Annotation of OpenXM/src/asir-contrib/testing/noro/new_pd.rr, Revision 1.9
1.9 ! ohara 1: /* $OpenXM: OpenXM/src/asir-contrib/testing/noro/new_pd.rr,v 1.8 2011/11/01 00:35:56 noro Exp $ */
1.1 noro 2: import("gr")$
3: module noro_pd$
1.8 noro 4: static GBCheck,F4,EProcs,Procs,SatHomo,GBRat,SuccSat,RepColon$
1.1 noro 5:
1.8 noro 6: localf radical_membership_sat$
1.4 noro 7: localf witness$
8: localf get_lc,tomonic,aa,ideal_intersection_m,redbase$
1.8 noro 9: localf para_exec,nd_gr_rat,competitive_exec,call_func,call_func_serial$
1.1 noro 10: localf call_ideal_list_intersection$
1.3 noro 11: localf call_colon,call_prime_dec$
1.7 noro 12: localf prime_dec2, prime_dec_main2$
1.1 noro 13: localf first_second$
14: localf third$
15: localf locsat,iso_comp_para,extract_qj,colon_prime_dec,extract_comp$
16: localf separator$
1.4 noro 17: localf member,mingen,compute_gbsyz,redcoef,recompute_trace,dtop,topnum$
1.1 noro 18: localf prepost$
19: localf monodec0,monodec,prod$
20: localf extract_qd,primary_check$
21: localf second$
1.8 noro 22: localf gbrat,succsat,repcolon,comp_third_tdeg,comp_tord$
1.1 noro 23: localf power$
24:
25: localf syci_dec, syc_dec$
26: localf syca_dec,syc0_dec$
27:
28: localf find_si0,find_si1,find_si2$
29: localf find_ssi0,find_ssi1,find_ssi2$
30:
31: localf init_pprocs, init_eprocs, init_procs, kill_procs$
32:
33: localf sy_dec, pseudo_dec, iso_comp, prima_dec$
34:
35: localf prime_dec, prime_dec_main, lex_predec1, zprimedec, zprimadec$
36: localf complete_qdecomp, partial_qdecomp, partial_qdecomp0, complete_decomp$
37: localf partial_decomp, partial_decomp0, zprimacomp, zprimecomp$
38: localf fast_gb, incremental_gb, elim_gb, ldim, make_mod_subst$
39: localf rsgn, find_npos, gen_minipoly, indepset$
1.8 noro 40: localf maxindep, maxindep2, contraction, contraction_m, ideal_list_intersection, ideal_intersection$
1.1 noro 41: localf radical_membership, modular_radical_membership$
42: localf radical_membership_rep, ideal_product, saturation$
1.4 noro 43: localf sat, satind, sat_ind, colon, isat$
1.1 noro 44: localf ideal_colon, ideal_sat, ideal_inclusion, qd_simp_comp, qd_remove_redundant_comp$
1.7 noro 45: localf pd_simp_comp, remove_identical_comp$
1.1 noro 46: localf pd_remove_redundant_comp, ppart, sq, gen_fctr, gen_nf, gen_gb_comp$
47: localf gen_mptop, lcfactor, compute_deg0, compute_deg, member$
48: localf elimination, setintersection, setminus, sep_list$
49: localf first, comp_tdeg, comp_tdeg_first, tdeg, comp_by_ord, comp_by_second$
50: localf gbcheck,f4,sathomo,qd_check,qdb_check$
51:
52: SatHomo=0$
53: GBCheck=1$
54: GBRat=0$
1.8 noro 55: SuccSat=0$
56: RepColon=0$
1.1 noro 57:
58: #define MAX(a,b) ((a)>(b)?(a):(b))
59: #define ACCUM_TIME(C,R) {T1 = time(); C += (T1[0]-T0[0])+(T1[1]-T0[1]); R += (T1[3]-T0[3]); }
