Annotation of OpenXM_contrib2/asir2000/lib/bfct, Revision 1.11
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: *
1.11 ! noro 48: * $OpenXM: OpenXM_contrib2/asir2000/lib/bfct,v 1.10 2000/12/15 01:34:31 noro Exp $
1.10 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: }
1.10 noro 76:
77: /* homogenized (heuristics) */
1.1 noro 78: dp_nelim(2);
1.10 noro 79: G0 = dp_weyl_gr_main(B,append(W,DW),1,0,6);
1.1 noro 80: G1 = [];
81: for ( T = G0; T != []; T = cdr(T) ) {
82: E = car(T); VL = vars(E);
83: if ( !member(y1,VL) && !member(y2,VL) )
84: G1 = cons(E,G1);
85: }
86: G2 = map(subst,G1,dt,1);
87: G3 = map(b_subst,G2,t);
88: G4 = map(subst,G3,t,-1-s);
89: return G4;
90: }
91:
1.10 noro 92: /*
93: * compute J_f|s=r, where r = the minimal integral root of global b_f(s)
94: * ann0(F) returns [MinRoot,Ideal]
95: */
96:
97: def ann0(F)
98: {
99: V = vars(F);
100: N = length(V);
101: D = newvect(N);
102:
103: for ( I = 0; I < N; I++ )
104: D[I] = [deg(F,V[I]),V[I]];
105: qsort(D,compare_first);
106: for ( V = [], I = 0; I < N; I++ )
107: V = cons(D[I][1],V);
108:
109: for ( I = N-1, DV = []; I >= 0; I-- )
110: DV = cons(strtov("d"+rtostr(V[I])),DV);
111:
112: /* XXX : heuristics */
113: W = append([y1,y2,t],reverse(V));
114: DW = append([dy1,dy2,dt],reverse(DV));
115: WDW = append(W,DW);
116:
117: B = [1-y1*y2,t-y1*F];
118: for ( I = 0; I < N; I++ ) {
119: B = cons(DV[I]+y1*diff(F,V[I])*dt,B);
120: }
121:
122: /* homogenized (heuristics) */
123: dp_nelim(2);
124: G0 = dp_weyl_gr_main(B,WDW,1,0,6);
125: G1 = [];
126: for ( T = G0; T != []; T = cdr(T) ) {
127: E = car(T); VL = vars(E);
128: if ( !member(y1,VL) && !member(y2,VL) )
129: G1 = cons(E,G1);
130: }
131: G2 = map(subst,G1,dt,1);
132: G3 = map(b_subst,G2,t);
133: G4 = map(subst,G3,t,-1-s);
134:
135: /* G4 = J_f(s) */
136:
137: V1 = cons(s,V); DV1 = cons(ds,DV); V1DV1 = append(V1,DV1);
138: G5 = dp_weyl_gr_main(cons(F,G4),V1DV1,0,1,0);
139: Bf = weyl_minipoly(G5,V1DV1,0,s);
140:
141: FList = cdr(fctr(Bf));
142: for ( T = FList, Min = 0; T != []; T = cdr(T) ) {
143: LF = car(car(T));
144: Root = -coef(LF,0)/coef(LF,1);
145: if ( dn(Root) == 1 && Root < Min )
146: Min = Root;
147: }
148: return [Min,map(subst,G4,s,Min)];
149: }
150:
1.7 noro 151: def indicial1(F,V)
1.6 noro 152: {
153: W = append([y1,t],V);
154: N = length(V);
155: B = [t-y1*F];
156: for ( I = N-1, DV = []; I >= 0; I-- )
157: DV = cons(strtov("d"+rtostr(V[I])),DV);
158: DW = append([dy1,dt],DV);
159: for ( I = 0; I < N; I++ ) {
160: B = cons(DV[I]+y1*diff(F,V[I])*dt,B);
161: }
162: dp_nelim(1);
1.10 noro 163:
164: /* homogenized (heuristics) */
1.7 noro 165: G0 = dp_weyl_gr_main(B,append(W,DW),1,0,6);
1.6 noro 166: G1 = map(subst,G0,y1,1);
