Annotation of OpenXM/src/asir-contrib/testing/noro/new_pd.rr, Revision 1.5
1.5 ! noro 1: /* $OpenXM: OpenXM/src/asir-contrib/testing/noro/new_pd.rr,v 1.4 2011/02/18 02:59:04 noro Exp $ */
1.1 noro 2: import("gr")$
3: module noro_pd$
4: static GBCheck,F4,EProcs,Procs,SatHomo,GBRat$
5:
1.4 noro 6: localf witness$
7: localf get_lc,tomonic,aa,ideal_intersection_m,redbase$
1.1 noro 8: localf para_exec,nd_gr_rat,competitive_exec,call_func$
9: localf call_ideal_list_intersection$
1.3 noro 10: localf call_colon,call_prime_dec$
1.1 noro 11: localf first_second$
12: localf third$
13: localf locsat,iso_comp_para,extract_qj,colon_prime_dec,extract_comp$
14: localf separator$
1.4 noro 15: localf member,mingen,compute_gbsyz,redcoef,recompute_trace,dtop,topnum$
1.1 noro 16: localf prepost$
17: localf monodec0,monodec,prod$
18: localf extract_qd,primary_check$
19: localf second$
20: localf gbrat,comp_third_tdeg,comp_tord$
21: localf power$
22:
23: localf syci_dec, syc_dec$
24: localf syca_dec,syc0_dec$
25:
26: localf find_si0,find_si1,find_si2$
27: localf find_ssi0,find_ssi1,find_ssi2$
28:
29: localf init_pprocs, init_eprocs, init_procs, kill_procs$
30:
31: localf sy_dec, pseudo_dec, iso_comp, prima_dec$
32:
33: localf prime_dec, prime_dec_main, lex_predec1, zprimedec, zprimadec$
34: localf complete_qdecomp, partial_qdecomp, partial_qdecomp0, complete_decomp$
35: localf partial_decomp, partial_decomp0, zprimacomp, zprimecomp$
36: localf fast_gb, incremental_gb, elim_gb, ldim, make_mod_subst$
37: localf rsgn, find_npos, gen_minipoly, indepset$
38: localf maxindep, contraction, ideal_list_intersection, ideal_intersection$
39: localf radical_membership, modular_radical_membership$
40: localf radical_membership_rep, ideal_product, saturation$
1.4 noro 41: localf sat, satind, sat_ind, colon, isat$
1.1 noro 42: localf ideal_colon, ideal_sat, ideal_inclusion, qd_simp_comp, qd_remove_redundant_comp$
43: localf pd_simp_comp$
44: localf pd_remove_redundant_comp, ppart, sq, gen_fctr, gen_nf, gen_gb_comp$
45: localf gen_mptop, lcfactor, compute_deg0, compute_deg, member$
46: localf elimination, setintersection, setminus, sep_list$
47: localf first, comp_tdeg, comp_tdeg_first, tdeg, comp_by_ord, comp_by_second$
48: localf gbcheck,f4,sathomo,qd_check,qdb_check$
49:
50: SatHomo=0$
51: GBCheck=1$
52: GBRat=0$
53:
54: #define MAX(a,b) ((a)>(b)?(a):(b))
55: #define ACCUM_TIME(C,R) {T1 = time(); C += (T1[0]-T0[0])+(T1[1]-T0[1]); R += (T1[3]-T0[3]); }
56:
57: def gbrat(A)
58: {
59: if ( A ) GBRat = 1;
60: else GBRat = 0;
61: }
62:
63: def gbcheck(A)
64: {
65: if ( A ) GBCheck = 1;
66: else GBCheck = -1;
67: }
68:
69: def f4(A)
70: {
71: if ( A ) F4 = 1;
72: else F4 = 0;
73: }
74:
75: def sathomo(A)
76: {
77: if ( A ) SatHomo = 1;
78: else SatHomo = 0;
79: }
80:
81: def init_eprocs()
82: {
83: if ( type(NoX=getopt(nox)) == -1 ) NoX = 0;
84: if ( !EProcs ) {
85: if ( NoX ) {
86: P0 = ox_launch_nox();
87: P1 = ox_launch_nox();
88: } else {
89: P0 = ox_launch();
90: P1 = ox_launch();
91: }
92: EProcs = [P0,P1];
93: }
94: }
95:
96: def init_pprocs(N)
97: {
98: if ( type(NoX=getopt(nox)) == -1 ) NoX = 0;
99: for ( R = [], I = 0; I < N; I++ ) {
100: P = NoX ? ox_launch_nox() : ox_launch();
101: R = cons(P,R);
102: }
103: return reverse(R);
104: }
105:
106: def init_procs()
107: {
108: if ( type(NoX=getopt(nox)) == -1 ) NoX = 0;
109: if ( !Procs ) {
110: if ( NoX ) {
111: P0 = ox_launch_nox();
112: P1 = ox_launch_nox();
113: } else {
114: P0 = ox_launch();
115: P1 = ox_launch();
116: }
117: Procs = [P0,P1];
118: }
119: }
120:
121: def kill_procs()
122: {
123: if ( Procs ) {
124: ox_shutdown(Procs[0]);
125: ox_shutdown(Procs[1]);
126: Procs = 0;
127: }
128: if ( EProcs ) {
129: ox_shutdown(EProcs[0]);
130: ox_shutdown(EProcs[1]);
131: EProcs = 0;
132: }
133: }
134:
135: def qd_check(B,V,QD)
136: {
137: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
138: G = nd_gr(B,V,Mod,0);
139: Iso = ideal_list_intersection(map(first,QD[0]),V,0|mod=Mod);
140: Emb = ideal_list_intersection(map(first,QD[1]),V,0|mod=Mod);
141: GG = ideal_intersection(Iso,Emb,V,0|mod=Mod);
142: return gen_gb_comp(G,GG,Mod);
143: }
144:
145: def primary_check(B,V)
146: {
147: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
148: G = nd_gr(B,V,Mod,0);
149: PL = prime_dec(G,V|indep=1,mod=Mod);
150: if ( length(PL) > 1 ) return 0;
151: P = PL[0][0]; Y = PL[0][1];
152: Z = setminus(V,Y);
153: H = elim_gb(G,Z,Y,Mod,[[0,length(Z)],[0,length(Y)]]);
154: H = contraction(H,Z|mod=Mod);
155: H = nd_gr(H,V,Mod,0);
156: if ( gen_gb_comp(G,H,Mod) ) return nd_gr(P,V,Mod,0);
157: else return 0;
158: }
159:
160: def qdb_check(B,V,QD)
161: {
162: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
163: G = nd_gr(B,V,Mod,0);
164: N = length(QD);
165: for ( I = 0, Q = [1]; I < N; I++ )
166: for ( J = 0, QL = map(first,QD[I]), L = length(QL);
167: J < L; J++ )
168: Q = ideal_intersection(Q,QL[J],V,0|mod=Mod);
169: if ( !gen_gb_comp(G,Q,Mod) )
170: return 0;
171: for ( I = 0; I < N; I++ ) {
172: T = QD[I];
173: M = length(T);
174: for ( J = 0; J < M; J++ ) {
175: P = primary_check(T[J][0],V|mod=Mod);
176: if ( !P ) return 0;
177: PP = nd_gr(T[J][1],V,Mod,0);
178: if ( !gen_gb_comp(P,PP,Mod) ) return 0;
179: }
180: }
181: return 1;
182: }
183:
184: def extract_qd(QD,V,Ind)
185: {
186: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
187: N = length(Ind);
188: for ( I = 0, Q = [1]; I < N; I++ )
189: for ( J = 0, QL = map(first,QD[Ind[I]]), L = length(QL);
190: J < L; J++ )
191: Q = ideal_intersection(Q,QL[J],V,0|mod=Mod);
192: return Q;
193: }
194:
195: /* SYC primary decomositions */
196:
197: def syc_dec(B,V)
198: {
199: if ( type(SI=getopt(si)) == -1 ) SI = 2;
200: SIFList=[find_ssi0, find_ssi1,find_ssi2];
201: if ( SI<0 || SI>2 ) error("sycb_dec : si should be 0,1,2");
202: SIF = SIFList[SI];
203:
204: if ( type(MaxLevel=getopt(level)) == -1 ) MaxLevel = -1;
205: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
206: if ( type(Lexdec=getopt(lexdec)) == -1 ) Lexdec = 0;
207: if ( type(Time=getopt(time)) == -1 ) Time = 0;
208: if ( type(Iso=getopt(iso)) == -1 ) Iso = 0;
209: if ( type(Colon=getopt(colon)) == -1 ) Colon = 1;
210: Ord = 0;
211: Tall = time();
212: C = Gt = G = fast_gb(B,V,Mod,Ord|trace=1);
213: Q = []; IntQ = [1]; First = 1;
214: Tpd = Tiso = Tsep = 0;
215: RTpd = RTiso = RTsep = 0;
216: for ( Level = 0; MaxLevel < 0 || Level <= MaxLevel; Level++ ) {
217: if ( type(Gt[0])==1 ) break;
218: T3 = T2 = T1 = T0 = time();
219: if ( First ) {
220: PtR = prime_dec(C,V|indep=1,lexdec=Lexdec,mod=Mod,radical=1);
221: Pt = PtR[0]; IntPt = PtR[1];
222: if ( gen_gb_comp(Gt,IntPt,Mod) ) {
223: /* Gt is radical and Gt = cap Pt */
224: for ( T = Pt, Qt = []; T != []; T = cdr(T) )
225: Qt = cons([car(T)[0],car(T)[0]],Qt);
226: return append(Q,[Qt]);
227: }
228: }
229: T1 = time(); Tpd += (T1[0]-T0[0])+(T1[1]-T0[1]); RTpd += (T1[3]-T0[3]);
230: Qt = iso_comp(Gt,Pt,V,Ord|mod=Mod,first=First,iso=Iso);
231: Q = append(Q,[Qt]);
232: for ( T = Qt; T != []; T = cdr(T) )
233: IntQ = ideal_intersection(IntQ,car(T)[0],V,Ord
234: |mod=Mod,
235: gbblock=[[0,length(IntQ)],[length(IntQ),length(car(T)[0])]]);
236: if ( First ) { IntP = IntPt; First = 0; }
237: if ( gen_gb_comp(IntQ,G,Mod) ) break;
238:
239: M = mingen(IntQ,V);
240: for ( Pt = [], C = [1], T = M; T != []; T = cdr(T) ) {
241: Ci = colon(G,car(T),V|isgb=1);
242: if ( type(Ci[0]) != 1 ) {
243: Pi = prime_dec(Ci,V|indep=1,lexdec=Lexdec,radical=1,mod=Mod);
244: C = ideal_intersection(C,Pi[1],V,Ord);
245: Pt = append(Pt,Pi[0]);
246: }
247: }
248: Pt = pd_simp_comp(Pt,V|first=1,mod=Mod);
249: if ( Colon ) C = ideal_colon(G,IntQ,V|mod=Mod);
250: T2 = time(); Tiso += (T2[0]-T1[0])+(T2[1]-T1[1]); RTiso += (T2[3]-T1[3]);
251: Ok = (*SIF)(C,G,IntQ,IntP,V,Ord|mod=Mod);
252: Gt = append(Ok,G);
253: T3 = time(); Tsep += (T3[0]-T2[0])+(T3[1]-T2[1]); RTsep += (T3[3]-T2[3]);
254: }
255: T4 = time(); RTall = (T4[3]-Tall[3]); Tall = (T4[0]-Tall[0])+(T3[1]-Tall[1]);
256: if ( Time ) {
257: print(["cpu","total",Tall,"pd",Tpd,"iso",Tiso,"sep",Tsep]);
258: print(["elapsed","total",RTall,"pd",RTpd,"iso",RTiso,"sep",RTsep]);
259: }
260: return Q;
261: }
262:
263: static Tint2, RTint2$
264:
265: def syci_dec(B,V)
266: {
267: if ( type(SI=getopt(si)) == -1 ) SI = 1;
268: if ( SI<0 || SI>2 ) error("sycb_assdec : si should be 0,1,2");
269: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
270: if ( type(Lexdec=getopt(lexdec)) == -1 ) Lexdec = 0;
271: if ( type(Time=getopt(time)) == -1 ) Time = 0;
272: if ( type(Iso=getopt(iso)) == -1 ) Iso = 0;
273: if ( type(Ass=getopt(ass)) == -1 ) Ass = 0;
274: if ( type(Colon=getopt(colon)) == -1 ) Colon = 0;
275: if ( type(Para=getopt(para)) == -1 ) Para = 0;
276: Ord = 0;
277: Tiso = Tint = Tpd = Text = Tint2 = 0;
278: RTiso = RTint = RTpd = RText = RTint2 = 0;
279: T00 = time();
280: G = fast_gb(B,V,Mod,Ord|trace=1);
281: IntQ = [1]; QL = RL = []; First = 1;
282: for ( Level = 0; ; Level++ ) {
283: T0 = time();
284: if ( First ) {
285: PtR = prime_dec(G,V|indep=1,lexdec=Lexdec,mod=Mod,radical=1);
286: Pt = PtR[0]; IntPt = PtR[1]; Rad = IntPt;
1.2 noro 287: if ( gen_gb_comp(G,Rad,Mod) ) {
288: /* Gt is radical and Gt = cap Pt */
289: for ( T = Pt, Qt = []; T != []; T = cdr(T) )
290: Qt = cons([car(T)[0],car(T)[0],car(T)[1]],Qt);
291: return [reverse(Qt)];
292: }
1.1 noro 293: } else
294: Pt = colon_prime_dec(G,IntQ,V|lexdec=Lexdec,mod=Mod,para=Para);
295: ACCUM_TIME(Tpd,RTpd)
296: T0 = time();
297: Rt = iso_comp(G,Pt,V,Ord|mod=Mod,iso=Iso,para=Para,intq=IntQ);
298: ACCUM_TIME(Tiso,RTiso)
299: T0 = time();
1.4 noro 300: if ( Iso != 3 ) {
301: IntQ = ideal_list_intersection(map(first,Rt),V,Ord|mod=Mod,para=Para,isgb=1);
302: RL = append(RL,[Rt]);
303: } else {
304: NI = length(Rt);
305: Q = IntQ;
306: for ( J = 0, T = []; J < NI; J++ ) {
307: TJ = extract_qj(Q,V,Rt[J],Rad,Mod,SI,Colon,-1);
308: T = cons(TJ,T);
309: IntQ = ideal_intersection_m(IntQ,TJ[0],V,Ord|mod=Mod);
310: }
311: print("");
312: IntQ = nd_gr(IntQ,V,Mod,Ord);
313: T = reverse(T); RL = append(RL,[T]);
314: }
1.1 noro 315: QL = append(QL,[IntQ]);
316: ACCUM_TIME(Tint,RTint)
