Annotation of OpenXM_contrib2/asir2000/lib/bfct, Revision 1.7
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: *
1.7 ! noro 48: * $OpenXM: OpenXM_contrib2/asir2000/lib/bfct,v 1.6 2000/12/13 05:37:31 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: 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: dp_nelim(2);
1.4 noro 67: G0 = dp_weyl_gr_main(B,append(W,DW),0,0,6);
1.1 noro 68: G1 = [];
69: for ( T = G0; T != []; T = cdr(T) ) {
70: E = car(T); VL = vars(E);
71: if ( !member(y1,VL) && !member(y2,VL) )
72: G1 = cons(E,G1);
73: }
74: G2 = map(subst,G1,dt,1);
75: G3 = map(b_subst,G2,t);
76: G4 = map(subst,G3,t,-1-s);
77: return G4;
78: }
79:
1.7 ! noro 80: def indicial1(F,V)
1.6 noro 81: {
82: V = vars(F);
83: W = append([y1,t],V);
84: N = length(V);
85: B = [t-y1*F];
86: for ( I = N-1, DV = []; I >= 0; I-- )
87: DV = cons(strtov("d"+rtostr(V[I])),DV);
88: DW = append([dy1,dt],DV);
89: for ( I = 0; I < N; I++ ) {
90: B = cons(DV[I]+y1*diff(F,V[I])*dt,B);
91: }
92: dp_nelim(1);
1.7 ! noro 93: /* we use homogenization (heuristically determined) */
! 94: G0 = dp_weyl_gr_main(B,append(W,DW),1,0,6);
1.6 noro 95: G1 = map(subst,G0,y1,1);
96: Mat = newmat(2,2,[[-1,1],[0,1]]);
97: G2 = map(psi,G1,t,dt);
98: G3 = map(subst,G2,t,-s-1);
99: return G3;
100: }
101:
102: def psi(F,T,DT)
103: {
104: D = dp_ptod(F,[T,DT]);
105: Wmax = weight(D);
106: D1 = dp_rest(D);
107: for ( ; D1; D1 = dp_rest(D1) )
108: if ( weight(D1) > Wmax )
109: Wmax = weight(D1);
110: for ( D1 = D, Dmax = 0; D1; D1 = dp_rest(D1) )
111: if ( weight(D1) == Wmax )
112: Dmax += dp_hm(D1);
113: if ( Wmax >= 0 )
114: Dmax = dp_weyl_mul(<<Wmax,0>>,Dmax);
115: else
116: Dmax = dp_weyl_mul(<<0,-Wmax>>,Dmax);
117: Rmax = dp_dtop(Dmax,[T,DT]);
118: R = b_subst(subst(Rmax,DT,1),T);
119: return R;
120: }
121:
122: def weight(D)
123: {
124: V = dp_etov(D);
125: return V[1]-V[0];
126: }
127:
128: def compare_first(A,B)
129: {
130: A0 = car(A);
131: B0 = car(B);
132: if ( A0 > B0 )
133: return 1;
134: else if ( A0 < B0 )
135: return -1;
136: else
137: return 0;
138: }
139:
1.1 noro 140: /* b-function of F ? */
141:
142: def bfct(F)
143: {
144: V = vars(F);
145: N = length(V);
1.6 noro 146: D = newvect(N);
1.7 ! noro 147:
1.6 noro 148: for ( I = 0; I < N; I++ )
149: D[I] = [deg(F,V[I]),V[I]];
150: qsort(D,compare_first);
151: for ( V = [], I = 0; I < N; I++ )
152: V = cons(D[I][1],V);
1.1 noro 153: for ( I = N-1, DV = []; I >= 0; I-- )
154: DV = cons(strtov("d"+rtostr(V[I])),DV);
1.6 noro 155: V1 = cons(s,V); DV1 = cons(ds,DV);
1.7 ! noro 156:
! 157: G0 = indicial1(F,reverse(V));
! 158: G1 = dp_weyl_gr_main(G0,append(V1,DV1),0,1,0);
! 159: Minipoly = weyl_minipoly(G1,append(V1,DV1),0,s);
1.6 noro 160: return Minipoly;
161: }
162:
163: def weyl_minipolym(G,V,O,M,V0)
164: {
165: N = length(V);
166: Len = length(G);
167: dp_ord(O);
168: setmod(M);
169: PS = newvect(Len);
170: PS0 = newvect(Len);
171:
172: for ( I = 0, T = G; T != []; T = cdr(T), I++ )
173: PS0[I] = dp_ptod(car(T),V);
174: for ( I = 0, T = G; T != []; T = cdr(T), I++ )