167: Mat = newmat(2,2,[[-1,1],[0,1]]);
168: G2 = map(psi,G1,t,dt);
169: G3 = map(subst,G2,t,-s-1);
170: return G3;
171: }
172:
173: def psi(F,T,DT)
174: {
175: D = dp_ptod(F,[T,DT]);
176: Wmax = weight(D);
177: D1 = dp_rest(D);
178: for ( ; D1; D1 = dp_rest(D1) )
179: if ( weight(D1) > Wmax )
180: Wmax = weight(D1);
181: for ( D1 = D, Dmax = 0; D1; D1 = dp_rest(D1) )
182: if ( weight(D1) == Wmax )
183: Dmax += dp_hm(D1);
184: if ( Wmax >= 0 )
185: Dmax = dp_weyl_mul(<<Wmax,0>>,Dmax);
186: else
187: Dmax = dp_weyl_mul(<<0,-Wmax>>,Dmax);
188: Rmax = dp_dtop(Dmax,[T,DT]);
189: R = b_subst(subst(Rmax,DT,1),T);
190: return R;
191: }
192:
193: def weight(D)
194: {
195: V = dp_etov(D);
196: return V[1]-V[0];
197: }
198:
199: def compare_first(A,B)
200: {
201: A0 = car(A);
202: B0 = car(B);
203: if ( A0 > B0 )
204: return 1;
205: else if ( A0 < B0 )
206: return -1;
207: else
208: return 0;
209: }
210:
1.1 noro 211: /* b-function of F ? */
212:
213: def bfct(F)
214: {
215: V = vars(F);
216: N = length(V);
1.6 noro 217: D = newvect(N);
1.7 noro 218:
1.6 noro 219: for ( I = 0; I < N; I++ )
220: D[I] = [deg(F,V[I]),V[I]];
221: qsort(D,compare_first);
222: for ( V = [], I = 0; I < N; I++ )
223: V = cons(D[I][1],V);
1.1 noro 224: for ( I = N-1, DV = []; I >= 0; I-- )
225: DV = cons(strtov("d"+rtostr(V[I])),DV);
1.6 noro 226: V1 = cons(s,V); DV1 = cons(ds,DV);
1.7 noro 227:
228: G0 = indicial1(F,reverse(V));
229: G1 = dp_weyl_gr_main(G0,append(V1,DV1),0,1,0);
230: Minipoly = weyl_minipoly(G1,append(V1,DV1),0,s);
1.6 noro 231: return Minipoly;
232: }
233:
234: def weyl_minipolym(G,V,O,M,V0)
235: {
236: N = length(V);
237: Len = length(G);
238: dp_ord(O);
239: setmod(M);
240: PS = newvect(Len);
241: PS0 = newvect(Len);
242:
243: for ( I = 0, T = G; T != []; T = cdr(T), I++ )
244: PS0[I] = dp_ptod(car(T),V);
245: for ( I = 0, T = G; T != []; T = cdr(T), I++ )
246: PS[I] = dp_mod(dp_ptod(car(T),V),M,[]);
247:
248: for ( I = Len - 1, GI = []; I >= 0; I-- )
249: GI = cons(I,GI);
250:
251: U = dp_mod(dp_ptod(V0,V),M,[]);
252:
253: T = dp_mod(<<0>>,M,[]);
254: TT = dp_mod(dp_ptod(1,V),M,[]);
255: G = H = [[TT,T]];
256:
257: for ( I = 1; ; I++ ) {
258: T = dp_mod(<<I>>,M,[]);
259:
260: TT = dp_weyl_nf_mod(GI,dp_weyl_mul_mod(TT,U,M),PS,1,M);
261: H = cons([TT,T],H);
262: L = dp_lnf_mod([TT,T],G,M);
263: if ( !L[0] )
264: return dp_dtop(L[1],[V0]);
265: else
266: G = insert(G,L);
267: }
268: }
269:
270: def weyl_minipoly(G0,V0,O0,V)
271: {
1.11 ! noro 272: HM = hmlist(G0,V0,O0);
1.6 noro 273: for ( I = 0; ; I++ ) {
274: Prime = lprime(I);
1.11 ! noro 275: if ( !valid_modulus(HM,Prime) )
! 276: continue;
1.6 noro 277: MP = weyl_minipolym(G0,V0,O0,Prime,V);
278: for ( D = deg(MP,V), TL = [], J = 0; J <= D; J++ )
