Annotation of OpenXM_contrib2/asir2000/lib/bfct, Revision 1.8
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'
34: * RIGHTS. NO FLL DEALER, AGENT, EMPLOYEES IS AUTHORIZED TO MAKE ANY
35: * MODIFICATIONS, EXTENSIONS, OR ADDITIONS TO THIS WARRANTY.
36: * UNDER NO CIRCUMSTANCES AND UNDER NO LEGAL THEORY, TORT, CONTRACT,
37: * OR OTHERWISE, SHALL FLL BE LIABLE TO YOU OR ANY OTHER PERSON FOR ANY
38: * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, PUNITIVE OR CONSEQUENTIAL
39: * DAMAGES OF ANY CHARACTER, INCLUDING, WITHOUT LIMITATION, DAMAGES
40: * ARISING OUT OF OR RELATING TO THE SOFTWARE OR THIS AGREEMENT, DAMAGES
41: * FOR LOSS OF GOODWILL, WORK STOPPAGE, OR LOSS OF DATA, OR FOR ANY
42: * DAMAGES, EVEN IF FLL SHALL HAVE BEEN INFORMED OF THE POSSIBILITY OF
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: *
1.8 ! noro 48: * $OpenXM: OpenXM_contrib2/asir2000/lib/bfct,v 1.7 2000/12/14 01:38:37 noro Exp $
1.2 noro 49: */
1.1 noro 50: /* requires 'primdec' */
51:
1.6 noro 52: /* annihilating ideal of F^s */
1.1 noro 53:
54: def ann(F)
55: {
56: V = vars(F);
57: N = length(V);
1.8 ! noro 58: D = newvect(N);
! 59:
! 60: for ( I = 0; I < N; I++ )
! 61: D[I] = [deg(F,V[I]),V[I]];
! 62: qsort(D,compare_first);
! 63: for ( V = [], I = N-1; I >= 0; I-- )
! 64: V = cons(D[I][1],V);
! 65:
1.1 noro 66: for ( I = N-1, DV = []; I >= 0; I-- )
67: DV = cons(strtov("d"+rtostr(V[I])),DV);
1.8 ! noro 68:
! 69: W = append([y1,y2,t],V);
1.1 noro 70: DW = append([dy1,dy2,dt],DV);
1.8 ! noro 71:
! 72: B = [1-y1*y2,t-y1*F];
1.1 noro 73: for ( I = 0; I < N; I++ ) {
74: B = cons(DV[I]+y1*diff(F,V[I])*dt,B);
75: }
76: dp_nelim(2);
1.4 noro 77: G0 = dp_weyl_gr_main(B,append(W,DW),0,0,6);
1.1 noro 78: G1 = [];
79: for ( T = G0; T != []; T = cdr(T) ) {
80: E = car(T); VL = vars(E);
81: if ( !member(y1,VL) && !member(y2,VL) )
82: G1 = cons(E,G1);
83: }
84: G2 = map(subst,G1,dt,1);
85: G3 = map(b_subst,G2,t);
86: G4 = map(subst,G3,t,-1-s);
87: return G4;
88: }
89:
1.7 noro 90: def indicial1(F,V)
1.6 noro 91: {
92: W = append([y1,t],V);
93: N = length(V);
94: B = [t-y1*F];
95: for ( I = N-1, DV = []; I >= 0; I-- )
96: DV = cons(strtov("d"+rtostr(V[I])),DV);
97: DW = append([dy1,dt],DV);
98: for ( I = 0; I < N; I++ ) {
99: B = cons(DV[I]+y1*diff(F,V[I])*dt,B);
100: }
101: dp_nelim(1);
1.7 noro 102: /* we use homogenization (heuristically determined) */
103: G0 = dp_weyl_gr_main(B,append(W,DW),1,0,6);
1.6 noro 104: G1 = map(subst,G0,y1,1);
105: Mat = newmat(2,2,[[-1,1],[0,1]]);
106: G2 = map(psi,G1,t,dt);
107: G3 = map(subst,G2,t,-s-1);
108: return G3;
109: }
110:
111: def psi(F,T,DT)
112: {