175: PS[I] = dp_mod(dp_ptod(car(T),V),M,[]);
176:
177: for ( I = Len - 1, GI = []; I >= 0; I-- )
178: GI = cons(I,GI);
179:
180: U = dp_mod(dp_ptod(V0,V),M,[]);
181:
182: T = dp_mod(<<0>>,M,[]);
183: TT = dp_mod(dp_ptod(1,V),M,[]);
184: G = H = [[TT,T]];
185:
186: for ( I = 1; ; I++ ) {
187: T = dp_mod(<<I>>,M,[]);
188:
189: TT = dp_weyl_nf_mod(GI,dp_weyl_mul_mod(TT,U,M),PS,1,M);
190: H = cons([TT,T],H);
191: L = dp_lnf_mod([TT,T],G,M);
192: if ( !L[0] )
193: return dp_dtop(L[1],[V0]);
194: else
195: G = insert(G,L);
196: }
197: }
198:
199: def weyl_minipoly(G0,V0,O0,V)
200: {
201: for ( I = 0; ; I++ ) {
202: Prime = lprime(I);
203: MP = weyl_minipolym(G0,V0,O0,Prime,V);
204: for ( D = deg(MP,V), TL = [], J = 0; J <= D; J++ )
205: TL = cons(V^J,TL);
206: dp_ord(O0);
207: NF = weyl_gennf(G0,TL,V0,O0)[0];
208:
209: LHS = weyl_nf_tab(-car(TL),NF,V0);
210: B = weyl_hen_ttob(cdr(TL),NF,LHS,V0,Prime);
211: if ( B ) {
212: R = ptozp(B[1]*car(TL)+B[0]);
213: return R;
214: }
215: }
216: }
217:
218: def weyl_gennf(G,TL,V,O)
219: {
220: N = length(V); Len = length(G); dp_ord(O); PS = newvect(Len);
221: for ( I = 0, T = G, HL = []; T != []; T = cdr(T), I++ ) {
222: PS[I] = dp_ptod(car(T),V); HL = cons(dp_ht(PS[I]),HL);
223: }
224: for ( I = 0, DTL = []; TL != []; TL = cdr(TL) )
225: DTL = cons(dp_ptod(car(TL),V),DTL);
226: for ( I = Len - 1, GI = []; I >= 0; I-- )
227: GI = cons(I,GI);
228: T = car(DTL); DTL = cdr(DTL);
229: H = [weyl_nf(GI,T,T,PS)];
1.1 noro 230:
1.6 noro 231: T0 = time()[0];
232: while ( DTL != [] ) {
233: T = car(DTL); DTL = cdr(DTL);
234: if ( dp_gr_print() )
235: print(".",2);
236: if ( L = search_redble(T,H) ) {
237: DD = dp_subd(T,L[1]);
238: NF = weyl_nf(GI,dp_weyl_mul(L[0],dp_subd(T,L[1])),dp_hc(L[1])*T,PS);
239: } else
240: NF = weyl_nf(GI,T,T,PS);
241: NF = remove_cont(NF);
242: H = cons(NF,H);
243: }
244: print("");
245: TNF = time()[0]-T0;
246: if ( dp_gr_print() )
247: print("gennf(TAB="+rtostr(TTAB)+" NF="+rtostr(TNF)+")");
248: return [H,PS,GI];
249: }
1.1 noro 250:
1.6 noro 251: def weyl_nf(B,G,M,PS)
252: {
253: for ( D = 0; G; ) {
254: for ( U = 0, L = B; L != []; L = cdr(L) ) {
255: if ( dp_redble(G,R=PS[car(L)]) > 0 ) {
256: GCD = igcd(dp_hc(G),dp_hc(R));
257: CG = idiv(dp_hc(R),GCD); CR = idiv(dp_hc(G),GCD);
258: U = CG*G-dp_weyl_mul(CR*dp_subd(G,R),R);
259: if ( !U )
260: return [D,M];
261: D *= CG; M *= CG;
262: break;
263: }
264: }
265: if ( U )
266: G = U;
267: else {
268: D += dp_hm(G); G = dp_rest(G);
269: }
270: }
271: return [D,M];
272: }
273:
274: def weyl_nf_mod(B,G,PS,Mod)
275: {
276: for ( D = 0; G; ) {
277: for ( U = 0, L = B; L != []; L = cdr(L) ) {
278: if ( dp_redble(G,R=PS[car(L)]) > 0 ) {
279: CR = dp_hc(G)/dp_hc(R);
280: U = G-dp_weyl_mul_mod(CR*dp_mod(dp_subd(G,R),Mod,[]),R,Mod);
281: if ( !U )
282: return D;
1.1 noro 283: break;
1.6 noro 284: }
285: }
286: if ( U )
287: G = U;
288: else {
289: D += dp_hm(G); G = dp_rest(G);
1.1 noro 290: }
291: }
1.6 noro 292: return D;
293: }
294:
295: def weyl_hen_ttob(T,NF,LHS,V,MOD)
296: {
297: T0 = time()[0]; M = etom(weyl_leq_nf(T,NF,LHS,V)); TE = time()[0] - T0;