279: TL = cons(V^J,TL);
280: dp_ord(O0);
281: NF = weyl_gennf(G0,TL,V0,O0)[0];
282:
283: LHS = weyl_nf_tab(-car(TL),NF,V0);
284: B = weyl_hen_ttob(cdr(TL),NF,LHS,V0,Prime);
285: if ( B ) {
286: R = ptozp(B[1]*car(TL)+B[0]);
287: return R;
288: }
289: }
290: }
291:
292: def weyl_gennf(G,TL,V,O)
293: {
294: N = length(V); Len = length(G); dp_ord(O); PS = newvect(Len);
295: for ( I = 0, T = G, HL = []; T != []; T = cdr(T), I++ ) {
296: PS[I] = dp_ptod(car(T),V); HL = cons(dp_ht(PS[I]),HL);
297: }
298: for ( I = 0, DTL = []; TL != []; TL = cdr(TL) )
299: DTL = cons(dp_ptod(car(TL),V),DTL);
300: for ( I = Len - 1, GI = []; I >= 0; I-- )
301: GI = cons(I,GI);
302: T = car(DTL); DTL = cdr(DTL);
303: H = [weyl_nf(GI,T,T,PS)];
1.1 noro 304:
1.6 noro 305: T0 = time()[0];
306: while ( DTL != [] ) {
307: T = car(DTL); DTL = cdr(DTL);
308: if ( dp_gr_print() )
309: print(".",2);
310: if ( L = search_redble(T,H) ) {
311: DD = dp_subd(T,L[1]);
312: NF = weyl_nf(GI,dp_weyl_mul(L[0],dp_subd(T,L[1])),dp_hc(L[1])*T,PS);
313: } else
314: NF = weyl_nf(GI,T,T,PS);
315: NF = remove_cont(NF);
316: H = cons(NF,H);
317: }
1.10 noro 318: print("");
1.6 noro 319: TNF = time()[0]-T0;
320: if ( dp_gr_print() )
321: print("gennf(TAB="+rtostr(TTAB)+" NF="+rtostr(TNF)+")");
322: return [H,PS,GI];
323: }
1.1 noro 324:
1.6 noro 325: def weyl_nf(B,G,M,PS)
326: {
327: for ( D = 0; G; ) {
328: for ( U = 0, L = B; L != []; L = cdr(L) ) {
329: if ( dp_redble(G,R=PS[car(L)]) > 0 ) {
330: GCD = igcd(dp_hc(G),dp_hc(R));
331: CG = idiv(dp_hc(R),GCD); CR = idiv(dp_hc(G),GCD);
332: U = CG*G-dp_weyl_mul(CR*dp_subd(G,R),R);
333: if ( !U )
334: return [D,M];
335: D *= CG; M *= CG;
336: break;
337: }
338: }
339: if ( U )
340: G = U;
341: else {
342: D += dp_hm(G); G = dp_rest(G);
343: }
344: }
345: return [D,M];
346: }
347:
348: def weyl_nf_mod(B,G,PS,Mod)
349: {
350: for ( D = 0; G; ) {
351: for ( U = 0, L = B; L != []; L = cdr(L) ) {
352: if ( dp_redble(G,R=PS[car(L)]) > 0 ) {
353: CR = dp_hc(G)/dp_hc(R);
354: U = G-dp_weyl_mul_mod(CR*dp_mod(dp_subd(G,R),Mod,[]),R,Mod);
355: if ( !U )
356: return D;
1.1 noro 357: break;
1.6 noro 358: }
359: }
360: if ( U )
361: G = U;
362: else {
363: D += dp_hm(G); G = dp_rest(G);
1.1 noro 364: }
365: }
1.6 noro 366: return D;
367: }
368:
369: def weyl_hen_ttob(T,NF,LHS,V,MOD)
370: {
371: T0 = time()[0]; M = etom(weyl_leq_nf(T,NF,LHS,V)); TE = time()[0] - T0;
372: T0 = time()[0]; U = henleq(M,MOD); TH = time()[0] - T0;
373: if ( dp_gr_print() ) {
374: print("(etom="+rtostr(TE)+" hen="+rtostr(TH)+")");
375: }
376: return U ? vtop(T,U,LHS) : 0;
377: }
378:
379: def weyl_leq_nf(TL,NF,LHS,V)
380: {
381: TLen = length(NF);
382: T = newvect(TLen); M = newvect(TLen);
383: for ( I = 0; I < TLen; I++ ) {