113: D = dp_ptod(F,[T,DT]);
114: Wmax = weight(D);
115: D1 = dp_rest(D);
116: for ( ; D1; D1 = dp_rest(D1) )
117: if ( weight(D1) > Wmax )
118: Wmax = weight(D1);
119: for ( D1 = D, Dmax = 0; D1; D1 = dp_rest(D1) )
120: if ( weight(D1) == Wmax )
121: Dmax += dp_hm(D1);
122: if ( Wmax >= 0 )
123: Dmax = dp_weyl_mul(<<Wmax,0>>,Dmax);
124: else
125: Dmax = dp_weyl_mul(<<0,-Wmax>>,Dmax);
126: Rmax = dp_dtop(Dmax,[T,DT]);
127: R = b_subst(subst(Rmax,DT,1),T);
128: return R;
129: }
130:
131: def weight(D)
132: {
133: V = dp_etov(D);
134: return V[1]-V[0];
135: }
136:
137: def compare_first(A,B)
138: {
139: A0 = car(A);
140: B0 = car(B);
141: if ( A0 > B0 )
142: return 1;
143: else if ( A0 < B0 )
144: return -1;
145: else
146: return 0;
147: }
148:
1.1 noro 149: /* b-function of F ? */
150:
151: def bfct(F)
152: {
153: V = vars(F);
154: N = length(V);
1.6 noro 155: D = newvect(N);
1.7 noro 156:
1.6 noro 157: for ( I = 0; I < N; I++ )
158: D[I] = [deg(F,V[I]),V[I]];
159: qsort(D,compare_first);
160: for ( V = [], I = 0; I < N; I++ )
161: V = cons(D[I][1],V);
1.1 noro 162: for ( I = N-1, DV = []; I >= 0; I-- )
163: DV = cons(strtov("d"+rtostr(V[I])),DV);
1.6 noro 164: V1 = cons(s,V); DV1 = cons(ds,DV);
1.7 noro 165:
166: G0 = indicial1(F,reverse(V));
167: G1 = dp_weyl_gr_main(G0,append(V1,DV1),0,1,0);
168: Minipoly = weyl_minipoly(G1,append(V1,DV1),0,s);
1.6 noro 169: return Minipoly;
170: }
171:
172: def weyl_minipolym(G,V,O,M,V0)
173: {
174: N = length(V);
175: Len = length(G);
176: dp_ord(O);
177: setmod(M);
178: PS = newvect(Len);
179: PS0 = newvect(Len);
180:
181: for ( I = 0, T = G; T != []; T = cdr(T), I++ )
182: PS0[I] = dp_ptod(car(T),V);
183: for ( I = 0, T = G; T != []; T = cdr(T), I++ )
184: PS[I] = dp_mod(dp_ptod(car(T),V),M,[]);
185:
186: for ( I = Len - 1, GI = []; I >= 0; I-- )
187: GI = cons(I,GI);
188:
189: U = dp_mod(dp_ptod(V0,V),M,[]);
190:
191: T = dp_mod(<<0>>,M,[]);
192: TT = dp_mod(dp_ptod(1,V),M,[]);
193: G = H = [[TT,T]];
194:
195: for ( I = 1; ; I++ ) {
196: T = dp_mod(<<I>>,M,[]);
197:
198: TT = dp_weyl_nf_mod(GI,dp_weyl_mul_mod(TT,U,M),PS,1,M);
199: H = cons([TT,T],H);
200: L = dp_lnf_mod([TT,T],G,M);
201: if ( !L[0] )
202: return dp_dtop(L[1],[V0]);
203: else
204: G = insert(G,L);
205: }
206: }
207:
208: def weyl_minipoly(G0,V0,O0,V)
209: {
210: for ( I = 0; ; I++ ) {
211: Prime = lprime(I);
212: MP = weyl_minipolym(G0,V0,O0,Prime,V);
213: for ( D = deg(MP,V), TL = [], J = 0; J <= D; J++ )
214: TL = cons(V^J,TL);
215: dp_ord(O0);
216: NF = weyl_gennf(G0,TL,V0,O0)[0];
217:
218: LHS = weyl_nf_tab(-car(TL),NF,V0);
219: B = weyl_hen_ttob(cdr(TL),NF,LHS,V0,Prime);