60:
61: def gbrat(A)
62: {
1.8 noro 63: GBRat = A;
64: }
65:
66: def succsat(A)
67: {
68: SuccSat = A;
69: }
70:
71: def repcolon(A)
72: {
73: RepColon = A;
1.1 noro 74: }
75:
76: def gbcheck(A)
77: {
78: if ( A ) GBCheck = 1;
79: else GBCheck = -1;
80: }
81:
82: def f4(A)
83: {
84: if ( A ) F4 = 1;
85: else F4 = 0;
86: }
87:
88: def sathomo(A)
89: {
90: if ( A ) SatHomo = 1;
91: else SatHomo = 0;
92: }
93:
94: def init_eprocs()
95: {
96: if ( type(NoX=getopt(nox)) == -1 ) NoX = 0;
97: if ( !EProcs ) {
98: if ( NoX ) {
99: P0 = ox_launch_nox();
100: P1 = ox_launch_nox();
101: } else {
102: P0 = ox_launch();
103: P1 = ox_launch();
104: }
105: EProcs = [P0,P1];
106: }
107: }
108:
109: def init_pprocs(N)
110: {
111: if ( type(NoX=getopt(nox)) == -1 ) NoX = 0;
112: for ( R = [], I = 0; I < N; I++ ) {
113: P = NoX ? ox_launch_nox() : ox_launch();
114: R = cons(P,R);
115: }
116: return reverse(R);
117: }
118:
119: def init_procs()
120: {
121: if ( type(NoX=getopt(nox)) == -1 ) NoX = 0;
122: if ( !Procs ) {
123: if ( NoX ) {
124: P0 = ox_launch_nox();
125: P1 = ox_launch_nox();
126: } else {
127: P0 = ox_launch();
128: P1 = ox_launch();
129: }
130: Procs = [P0,P1];
131: }
132: }
133:
134: def kill_procs()
135: {
136: if ( Procs ) {
137: ox_shutdown(Procs[0]);
138: ox_shutdown(Procs[1]);
139: Procs = 0;
140: }
141: if ( EProcs ) {
142: ox_shutdown(EProcs[0]);
143: ox_shutdown(EProcs[1]);
144: EProcs = 0;
145: }
146: }
147:
148: def qd_check(B,V,QD)
149: {
150: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
151: G = nd_gr(B,V,Mod,0);
152: Iso = ideal_list_intersection(map(first,QD[0]),V,0|mod=Mod);
153: Emb = ideal_list_intersection(map(first,QD[1]),V,0|mod=Mod);
154: GG = ideal_intersection(Iso,Emb,V,0|mod=Mod);
155: return gen_gb_comp(G,GG,Mod);
156: }
157:
158: def primary_check(B,V)
159: {
160: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
161: G = nd_gr(B,V,Mod,0);
162: PL = prime_dec(G,V|indep=1,mod=Mod);
163: if ( length(PL) > 1 ) return 0;
164: P = PL[0][0]; Y = PL[0][1];
165: Z = setminus(V,Y);
166: H = elim_gb(G,Z,Y,Mod,[[0,length(Z)],[0,length(Y)]]);
167: H = contraction(H,Z|mod=Mod);
168: H = nd_gr(H,V,Mod,0);
169: if ( gen_gb_comp(G,H,Mod) ) return nd_gr(P,V,Mod,0);
170: else return 0;
171: }
172:
173: def qdb_check(B,V,QD)
174: {
175: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
176: G = nd_gr(B,V,Mod,0);
177: N = length(QD);
178: for ( I = 0, Q = [1]; I < N; I++ )
179: for ( J = 0, QL = map(first,QD[I]), L = length(QL);
180: J < L; J++ )
1.8 noro 181: Q = ideal_intersection_m(Q,QL[J],V,0|mod=Mod);
182: Q = nd_gr(Q,V,0,0);
1.1 noro 183: if ( !gen_gb_comp(G,Q,Mod) )
184: return 0;
185: for ( I = 0; I < N; I++ ) {
186: T = QD[I];