298: T0 = time()[0]; U = henleq(M,MOD); TH = time()[0] - T0;
299: if ( dp_gr_print() ) {
300: print("(etom="+rtostr(TE)+" hen="+rtostr(TH)+")");
301: }
302: return U ? vtop(T,U,LHS) : 0;
303: }
304:
305: def weyl_leq_nf(TL,NF,LHS,V)
306: {
307: TLen = length(NF);
308: T = newvect(TLen); M = newvect(TLen);
309: for ( I = 0; I < TLen; I++ ) {
310: T[I] = dp_ht(NF[I][1]);
311: M[I] = dp_hc(NF[I][1]);
312: }
313: Len = length(TL); INDEX = newvect(Len); COEF = newvect(Len);
314: for ( L = TL, J = 0; L != []; L = cdr(L), J++ ) {
315: D = dp_ptod(car(L),V);
316: for ( I = 0; I < TLen; I++ )
317: if ( D == T[I] )
318: break;
319: INDEX[J] = I; COEF[J] = strtov("u"+rtostr(J));
320: }
321: if ( !LHS ) {
322: COEF[0] = 1; NM = 0; DN = 1;
323: } else {
324: NM = LHS[0]; DN = LHS[1];
325: }
326: for ( J = 0, S = -NM; J < Len; J++ ) {
327: DNJ = M[INDEX[J]];
328: GCD = igcd(DN,DNJ); CS = DNJ/GCD; CJ = DN/GCD;
329: S = CS*S + CJ*NF[INDEX[J]][0]*COEF[J];
330: DN *= CS;
331: }
332: for ( D = S, E = []; D; D = dp_rest(D) )
333: E = cons(dp_hc(D),E);
334: BOUND = LHS ? 0 : 1;
335: for ( I = Len - 1, W = []; I >= BOUND; I-- )
336: W = cons(COEF[I],W);
337: return [E,W];
338: }
339:
340: def weyl_nf_tab(A,NF,V)
341: {
342: TLen = length(NF);
343: T = newvect(TLen); M = newvect(TLen);
344: for ( I = 0; I < TLen; I++ ) {
345: T[I] = dp_ht(NF[I][1]);
346: M[I] = dp_hc(NF[I][1]);
347: }
348: A = dp_ptod(A,V);
349: for ( Z = A, Len = 0; Z; Z = dp_rest(Z), Len++ );
350: INDEX = newvect(Len); COEF = newvect(Len);
351: for ( Z = A, J = 0; Z; Z = dp_rest(Z), J++ ) {
352: D = dp_ht(Z);
353: for ( I = 0; I < TLen; I++ )
354: if ( D == T[I] )
355: break;
356: INDEX[J] = I; COEF[J] = dp_hc(Z);
357: }
358: for ( J = 0, S = 0, DN = 1; J < Len; J++ ) {
359: DNJ = M[INDEX[J]];
360: GCD = igcd(DN,DNJ); CS = DNJ/GCD; CJ = DN/GCD;
361: S = CS*S + CJ*NF[INDEX[J]][0]*COEF[J];
362: DN *= CS;
363: }
364: return [S,DN];
1.1 noro 365: }
366:
367: def remove_zero(L)
368: {
369: for ( R = []; L != []; L = cdr(L) )
370: if ( car(L) )
371: R = cons(car(L),R);
372: return R;
373: }
374:
375: def z_subst(F,V)
376: {
377: for ( ; V != []; V = cdr(V) )
378: F = subst(F,car(V),0);
379: return F;
380: }
381:
382: def flatmf(L) {
383: for ( S = []; L != []; L = cdr(L) )
384: if ( type(F=car(car(L))) != NUM )
385: S = append(S,[F]);
386: return S;
387: }
388:
389: def member(A,L) {
390: for ( ; L != []; L = cdr(L) )
391: if ( A == car(L) )
392: return 1;
393: return 0;
394: }
395:
396: def intersection(A,B)
397: {
398: for ( L = []; A != []; A = cdr(A) )
399: if ( member(car(A),B) )
400: L = cons(car(A),L);
401: return L;
402: }
403:
404: def b_subst(F,V)
405: {
406: D = deg(F,V);
407: C = newvect(D+1);
408: for ( I = D; I >= 0; I-- )
409: C[I] = coef(F,I,V);
410: for ( I = 0, R = 0; I <= D; I++ )
411: if ( C[I] )
412: R += C[I]*v_factorial(V,I);
413: return R;
414: }
415:
416: def v_factorial(V,N)
417: {
418: for ( J = N-1, R = 1; J >= 0; J-- )
419: R *= V-J;
420: return R;
421: }
422: end$
423:
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