317: if ( gen_gb_comp(IntQ,G,Mod) ) break;
318: First = 0;
319: }
320: T0 = time();
1.4 noro 321: if ( Iso != 3 && !Ass )
1.1 noro 322: RL = extract_comp(QL,RL,V,Rad|mod=Mod,para=Para,si=SI,colon=Colon,ass=Ass);
323: ACCUM_TIME(Text,RText)
324: if ( Time ) {
325: T1 = time();
326: Tall = T1[0]-T00[0]+T1[1]-T00[1]; RTall += T1[3]-T00[3];
327: Tass = Tall-Text; RTass = RTall-RText;
328: print(["total",Tall,"ass",Tass,"pd",Tpd,"iso",Tiso,"int",Tint,"ext",Text]);
329: print(["elapsed",RTall,"ass",RTass,"pd",RTpd,"iso",RTiso,"int",RTint,"ext",RText]);
330: }
331: return RL;
332: }
333:
334: def extract_comp(QL,RL,V,Rad) {
335: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
336: if ( type(Para=getopt(para)) == -1 ) Para = 0;
337: if ( type(Colon=getopt(colon)) == -1 ) Colon = 0;
338: if ( type(SI=getopt(si)) == -1 ) SI = 1;
339: if ( type(Ass=getopt(ass)) == -1 ) Ass = 0;
340:
341: L = length(QL);
342: if ( Para ) {
343: for ( Task = [], I = 1; I < L; I++ ) {
344: QI = QL[I-1]; RI = RL[I]; NI = length(RI);
345: for ( J = 0, TI = []; J < NI; J++ ) {
346: T = ["noro_pd.extract_qj",QI,V,RI[J],Rad,Mod,SI,Colon,I];
347: Task = cons(T,Task);
348: }
349: }
350: print("comps:",2); print(length(Task),2); print("");
351: R = para_exec(Para,Task);
352: S = vector(L);
353: for ( I = 1; I < L; I++ ) S[I] = [];
354: S[0] = RL[0];
355: for ( T = R; T != []; T = cdr(T) ) {
356: U = car(T); Level = U[0]; Body = U[1];
357: S[Level] = cons(Body,S[Level]);
358: }
359: return vtol(S);
360: } else {
361: TL = [RL[0]];
362: for ( I = 1; I < L; I++ ) {
363: print("level:",2); print(I,2);
364: print(" comps:",2); print(length(RL[I]),2); print("");
365: QI = QL[I-1]; RI = RL[I]; NI = length(RI);
366: for ( J = 0, TI = []; J < NI; J++ ) {
367: TIJ = extract_qj(QI,V,RI[J],Rad,Mod,SI,Colon,-1);
368: TI = cons(TIJ,TI);
369: }
370: TI = reverse(TI); TL = cons(TI,TL);
371: }
372: TL = reverse(TL);
373: }
374: return TL;
375: }
376:
377: def colon_prime_dec(G,IntQ,V) {
378: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
379: if ( type(Lexdec=getopt(lexdec)) == -1 ) Lexdec = 0;
380: if ( type(Para=getopt(para)) == -1 ) Para = 0;
1.3 noro 381: if ( !Para ) {
382: print("colon_pd:",2); print(length(IntQ),2);
383: }
1.1 noro 384: if ( !Mod ) M = mingen(IntQ,V);
385: else M = IntQ;
386: if ( Para ) {
387: L = length(M);
1.3 noro 388: for ( Task = [], J = 0; J < L; J++ )
1.1 noro 389: if ( gen_nf(M[J],G,V,Ord,Mod) ) {
1.3 noro 390: T = ["noro_pd.call_colon",G,M[J],V,Mod,1];
1.1 noro 391: Task = cons(T,Task);
392: }
393: Task = reverse(Task);
394: R = para_exec(Para,Task);
1.3 noro 395: R = pd_simp_comp(R,V|mod=Mod); L = length(R);
396:
397: for ( Task = [], J = 0; J < L; J++ ) {
398: T = ["noro_pd.call_prime_dec",R[J],V,1,Lexdec,Mod];
399: Task = cons(T,Task);
400: }
401: Task = reverse(Task);
402: R = para_exec(Para,Task);
403:
1.1 noro 404: for ( Pt = [], T = R; T != []; T = cdr(T) ) Pt = append(Pt,car(T));
405: } else {
1.3 noro 406: for ( R = [], T = M; T != []; T = cdr(T) ) {
407: Ci = colon(G,car(T),V|isgb=1,mod=Mod);
408: R = cons(Ci,R);
409: }
410: print("->",2); print(length(M),2);
411: R = pd_simp_comp(R,V|mod=Mod);
412: print("->",2); print(length(R));
413: for ( Pt = [], T = R; T != []; T = cdr(T) ) {
414: Pi = prime_dec(car(T),V|indep=1,lexdec=Lexdec,mod=Mod);
1.1 noro 415: Pt = append(Pt,Pi);
416: }
417: }
418: Pt = pd_simp_comp(Pt,V|first=1,mod=Mod);
419: return Pt;
420: }
421:
1.3 noro 422: def call_colon(G,F,V,Mod,IsGB)
423: {
424: return colon(G,F,V|isgb=1,mod=Mod);
425: }
426:
427: def call_prime_dec(G,V,Indep,Lexdec,Mod)
1.1 noro 428: {
1.3 noro 429: if ( type(G[0]) != 1 )
430: Pi = prime_dec(G,V|indep=Indep,lexdec=Lexdec,mod=Mod);
1.1 noro 431: else
432: Pi = [];
433: return Pi;
434: }
435:
436: def extract_qj(Q,V,QL,Rad,Mod,SI,Colon,Level)
437: {
438: SIFList=[find_ssi0, find_ssi1,find_ssi2];
439: SIF = SIFList[SI];
440: G = QL[0]; P = QL[1]; PV = QL[2];
1.4 noro 441: if ( Q != [1] ) {
442: C = Colon ? ideal_colon(G,Q,V|mod=Mod) : P;
443: Ok = (*SIF)(C,G,Q,Rad,V,0|mod=Mod);
444: } else
445: Ok = [];
1.1 noro 446: V0 = setminus(V,PV);
447: HJ = elim_gb(append(Ok,G),V0,PV,Mod,[[0,length(V0)],[0,length(PV)]]);
448: HJ = contraction(HJ,V0|mod=Mod);
449: IJ = nd_gr(HJ,V,Mod,Ord);
450: return Level >= 0 ? [Level,[IJ,P]] : [IJ,P];
451: }
452:
453: def syca_dec(B,V)
454: {
455: T00 = time();
456: if ( type(SI=getopt(si)) == -1 ) SI = 2;
457: SIFList=[find_si0, find_si1,find_si2]; SIF = SIFList[SI];
458: if ( !SIF ) error("syca_dec : si should be 0,1,2");
459:
460: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
461: if ( type(Lexdec=getopt(lexdec)) == -1 ) Lexdec = 0;
462: if ( type(NoSimp=getopt(nosimp)) == -1 ) NoSimp = 0;
463: if ( type(Time=getopt(time)) == -1 ) Time = 0;
464: if ( type(Iso=getopt(iso)) == -1 ) Iso = 0;
465: Ord = 0;
466: Gt = G0 = G = fast_gb(B,V,Mod,Ord|trace=1);
467: Q0 = Q = []; IntQ0 = IntQ = [1]; First = 1;
468: C = 0;
469:
470: Tass = Tiso = Tcolon = Tsep = Tirred = 0;
471: Rass = Riso = Rcolon = Rsep = Rirred = 0;
472: while ( 1 ) {
473: if ( type(Gt[0])==1 ) break;
474: T0 = time();
475: PtR = prime_dec(Gt,V|indep=1,lexdec=Lexdec,mod=Mod,radical=1);
476: T1 = time(); Tass += T1[0]-T0[0]+T1[1]-T0[1]; Rass += T1[3]-T0[3];
477: Pt = PtR[0]; IntPt = PtR[1];
478: if ( gen_gb_comp(Gt,IntPt,Mod) ) {
479: /* Gt is radical and Gt = cap Pt */
480: for ( T = Pt, Qt = []; T != []; T = cdr(T) )
481: Qt = cons([car(T)[0],car(T)[0]],Qt);
482: if ( First )
483: return [Qt,[]];
484: else
485: Q0 = append(Qt,Q0);
486: break;
487: }
488: T0 = time();
489: Qt = iso_comp(Gt,Pt,V,Ord|mod=Mod,isgb=1,iso=Iso);
490: T1 = time(); Tiso += T1[0]-T0[0]+T1[1]-T0[1]; Riso += T1[3]-T0[3];
491: IntQt = ideal_list_intersection(map(first,Qt),V,Ord|mod=Mod);
492: if ( First ) {
493: IntQ0 = IntQ = IntQt; IntP = IntPt; Qi = Qt; First = 0;
494: } else {
495: IntQ1 = ideal_intersection(IntQ,IntQt,V,Ord|mod=Mod);
496: if ( gen_gb_comp(IntQ,IntQ1,Mod) ) {
497: G = Gt; IntP = IntPt; Q = []; IntQ = [1]; C = 0;
498: continue;
499: } else {
500: IntQ = IntQ1;
501: IntQ1 = ideal_intersection(IntQ0,IntQt,V,Ord|mod=Mod);
502: if ( !gen_gb_comp(IntQ0,IntQ1,Mod) ) {
503: Q = append(Qt,Q);
504: for ( T = Qt; T != []; T = cdr(T) )
505: if ( !ideal_inclusion(IntQ0,car(T)[0],V,Ord|mod=Mod) )
506: Q0 = append(Q0,[car(T)]);
507: IntQ0 = IntQ1;
508: }
509: }
510: }
511: if ( gen_gb_comp(IntQt,Gt,Mod) || gen_gb_comp(IntQ,G,Mod) || gen_gb_comp(IntQ0,G0,Mod) ) break;
512: T0 = time();
513: C1 = ideal_colon(G,IntQ,V|mod=Mod);
514: T1 = time(); Tcolon += T1[0]-T0[0]+T1[1]-T0[1]; Rcolon += T1[3]-T0[3];
515: if ( C && gen_gb_comp(C,C1,Mod) ) {
516: G = Gt; IntP = IntPt; Q = []; IntQ = [1]; C = 0;
517: continue;
518: } else C = C1;
519: T0 = time();
520: Ok = (*SIF)(C,G,IntQ,IntP,V,Ord|mod=Mod);
521: G1 = append(Ok,G);
522: Gt1 = incremental_gb(G1,V,Ord|mod=Mod);
523: T1 = time(); Tsep += T1[0]-T0[0]+T1[1]-T0[1]; Rsep += T1[3]-T0[3];
524: Gt = Gt1;
525: }
526: T0 = time();
527: if ( !NoSimp ) Q1 = qd_remove_redundant_comp(G0,Qi,Q0,V,Ord|mod=Mod);
528: else Q1 = Q0;
529: if ( Time ) {
530: T1 = time(); Tirred += T1[0]-T0[0]+T1[1]-T0[1]; Rirred += T1[3]-T0[3];
531: Tall = T1[0]-T00[0]+T1[1]-T00[1]; Rall += T1[3]-T00[3];
532: print(["total",Tall,"ass",Tass,"iso",Tiso, "colon",Tcolon,"sep",Tsep,"irred",Tirred]);
533: print(["Rtotal",Rall,"Rass",Rass,"Riso",Riso, "Rcolon",Rcolon,"Rsep",Rsep,"Rirred",Rirred]);
534: print(["iso",length(Qi),"emb",length(Q0),"->",length(Q1)]);
535: }
536: return [Qi,Q1];
537: }
538:
539: def syc0_dec(B,V)
540: {
541: T00 = time();
542: if ( type(SI=getopt(si)) == -1 ) SI = 1;
543: SIFList=[find_si0, find_si1,find_si2,find_ssi0,find_ssi1,find_ssi2]; SIF = SIFList[SI];
544: if ( !SIF ) error("syc0_dec : si should be 0,1,2");
545: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
546: if ( type(Lexdec=getopt(lexdec)) == -1 ) Lexdec = 0;
547: if ( type(NoSimp=getopt(nosimp)) == -1 ) NoSimp = 0;
548: if ( type(Time=getopt(time)) == -1 ) Time = 0;
549: Ord = 0;
550: G = fast_gb(B,V,Mod,Ord);
551: Q = []; IntQ = [1]; Gt = G; First = 1;
552: Tass = Tiso = Tcolon = Tsep = Tirred = 0;
553: Rass = Riso = Rcolon = Rsep = Rirred = 0;
554: while ( 1 ) {
555: if ( type(Gt[0])==1 ) break;
556: T0 = time();
557: PtR = prime_dec(Gt,V|indep=1,lexdec=Lexdec,mod=Mod,radical=1);
558: T1 = time(); Tass += T1[0]-T0[0]+T1[1]-T0[1]; Rass += T1[3]-T0[3];
559: Pt = PtR[0]; IntPt = PtR[1];
560: if ( gen_gb_comp(Gt,IntPt,Mod) ) {
561: /* Gt is radical and Gt = cap Pt */
562: for ( T = Pt, Qt = []; T != []; T = cdr(T) )
563: Qt = cons([car(T)[0],car(T)[0]],Qt);
564: if ( First )
565: return [Qt,[]];
566: else
567: Q = append(Qt,Q);
568: break;
569: }
570:
571: T0 = time();
572: Qt = iso_comp(Gt,Pt,V,Ord|mod=Mod,isgb=1);
573: T1 = time(); Tiso += T1[0]-T0[0]+T1[1]-T0[1]; Riso += T1[3]-T0[3];
574: IntQt = ideal_list_intersection(map(first,Qt),V,Ord|mod=Mod);
575: if ( First ) {
576: IntQ = IntQt; Qi = Qt; First = 0;
577: } else {
578: IntQ1 = ideal_intersection(IntQ,IntQt,V,Ord|mod=Mod);
579: if ( !gen_gb_comp(IntQ1,IntQ,Mod) )
580: Q = append(Qt,Q);
581: }
582: if ( gen_gb_comp(IntQ,G,Mod) || gen_gb_comp(IntQt,Gt,Mod) )
583: break;
584: T0 = time();
585: C = ideal_colon(Gt,IntQt,V|mod=Mod);
586: T1 = time(); Tcolon += T1[0]-T0[0]+T1[1]-T0[1]; Rcolon += T1[3]-T0[3];
587: T0 = time();
588: Ok = (*SIF)(C,Gt,IntQt,IntPt,V,Ord|mod=Mod);
589: G1 = append(Ok,Gt);
590: Gt = incremental_gb(G1,V,Ord|mod=Mod);
591: T1 = time(); Tsep += T1[0]-T0[0]+T1[1]-T0[1]; Rsep += T1[3]-T0[3];
592: }
593: T0 = time();
594: if ( !NoSimp ) Q1 = qd_remove_redundant_comp(G,Qi,Q,V,Ord|mod=Mod);
595: else Q1 = Q;
596: T1 = time(); Tirred += T1[0]-T0[0]+T1[1]-T0[1]; Rirred += T1[3]-T0[3];
597: Tall = T1[0]-T00[0]+T1[1]-T00[1]; Rall += T1[3]-T00[3];
598: if ( Time ) {
599: print(["total",Tall,"ass",Tass,"iso",Tiso, "colon",Tcolon,"sep",Tsep,"irred",Tirred]);
600: print(["Rtotal",Rall,"Rass",Rass,"Riso",Riso, "Rcolon",Rcolon,"Rsep",Rsep,"Rirred",Rirred]);
601: print(["iso",length(Qi),"emb",length(Q),"->",length(Q1)]);
602: }
603: return [Qi,Q1];
604: }
605:
606: def power(A,I) { return A^I; }
607:
608:
609: /* functions for computating a separing ideal */