187: M = length(T);
188: for ( J = 0; J < M; J++ ) {
189: P = primary_check(T[J][0],V|mod=Mod);
190: if ( !P ) return 0;
191: PP = nd_gr(T[J][1],V,Mod,0);
192: if ( !gen_gb_comp(P,PP,Mod) ) return 0;
193: }
194: }
195: return 1;
196: }
197:
198: def extract_qd(QD,V,Ind)
199: {
200: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
201: N = length(Ind);
202: for ( I = 0, Q = [1]; I < N; I++ )
203: for ( J = 0, QL = map(first,QD[Ind[I]]), L = length(QL);
204: J < L; J++ )
205: Q = ideal_intersection(Q,QL[J],V,0|mod=Mod);
206: return Q;
207: }
208:
209: /* SYC primary decomositions */
210:
211: def syc_dec(B,V)
212: {
213: if ( type(SI=getopt(si)) == -1 ) SI = 2;
214: SIFList=[find_ssi0, find_ssi1,find_ssi2];
215: if ( SI<0 || SI>2 ) error("sycb_dec : si should be 0,1,2");
216: SIF = SIFList[SI];
217:
218: if ( type(MaxLevel=getopt(level)) == -1 ) MaxLevel = -1;
219: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
220: if ( type(Lexdec=getopt(lexdec)) == -1 ) Lexdec = 0;
221: if ( type(Time=getopt(time)) == -1 ) Time = 0;
222: if ( type(Iso=getopt(iso)) == -1 ) Iso = 0;
223: if ( type(Colon=getopt(colon)) == -1 ) Colon = 1;
224: Ord = 0;
225: Tall = time();
226: C = Gt = G = fast_gb(B,V,Mod,Ord|trace=1);
227: Q = []; IntQ = [1]; First = 1;
228: Tpd = Tiso = Tsep = 0;
229: RTpd = RTiso = RTsep = 0;
230: for ( Level = 0; MaxLevel < 0 || Level <= MaxLevel; Level++ ) {
231: if ( type(Gt[0])==1 ) break;
232: T3 = T2 = T1 = T0 = time();
233: if ( First ) {
234: PtR = prime_dec(C,V|indep=1,lexdec=Lexdec,mod=Mod,radical=1);
235: Pt = PtR[0]; IntPt = PtR[1];
236: if ( gen_gb_comp(Gt,IntPt,Mod) ) {
237: /* Gt is radical and Gt = cap Pt */
238: for ( T = Pt, Qt = []; T != []; T = cdr(T) )
239: Qt = cons([car(T)[0],car(T)[0]],Qt);
240: return append(Q,[Qt]);
241: }
242: }
243: T1 = time(); Tpd += (T1[0]-T0[0])+(T1[1]-T0[1]); RTpd += (T1[3]-T0[3]);
244: Qt = iso_comp(Gt,Pt,V,Ord|mod=Mod,first=First,iso=Iso);
245: Q = append(Q,[Qt]);
246: for ( T = Qt; T != []; T = cdr(T) )
247: IntQ = ideal_intersection(IntQ,car(T)[0],V,Ord
248: |mod=Mod,
249: gbblock=[[0,length(IntQ)],[length(IntQ),length(car(T)[0])]]);
250: if ( First ) { IntP = IntPt; First = 0; }
251: if ( gen_gb_comp(IntQ,G,Mod) ) break;
252:
253: M = mingen(IntQ,V);
254: for ( Pt = [], C = [1], T = M; T != []; T = cdr(T) ) {
255: Ci = colon(G,car(T),V|isgb=1);
256: if ( type(Ci[0]) != 1 ) {
257: Pi = prime_dec(Ci,V|indep=1,lexdec=Lexdec,radical=1,mod=Mod);
258: C = ideal_intersection(C,Pi[1],V,Ord);
259: Pt = append(Pt,Pi[0]);
260: }
261: }
262: Pt = pd_simp_comp(Pt,V|first=1,mod=Mod);
263: if ( Colon ) C = ideal_colon(G,IntQ,V|mod=Mod);
264: T2 = time(); Tiso += (T2[0]-T1[0])+(T2[1]-T1[1]); RTiso += (T2[3]-T1[3]);
265: Ok = (*SIF)(C,G,IntQ,IntP,V,Ord|mod=Mod);
