gr_main(G6_0,[s],0,0,0)[0])));
                    123:        for ( T = F0, BF = []; T != []; T = cdr(T) ) {
                    124:                FI = car(T);
                    125:                for ( J = 1; ; J++ ) {
                    126:                        S = map(srem,map(z_subst,idealquo(G6,[FI^J],V1,0),V),FI);
                    127:                        for ( ; S != [] && !car(S); S = cdr(S) );
                    128:                        if ( S != [] )
                    129:                                break;
                    130:                }
                    131:                BF = cons([FI,J],BF);
                    132:        }
                    133:        return BF;
                    134: }
                    135:
                    136: def remove_zero(L)
                    137: {
                    138:        for ( R = []; L != []; L = cdr(L) )
                    139:                if ( car(L) )
                    140:                        R = cons(car(L),R);
                    141:        return R;
                    142: }
                    143:
                    144: def z_subst(F,V)
                    145: {
                    146:        for ( ; V != []; V = cdr(V) )
                    147:                F = subst(F,car(V),0);
                    148:        return F;
                    149: }
                    150:
                    151: def flatmf(L) {
                    152:     for ( S = []; L != []; L = cdr(L) )
                    153:                if ( type(F=car(car(L))) != NUM )
                    154:                        S = append(S,[F]);
                    155:        return S;
                    156: }
                    157:
                    158: def member(A,L) {
                    159:     for ( ; L != []; L = cdr(L) )
                    160:                if ( A == car(L) )
                    161:                        return 1;
                    162:        return 0;
                    163: }
                    164:
                    165: def intersection(A,B)
                    166: {
                    167:        for ( L = []; A != []; A = cdr(A) )
                    168:        if ( member(car(A),B) )
                    169:                L = cons(car(A),L);
                    170:        return L;
                    171: }
                    172:
                    173: def b_subst(F,V)
                    174: {
                    175:        D = deg(F,V);
                    176:        C = newvect(D+1);
                    177:        for ( I = D; I >= 0; I-- )
                    178:                C[I] = coef(F,I,V);
                    179:        for ( I = 0, R = 0; I <= D; I++ )
                    180:                if ( C[I] )
                    181:                        R += C[I]*v_factorial(V,I);
                    182:        return R;
                    183: }
                    184:
                    185: def v_factorial(V,N)
                    186: {
                    187:        for ( J = N-1, R = 1; J >= 0; J-- )
                    188:                R *= V-J;
                    189:        return R;
                    190: }
                    191: end$
                    192:

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