610: /* C=G:Q, Rad=rad(Q), return J s.t. Q cap (G+J) = G */
611:
612: def find_si0(C,G,Q,Rad,V,Ord) {
613: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
614: for ( CI = C, I = 1; ; I++ ) {
615: for ( T = CI, S = []; T != []; T = cdr(T) )
616: if ( gen_nf(car(T),Q,V,Ord,Mod) ) S = cons(car(T),S);
617: if ( S == [] )
618: error("find_si0 : cannot happen");
619: G1 = append(S,G);
620: Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
621: /* check whether (Q cap (G+S)) = G */
622: if ( gen_gb_comp(Int,G,Mod) ) { print([0]); return reverse(S); }
623: CI = ideal_product(CI,C,V|mod=Mod);
624: }
625: }
626:
627: def find_si1(C,G,Q,Rad,V,Ord) {
628: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
629: for ( T = C, S = []; T != []; T = cdr(T) )
630: if ( gen_nf(car(T),Q,V,Ord,Mod) ) S = cons(car(T),S);
631: if ( S == [] )
632: error("find_si1 : cannot happen");
633: G1 = append(S,G);
634: Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
635: /* check whether (Q cap (G+S)) = G */
636: if ( gen_gb_comp(Int,G,Mod) ) { print([0]); return reverse(S); }
637:
638: C = qsort(C,comp_tdeg);
639:
640: Tmp = ttttt; TV = cons(Tmp,V); Ord1 = [[0,1],[Ord,length(V)]];
641: Int0 = incremental_gb(append(vtol(ltov(G)*Tmp),vtol(ltov(Q)*(1-Tmp))),
642: TV,Ord1|gbblock=[[0,length(G)]],mod=Mod);
643: Dp = dp_gr_print(); dp_gr_print(0);
644: for ( T = C, S = []; T != []; T = cdr(T) ) {
645: if ( !gen_nf(car(T),Rad,V,Ord,Mod) ) continue;
646: Ui = U = car(T);
647: for ( I = 1; ; I++ ) {
648: G1 = cons(Ui,G);
649: Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
650: if ( gen_gb_comp(Int,G,Mod) ) break;
651: else
652: Ui = gen_nf(Ui*U,G,V,Ord,Mod);
653: }
654: print([length(T),I],2);
655: Int1 = incremental_gb(append(Int0,[Tmp*Ui]),TV,Ord1
656: |gbblock=[[0,length(Int0)]],mod=Mod);
657: Int = elimination(Int1,V);
658: if ( !gen_gb_comp(Int,G,Mod) ) {
659: break;
660: } else {
661: Int0 = Int1;
662: S = cons(Ui,S);
663: }
664: }
665: print("");
666: dp_gr_print(Dp);
667: return reverse(S);
668: }
669:
670: def find_si2(C,G,Q,Rad,V,Ord) {
671: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
672: for ( T = C, S = []; T != []; T = cdr(T) )
673: if ( gen_nf(car(T),Q,V,Ord,Mod) ) S = cons(car(T),S);
674: if ( S == [] )
675: error("find_si2 : cannot happen");
676: G1 = append(S,G);
677: Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
678: /* check whether (Q cap (G+S)) = G */
679: if ( gen_gb_comp(Int,G,Mod) ) { print([0]); return reverse(S); }
680:
681: C = qsort(C,comp_tdeg);
682:
683: Dp = dp_gr_print(); dp_gr_print(0);
684: Tmp = ttttt; TV = cons(Tmp,V); Ord1 = [[0,1],[Ord,length(V)]];
685: Int0 = incremental_gb(append(vtol(ltov(G)*Tmp),vtol(ltov(Q)*(1-Tmp))),
686: TV,Ord1|gbblock=[[0,length(G)]],mod=Mod);
687: for ( T = C, S = []; T != []; T = cdr(T) ) {
688: if ( !gen_nf(car(T),Rad,V,Ord,Mod) ) continue;
689: Ui = U = car(T);
690: for ( I = 1; ; I++ ) {
691: Int1 = incremental_gb(append(Int0,[Tmp*Ui]),TV,Ord1
692: |gbblock=[[0,length(Int0)]],mod=Mod);
693: Int = elimination(Int1,V);
694: if ( gen_gb_comp(Int,G,Mod) ) break;
695: else
696: Ui = gen_nf(Ui*U,G,V,Ord,Mod);
697: }
698: print([length(T),I],2);
699: S = cons(Ui,S);
700: }
701: S = qsort(S,comp_tdeg);
702: print("");
703: End = Len = length(S);
704:
705: Tmp = ttttt; TV = cons(Tmp,V); Ord1 = [[0,1],[Ord,length(V)]];
706: Prev = 1;
707: G1 = append(G,[S[0]]);
708: Int0 = incremental_gb(append(vtol(ltov(G1)*Tmp),vtol(ltov(Q)*(1-Tmp))),
709: TV,Ord1|gbblock=[[0,length(G)]],mod=Mod);
710: if ( End > 1 ) {
711: Cur = 2;
712: while ( Prev < Cur ) {
713: for ( St = [], I = Prev; I < Cur; I++ ) St = cons(Tmp*S[I],St);
714: Int1 = incremental_gb(append(Int0,St),TV,Ord1
715: |gbblock=[[0,length(Int0)]],mod=Mod);
716: Int = elimination(Int1,V);
717: if ( gen_gb_comp(Int,G,Mod) ) {
718: print([Cur],2);
719: Prev = Cur;
720: Cur = Cur+idiv(End-Cur+1,2);
721: Int0 = Int1;
722: } else {
723: End = Cur;
724: Cur = Prev + idiv(Cur-Prev,2);
725: }
726: }
727: for ( St = [], I = 0; I < Prev; I++ ) St = cons(S[I],St);
728: } else
729: St = [S[0]];
730: print("");
731: for ( I = Prev; I < Len; I++ ) {
732: Int1 = incremental_gb(append(Int0,[Tmp*S[I]]),TV,Ord1
733: |gbblock=[[0,length(Int0)]],mod=Mod);
734: Int = elimination(Int1,V);
735: if ( gen_gb_comp(Int,G,Mod) ) {
736: print([I],2);
737: St = cons(S[I],St);
738: Int0 = Int1;
739: }
740: }
741: Ok = reverse(St);
742: print("");
743: print([length(S),length(Ok)]);
744: dp_gr_print(Dp);
745: return Ok;
746: }
747:
748: /* functions for computing a saturated separating ideal */
749:
750: def find_ssi0(C,G,Q,Rad,V,Ord) {
751: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
752: if ( type(Reduce=getopt(red)) == -1 ) Reduce = 0;
753: for ( T = C, S = []; T != []; T = cdr(T) )
754: if ( gen_nf(car(T),Q,V,Ord,Mod) ) S = cons(car(T),S);
755: if ( S == [] )
756: error("find_ssi0 : cannot happen");
757: G1 = append(S,G);
758: Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
759: /* check whether (Q cap (G+S)) = G */
760: if ( gen_gb_comp(Int,G,Mod) ) { print([0]); return reverse(S); }
761:
762: if ( Reduce ) {
763: for ( T = C, U = []; T != []; T = cdr(T) )
764: if ( gen_nf(car(T),Rad,V,Ord,Mod) ) U = cons(car(T),U);
765: U = reverse(U);
766: } else
767: U = C;
768:
769: for ( I = 1; ; I++ ) {
770: print([I],2);
771: S = map(power,U,I);
772: G1 = append(S,G);
773: Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
774: /* check whether (Q cap (G+S)) = G */
775: if ( gen_gb_comp(Int,G,Mod) ) { print(""); return reverse(S); }
776: }
777: }
778:
779: def find_ssi1(C,G,Q,Rad,V,Ord) {
780: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
781: if ( type(Reduce=getopt(red)) == -1 ) Reduce = 0;
782: for ( T = C, S = []; T != []; T = cdr(T) )
783: if ( gen_nf(car(T),Q,V,Ord,Mod) ) S = cons(car(T),S);
784: if ( S == [] )
785: error("find_ssi1 : cannot happen");
786: G1 = append(S,G);
787: Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
788: /* check whether (Q cap (G+S)) = G */
789: if ( gen_gb_comp(Int,G,Mod) ) { print([0]); return reverse(S); }
790:
791: dp_ord(Ord); DC = map(dp_ptod,C,V);
792: DC = qsort(DC,comp_tord); C = map(dp_dtop,DC,V);
793: print(length(C),2);
794: if ( Reduce ) {
795: SC = map(sq,C,Mod);
796: SC = reverse(SC); C = reverse(C);
797: for ( T = C, C1 = [], R1 = append(SC,Rad); T != []; T = cdr(T) ) {
798: R0 = car(R1); R1 = cdr(R1);
799: if ( !gen_nf(car(T),Rad,V,Ord,Mod) ) continue;
800: if ( radical_membership(R0,R1,V|mod=Mod) ) {
801: C1 = cons(car(T),C1);
802: R1 = append(R1,[R0]);
803: }
804: }
805: print("->",0); print(length(C1),2);
806: C = C1;
807: }
808: print(" ",2);
809:
810: Tmp = ttttt; TV = cons(Tmp,V); Ord1 = [[0,1],[Ord,length(V)]];
811: Int0 = incremental_gb(append(vtol(ltov(G)*Tmp),vtol(ltov(Q)*(1-Tmp))),
812: TV,Ord1|gbblock=[[0,length(G)]],mod=Mod);
813: Dp = dp_gr_print(); dp_gr_print(0);
814: for ( J = 0, T = C, S = [], GS = G; T != []; T = cdr(T), J++ ) {
815: if ( !gen_nf(car(T),Rad,V,Ord,Mod) ) continue;
816: Ui = U = car(T);
817: for ( I = 1; ; I++ ) {
818: Int1 = nd_gr(append(Int0,[Tmp*Ui]),TV,Mod,Ord1
819: |gbblock=[[0,length(Int0)]],newelim=1);
820: if ( Int1 ) {
821: Int = elimination(Int1,V);
822: if ( gen_gb_comp(Int,G,Mod) ) break;
823: }
824: print("x",2);
825: Ui = gen_nf(Ui*U,G,V,Ord,Mod);
826: }
827: print(J,2);
828: Int0 = Int1;
829: S = cons(Ui,S);
830: }
831: print("");
832: dp_gr_print(Dp);
833: return reverse(S);
834: }
835:
836: def find_ssi2(C,G,Q,Rad,V,Ord) {
837: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
838: if ( type(Reduce=getopt(red)) == -1 ) Reduce = 0;
839: for ( T = C, S = []; T != []; T = cdr(T) )
840: if ( gen_nf(car(T),Q,V,Ord,Mod) ) S = cons(car(T),S);
841: if ( S == [] )
842: error("find_ssi2 : cannot happen");
843: G1 = append(S,G);
844: Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
845: /* check whether (Q cap (G+S)) = G */
846: if ( gen_gb_comp(Int,G,Mod) ) { print([0]); return reverse(S); }
847:
848: #if 0
849: dp_ord(Ord); DC = map(dp_ptod,C,V);
850: DC = qsort(DC,comp_tord); C = map(dp_dtop,DC,V);
851: #else
852: C = qsort(C,comp_tdeg);
853: #endif
854: if ( Reduce ) {
855: for ( T = C, C1 = [], R1 = Rad; T != []; T = cdr(T) ) {
856: if ( !gen_nf(car(T),Rad,V,Ord,Mod) ) continue;
1.4 noro 857: if ( radical_membership(car(T),R1,V|mod=Mod) ) {
1.1 noro 858: C1 = cons(car(T),C1);
859: R1 = cons(sq(car(T),Mod),R1);
860: }
861: }
862: print(["C",length(C),"->",length(C1)]);
863: C = reverse(C1);
864: }
865: for ( T = C, S = []; T != []; T = cdr(T) ) {
866: if ( !gen_nf(car(T),Rad,V,Ord,Mod) ) continue;
867: Ui = U = car(T);
868: S = cons([Ui,U],S);
869: }
870: S = qsort(S,comp_tdeg_first);
871: print("");
872:
873: Dp = dp_gr_print(); dp_gr_print(0);
874: Tmp = ttttt; TV = cons(Tmp,V); Ord1 = [[0,1],[Ord,length(V)]];
875: Int0 = incremental_gb(append(vtol(ltov(G)*Tmp),vtol(ltov(Q)*(1-Tmp))),
876: TV,Ord1|gbblock=[[0,length(G)]],mod=Mod);
877: OK = [];
878: while ( S != [] ) {
879: Len = length(S); print("remaining gens : ",0); print(Len);
880: S1 = [];
881: for ( Start = Prev = 0; Start < Len; Start = Prev ) {
882: Cur = Start+1;
883: print(Start,2);
884: while ( Prev < Len ) {
885: for ( St = [], I = Prev; I < Cur; I++ ) St = cons(Tmp*S[I][0],St);
886: Int1 = nd_gr(append(Int0,St),TV,Mod,Ord1|gbblock=[[0,length(Int0)]],newelim=1);
887: if ( !Int1 ) {
888: print("x",0); break;
889: }
890: Int = elimination(Int1,V);
891: if ( gen_gb_comp(Int,G,Mod) ) {
892: print([Prev,Cur-1],2);
893: Prev = Cur;
894: Cur += (Prev-Start)+1;
895: if ( Cur > Len ) Cur = Len;
896: Int0 = Int1;
897: } else
898: break;
899: }
900: for ( I = Start; I < Prev; I++ ) OK = cons(S[I][0],OK);
901: if ( Prev == Start ) {
902: Ui = S[I][0]; U = S[I][1];
903: Ui = gen_nf(Ui*U,G,V,Ord,Mod);
904: S1 = cons([Ui,U],S1);
905: Prev++;
906: }
907: }
908: S = reverse(S1);
909: print("");
910: }
911: print("");
912: OK = reverse(OK);
913: dp_gr_print(Dp);
914: return OK;
915: }
916:
917: /* SY primary decompsition */
918:
919: def sy_dec(B,V)
920: {
921: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
922: if ( type(Lexdec=getopt(lexdec)) == -1 ) Lexdec = 0;