266: Gt = append(Ok,G);
267: T3 = time(); Tsep += (T3[0]-T2[0])+(T3[1]-T2[1]); RTsep += (T3[3]-T2[3]);
268: }
269: T4 = time(); RTall = (T4[3]-Tall[3]); Tall = (T4[0]-Tall[0])+(T3[1]-Tall[1]);
270: if ( Time ) {
271: print(["cpu","total",Tall,"pd",Tpd,"iso",Tiso,"sep",Tsep]);
272: print(["elapsed","total",RTall,"pd",RTpd,"iso",RTiso,"sep",RTsep]);
273: }
274: return Q;
275: }
276:
277: static Tint2, RTint2$
278:
279: def syci_dec(B,V)
280: {
281: if ( type(SI=getopt(si)) == -1 ) SI = 1;
282: if ( SI<0 || SI>2 ) error("sycb_assdec : si should be 0,1,2");
283: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
284: if ( type(Lexdec=getopt(lexdec)) == -1 ) Lexdec = 0;
285: if ( type(Time=getopt(time)) == -1 ) Time = 0;
286: if ( type(Iso=getopt(iso)) == -1 ) Iso = 0;
287: if ( type(Ass=getopt(ass)) == -1 ) Ass = 0;
288: if ( type(Colon=getopt(colon)) == -1 ) Colon = 0;
289: if ( type(Para=getopt(para)) == -1 ) Para = 0;
1.8 noro 290: if ( type(Trace=getopt(trace)) == -1 ) Trace = 0;
1.1 noro 291: Ord = 0;
292: Tiso = Tint = Tpd = Text = Tint2 = 0;
293: RTiso = RTint = RTpd = RText = RTint2 = 0;
294: T00 = time();
1.8 noro 295: G = fast_gb(B,V,Mod,Ord|trace=Trace);
1.1 noro 296: IntQ = [1]; QL = RL = []; First = 1;
297: for ( Level = 0; ; Level++ ) {
298: T0 = time();
1.8 noro 299: if ( !Level ) {
1.1 noro 300: PtR = prime_dec(G,V|indep=1,lexdec=Lexdec,mod=Mod,radical=1);
1.8 noro 301: ACCUM_TIME(Tfpd,RTfpd)
1.1 noro 302: Pt = PtR[0]; IntPt = PtR[1]; Rad = IntPt;
1.2 noro 303: if ( gen_gb_comp(G,Rad,Mod) ) {
304: /* Gt is radical and Gt = cap Pt */
305: for ( T = Pt, Qt = []; T != []; T = cdr(T) )
306: Qt = cons([car(T)[0],car(T)[0],car(T)[1]],Qt);
307: return [reverse(Qt)];
308: }
1.1 noro 309: } else
310: Pt = colon_prime_dec(G,IntQ,V|lexdec=Lexdec,mod=Mod,para=Para);
311: ACCUM_TIME(Tpd,RTpd)
312: T0 = time();
313: Rt = iso_comp(G,Pt,V,Ord|mod=Mod,iso=Iso,para=Para,intq=IntQ);
314: ACCUM_TIME(Tiso,RTiso)
1.8 noro 315: if ( !Level ) {
316: if ( Iso == 3 ) {
317: NI = length(Rt);
318: Q = IntQ;
319: T0 = time();
320: if ( Para ) {
321: for ( J = 0, Task = []; J < NI; J++ ) {
322: T = ["noro_pd.extract_qj",Q,V,Rt[J],Rad,Mod,SI,Colon,-1];
323: Task = cons(T,Task);
324: }
325: Task = reverse(Task);
326: print("comps:",2); print(length(Task),2);
327: Rt = para_exec(Para,Task);
328: } else {
329: for ( J = 0, T = []; J < NI; J++ ) {
330: TJ = extract_qj(Q,V,Rt[J],Rad,Mod,SI,Colon,-1);
331: T = cons(TJ,T);
332: }
333: Rt = reverse(T);
334: }
335: ACCUM_TIME(Text,RText)
336: }
337: print("");
338: T0 = time();
339: Int = Rad;
340: for ( T = Rt; T != []; T = cdr(T) )
341: if ( !gb_comp(car(T)[0],car(T)[1]) )
342: Int = ideal_intersection_m(Int,car(T)[0],V,Ord|mod=Mod);
343: IntQ = nd_gr(Int,V,Mod,Ord);