220: if ( B ) {
221: R = ptozp(B[1]*car(TL)+B[0]);
222: return R;
223: }
224: }
225: }
226:
227: def weyl_gennf(G,TL,V,O)
228: {
229: N = length(V); Len = length(G); dp_ord(O); PS = newvect(Len);
230: for ( I = 0, T = G, HL = []; T != []; T = cdr(T), I++ ) {
231: PS[I] = dp_ptod(car(T),V); HL = cons(dp_ht(PS[I]),HL);
232: }
233: for ( I = 0, DTL = []; TL != []; TL = cdr(TL) )
234: DTL = cons(dp_ptod(car(TL),V),DTL);
235: for ( I = Len - 1, GI = []; I >= 0; I-- )
236: GI = cons(I,GI);
237: T = car(DTL); DTL = cdr(DTL);
238: H = [weyl_nf(GI,T,T,PS)];
1.1 noro 239:
1.6 noro 240: T0 = time()[0];
241: while ( DTL != [] ) {
242: T = car(DTL); DTL = cdr(DTL);
243: if ( dp_gr_print() )
244: print(".",2);
245: if ( L = search_redble(T,H) ) {
246: DD = dp_subd(T,L[1]);
247: NF = weyl_nf(GI,dp_weyl_mul(L[0],dp_subd(T,L[1])),dp_hc(L[1])*T,PS);
248: } else
249: NF = weyl_nf(GI,T,T,PS);
250: NF = remove_cont(NF);
251: H = cons(NF,H);
252: }
253: print("");
254: TNF = time()[0]-T0;
255: if ( dp_gr_print() )
256: print("gennf(TAB="+rtostr(TTAB)+" NF="+rtostr(TNF)+")");
257: return [H,PS,GI];
258: }
1.1 noro 259:
1.6 noro 260: def weyl_nf(B,G,M,PS)
261: {
262: for ( D = 0; G; ) {
263: for ( U = 0, L = B; L != []; L = cdr(L) ) {
264: if ( dp_redble(G,R=PS[car(L)]) > 0 ) {
265: GCD = igcd(dp_hc(G),dp_hc(R));
266: CG = idiv(dp_hc(R),GCD); CR = idiv(dp_hc(G),GCD);
267: U = CG*G-dp_weyl_mul(CR*dp_subd(G,R),R);
268: if ( !U )
269: return [D,M];
270: D *= CG; M *= CG;
271: break;
272: }
273: }
274: if ( U )
275: G = U;
276: else {
277: D += dp_hm(G); G = dp_rest(G);
278: }
279: }
280: return [D,M];
281: }
282:
283: def weyl_nf_mod(B,G,PS,Mod)
284: {
285: for ( D = 0; G; ) {
286: for ( U = 0, L = B; L != []; L = cdr(L) ) {
287: if ( dp_redble(G,R=PS[car(L)]) > 0 ) {
288: CR = dp_hc(G)/dp_hc(R);
289: U = G-dp_weyl_mul_mod(CR*dp_mod(dp_subd(G,R),Mod,[]),R,Mod);
290: if ( !U )
291: return D;
1.1 noro 292: break;
1.6 noro 293: }
294: }
295: if ( U )
296: G = U;
297: else {
298: D += dp_hm(G); G = dp_rest(G);
1.1 noro 299: }
300: }
1.6 noro 301: return D;
302: }
303:
304: def weyl_hen_ttob(T,NF,LHS,V,MOD)
305: {
306: T0 = time()[0]; M = etom(weyl_leq_nf(T,NF,LHS,V)); TE = time()[0] - T0;
307: T0 = time()[0]; U = henleq(M,MOD); TH = time()[0] - T0;
308: if ( dp_gr_print() ) {
309: print("(etom="+rtostr(TE)+" hen="+rtostr(TH)+")");
310: }
311: return U ? vtop(T,U,LHS) : 0;
312: }
313:
314: def weyl_leq_nf(TL,NF,LHS,V)
315: {
316: TLen = length(NF);
317: T = newvect(TLen); M = newvect(TLen);
318: for ( I = 0; I < TLen; I++ ) {
319: T[I] = dp_ht(NF[I][1]);
320: M[I] = dp_hc(NF[I][1]);
321: }