384: T[I] = dp_ht(NF[I][1]);
385: M[I] = dp_hc(NF[I][1]);
386: }
387: Len = length(TL); INDEX = newvect(Len); COEF = newvect(Len);
388: for ( L = TL, J = 0; L != []; L = cdr(L), J++ ) {
389: D = dp_ptod(car(L),V);
390: for ( I = 0; I < TLen; I++ )
391: if ( D == T[I] )
392: break;
393: INDEX[J] = I; COEF[J] = strtov("u"+rtostr(J));
394: }
395: if ( !LHS ) {
396: COEF[0] = 1; NM = 0; DN = 1;
397: } else {
398: NM = LHS[0]; DN = LHS[1];
399: }
400: for ( J = 0, S = -NM; J < Len; J++ ) {
401: DNJ = M[INDEX[J]];
402: GCD = igcd(DN,DNJ); CS = DNJ/GCD; CJ = DN/GCD;
403: S = CS*S + CJ*NF[INDEX[J]][0]*COEF[J];
404: DN *= CS;
405: }
406: for ( D = S, E = []; D; D = dp_rest(D) )
407: E = cons(dp_hc(D),E);
408: BOUND = LHS ? 0 : 1;
409: for ( I = Len - 1, W = []; I >= BOUND; I-- )
410: W = cons(COEF[I],W);
411: return [E,W];
412: }
413:
414: def weyl_nf_tab(A,NF,V)
415: {
416: TLen = length(NF);
417: T = newvect(TLen); M = newvect(TLen);
418: for ( I = 0; I < TLen; I++ ) {
419: T[I] = dp_ht(NF[I][1]);
420: M[I] = dp_hc(NF[I][1]);
421: }
422: A = dp_ptod(A,V);
423: for ( Z = A, Len = 0; Z; Z = dp_rest(Z), Len++ );
424: INDEX = newvect(Len); COEF = newvect(Len);
425: for ( Z = A, J = 0; Z; Z = dp_rest(Z), J++ ) {
426: D = dp_ht(Z);
427: for ( I = 0; I < TLen; I++ )
428: if ( D == T[I] )
429: break;
430: INDEX[J] = I; COEF[J] = dp_hc(Z);
431: }
432: for ( J = 0, S = 0, DN = 1; J < Len; J++ ) {
433: DNJ = M[INDEX[J]];
434: GCD = igcd(DN,DNJ); CS = DNJ/GCD; CJ = DN/GCD;
435: S = CS*S + CJ*NF[INDEX[J]][0]*COEF[J];
436: DN *= CS;
437: }
438: return [S,DN];
1.1 noro 439: }
440:
441: def remove_zero(L)
442: {
443: for ( R = []; L != []; L = cdr(L) )
444: if ( car(L) )
445: R = cons(car(L),R);
446: return R;
447: }
448:
449: def z_subst(F,V)
450: {
451: for ( ; V != []; V = cdr(V) )
452: F = subst(F,car(V),0);
453: return F;
454: }
455:
456: def flatmf(L) {
457: for ( S = []; L != []; L = cdr(L) )
458: if ( type(F=car(car(L))) != NUM )
459: S = append(S,[F]);
460: return S;
461: }
462:
463: def member(A,L) {
464: for ( ; L != []; L = cdr(L) )
465: if ( A == car(L) )
466: return 1;
467: return 0;
468: }
469:
470: def intersection(A,B)
471: {
472: for ( L = []; A != []; A = cdr(A) )
473: if ( member(car(A),B) )
474: L = cons(car(A),L);
475: return L;
476: }
477:
478: def b_subst(F,V)
479: {
480: D = deg(F,V);
481: C = newvect(D+1);
482: for ( I = D; I >= 0; I-- )
483: C[I] = coef(F,I,V);
484: for ( I = 0, R = 0; I <= D; I++ )
485: if ( C[I] )
486: R += C[I]*v_factorial(V,I);
487: return R;
488: }
489:
490: def v_factorial(V,N)
491: {
492: for ( J = N-1, R = 1; J >= 0; J-- )
493: R *= V-J;
494: return R;
495: }
496: end$
497:
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