344: ACCUM_TIME(Tint,RTint)
345: RL = append(RL,[Rt]);
346: } else if ( Iso != 3 ) {
1.1 noro 347: T0 = time();
1.8 noro 348: IntQ = ideal_list_intersection(map(first,Rt),V,Ord|mod=Mod,isgb=1);
1.4 noro 349: RL = append(RL,[Rt]);
1.8 noro 350: ACCUM_TIME(Tint,RTint)
1.4 noro 351: } else {
352: NI = length(Rt);
353: Q = IntQ;
1.8 noro 354: if ( Para ) {
355: for ( J = 0, Task = []; J < NI; J++ ) {
356: T = ["noro_pd.extract_qj",Q,V,Rt[J],Rad,Mod,SI,Colon,-1];
357: Task = cons(T,Task);
358: }
359: Task = reverse(Task);
360: print("comps:",2); print(length(Task),2);
361: T0 = time();
362: R = para_exec(Para,Task);
363: ACCUM_TIME(Text,RText)
364: print("");
365: T0 = time();
366: IntQ = ideal_list_intersection(cons(IntQ,map(first,R)),V,Ord|mod=Mod);
367: ACCUM_TIME(Tint,RTint)
368: RL = append(RL,[R]);
369: } else {
370: for ( J = 0, T = []; J < NI; J++ ) {
371: T0 = time();
372: TJ = extract_qj(Q,V,Rt[J],Rad,Mod,SI,Colon,-1);
373: ACCUM_TIME(Text,RText)
374: T = cons(TJ,T);
375: T0 = time();
376: IntQ = ideal_intersection_m(IntQ,TJ[0],V,Ord|mod=Mod);
377: ACCUM_TIME(Tint,RTint)
378: }
379: print("");
380: T0 = time();
381: IntQ = nd_gr(IntQ,V,Mod,Ord);
382: ACCUM_TIME(Tint,RTint)
383: T = reverse(T); RL = append(RL,[T]);
1.4 noro 384: }
385: }
1.1 noro 386: QL = append(QL,[IntQ]);
387: if ( gen_gb_comp(IntQ,G,Mod) ) break;
388: }
389: T0 = time();
1.4 noro 390: if ( Iso != 3 && !Ass )
1.1 noro 391: RL = extract_comp(QL,RL,V,Rad|mod=Mod,para=Para,si=SI,colon=Colon,ass=Ass);
392: ACCUM_TIME(Text,RText)
393: if ( Time ) {
394: T1 = time();
395: Tall = T1[0]-T00[0]+T1[1]-T00[1]; RTall += T1[3]-T00[3];
396: Tass = Tall-Text; RTass = RTall-RText;
1.8 noro 397: print(["total",Tall,"ass",Tass,"pd",Tpd,"(fpd)",Tfpd,"iso",Tiso,"int",Tint,"ext",Text]);
398: print(["elapsed",RTall,"ass",RTass,"pd",RTpd,"(fpd)",RTfpd,"iso",RTiso,"int",RTint,"ext",RText]);
1.1 noro 399: }
400: return RL;
401: }
402:
403: def extract_comp(QL,RL,V,Rad) {
404: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
405: if ( type(Para=getopt(para)) == -1 ) Para = 0;
406: if ( type(Colon=getopt(colon)) == -1 ) Colon = 0;
407: if ( type(SI=getopt(si)) == -1 ) SI = 1;
408: if ( type(Ass=getopt(ass)) == -1 ) Ass = 0;
409:
410: L = length(QL);
411: if ( Para ) {
412: for ( Task = [], I = 1; I < L; I++ ) {
413: QI = QL[I-1]; RI = RL[I]; NI = length(RI);
414: for ( J = 0, TI = []; J < NI; J++ ) {
415: T = ["noro_pd.extract_qj",QI,V,RI[J],Rad,Mod,SI,Colon,I];
416: Task = cons(T,Task);
417: }
418: }
1.8 noro 419: Task = reverse(Task);
1.1 noro 420: print("comps:",2); print(length(Task),2); print("");
421: R = para_exec(Para,Task);
422: S = vector(L);
423: for ( I = 1; I < L; I++ ) S[I] = [];
424: S[0] = RL[0];
425: for ( T = R; T != []; T = cdr(T) ) {