322: Len = length(TL); INDEX = newvect(Len); COEF = newvect(Len);
323: for ( L = TL, J = 0; L != []; L = cdr(L), J++ ) {
324: D = dp_ptod(car(L),V);
325: for ( I = 0; I < TLen; I++ )
326: if ( D == T[I] )
327: break;
328: INDEX[J] = I; COEF[J] = strtov("u"+rtostr(J));
329: }
330: if ( !LHS ) {
331: COEF[0] = 1; NM = 0; DN = 1;
332: } else {
333: NM = LHS[0]; DN = LHS[1];
334: }
335: for ( J = 0, S = -NM; J < Len; J++ ) {
336: DNJ = M[INDEX[J]];
337: GCD = igcd(DN,DNJ); CS = DNJ/GCD; CJ = DN/GCD;
338: S = CS*S + CJ*NF[INDEX[J]][0]*COEF[J];
339: DN *= CS;
340: }
341: for ( D = S, E = []; D; D = dp_rest(D) )
342: E = cons(dp_hc(D),E);
343: BOUND = LHS ? 0 : 1;
344: for ( I = Len - 1, W = []; I >= BOUND; I-- )
345: W = cons(COEF[I],W);
346: return [E,W];
347: }
348:
349: def weyl_nf_tab(A,NF,V)
350: {
351: TLen = length(NF);
352: T = newvect(TLen); M = newvect(TLen);
353: for ( I = 0; I < TLen; I++ ) {
354: T[I] = dp_ht(NF[I][1]);
355: M[I] = dp_hc(NF[I][1]);
356: }
357: A = dp_ptod(A,V);
358: for ( Z = A, Len = 0; Z; Z = dp_rest(Z), Len++ );
359: INDEX = newvect(Len); COEF = newvect(Len);
360: for ( Z = A, J = 0; Z; Z = dp_rest(Z), J++ ) {
361: D = dp_ht(Z);
362: for ( I = 0; I < TLen; I++ )
363: if ( D == T[I] )
364: break;
365: INDEX[J] = I; COEF[J] = dp_hc(Z);
366: }
367: for ( J = 0, S = 0, DN = 1; J < Len; J++ ) {
368: DNJ = M[INDEX[J]];
369: GCD = igcd(DN,DNJ); CS = DNJ/GCD; CJ = DN/GCD;
370: S = CS*S + CJ*NF[INDEX[J]][0]*COEF[J];
371: DN *= CS;
372: }
373: return [S,DN];
1.1 noro 374: }
375:
376: def remove_zero(L)
377: {
378: for ( R = []; L != []; L = cdr(L) )
379: if ( car(L) )
380: R = cons(car(L),R);
381: return R;
382: }
383:
384: def z_subst(F,V)
385: {
386: for ( ; V != []; V = cdr(V) )
387: F = subst(F,car(V),0);
388: return F;
389: }
390:
391: def flatmf(L) {
392: for ( S = []; L != []; L = cdr(L) )
393: if ( type(F=car(car(L))) != NUM )
394: S = append(S,[F]);
395: return S;
396: }
397:
398: def member(A,L) {
399: for ( ; L != []; L = cdr(L) )
400: if ( A == car(L) )
401: return 1;
402: return 0;
403: }
404:
405: def intersection(A,B)
406: {
407: for ( L = []; A != []; A = cdr(A) )
408: if ( member(car(A),B) )
409: L = cons(car(A),L);
410: return L;
411: }
412:
413: def b_subst(F,V)
414: {
415: D = deg(F,V);
416: C = newvect(D+1);
417: for ( I = D; I >= 0; I-- )
418: C[I] = coef(F,I,V);
419: for ( I = 0, R = 0; I <= D; I++ )
420: if ( C[I] )
421: R += C[I]*v_factorial(V,I);
422: return R;
423: }
424:
425: def v_factorial(V,N)
426: {
427: for ( J = N-1, R = 1; J >= 0; J-- )
428: R *= V-J;
429: return R;
430: }
431: end$
432:
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