923: Ord = 0;
924: G = fast_gb(B,V,Mod,Ord);
925: Q = [];
926: IntQ = [1];
927: Gt = G;
928: First = 1;
929: while ( 1 ) {
930: if ( type(Gt[0]) == 1 ) break;
931: Pt = prime_dec(Gt,V|indep=1,lexdec=Lexdec,mod=Mod);
932: L = pseudo_dec(Gt,Pt,V,Ord|mod=Mod);
933: Qt = L[0]; Rt = L[1]; St = L[2];
934: IntQt = ideal_list_intersection(map(first,Qt),V,Ord|mod=Mod);
935: if ( First ) {
936: IntQ = IntQt;
937: Qi = Qt;
938: First = 0;
939: } else {
940: IntQ = ideal_intersection(IntQ,IntQt,V,Ord|mod=Mod);
941: Q = append(Qt,Q);
942: }
943: if ( gen_gb_comp(IntQ,G,Mod) ) break;
944: for ( T = Rt; T != []; T = cdr(T) ) {
945: if ( type(car(T)[0]) == 1 ) continue;
946: U = sy_dec(car(T),V|lexdec=Lexdec,mod=Mod);
947: IntQ = ideal_list_intersection(cons(IntQ,map(first,U)),
948: V,Ord|mod=Mod);
949: Q = append(U,Q);
950: if ( gen_gb_comp(IntQ,G,Mod) ) break;
951: }
952: Gt = fast_gb(append(Gt,St),V,Mod,Ord);
953: }
954: Q = qd_remove_redundant_comp(G,Qi,Q,V,Ord|mod=Mod);
955: return append(Qi,Q);
956: }
957:
958: def pseudo_dec(G,L,V,Ord)
959: {
960: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
961: N = length(L);
962: S = vector(N);
963: Q = vector(N);
964: R = vector(N);
965: L0 = map(first,L);
966: for ( I = 0; I < N; I++ ) {
967: LI = setminus(L0,[L0[I]]);
968: PI = ideal_list_intersection(LI,V,Ord|mod=Mod);
969: PI = qsort(PI,comp_tdeg);
970: for ( T = PI; T != []; T = cdr(T) )
971: if ( gen_nf(car(T),L0[I],V,Ord,Mod) ) break;
972: if ( T == [] ) error("separator : cannot happen");
973: SI = satind(G,car(T),V|mod=Mod);
974: QI = SI[0];
975: S[I] = car(T)^SI[1];
976: PV = L[I][1];
977: V0 = setminus(V,PV);
978: #if 0
979: GI = fast_gb(QI,append(V0,PV),Mod,
980: [[Ord,length(V0)],[Ord,length(PV)]]);
981: #else
982: GI = fast_gb(QI,append(V0,PV),Mod,
983: [[2,length(V0)],[Ord,length(PV)]]);
984: #endif
985: LCFI = lcfactor(GI,V0,Ord,Mod);
986: for ( F = 1, T = LCFI, Gt = QI; T != []; T = cdr(T) ) {
987: St = satind(Gt,T[0],V|mod=Mod);
988: Gt = St[0]; F *= T[0]^St[1];
989: }
990: Q[I] = [Gt,L0[I]];
991: R[I] = fast_gb(cons(F,QI),V,Mod,Ord);
992: }
993: return [vtol(Q),vtol(R),vtol(S)];
994: }
995:
996: def iso_comp(G,L,V,Ord)
997: {
998: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
999: if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0;
1000: if ( type(Iso=getopt(iso)) == -1 ) Iso = 0;
1001: if ( type(Para=getopt(para)) == -1 ) Para = 0;
1002: if ( type(Q=getopt(intq)) == -1 ) Q = 0;
1.4 noro 1003: if ( type(S=getopt(sep)) == -1 ) S = 0;
1.1 noro 1004:
1.4 noro 1005: if ( !S ) S = separator(L,V|mod=Mod);
1.1 noro 1006: N = length(L);
1007: print("comps : ",2); print(N); print("",2);
1008: if ( Para ) {
1009: Task = [];
1010: for ( I = 0; I < N; I++ ) {
1011: T = ["noro_pd.locsat",G,V,L[I],S[I],Mod,IsGB,Iso,Q];
1012: Task = cons(T,Task);
1013: }
1014: Task = reverse(Task);
1015: R = para_exec(Para,Task);
1016: return R;
1017: } else {
1018: for ( I = 0, R = []; I < N; I++ ) {
1019: QI = locsat(G,V,L[I],S[I],Mod,IsGB,Iso,Q);
1020: if ( type(QI[0][0])==1 )
1021: error("iso_comp : cannot happen");
1022: print(".",2);
1023: R = cons(QI,R);
1024: }
1025: print("");
1026: return reverse(R);
1027: }
1028: }
1029:
1030: def locsat(G,V,L,S,Mod,IsGB,Iso,Q)
1031: {
1032: P = L[0]; PV = L[1]; V0 = setminus(V,PV);
1033: if ( Iso==1 ) {
1034: QI = sat(G,S,V|isgb=IsGB,mod=Mod);
1035: GI = elim_gb(QI,V0,PV,Mod,[[0,length(V0)],[0,length(PV)]]);
1036: GI = nd_gr(contraction(GI,V0|mod=Mod),V,Mod,0);
1037: } else if ( Iso==0 ) {
1038: HI = elim_gb(G,V0,PV,Mod,[[0,length(V0)],[0,length(PV)]]);
1039: GI = nd_gr(contraction(HI,V0|mod=Mod),V,Mod,0);
1040: GI = sat(GI,S,V|isgb=IsGB,mod=Mod);
1041: } else if ( Iso==2 ) {
1042: HI = elim_gb(G,V0,PV,Mod,[[0,length(V0)],[0,length(PV)]]);
1043: TV = ttttt;
1044: if ( Mod )
1045: GI = nd_gr(cons(TV*S-1,HI),cons(TV,V0),Mod,[[0,1],[0,length(V0)]]);
1046: else
1047: GI = nd_gr_trace(append(HI,[TV*S-1]),cons(TV,V0),
1048: 1,1,[[0,1],[0,length(V0)]]|gbblock=[[0,length(HI)]]);
1049: GI = elimination(GI,V);
1050: GI = nd_gr(contraction(GI,V0|mod=Mod),V,Mod,0);
1.4 noro 1051: } else if ( Iso==3 ) {
1052: GI = sat(G,S,V|isgb=IsGB,mod=Mod);
1.1 noro 1053: }
1054: if ( Q )
1055: GI = ideal_intersection(Q,GI,V,0|mod=Mod);
1056: return [GI,P,PV];
1057: }
1058:
1059: /* GTZ primary decompsition */
1060:
1061: def prima_dec(B,V)
1062: {
1063: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1064: if ( type(Ord=getopt(ord)) == -1 ) Ord = 0;
1065: G0 = fast_gb(B,V,Mod,0);
1066: G = fast_gb(G0,V,Mod,Ord);
1067: IntP = [1];
1068: QD = [];
1069: while ( 1 ) {
1070: if ( type(G[0])==1 || ideal_inclusion(IntP,G0,V,0|mod=Mod) )
1071: break;
1072: W = maxindep(G,V,Ord); NP = length(W);
1073: V0 = setminus(V,W); N = length(V0);
1074: V1 = append(V0,W);
1075: G1 = fast_gb(G,V1,Mod,[[Ord,N],[Ord,NP]]);
1076: LCF = lcfactor(G1,V0,Ord,Mod);
1077: L = zprimacomp(G,V0|mod=Mod);
1078: F = 1;
1079: for ( T = LCF, G2 = G; T != []; T = cdr(T) ) {
1080: S = satind(G2,T[0],V1|mod=Mod);
1081: G2 = S[0]; F *= T[0]^S[1];
1082: }
1083: for ( T = L, QL = []; T != []; T = cdr(T) )
1084: QL = cons(car(T)[0],QL);
1085: Int = ideal_list_intersection(QL,V,0|mod=Mod);
1086: IntP = ideal_intersection(IntP,Int,V,0|mod=Mod);
1087: QD = append(QD,L);
1088: F = gen_nf(F,G,V,0,Mod);
1089: G = fast_gb(cons(F,G),V,Mod,Ord);
1090: }
1091: QD = qd_remove_redundant_comp(G0,[],QD,V,0);
1092: return QD;
1093: }
1094:
1095: /* SL prime decomposition */
1096:
1097: def prime_dec(B,V)
1098: {
1099: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1100: if ( type(Indep=getopt(indep)) == -1 ) Indep = 0;
1101: if ( type(NoLexDec=getopt(lexdec)) == -1 ) LexDec = 0;
1102: if ( type(Rad=getopt(radical)) == -1 ) Rad = 0;
1103: B = map(sq,B,Mod);
1104: if ( LexDec )
1105: PD = lex_predec1(B,V|mod=Mod);
1106: else
1107: PD = [B];
1108: if ( length(PD) > 1 ) {
1109: G = ideal_list_intersection(PD,V,0|mod=Mod);
1110: PD = pd_remove_redundant_comp(G,PD,V,0|mod=Mod);
1111: }
1112: R = [];
1113: for ( T = PD; T != []; T = cdr(T) )
1114: R = append(prime_dec_main(car(T),V|indep=Indep,mod=Mod),R);
1115: if ( Indep ) {
1116: G = ideal_list_intersection(map(first,R),V,0|mod=Mod);
1117: if ( LexDec ) R = pd_simp_comp(R,V|first=1,mod=Mod);
1118: } else {
1119: G = ideal_list_intersection(R,V,0|mod=Mod);
1120: if ( LexDec ) R = pd_simp_comp(R,V|first=1,mod=Mod);
1121: }
1122: return Rad ? [R,G] : R;
1123: }
1124:
1125: def prime_dec_main(B,V)
1126: {
1127: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1128: if ( type(Indep=getopt(indep)) == -1 ) Indep = 0;
1129: G = fast_gb(B,V,Mod,0);
1130: IntP = [1];
1131: PD = [];
1.4 noro 1132: DG = ltov(map(dp_ptod,G,V));
1133: for ( Ind = [], I = length(G)-1; I >= 0; I-- ) Ind = cons(I,Ind);
1134: if ( Mod ) DG = map(dp_mod,DG,Mod,[]);
1.1 noro 1135: while ( 1 ) {
1136: /* rad(G) subset IntP */
1137: /* check if IntP subset rad(G) */
1.4 noro 1138: /* print([length(PD),length(IntP)],2); */
1.1 noro 1139: for ( T = IntP; T != []; T = cdr(T) ) {
1.4 noro 1140: if ( (GNV = radical_membership(car(T),G,V|mod=Mod,isgb=1,dg=[DG,Ind])) ) {
1.1 noro 1141: F = car(T);
1142: break;
1143: }
1144: }
1145: if ( T == [] ) return PD;
1146:
1147: /* GNV = [GB(<NV*F-1,G>),NV] */
1148: G1 = fast_gb(GNV[0],cons(GNV[1],V),Mod,[[0,1],[0,length(V)]]);
1149: G0 = elimination(G1,V);
1150: PD0 = zprimecomp(G0,V,Indep|mod=Mod);
1151: if ( Indep ) {
1152: Int = ideal_list_intersection(PD0[0],V,0|mod=Mod);
1153: IndepSet = PD0[1];
1154: for ( PD1 = [], T = PD0[0]; T != []; T = cdr(T) )
1155: PD1 = cons([car(T),IndepSet],PD1);
1156: PD = append(PD,reverse(PD1));
1157: } else {
1158: Int = ideal_list_intersection(PD0,V,0|mod=Mod);
1159: PD = append(PD,PD0);
1160: }
1.4 noro 1161: #if 0
1162: IntP = ideal_intersection_m(IntP,Int,V,0|mod=Mod);
1163: #else
1164: IntP = ideal_intersection(IntP,Int,V,0
1165: |mod=Mod,gbblock=[[0,length(IntP)]]);
1166: #endif
1.1 noro 1167: }
1168: }
1169:
1170: /* pre-decomposition */
1171:
1172: def lex_predec1(B,V)
1173: {
1174: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1175: G = fast_gb(B,V,Mod,2);
1176: for ( T = G; T != []; T = cdr(T) ) {
1177: F = gen_fctr(car(T),Mod);
1178: if ( length(F) > 2 || length(F) == 2 && F[1][1] > 1 ) {
1179: for ( R = [], S = cdr(F); S != []; S = cdr(S) ) {
1180: Ft = car(S)[0];
1181: Gt = map(ptozp,map(gen_nf,G,[Ft],V,0,Mod));
1182: R1 = fast_gb(cons(Ft,Gt),V,Mod,0);
1183: R = cons(R1,R);
1184: }
1185: return R;
1186: }
1187: }
1188: return [G];
1189: }
1190:
1191: /* zero-dimensional prime/primary decomosition */
1192:
1193: def zprimedec(B,V,Mod)
1194: {
1195: L = partial_decomp(B,V,Mod);
1196: P = L[0]; NP = L[1];
1197: R = [];
1198: for ( ; P != []; P = cdr(P) ) R = cons(car(car(P)),R);
1199: for ( T = NP; T != []; T = cdr(T) ) {
1200: R1 = complete_decomp(car(T),V,Mod);
1201: R = append(R1,R);
1202: }
1203: return R;
1204: }
1205:
1206: def zprimadec(B,V,Mod)
1207: {
1208: L = partial_qdecomp(B,V,Mod);
1209: Q = L[0]; NQ = L[1];
1210: R = [];
1211: for ( ; Q != []; Q = cdr(Q) ) {
1212: T = car(Q); R = cons([T[0],T[1]],R);
1213: }
1214: for ( T = NQ; T != []; T = cdr(T) ) {
1215: R1 = complete_qdecomp(car(T),V,Mod);
1216: R = append(R1,R);
1217: }
1218: return R;
1219: }
1220:
1221: def complete_qdecomp(GD,V,Mod)
1222: {
1223: GQ = GD[0]; GP = GD[1]; D = GD[2];
1224: W = vars(GP);
1225: PV = setminus(W,V);
1226: N = length(V); PN = length(PV);
1227: U = find_npos([GP,D],V,PV,Mod);
1228: NV = ttttt;
1229: M = gen_minipoly(cons(NV-U,GQ),cons(NV,V),PV,0,NV,Mod);
1230: M = ppart(M,NV,Mod);
1231: MF = Mod ? modfctr(M) : fctr(M);
1232: R = [];
1233: for ( T = cdr(MF); T != []; T = cdr(T) ) {
1234: S = car(T);
1235: Mt = subst(S[0],NV,U);
1236: GP1 = fast_gb(cons(Mt,GP),W,Mod,0);
1237: GQ1 = fast_gb(cons(Mt^S[1],GQ),W,Mod,0);
1238: if ( PV != [] ) {
1239: GP1 = elim_gb(GP1,V,PV,Mod,[[0,N],[0,PN]]);
1240: GQ1 = elim_gb(GQ1,V,PV,Mod,[[0,N],[0,PN]]);
1241: }
1242: R = cons([GQ1,GP1],R);
1243: }
1244: return R;
1245: }
1246:
1247: def partial_qdecomp(B,V,Mod)
1248: {
1249: Elim = (Elim=getopt(elim))&&type(Elim)!=-1 ? 1 : 0;
1250: N = length(V);
1251: W = vars(B);
1252: PV = setminus(W,V);