426: U = car(T); Level = U[0]; Body = U[1];
427: S[Level] = cons(Body,S[Level]);
428: }
429: return vtol(S);
430: } else {
431: TL = [RL[0]];
432: for ( I = 1; I < L; I++ ) {
433: print("level:",2); print(I,2);
434: print(" comps:",2); print(length(RL[I]),2); print("");
435: QI = QL[I-1]; RI = RL[I]; NI = length(RI);
436: for ( J = 0, TI = []; J < NI; J++ ) {
437: TIJ = extract_qj(QI,V,RI[J],Rad,Mod,SI,Colon,-1);
438: TI = cons(TIJ,TI);
439: }
440: TI = reverse(TI); TL = cons(TI,TL);
441: }
442: TL = reverse(TL);
443: }
444: return TL;
445: }
446:
447: def colon_prime_dec(G,IntQ,V) {
448: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
449: if ( type(Lexdec=getopt(lexdec)) == -1 ) Lexdec = 0;
450: if ( type(Para=getopt(para)) == -1 ) Para = 0;
1.3 noro 451: if ( !Para ) {
452: print("colon_pd:",2); print(length(IntQ),2);
453: }
1.1 noro 454: if ( !Mod ) M = mingen(IntQ,V);
455: else M = IntQ;
456: if ( Para ) {
457: L = length(M);
1.3 noro 458: for ( Task = [], J = 0; J < L; J++ )
1.1 noro 459: if ( gen_nf(M[J],G,V,Ord,Mod) ) {
1.3 noro 460: T = ["noro_pd.call_colon",G,M[J],V,Mod,1];
1.1 noro 461: Task = cons(T,Task);
462: }
463: Task = reverse(Task);
464: R = para_exec(Para,Task);
1.3 noro 465: R = pd_simp_comp(R,V|mod=Mod); L = length(R);
466:
467: for ( Task = [], J = 0; J < L; J++ ) {
468: T = ["noro_pd.call_prime_dec",R[J],V,1,Lexdec,Mod];
469: Task = cons(T,Task);
470: }
471: Task = reverse(Task);
472: R = para_exec(Para,Task);
473:
1.1 noro 474: for ( Pt = [], T = R; T != []; T = cdr(T) ) Pt = append(Pt,car(T));
475: } else {
1.3 noro 476: for ( R = [], T = M; T != []; T = cdr(T) ) {
477: Ci = colon(G,car(T),V|isgb=1,mod=Mod);
478: R = cons(Ci,R);
479: }
480: print("->",2); print(length(M),2);
481: R = pd_simp_comp(R,V|mod=Mod);
482: print("->",2); print(length(R));
1.8 noro 483: #if 1
1.3 noro 484: for ( Pt = [], T = R; T != []; T = cdr(T) ) {
485: Pi = prime_dec(car(T),V|indep=1,lexdec=Lexdec,mod=Mod);
1.1 noro 486: Pt = append(Pt,Pi);
487: }
1.8 noro 488: #else
489: J = ideal_list_intersection(R,V,0|mod=Mod);
490: Pt = prime_dec(J,V|indep=1,lexdec=Lexdec,mod=Mod);
491: #endif
1.1 noro 492: }
1.8 noro 493: #if 1
1.1 noro 494: Pt = pd_simp_comp(Pt,V|first=1,mod=Mod);
1.8 noro 495: #endif
1.1 noro 496: return Pt;
497: }
498:
1.3 noro 499: def call_colon(G,F,V,Mod,IsGB)
500: {
501: return colon(G,F,V|isgb=1,mod=Mod);
502: }
503:
504: def call_prime_dec(G,V,Indep,Lexdec,Mod)
1.1 noro 505: {
1.3 noro 506: if ( type(G[0]) != 1 )
507: Pi = prime_dec(G,V|indep=Indep,lexdec=Lexdec,mod=Mod);
1.1 noro 508: else
509: Pi = [];
510: return Pi;
511: }
512:
513: def extract_qj(Q,V,QL,Rad,Mod,SI,Colon,Level)
514: {
515: SIFList=[find_ssi0, find_ssi1,find_ssi2];
516: SIF = SIFList[SI];