1253: NP = length(PV);
1254: W = append(V,PV);
1255: if ( Elim && PV != [] ) Ord = [[0,N],[0,NP]];
1256: else Ord = 0;
1257: if ( Mod )
1258: B = nd_f4(B,W,Mod,Ord);
1259: else
1260: B = nd_gr_trace(B,W,1,GBCheck,Ord);
1261: Q = []; NQ = [[B,B,vector(N+1)]];
1262: for ( I = length(V)-1; I >= 0; I-- ) {
1263: NQ1 = [];
1264: for ( T = NQ; T != []; T = cdr(T) ) {
1265: L = partial_qdecomp0(car(T),V,PV,Ord,I,Mod);
1266: Q = append(L[0],Q);
1267: NQ1 = append(L[1],NQ1);
1268: }
1269: NQ = NQ1;
1270: }
1271: return [Q,NQ];
1272: }
1273:
1274: def partial_qdecomp0(GD,V,PV,Ord,I,Mod)
1275: {
1276: GQ = GD[0]; GP = GD[1]; D = GD[2];
1277: N = length(V); PN = length(PV);
1278: W = append(V,PV);
1279: VI = V[I];
1280: M = gen_minipoly(GQ,V,PV,Ord,VI,Mod);
1281: M = ppart(M,VI,Mod);
1282: if ( Mod )
1283: MF = modfctr(M,Mod);
1284: else
1285: MF = fctr(M);
1286: Q = []; NQ = [];
1287: if ( length(MF) == 2 && MF[1][1] == 1 ) {
1288: D1 = D*1; D1[I] = M;
1289: GQelim = elim_gb(GQ,V,PV,Mod,Ord);
1290: GPelim = elim_gb(GP,V,PV,Mod,Ord);
1291: LD = ldim(GQelim,V);
1292: if ( deg(M,VI) == LD )
1293: Q = cons([GQelim,GPelim,D1],Q);
1294: else
1295: NQ = cons([GQelim,GPelim,D1],NQ);
1296: return [Q,NQ];
1297: }
1298: for ( T = cdr(MF); T != []; T = cdr(T) ) {
1299: S = car(T); Mt = S[0]; D1 = D*1; D1[I] = Mt;
1300:
1301: GQ1 = fast_gb(cons(Mt^S[1],GQ),W,Mod,Ord);
1302: GQelim = elim_gb(GQ1,V,PV,Mod,Ord);
1303: GP1 = fast_gb(cons(Mt,GP),W,Mod,Ord);
1304: GPelim = elim_gb(GP1,V,PV,Mod,Ord);
1305:
1306: D1[N] = LD = ldim(GPelim,V);
1307:
1308: for ( J = 0; J < N; J++ )
1309: if ( D1[J] && deg(D1[J],V[J]) == LD ) break;
1310: if ( J < N )
1311: Q = cons([GQelim,GPelim,D1],Q);
1312: else
1313: NQ = cons([GQelim,GPelim,D1],NQ);
1314: }
1315: return [Q,NQ];
1316: }
1317:
1318: def complete_decomp(GD,V,Mod)
1319: {
1320: G = GD[0]; D = GD[1];
1321: W = vars(G);
1322: PV = setminus(W,V);
1323: N = length(V); PN = length(PV);
1324: U = find_npos(GD,V,PV,Mod);
1325: NV = ttttt;
1326: M = gen_minipoly(cons(NV-U,G),cons(NV,V),PV,0,NV,Mod);
1327: M = ppart(M,NV,Mod);
1328: MF = Mod ? modfctr(M) : fctr(M);
1329: if ( length(MF) == 2 ) return [G];
1330: R = [];
1331: for ( T = cdr(MF); T != []; T = cdr(T) ) {
1332: Mt = subst(car(car(T)),NV,U);
1333: G1 = fast_gb(cons(Mt,G),W,Mod,0);
1334: if ( PV != [] ) G1 = elim_gb(G1,V,PV,Mod,[[0,N],[0,PN]]);
1335: R = cons(G1,R);
1336: }
1337: return R;
1338: }
1339:
1340: def partial_decomp(B,V,Mod)
1341: {
1342: Elim = (Elim=getopt(elim))&&type(Elim)!=-1 ? 1 : 0;
1343: N = length(V);
1344: W = vars(B);
1345: PV = setminus(W,V);
1346: NP = length(PV);
1347: W = append(V,PV);
1348: if ( Elim && PV != [] ) Ord = [[0,N],[0,NP]];
1349: else Ord = 0;
1350: if ( Mod )
1351: B = nd_f4(B,W,Mod,Ord);
1352: else
1353: B = nd_gr_trace(B,W,1,GBCheck,Ord);
1354: P = []; NP = [[B,vector(N+1)]];
1355: for ( I = length(V)-1; I >= 0; I-- ) {
1356: NP1 = [];
1357: for ( T = NP; T != []; T = cdr(T) ) {
1358: L = partial_decomp0(car(T),V,PV,Ord,I,Mod);
1359: P = append(L[0],P);
1360: NP1 = append(L[1],NP1);
1361: }
1362: NP = NP1;
1363: }
1364: return [P,NP];
1365: }
1366:
1367: def partial_decomp0(GD,V,PV,Ord,I,Mod)
1368: {
1369: G = GD[0]; D = GD[1];
1370: N = length(V); PN = length(PV);
1371: W = append(V,PV);
1372: VI = V[I];
1373: M = gen_minipoly(G,V,PV,Ord,VI,Mod);
1374: M = ppart(M,VI,Mod);
1375: if ( Mod )
1376: MF = modfctr(M,Mod);
1377: else
1378: MF = fctr(M);
1379: if ( length(MF) == 2 && MF[1][1] == 1 ) {
1380: D1 = D*1;
1381: D1[I] = M;
1382: Gelim = elim_gb(G,V,PV,Mod,Ord);
1383: D1[N] = LD = ldim(Gelim,V);
1384: GD1 = [Gelim,D1];
1385: for ( J = 0; J < N; J++ )
1386: if ( D1[J] && deg(D1[J],V[J]) == LD )
1387: return [[GD1],[]];
1388: return [[],[GD1]];
1389: }
1390: P = []; NP = [];
1391: GI = elim_gb(G,V,PV,Mod,Ord);
1392: for ( T = cdr(MF); T != []; T = cdr(T) ) {
1393: Mt = car(car(T));
1394: D1 = D*1;
1395: D1[I] = Mt;
1396: GIt = map(gen_nf,GI,[Mt],V,Ord,Mod);
1397: G1 = cons(Mt,GIt);
1398: Gelim = elim_gb(G1,V,PV,Mod,Ord);
1399: D1[N] = LD = ldim(Gelim,V);
1400: for ( J = 0; J < N; J++ )
1401: if ( D1[J] && deg(D1[J],V[J]) == LD ) break;
1402: if ( J < N )
1403: P = cons([Gelim,D1],P);
1404: else
1405: NP = cons([Gelim,D1],NP);
1406: }
1407: return [P,NP];
1408: }
1409:
1410: /* prime/primary components over rational function field */
1411:
1412: def zprimacomp(G,V) {
1413: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1414: L = zprimadec(G,V,0|mod=Mod);
1415: R = [];
1416: dp_ord(0);
1417: for ( T = L; T != []; T = cdr(T) ) {
1418: S = car(T);
1419: UQ = contraction(S[0],V|mod=Mod);
1420: UP = contraction(S[1],V|mod=Mod);
1421: R = cons([UQ,UP],R);
1422: }
1423: return R;
1424: }
1425:
1426: def zprimecomp(G,V,Indep) {
1427: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1428: W = maxindep(G,V,0|mod=Mod);
1429: V0 = setminus(V,W);
1430: V1 = append(V0,W);
1431: #if 0
1432: O1 = [[0,length(V0)],[0,length(W)]];
1433: G1 = fast_gb(G,V1,Mod,O1);
1434: dp_ord(0);
1435: #else
1436: G1 = G;
1437: #endif
1438: PD = zprimedec(G1,V0,Mod);
1439: dp_ord(0);
1440: R = [];
1441: for ( T = PD; T != []; T = cdr(T) ) {
1442: U = contraction(car(T),V0|mod=Mod);
1443: U = nd_gr(U,V,Mod,0);
1444: R = cons(U,R);
1445: }
1446: if ( Indep ) return [R,W];
1447: else return R;
1448: }
1449:
1450: def fast_gb(B,V,Mod,Ord)
1451: {
1452: if ( type(Block=getopt(gbblock)) == -1 ) Block = 0;
1453: if ( type(NoRA=getopt(nora)) == -1 ) NoRA = 0;
1454: if ( type(Trace=getopt(trace)) == -1 ) Trace = 0;
1455: if ( Mod )
1456: G = nd_f4(B,V,Mod,Ord|nora=NoRA);
1457: else if ( F4 )
1458: G = map(ptozp,f4_chrem(B,V,Ord));
1459: else if ( Trace ) {
1460: if ( Block )
1461: G = nd_gr_trace(B,V,1,1,Ord|nora=NoRA,gbblock=Block);
1462: else
1463: G = nd_gr_trace(B,V,1,1,Ord|nora=NoRA);
1464: } else {
1465: if ( Block )
1466: G = nd_gr(B,V,0,Ord|nora=NoRA,gbblock=Block);
1467: else
1468: G = nd_gr(B,V,0,Ord|nora=NoRA);
1469: }
1470: return G;
1471: }
1472:
1473: def incremental_gb(A,V,Ord)
1474: {
1475: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1476: if ( type(Block=getopt(gbblock)) == -1 ) Block = 0;
1477: if ( Mod ) {
1478: if ( Block )
1479: G = nd_gr(A,V,Mod,Ord|gbblock=Block);
1480: else
1481: G = nd_gr(A,V,Mod,Ord);
1482: } else if ( Procs ) {
1483: Arg0 = ["nd_gr",A,V,0,Ord];
1484: Arg1 = ["nd_gr_trace",A,V,1,GBCheck,Ord];
1485: G = competitive_exec(Procs,Arg0,Arg1);
1486: } else if ( Block )
1487: G = nd_gr(A,V,0,Ord|gbblock=Block);
1488: else
1489: G = nd_gr(A,V,0,Ord);
1490: return G;
1491: }
1492:
1493: def elim_gb(G,V,PV,Mod,Ord)
1494: {
1495: N = length(V); PN = length(PV);
1496: O1 = [[0,N],[0,PN]];
1497: if ( Ord == O1 )
1498: Ord = Ord[0][0];
1499: if ( Mod ) /* XXX */ {
1500: for ( T = G, H = []; T != []; T = cdr(T) )
1501: if ( car(T) ) H = cons(car(T),H);
1502: G = reverse(H);
1503: G = dp_gr_mod_main(G,V,0,Mod,Ord);
1504: } else if ( EProcs ) {
1505: #if 1
1506: Arg0 = ["dp_gr_main",G,V,0,0,Ord];
1507: #else
1508: Arg0 = ["nd_gr",G,V,0,Ord];
1509: #endif
1510: Arg1 = ["noro_pd.nd_gr_rat",G,V,PV,O1,Ord];
1511: G = competitive_exec(EProcs,Arg0,Arg1);
1512: } else if ( GBRat ) {
1513: G1 = nd_gr(G,append(V,PV),0,O1);
1514: G1 = nd_gr_postproc(G1,V,0,Ord,0);
1515: return G1;
1516: } else
1517: #if 1
1.2 noro 1518: #if 0
1.1 noro 1519: G = dp_gr_main(G,V,0,0,Ord);
1520: #else
1521: G = nd_gr_trace(G,V,1,1,Ord);
1522: #endif
1523: #else
1524: G = nd_gr(G,V,0,Ord);
1525: #endif
1526: return G;
1527: }
1528:
1529: def ldim(G,V)
1530: {
1531: O0 = dp_ord(); dp_ord(0);
1532: D = length(dp_mbase(map(dp_ptod,G,V)));
1533: dp_ord(O0);
1534: return D;
1535: }
1536:
1537: /* over Q only */
1538:
1539: def make_mod_subst(GD,V,PV,HC)
1540: {
1541: N = length(V);
1542: PN = length(PV);
1543: G = GD[0]; D = GD[1];
1544: for ( I = 0; ; I = (I+1)%100 ) {
1545: Mod = lprime(I);
1546: S = [];
1547: for ( J = PN-1; J >= 0; J-- )
1548: S = append([PV[J],random()%Mod],S);
1549: for ( T = HC; T != []; T = cdr(T) )
1550: if ( !(subst(car(T),S)%Mod) ) break;
1551: if ( T != [] ) continue;
1552: for ( J = 0; J < N; J++ ) {
1553: M = subst(D[J],S);
1554: F = modsqfr(M,Mod);
1555: if ( length(F) != 2 || F[1][1] != 1 ) break;
1556: }
1557: if ( J < N ) continue;
1558: G0 = map(subst,G,S);
1559: return [G0,Mod];
1560: }
1561: }
1562:
1563: def rsgn()
1564: {
1565: return random()%2 ? 1 : -1;
1566: }
1567:
1568: def find_npos(GD,V,PV,Mod)
1569: {
1570: N = length(V); PN = length(PV);
1571: G = GD[0]; D = GD[1]; LD = D[N];
1.5 ! noro 1572: DH = map(dp_dtop,map(dp_ht,map(dp_ptod,D,V)),V);
1.1 noro 1573: Ord0 = dp_ord(); dp_ord(0);
1574: HC = map(dp_hc,map(dp_ptod,G,V));
1575: dp_ord(Ord0);
1576: if ( !Mod ) {
1577: W = append(V,PV);
1578: G1 = nd_gr_trace(G,W,1,GBCheck,[[0,N],[0,PN]]);
1579: L = make_mod_subst([G1,D],V,PV,HC);
1580: return find_npos([L[0],D],V,[],L[1]);
1581: }
1582: N = length(V);
1583: NV = ttttt;
1584: for ( B = 2; ; B++ ) {
1585: for ( J = N-2; J >= 0; J-- ) {
1.5 ! noro 1586: for ( U = 0, K = J; K < N; K++ ) {
! 1587: if ( DH[K] == V[K] ) continue;
1.1 noro 1588: U += rsgn()*((random()%B+1))*V[K];
1.5 ! noro 1589: }
1.1 noro 1590: M = minipolym(G,V,0,U,NV,Mod);
1591: if ( deg(M,NV) == LD ) return U;
1592: }
1593: }
1594: }
1595:
1596: def gen_minipoly(G,V,PV,Ord,VI,Mod)
1597: {
1598: if ( PV == [] ) {
1599: NV = sssss;
1600: if ( Mod )
1601: M = minipolym(G,V,Ord,VI,NV,Mod);
1602: else
1603: M = minipoly(G,V,Ord,VI,NV);
1604: return subst(M,NV,VI);
1605: }
1606: W = setminus(V,[VI]);
1607: PV1 = cons(VI,PV);
1608: #if 0
1609: while ( 1 ) {
1610: V1 = append(W,PV1);
1611: if ( Mod )
1612: G = nd_gr(G,V1,Mod,[[0,1],[0,length(V1)-1]]|nora=1);
1613: else
1614: G = nd_gr_trace(G,V1,1,GBCheck,[[0,1],[0,length(V1)-1]]|nora=1);
1615: if ( W == [] ) break;
1616: else {
1617: W = cdr(W);
1618: G = elimination(G,cdr(V1));
1619: }
1620: }
1621: #elif 1
1622: if ( Mod ) {
1623: V1 = append(W,PV1);
1624: G = nd_gr(G,V1,Mod,[[0,length(W)],[0,length(PV1)]]);
1625: G = elimination(G,PV1);
1626: } else {
1627: PV2 = setminus(PV1,[PV1[length(PV1)-1]]);
1628: V2 = append(W,PV2);
1629: G = nd_gr_trace(G,V2,1,GBCheck,[[0,length(W)],[0,length(PV2)]]|nora=1);
1630: G = elimination(G,PV1);
1631: }
1632: #else
1633: V1 = append(W,PV1);
1634: if ( Mod )
1635: G = nd_gr(G,V1,Mod,[[0,length(W)],[0,length(PV1)]]|nora=1);
1636: else
1637: G = nd_gr_trace(G,V1,1,GBCheck,[[0,length(W)],[0,length(PV1)]]|nora=1);
1638: G = elimination(G,PV1);
1639: #endif
1640: if ( Mod )
1641: G = nd_gr(G,PV1,Mod,[[0,1],[0,length(PV)]]|nora=1);
1642: else
1643: G = nd_gr_trace(G,PV1,1,GBCheck,[[0,1],[0,length(PV)]]|nora=1);
1644: for ( M = car(G), T = cdr(G); T != []; T = cdr(T) )
1645: if ( deg(car(T),VI) < deg(M,VI) ) M = car(T);
1646: return M;
1647: }
1648:
1649: def indepset(V,H)
1650: {
1651: if ( H == [] ) return V;
1652: N = -1;
1653: for ( T = V; T != []; T = cdr(T) ) {
1654: VI = car(T);
1655: HI = [];
1656: for ( S = H; S != []; S = cdr(S) )
1657: if ( !tdiv(car(S),VI) ) HI = cons(car(S),HI);
1658: RI = indepset(setminus(V,[VI]),HI);
1659: if ( length(RI) > N ) {
1660: R = RI; N = length(RI);
1661: }
1662: }
1663: return R;
1664: }
1665:
1666: def maxindep(B,V,O)
1667: {
1668: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1669: G = fast_gb(B,V,Mod,O);
1670: Old = dp_ord();
1671: dp_ord(O);
1672: H = map(dp_dtop,map(dp_ht,map(dp_ptod,G,V)),V);
1673: H = map(sq,H,0);
1674: H = nd_gr(H,V,0,0);
1675: H = monodec0(H,V);
1676: N = length(V);
1677: Dep = [];
1678: for ( T = H, Len = N+1; T != []; T = cdr(T) ) {
1679: M = length(car(T));
1680: if ( M < Len ) {
1681: Dep = [car(T)];
1682: Len = M;
1683: } else if ( M == Len )
1684: Dep = cons(car(T),Dep);
1685: }
1686: R = setminus(V,Dep[0]);
1687: dp_ord(Old);
1688: return R;
1689: }
1690:
1691: /* ideal operations */
1692: def contraction(G,V)
1693: {
1694: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1695: C = [];
1696: for ( T = G; T != []; T = cdr(T) ) {
1697: C1 = dp_hc(dp_ptod(car(T),V));
1698: S = gen_fctr(C1,Mod);
1699: for ( S = cdr(S); S != []; S = cdr(S) )
1700: if ( !member(S[0][0],C) ) C = cons(S[0][0],C);
1701: }
1702: W = vars(G);
1703: PV = setminus(W,V);
1704: W = append(V,PV);
1705: NV = ttttt;
1706: for ( T = C, S = 1; T != []; T = cdr(T) )
1707: S *= car(T);
1708: G = saturation([G,NV],S,W|mod=Mod);
1709: return G;
1710: }
1711:
1712: def ideal_list_intersection(L,V,Ord)
1713: {
1714: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1.4 noro 1715: if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0;
1.1 noro 1716: if ( type(Para=getopt(para)) == -1 || type(Para) != 4 ) Para = [];
1717: N = length(L);
1718: if ( N == 0 ) return [1];
1.4 noro 1719: if ( N == 1 )
1720: return IsGB ? L[0] : fast_gb(L[0],V,Mod,Ord);
1.2 noro 1721: if ( N > 2 && (Len = length(Para)) >= 2 ) {
1722: Div = N >= 2*Len ? Len : 2;
1723: QR = iqr(N,Div); Q = QR[0]; R = QR[1];
1724: T = []; K = 0;
1725: for ( I = 0; I < Div; I++ ) {
1726: LenI = I<R? Q+1 : Q;
1727: if ( LenI ) {
1728: for ( LI = [], J = 0; J < LenI; J++ ) LI = cons(L[K++],LI);
1.4 noro 1729: TI = ["noro_pd.call_ideal_list_intersection",LI,V,Mod,Ord,IsGB];
1.2 noro 1730: T = cons(TI,T);
1731: }
1732: }
1733: Tint = para_exec(Para,T);
1.4 noro 1734: return ideal_list_intersection(Tint,V,Ord|mod=Mod,para=Para,isgb=IsGB);
1.1 noro 1735: } else {
1.4 noro 1736: for ( I = 0, T = [1]; I < N; I++ )
1737: T = ideal_intersection_m(T,L[I],V,Ord|mod=Mod);
1738: T = nd_gr(T,V,Mod,Ord);
1739: return T;
1.1 noro 1740: }
1741: }
1742:
1.4 noro 1743: def call_ideal_list_intersection(L,V,Mod,Ord,IsGB)
1.1 noro 1744: {
1.4 noro 1745: return ideal_list_intersection(L,V,Ord|mod=Mod,isgb=IsGB);
1.1 noro 1746: }
1747:
1748: def ideal_intersection(A,B,V,Ord)
1749: {
1750: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1751: if ( type(Block=getopt(gbblock)) == -1 ) Block = 0;
1752: T = ttttt;
1753: if ( Mod ) {
1754: if ( Block )
1755: G = nd_gr(append(vtol(ltov(A)*T),vtol(ltov(B)*(1-T))),
1756: cons(T,V),Mod,[[0,1],[Ord,length(V)]]|gbblock=Block,nora=0);
1757: else
1758: G = nd_gr(append(vtol(ltov(A)*T),vtol(ltov(B)*(1-T))),
1759: cons(T,V),Mod,[[0,1],[Ord,length(V)]]|nora=0);
1760: } else
1761: if ( Procs ) {
1762: Arg0 = ["nd_gr",
1763: append(vtol(ltov(A)*T),vtol(ltov(B)*(1-T))),
1764: cons(T,V),0,[[0,1],[Ord,length(V)]]];
1765: Arg1 = ["nd_gr_trace",
1766: append(vtol(ltov(A)*T),vtol(ltov(B)*(1-T))),
1767: cons(T,V),1,GBCheck,[[0,1],[Ord,length(V)]]];
1768: G = competitive_exec(Procs,Arg0,Arg1);
1769: } else {
1770: if ( Block )
1771: G = nd_gr(append(vtol(ltov(A)*T),vtol(ltov(B)*(1-T))),
1772: cons(T,V),0,[[0,1],[Ord,length(V)]]|gbblock=Block,nora=0);
1773: else
1774: G = nd_gr(append(vtol(ltov(A)*T),vtol(ltov(B)*(1-T))),
1775: cons(T,V),0,[[0,1],[Ord,length(V)]]|nora=0);
1776: }
1777: G0 = elimination(G,V);
1778: if ( 0 && !Procs )
1779: G0 = nd_gr_postproc(G0,V,Mod,Ord,0);
1780: return G0;
1781: }
1782:
1.4 noro 1783:
1784: def aa(A) { return [A,A]; }
1785:
1786: def ideal_intersection_m(A,B,V,Ord)
1787: {
1788: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1789:
1790: dp_ord(Ord);
1791: DA = map(dp_ptod,A,V); DB = ltov(map(dp_ptod,B,V));
1792: if ( Mod ) {
1793: DA = map(dp_mod,DA,Mod,[]); DB = map(dp_mod,DB,Mod,[]);
1794: setmod(Mod);
1795: }
1796: N = length(B);
1797: for ( Ind = [], I = N-1; I >= 0; I-- ) Ind = cons(I,Ind);
1798: for ( T = DA, C = []; T != []; T = cdr(T) ) {
1799: L = Mod?dp_true_nf_mod(Ind,car(T),DB,1,Mod):dp_true_nf(Ind,car(T),DB,1);
1800: R = dp_dtop(L[0],V); Q = dp_dtop(car(T)*L[1]-L[0],V);
1801: C = cons([R,-Q],C);
1802: }
1803: G = nd_gr(append(C,map(aa,B)),V,Mod,[1,Ord]|intersect=1);
1804: G = map(second,G);
1805: return G;
1806: }
1807:
1.1 noro 1808: /* returns GB if F notin rad(G) */
1809:
1810: def radical_membership(F,G,V) {
1811: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1812: if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0;
1.4 noro 1813: if ( type(L=getopt(dg)) == -1 ) L = 0;
1814: dp_ord(0);
1815: if ( L ) { DG = L[0]; Ind = L[1]; }
1816: else {
1817: DG = ltov(map(dp_ptod,G,V));
1818: if ( Mod ) DG = map(dp_mod,DG,Mod,[]);
1819: for ( Ind = [], I = length(G)-1; I >= 0; I-- ) Ind = cons(I,Ind);
1820: }
1821: DF = dp_ptod(F,V); DFI = dp_ptod(1,V);
1822: if ( Mod ) {
1823: DF = dp_mod(DF,Mod,[]); DFI = dp_mod(DFI,Mod,[]);
1824: setmod(Mod);
1825: }
1826: for ( I = 0; I < 3; I++ ) {
1827: DFI = Mod?dp_nf_mod(Ind,DF*DFI,DG,0,Mod):dp_nf(Ind,DF*DFI,DG,0);
1828: if ( !DFI ) return 0;
1829: }
1.1 noro 1830: NV = ttttt;
1831: if ( IsGB )
1832: T = nd_gr(append(G,[NV*F-1]),cons(NV,V),Mod,0
1833: |gbblock=[[0,length(G)]]);
1834: else
1835: T = nd_gr(append(G,[NV*F-1]),cons(NV,V),Mod,0);
1836: if ( type(car(T)) != 1 ) return [T,NV];
1837: else return 0;
1838: }
1839:
1840: def modular_radical_membership(F,G,V) {
1841: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1842: if ( Mod )
1843: return radical_membership(F,G,V|mod=Mod);
1844:
1845: F = gen_nf(F,G,V,0,0);
1846: if ( !F ) return 0;
1847: NV = ttttt;
1848: for ( J = 0; ; J++ ) {
1849: Mod = lprime(J);
1850: H = map(dp_hc,map(dp_ptod,G,V));
1851: for ( ; H != []; H = cdr(H) ) if ( !(car(H)%Mod) ) break;
1852: if ( H != [] ) continue;
1853:
1854: T = nd_f4(cons(NV*F-1,G),cons(NV,V),Mod,0);
1855: if ( type(car(T)) == 1 ) {
1856: I = radical_membership_rep(F,G,V,-1,0,Mod);
1857: I1 = radical_membership_rep(F,G,V,I,0,0);
1858: if ( I1 > 0 ) return 0;
1859: }
1860: return radical_membership(F,G,V);
1861: }
1862: }
1863:
1864: def radical_membership_rep(F,G,V,Max,Ord,Mod) {
1865: Ft = F;
1866: I = 1;
1867: while ( Max < 0 || I <= Max ) {
1868: Ft = gen_nf(Ft,G,V,Ord,Mod);
1869: if ( !Ft ) return I;
1870: Ft *= F;
1871: I++;
1872: }
1873: return -1;
1874: }
1875:
1876: def ideal_product(A,B,V)
1877: {
1878: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1879: dp_ord(0);
1880: DA = map(dp_ptod,A,V);
1881: DB = map(dp_ptod,B,V);
1882: DegA = map(dp_td,DA);
1883: DegB = map(dp_td,DB);
1884: for ( PA = [], T = A, DT = DegA; T != []; T = cdr(T), DT = cdr(DT) )
1885: PA = cons([car(T),car(DT)],PA);
1886: PA = reverse(PA);
1887: for ( PB = [], T = B, DT = DegB; T != []; T = cdr(T), DT = cdr(DT) )
1888: PB = cons([car(T),car(DT)],PB);
1889: PB = reverse(PB);
1890: R = [];
1891: for ( T = PA; T != []; T = cdr(T) )
1892: for ( S = PB; S != []; S = cdr(S) )
1893: R = cons([car(T)[0]*car(S)[0],car(T)[1]+car(S)[1]],R);
1894: T = qsort(R,comp_by_second);
1895: T = map(first,T);
1896: Len = length(A)>length(B)?length(A):length(B);
1897: Len *= 2;
1898: L = sep_list(T,Len); B0 = L[0]; B1 = L[1];
1899: R = fast_gb(B0,V,Mod,0);
1900: while ( B1 != [] ) {
1901: print(length(B1));
1902: L = sep_list(B1,Len);
1903: B0 = L[0]; B1 = L[1];
1904: R = fast_gb(append(R,B0),V,Mod,0|gbblock=[[0,length(R)]],nora=1);
1905: }
1906: return R;
1907: }
1908:
1909: def saturation(GNV,F,V)
1910: {
1911: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1912: G = GNV[0]; NV = GNV[1];
1913: if ( Mod )
1914: G1 = nd_gr(cons(NV*F-1,G),cons(NV,V),Mod,[[0,1],[0,length(V)]]);
1915: else if ( Procs ) {
1916: Arg0 = ["nd_gr_trace",
1917: cons(NV*F-1,G),cons(NV,V),0,GBCheck,[[0,1],[0,length(V)]]];
1918: Arg1 = ["nd_gr_trace",
1919: cons(NV*F-1,G),cons(NV,V),1,GBCheck,[[0,1],[0,length(V)]]];
1920: G1 = competitive_exec(Procs,Arg0,Arg1);
1921: } else
1922: G1 = nd_gr(cons(NV*F-1,G),cons(NV,V),0,[[0,1],[0,length(V)]]);
1923: return elimination(G1,V);
1924: }
1925:
1926: def sat(G,F,V)
1927: {
1928: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1929: if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0;
1930: NV = ttttt;
1931: if ( Mod )
1932: G1 = nd_gr(cons(NV*F-1,G),cons(NV,V),Mod,[[0,1],[0,length(V)]]);
1933: else if ( Procs ) {
1934: Arg0 = ["nd_gr_trace",
1935: cons(NV*F-1,G),cons(NV,V),0,GBCheck,[[0,1],[0,length(V)]]];
1936: Arg1 = ["nd_gr_trace",
1937: cons(NV*F-1,G),cons(NV,V),1,GBCheck,[[0,1],[0,length(V)]]];
1938: G1 = competitive_exec(Procs,Arg0,Arg1);
1939: } else {
1940: B1 = append(G,[NV*F-1]);
1941: V1 = cons(NV,V);
1942: Ord1 = [[0,1],[0,length(V)]];
1943: if ( IsGB )
1944: G1 = nd_gr(B1,V1,0,Ord1|gbblock=[[0,length(G)]]);
1945: else
1946: G1 = nd_gr(B1,V1,0,Ord1);
1947: }
1948: return elimination(G1,V);
1949: }
1950:
1.4 noro 1951: def isat(B,S,V)
1952: {
1953: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1954: if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0;
1955: F = cdr(fctr(S));
1956: R = B;
1957: for ( T = F; T != []; T = cdr(T) )
1958: R = sat(R,car(T)[0],V|mod=Mod,isgb=IsGB);
1959: return R;
1960: }
1961:
1.1 noro 1962: def satind(G,F,V)
1963: {
1964: if ( type(Block=getopt(gbblock)) == -1 ) Block = 0;
1965: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1966: NV = ttttt;
1967: N = length(V);
1968: B = append(G,[NV*F-1]);
1969: V1 = cons(NV,V);
1970: Ord1 = [[0,1],[0,N]];
1971: if ( Mod )
1972: if ( Block )
1973: D = nd_gr(B,V1,Mod,Ord1|nora=1,gentrace=1,gbblock=Block);
1974: else
1975: D = nd_gr(B,V1,Mod,Ord1|nora=1,gentrace=1);
1976: else
1977: if ( Block )
1978: D = nd_gr_trace(B,V1,SatHomo,GBCheck,Ord1
1979: |nora=1,gentrace=1,gbblock=Block);
1980: else
1981: D = nd_gr_trace(B,V1,SatHomo,GBCheck,Ord1
1982: |nora=1,gentrace=1);
1983: G1 = D[0];
1984: Len = length(G1);
1985: Deg = compute_deg(B,V1,NV,D);
1986: D1 = 0;
1987: R = [];
1988: M = length(B);
1989: for ( I = 0; I < Len; I++ ) {
1990: if ( !member(NV,vars(G1[I])) ) {
1991: for ( J = 1; J < M; J++ )
1992: D1 = MAX(D1,Deg[I][J]);
1993: R = cons(G1[I],R);
1994: }
1995: }
1996: return [reverse(R),D1];
1997: }
1998:
1999: def sat_ind(G,F,V)
2000: {
2001: if ( type(Ord=getopt(ord)) == -1 ) Ord = 0;
2002: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2003: NV = ttttt;
2004: F = gen_nf(F,G,V,Ord,Mod);
2005: for ( I = 0, GI = G; ; I++ ) {
2006: G1 = colon(GI,F,V|mod=Mod,ord=Ord);
2007: if ( ideal_inclusion(G1,GI,V,Ord|mod=Mod) ) {
2008: return [GI,I];
2009: }
2010: else GI = G1;
2011: }
2012: }
2013:
2014: def colon(G,F,V)
2015: {
2016: if ( type(Ord=getopt(ord)) == -1 ) Ord = 0;
2017: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2018: if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0;
2019: F = gen_nf(F,G,V,Ord,Mod);
2020: if ( !F ) return [1];
2021: if ( IsGB )
2022: T = ideal_intersection(G,[F],V,Ord|gbblock=[[0,length(G)]],mod=Mod);
2023: else
2024: T = ideal_intersection(G,[F],V,Ord|mod=Mod);
1.4 noro 2025: Gen = Mod?map(sdivm,T,F,Mod):map(ptozp,map(sdiv,T,F));
2026: return nd_gr(Gen,V,Mod,Ord);
1.1 noro 2027: }
2028:
2029: #if 1
2030: def ideal_colon(G,F,V)
2031: {
2032: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2033: G = nd_gr(G,V,Mod,0);
2034: C = [1];
2035: TV = ttttt;
2036: F = qsort(F,comp_tdeg);
2037: for ( T = F; T != []; T = cdr(T) ) {
2038: S = colon(G,car(T),V|isgb=1,mod=Mod);
2039: if ( type(S[0])!= 1 ) {
2040: C = nd_gr(append(vtol(ltov(C)*TV),vtol(ltov(S)*(1-TV))),
2041: cons(TV,V),Mod,[[0,1],[Ord,length(V)]]|gbblock=[[0,length(C)]]);
2042: C = elimination(C,V);
2043: }
2044: }
2045: return C;
2046: }
2047: #else
2048: def ideal_colon(G,F,V)
2049: {
2050: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2051: G = nd_gr(G,V,Mod,0);
2052: for ( T = F, L = []; T != []; T = cdr(T) ) {
2053: C = colon(G,car(T),V|isgb=1,mod=Mod);
2054: if ( type(C[0]) != 1 ) L = cons(C,L);
2055: }
2056: L = reverse(L);
2057: return ideal_list_intersection(L,V,0|mod=Mod);
2058: }
2059:
2060: #endif
2061:
2062: def member(A,L)
2063: {
2064: for ( ; L != []; L = cdr(L) )
2065: if ( car(L) == A ) return 1;
2066: return 0;
2067: }
2068:
2069: def mingen(B,V) {
2070: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2071: Data = nd_gr(B,V,Mod,O|gentrace=1,gensyz=1);
1.4 noro 2072: G = Data[0]; STrace = Data[6];
1.1 noro 2073: N = length(G);
1.4 noro 2074: S = compute_gbsyz(N,V,STrace,Mod);
2075: for ( T = S, R = []; T != []; T = cdr(T) ) {
2076: for ( A = car(T); A1 = dp_rest(A); A = A1);
2077: if ( type(dp_hc(A)) ==1 ) R = cons(dp_etov(A)[0],R);
2078: }
2079: for ( I = 0, U = []; I < N; I++ ) if ( !member(I,R) ) U = cons(G[I],U);
1.1 noro 2080: return U;
2081: }
2082:
1.4 noro 2083: def compute_gbsyz(N,V,Trace,Mod)
1.1 noro 2084: {
2085: P = vector(N);
1.4 noro 2086: for ( I = 0; I < N; I++ ) P[I] = dp_ptod(x^I,[x]);
2087: for ( U = [], T = Trace; T != []; T = cdr(T) ) {
1.1 noro 2088: Ti = car(T);
2089: if ( Ti[0] != -1 ) error("Input is not a GB");
1.4 noro 2090: R = recompute_trace(Ti[1],P,V,Mod);
2091: U = cons(R,U);
1.1 noro 2092: }
2093: return reverse(U);
2094: }
2095:
1.4 noro 2096: def recompute_trace(Ti,P,V,Mod)
1.1 noro 2097: {
2098: for ( Num = 0, Den = 1; Ti != []; Ti = cdr(Ti) ) {
1.4 noro 2099: Sj = car(Ti); Dj = Sj[0]; Ij =Sj[1]; Mj = dp_dtop(Sj[2],V); Cj = Sj[3];
1.1 noro 2100: /* Num/Den <- (Dj*Num+Den*Mj*P[Ij])/(Den*Cj) */
1.4 noro 2101: if ( Dj ) Num = (Dj*Num+Den*Mj*P[Ij]);
1.1 noro 2102: Den *= Cj;
2103: }
1.4 noro 2104: return Num;
1.1 noro 2105: }
2106:
2107: def ideal_sat(G,F,V)
2108: {
2109: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2110: G = nd_gr(G,V,Mod,0);
2111: for ( T = F, L = []; T != []; T = cdr(T) )
2112: L = cons(sat(G,car(T),V|mod=Mod),L);
2113: L = reverse(L);
2114: return ideal_list_intersection(L,V,0|mod=Mod);
2115: }
2116:
2117: def ideal_inclusion(F,G,V,O)
2118: {
2119: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2120: for ( T = F; T != []; T = cdr(T) )
2121: if ( gen_nf(car(T),G,V,O,Mod) ) return 0;
2122: return 1;
2123: }
2124:
2125: /* remove redundant components */
2126:
2127: def qd_simp_comp(QP,V)
2128: {
2129: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2130: R = ltov(QP);
2131: N = length(R);
2132: for ( I = 0; I < N; I++ ) {
2133: if ( R[I] ) {
2134: QI = R[I][0]; PI = R[I][1];
2135: for ( J = I+1; J < N; J++ )
2136: if ( R[J] && gen_gb_comp(PI,R[J][1],Mod) ) {
2137: QI = ideal_intersection(QI,R[J][0],V,0|mod=Mod);
2138: R[J] = 0;
2139: }
2140: R[I] = [QI,PI];
2141: }
2142: }
2143: for ( I = N-1, S = []; I >= 0; I-- )
2144: if ( R[I] ) S = cons(R[I],S);
2145: return S;
2146: }
2147:
2148: def qd_remove_redundant_comp(G,Iso,Emb,V,Ord)
2149: {
2150: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2151: IsoInt = ideal_list_intersection(map(first,Iso),V,Ord|mod=Mod);
2152: Emb = qd_simp_comp(Emb,V|mod=Mod);
2153: Emb = reverse(qsort(Emb));
2154: A = ltov(Emb); N = length(A);
2155: Pre = IsoInt; Post = vector(N+1);
2156: for ( Post[N] = IsoInt, I = N-1; I >= 1; I-- )
2157: Post[I] = ideal_intersection(Post[I+1],A[I][0],V,Ord|mod=Mod);
2158: for ( I = 0; I < N; I++ ) {
2159: print(".",2);
2160: Int = ideal_intersection(Pre,Post[I+1],V,Ord|mod=Mod);
2161: if ( gen_gb_comp(Int,G,Mod) ) A[I] = 0;
2162: else
2163: Pre = ideal_intersection(Pre,A[I][0],V,Ord|mod=Mod);
2164: }
2165: for ( T = [], I = 0; I < N; I++ )
2166: if ( A[I] ) T = cons(A[I],T);
2167: return reverse(T);
2168: }
2169:
2170: def pd_simp_comp(PL,V)
2171: {
2172: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2173: if ( type(First=getopt(first)) == -1 ) First = 0;
2174: A = ltov(PL); N = length(A);
2175: if ( N == 1 ) return PL;
2176: for ( I = 0; I < N; I++ ) {
2177: if ( !A[I] ) continue;
2178: AI = First?A[I][0]:A[I];
2179: for ( J = 0; J < N; J++ ) {
2180: if ( J == I || !A[J] ) continue;
2181: AJ = First?A[J][0]:A[J];
2182: if ( gen_gb_comp(AI,AJ,Mod) || ideal_inclusion(AI,AJ,V,Ord|mod=Mod) )
2183: A[J] = 0;
2184: }
2185: }
2186: for ( I = 0, T = []; I < N; I++ ) if ( A[I] ) T = cons(A[I],T);
2187: return reverse(T);
2188: }
2189:
2190: def pd_remove_redundant_comp(G,P,V,Ord)
2191: {
2192: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2193: if ( type(First=getopt(first)) == -1 ) First = 0;
2194: if ( length(P) == 1 ) return P;
2195:
2196: A = ltov(P); N = length(A);
2197: for ( I = 0; I < N; I++ ) {
2198: if ( !A[I] ) continue;
2199: for ( J = I+1; J < N; J++ )
2200: if ( A[J] &&
2201: gen_gb_comp(First?A[I][0]:A[I],First?A[J][0]:A[J],Mod) ) A[J] = 0;
2202: }
2203: for ( I = 0, T = []; I < N; I++ ) if ( A[I] ) T = cons(A[I],T);
2204: A = ltov(reverse(T)); N = length(A);
2205: Pre = [1]; Post = vector(N+1);
2206: for ( Post[N] = [1], I = N-1; I >= 1; I-- )
2207: Post[I] = ideal_intersection(Post[I+1],First?A[I][0]:A[I],V,Ord|mod=Mod);
2208: for ( I = 0; I < N; I++ ) {
2209: Int = ideal_intersection(Pre,Post[I+1],V,Ord|mod=Mod);
2210: if ( gen_gb_comp(Int,G,Mod) ) A[I] = 0;
2211: else
2212: Pre = ideal_intersection(Pre,First?A[I][0]:A[I],V,Ord|mod=Mod);
2213: }
2214: for ( T = [], I = 0; I < N; I++ ) if ( A[I] ) T = cons(A[I],T);
2215: return reverse(T);
2216: }
2217:
2218: /* polynomial operations */
2219:
2220: def ppart(F,V,Mod)
2221: {
2222: if ( !Mod )
2223: G = nd_gr([F],[V],0,0);
2224: else
2225: G = dp_gr_mod_main([F],[V],0,Mod,0);
2226: return G[0];
2227: }
2228:
2229:
2230: def sq(F,Mod)
2231: {
2232: if ( !F ) return 0;
2233: A = cdr(gen_fctr(F,Mod));
2234: for ( R = 1; A != []; A = cdr(A) )
2235: R *= car(car(A));
2236: return R;
2237: }
2238:
2239: def lcfactor(G,V,O,Mod)
2240: {
2241: O0 = dp_ord(); dp_ord(O);
2242: C = [];
2243: for ( T = G; T != []; T = cdr(T) ) {
2244: C1 = dp_hc(dp_ptod(car(T),V));
2245: S = gen_fctr(C1,Mod);
2246: for ( S = cdr(S); S != []; S = cdr(S) )
2247: if ( !member(S[0][0],C) ) C = cons(S[0][0],C);
2248: }
2249: dp_ord(O0);
2250: return C;
2251: }
2252:
2253: def gen_fctr(F,Mod)
2254: {
2255: if ( Mod ) return modfctr(F,Mod);
2256: else return fctr(F);
2257: }
2258:
2259: def gen_mptop(F)
2260: {
2261: if ( !F ) return F;
2262: else if ( type(F)==1 )
2263: if ( ntype(F)==5 ) return mptop(F);
2264: else return F;
2265: else {
2266: V = var(F);
2267: D = deg(F,V);
2268: for ( R = 0, I = 0; I <= D; I++ )
2269: if ( C = coef(F,I,V) ) R += gen_mptop(C)*V^I;
2270: return R;
2271: }
2272: }
2273:
2274: def gen_nf(F,G,V,Ord,Mod)
2275: {
2276: if ( !Mod ) return p_nf(F,G,V,Ord);
2277:
2278: setmod(Mod);
2279: dp_ord(Ord); DF = dp_mod(dp_ptod(F,V),Mod,[]);
2280: N = length(G); DG = newvect(N);
2281: for ( I = N-1, IL = []; I >= 0; I-- ) {
2282: DG[I] = dp_mod(dp_ptod(G[I],V),Mod,[]);
2283: IL = cons(I,IL);
2284: }
2285: T = dp_nf_mod(IL,DF,DG,1,Mod);
2286: for ( R = 0; T; T = dp_rest(T) )
2287: R += gen_mptop(dp_hc(T))*dp_dtop(dp_ht(T),V);
2288: return R;
2289: }
2290:
2291: /* Ti = [D,I,M,C] */
2292:
2293: def compute_deg0(Ti,P,V,TV)
2294: {
2295: N = length(P[0]);
2296: Num = vector(N);
2297: for ( I = 0; I < N; I++ ) Num[I] = -1;
2298: for ( ; Ti != []; Ti = cdr(Ti) ) {
2299: Sj = car(Ti);
2300: Dj = Sj[0];
2301: Ij =Sj[1];
2302: Mj = deg(type(Sj[2])==9?dp_dtop(Sj[2],V):Sj[2],TV);
2303: Pj = P[Ij];
2304: if ( Dj )
2305: for ( I = 0; I < N; I++ )
2306: if ( Pj[I] >= 0 ) {
2307: T = Mj+Pj[I];
2308: Num[I] = MAX(Num[I],T);
2309: }
2310: }
2311: return Num;
2312: }
2313:
2314: def compute_deg(B,V,TV,Data)
2315: {
2316: GB = Data[0];
2317: Homo = Data[1];
2318: Trace = Data[2];
2319: IntRed = Data[3];
2320: Ind = Data[4];
2321: DB = map(dp_ptod,B,V);
2322: if ( Homo ) {
2323: DB = map(dp_homo,DB);
2324: V0 = append(V,[hhh]);
2325: } else
2326: V0 = V;
2327: Perm = Trace[0]; Trace = cdr(Trace);
2328: for ( I = length(Perm)-1, T = Trace; T != []; T = cdr(T) )
2329: if ( (J=car(T)[0]) > I ) I = J;
2330: N = I+1;
2331: N0 = length(B);
2332: P = vector(N);
2333: for ( T = Perm, I = 0; T != []; T = cdr(T), I++ ) {
2334: Pi = car(T);
2335: C = vector(N0);
2336: for ( J = 0; J < N0; J++ ) C[J] = -1;
2337: C[Pi[1]] = 0;
2338: P[Pi[0]] = C;
2339: }
2340: for ( T = Trace; T != []; T = cdr(T) ) {
2341: Ti = car(T); P[Ti[0]] = compute_deg0(Ti[1],P,V0,TV);
2342: }
2343: M = length(Ind);
2344: for ( T = IntRed; T != []; T = cdr(T) ) {
2345: Ti = car(T); P[Ti[0]] = compute_deg0(Ti[1],P,V,TV);
2346: }
2347: R = [];
2348: for ( J = 0; J < M; J++ ) {
2349: U = P[Ind[J]];
2350: R = cons(U,R);
2351: }
2352: return reverse(R);
2353: }
2354:
2355: /* set theoretic functions */
2356:
2357: def member(A,S)
2358: {
2359: for ( ; S != []; S = cdr(S) )
2360: if ( car(S) == A ) return 1;
2361: return 0;
2362: }
2363:
2364: def elimination(G,V) {
2365: for ( R = [], T = G; T != []; T = cdr(T) )
2366: if ( setminus(vars(car(T)),V) == [] ) R =cons(car(T),R);
2367: return R;
2368: }
2369:
2370: def setintersection(A,B)
2371: {
2372: for ( L = []; A != []; A = cdr(A) )
2373: if ( member(car(A),B) )
2374: L = cons(car(A),L);
2375: return L;
2376: }
2377:
2378: def setminus(A,B) {
2379: for ( T = reverse(A), R = []; T != []; T = cdr(T) ) {
2380: for ( S = B, M = car(T); S != []; S = cdr(S) )
2381: if ( car(S) == M ) break;
2382: if ( S == [] ) R = cons(M,R);
2383: }
2384: return R;
2385: }
2386:
2387: def sep_list(L,N)
2388: {
2389: if ( length(L) <= N ) return [L,[]];
2390: R = [];
2391: for ( T = L, I = 0; I < N; I++, T = cdr(T) )
2392: R = cons(car(T),R);
2393: return [reverse(R),T];
2394: }
2395:
2396: def first(L)
2397: {
2398: return L[0];
2399: }
2400:
2401: def second(L)
2402: {
2403: return L[1];
2404: }
2405:
2406: def third(L)
2407: {
2408: return L[2];
2409: }
2410:
2411: def first_second(L)
2412: {
2413: return [L[0],L[1]];
2414: }
2415:
2416: def comp_tord(A,B)
2417: {
2418: DA = dp_ht(A);
2419: DB = dp_ht(B);
2420: if ( DA > DB ) return 1;
2421: else if ( DA < DB ) return -1;
2422: else return 0;
2423: }
2424:
2425: def comp_tdeg(A,B)
2426: {
2427: DA = tdeg(A);
2428: DB = tdeg(B);
2429: if ( DA > DB ) return 1;
2430: else if ( DA < DB ) return -1;
2431: else return 0;
2432: }
2433:
2434: def comp_tdeg_first(A,B)
2435: {
2436: DA = tdeg(A[0]);
2437: DB = tdeg(B[0]);
2438: if ( DA > DB ) return 1;
2439: else if ( DA < DB ) return -1;
2440: else return 0;
2441: }
2442:
2443: def comp_third_tdeg(A,B)
2444: {
2445: if ( A[2] > B[2] ) return 1;
2446: if ( A[2] < B[2] ) return -1;
2447: DA = tdeg(A[0]);
2448: DB = tdeg(B[0]);
2449: if ( DA > DB ) return 1;
2450: else if ( DA < DB ) return -1;
2451: else return 0;
2452: }
2453:
2454: def tdeg(P)
2455: {
2456: dp_ord(0);
2457: return dp_td(dp_ptod(P,vars(P)));
2458: }
2459:
2460: def comp_by_ord(A,B)
2461: {
2462: if ( dp_ht(A) > dp_ht(B) ) return 1;
2463: else if ( dp_ht(A) < dp_ht(B) ) return -1;
2464: else return 0;
2465: }
2466:
2467: def comp_by_second(A,B)
2468: {
2469: if ( A[1] > B[1] ) return 1;
2470: else if ( A[1] < B[1] ) return -1;
2471: else return 0;
2472: }
2473:
2474: def get_lc(F)
2475: {
2476: if ( type(F)==1 ) return F;
2477: V = var(F);
2478: D = deg(F,V);
2479: return get_lc(coef(F,D,V));
2480: }
2481:
2482: def tomonic(F,Mod)
2483: {
2484: C = get_lc(F);
2485: IC = inv(C,Mod);
2486: return (IC*F)%Mod;
2487: }
2488:
2489: def gen_gb_comp(A,B,Mod)
2490: {
2491: if ( !Mod ) return gb_comp(A,B);
2492: LA = length(A); LB = length(B);
2493: if ( LA != LB ) return 0;
2494: A = map(tomonic,A,Mod);
2495: B = map(tomonic,B,Mod);
2496: A = qsort(A); B = qsort(B);
2497: if ( A != B ) return 0;
2498: return 1;
2499: }
2500:
2501: def prod(L)
2502: {
2503: for ( R = 1; L != []; L = cdr(L) )
2504: R *= car(L);
2505: return R;
2506: }
2507:
2508: def monodec0(B,V)
2509: {
2510: M = monodec(B,V);
2511: return map(vars,M);
2512: }
2513:
2514: def monodec(B,V)
2515: {
2516: B = map(sq,B,0);
2517: G = nd_gr_postproc(B,V,0,0,0);
2518: V = vars(G);
2519: N = length(V);
2520: if ( N == 0 ) return G == [] ? [[]] : [];
2521: if ( N == 1 ) return G;
2522: if ( N < 20 ) {
2523: T = dp_mono_raddec(G,V);
2524: return map(prod,T);
2525: }
2526: X = car(V); W = cdr(V);
2527: D0 = monodec(map(subst,B,X,0),W);
2528: T0 = map(dp_ptod,D0,W);
2529: D1 = monodec(map(subst,B,X,1),W);
2530: T1 = map(dp_ptod,D1,W);
1.4 noro 2531: #if 0
1.1 noro 2532: for ( T = T1; T != []; T = cdr(T) ) {
2533: for ( M = car(T), S1 = [], S = T0; S != []; S = cdr(S) )
2534: if ( !dp_redble(car(S),M) ) S1= cons(car(S),S1);
2535: T0 = S1;
2536: }
1.4 noro 2537: #else
2538: T0 = dp_mono_reduce(T0,T1);
2539: #endif
1.1 noro 2540: D0 = map(dp_dtop,T0,W);
2541: D0 = vtol(X*ltov(D0));
2542: return append(D0,D1);
2543: }
2544:
2545: def separator(P,V)
2546: {
2547: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2548: N = length(P);
1.4 noro 2549: dp_ord(0);
2550: DP = vector(N);
2551: for ( I = 0; I < N; I++ ) DP[I] = qsort(ltov(map(dp_ptod,P[I][0],V)),comp_tord);
2552: if ( Mod )
2553: for ( I = 0; I < N; I++ ) DP[I] = map(dp_mod,DP[I],Mod,[]);
2554: Ind = vector(N);
2555: for ( I = 0; I < N; I++ ) {
2556: for ( K = [], J = length(DP[I])-1; J >= 0; J-- ) K = cons(J,K);
2557: Ind[I] = K;
2558: }
2559: S = vector(N);
2560: for ( I = 0; I < N; I++ ) S[I] = 1;
1.1 noro 2561: for ( I = 0; I < N; I++ ) {
1.4 noro 2562: print(".",2);
1.1 noro 2563: for ( J = 0; J < N; J++ ) {
2564: if ( J == I ) continue;
1.4 noro 2565: T = DP[I]; L = length(T);
2566: if ( Mod ) {
2567: for ( K = 0; K < L; K++ )
2568: if ( dp_nf_mod(Ind[J],T[K],DP[J],0,Mod) ) break;
2569: } else {
2570: for ( K = 0; K < L; K++ )
2571: if ( dp_nf(Ind[J],T[K],DP[J],0) ) break;
2572: }
2573: S[J] = lcm(S[J],dp_dtop(T[K],V));
1.1 noro 2574: }
2575: }
1.4 noro 2576: print("");
1.1 noro 2577: return S;
2578: }
2579:
2580: def prepost(PL,V)
1.4 noro 2581: {
2582: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1.1 noro 2583: A = ltov(PL); N = length(A);
2584: Pre = vector(N);
2585: Post = vector(N);
2586: R = vector(N);
2587: Pre[0] = [1];
2588: print("pre ",2);
2589: for ( I = 1; I < N; I++, print(".",2) )
1.4 noro 2590: Pre[I] = ideal_intersection_m(Pre[I-1],A[I-1],V,0|mod=Mod);
1.1 noro 2591: print("done");
2592: print("post ",2);
2593: Post[N-1] = [1];
2594: for ( I = N-2; I >= 0; I--, print(".",2) )
1.4 noro 2595: Post[I] = ideal_intersection_m(Post[I+1],A[I+1],V,0|mod=Mod);
1.1 noro 2596: print("done");
2597: print("int ",2);
2598: for ( I = 0; I < N; I++, print(".",2) )
1.4 noro 2599: R[I] = ideal_intersection_m(Pre[I],Post[I],V,0|mod=Mod);
1.1 noro 2600: print("done");
2601: return R;
2602: }
2603:
2604: /* XXX */
2605:
2606: def call_func(Arg)
2607: {
2608: F = car(Arg);
2609: return call(strtov(F),cdr(Arg));
2610: }
2611:
2612: def competitive_exec(P,Arg0,Arg1)
2613: {
2614: P0 = P[0]; P1 = P[1];
2615: ox_cmo_rpc(P0,"noro_pd.call_func",Arg0|sync=1);
2616: ox_cmo_rpc(P1,"noro_pd.call_func",Arg1|sync=1);
2617: F = ox_select(P);
2618: R = ox_get(F[0]);
2619: if ( length(F) == 2 ) {
2620: ox_get(F[1]);
2621: } else {
2622: U = setminus(P,F);
2623: ox_reset(U[0]);
2624: }
2625: return R;
2626: }
2627:
2628:
2629: def nd_gr_rat(B,V,PV,Ord1,Ord)
2630: {
2631: G = nd_gr(B,append(V,PV),0,Ord1);
2632: G1 = nd_gr_postproc(G,V,0,Ord,0);
2633: return G1;
2634: }
2635:
2636: /* Task[i] = [fname,[arg0,...,argn]] */
2637:
2638: def para_exec(Proc,Task) {
2639: Free = Proc;
2640: N = length(Task);
2641: R = [];
2642: while ( N ) {
2643: while ( Task != [] && Free != [] ) {
2644: T = car(Task); Task = cdr(Task);
2645: ox_cmo_rpc(car(Free),"noro_pd.call_func",T);
2646: ox_push_cmd(car(Free),258); Free = cdr(Free);
2647: }
2648: Finish0 = Finish = ox_select(Proc);
2649: for ( ; Finish != []; Finish = cdr(Finish) ) {
2650: print(".",2);
2651: L = ox_get(car(Finish));
2652: R = cons(L,R);
2653: N--;
2654: }
2655: Free = append(Free,Finish0);
2656: }
2657: print("");
2658: return reverse(R);
2659: }
1.4 noro 2660:
2661: def redbase(B,V,Mod,Ord)
2662: {
2663: M = nd_gr_postproc(B,V,Mod,Ord,0);
2664: dp_ord(Ord);
2665: DM = ltov(map(dp_ptod,M,V));
2666: if ( Mod ) DM = map(dp_mod,DM,Mod,[]);
2667: N = length(DM);
2668: for ( Ind = [], I = N-1; I >= 0; I-- ) Ind = cons(I,Ind);
2669: for ( T = B, R = vtol(DM); T != []; T = cdr(T) ) {
2670: D = dp_ptod(car(T),V);
2671: if ( Mod ) D = dp_mod(D,Mod,[]);
2672: D = Mod?dp_nf_mod(Ind,D,DM,1,Mod):dp_nf(Ind,D,DM,1);
2673: if ( D ) R = cons(D,R);
2674: }
2675: D = qsort(R,comp_tord);
2676: return map(dp_dtop,D,V);
2677: }
2678:
2679: def witness(A,B,V)
2680: {
2681: G = nd_gr(B,V,0,Mod);
2682: L = length(A);
2683: QL = []; PL = [];
2684: for ( I = L-1; I >= 0; I-- ) {
2685: QL = append(map(first,A[I]),QL);
2686: PL = append(map(second,A[I]),PL);
2687: }
2688: N = length(QL);
2689: Qhat = prepost(QL,V);
2690: for ( I = 0, W = []; I < N; I++ ) {
2691: for ( T = Qhat[I]; T != []; T = cdr(T) )
2692: if ( gen_nf(car(T),QL[I],V,0,Mod) ) break;
2693: Ai = car(T);
2694: Ji = colon(G,Ai,V|isgb=1,mod=Mod);
2695: Ji = nd_gr(Ji,V,Mod,0);
2696: if ( gen_gb_comp(Ji,PL[I],Mod) ) Bi = 1;
2697: else {
2698: Ki = ideal_colon(Ji,PL[I],V|mod=Mod);
2699: for ( T = Ki; T != []; T = cdr(T) )
2700: if ( gen_nf(car(T),Ji,V,0,Mod) ) break;
2701: Bi = car(T);
2702: }
2703: W = cons(Ai*Bi,W);
2704: Li = colon(G,W[0],V|isgb=1,mod=Mod);
2705: Li = nd_gr(Li,V,Mod,0);
2706: if ( !gen_gb_comp(Li,PL[I],Mod) )
2707: error("afo");
2708: }
2709: return reverse(W);
2710: }
1.1 noro 2711: endmodule$
2712: end$
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