517: G = QL[0]; P = QL[1]; PV = QL[2];
1.4 noro 518: if ( Q != [1] ) {
519: C = Colon ? ideal_colon(G,Q,V|mod=Mod) : P;
520: Ok = (*SIF)(C,G,Q,Rad,V,0|mod=Mod);
521: } else
522: Ok = [];
1.1 noro 523: V0 = setminus(V,PV);
524: HJ = elim_gb(append(Ok,G),V0,PV,Mod,[[0,length(V0)],[0,length(PV)]]);
525: HJ = contraction(HJ,V0|mod=Mod);
526: IJ = nd_gr(HJ,V,Mod,Ord);
527: return Level >= 0 ? [Level,[IJ,P]] : [IJ,P];
528: }
529:
530: def syca_dec(B,V)
531: {
532: T00 = time();
533: if ( type(SI=getopt(si)) == -1 ) SI = 2;
534: SIFList=[find_si0, find_si1,find_si2]; SIF = SIFList[SI];
535: if ( !SIF ) error("syca_dec : si should be 0,1,2");
536:
537: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
538: if ( type(Lexdec=getopt(lexdec)) == -1 ) Lexdec = 0;
539: if ( type(NoSimp=getopt(nosimp)) == -1 ) NoSimp = 0;
540: if ( type(Time=getopt(time)) == -1 ) Time = 0;
541: if ( type(Iso=getopt(iso)) == -1 ) Iso = 0;
542: Ord = 0;
543: Gt = G0 = G = fast_gb(B,V,Mod,Ord|trace=1);
544: Q0 = Q = []; IntQ0 = IntQ = [1]; First = 1;
545: C = 0;
546:
547: Tass = Tiso = Tcolon = Tsep = Tirred = 0;
548: Rass = Riso = Rcolon = Rsep = Rirred = 0;
549: while ( 1 ) {
550: if ( type(Gt[0])==1 ) break;
551: T0 = time();
552: PtR = prime_dec(Gt,V|indep=1,lexdec=Lexdec,mod=Mod,radical=1);
553: T1 = time(); Tass += T1[0]-T0[0]+T1[1]-T0[1]; Rass += T1[3]-T0[3];
554: Pt = PtR[0]; IntPt = PtR[1];
555: if ( gen_gb_comp(Gt,IntPt,Mod) ) {
556: /* Gt is radical and Gt = cap Pt */
557: for ( T = Pt, Qt = []; T != []; T = cdr(T) )
558: Qt = cons([car(T)[0],car(T)[0]],Qt);
559: if ( First )
560: return [Qt,[]];
561: else
562: Q0 = append(Qt,Q0);
563: break;
564: }
565: T0 = time();
566: Qt = iso_comp(Gt,Pt,V,Ord|mod=Mod,isgb=1,iso=Iso);
567: T1 = time(); Tiso += T1[0]-T0[0]+T1[1]-T0[1]; Riso += T1[3]-T0[3];
568: IntQt = ideal_list_intersection(map(first,Qt),V,Ord|mod=Mod);
569: if ( First ) {
570: IntQ0 = IntQ = IntQt; IntP = IntPt; Qi = Qt; First = 0;
571: } else {
572: IntQ1 = ideal_intersection(IntQ,IntQt,V,Ord|mod=Mod);
573: if ( gen_gb_comp(IntQ,IntQ1,Mod) ) {
574: G = Gt; IntP = IntPt; Q = []; IntQ = [1]; C = 0;
575: continue;
576: } else {
577: IntQ = IntQ1;
578: IntQ1 = ideal_intersection(IntQ0,IntQt,V,Ord|mod=Mod);
579: if ( !gen_gb_comp(IntQ0,IntQ1,Mod) ) {
580: Q = append(Qt,Q);
581: for ( T = Qt; T != []; T = cdr(T) )
582: if ( !ideal_inclusion(IntQ0,car(T)[0],V,Ord|mod=Mod) )
583: Q0 = append(Q0,[car(T)]);
584: IntQ0 = IntQ1;
585: }
586: }
587: }
588: if ( gen_gb_comp(IntQt,Gt,Mod) || gen_gb_comp(IntQ,G,Mod) || gen_gb_comp(IntQ0,G0,Mod) ) break;
589: T0 = time();
590: C1 = ideal_colon(G,IntQ,V|mod=Mod);
591: T1 = time(); Tcolon += T1[0]-T0[0]+T1[1]-T0[1]; Rcolon += T1[3]-T0[3];
592: if ( C && gen_gb_comp(C,C1,Mod) ) {
593: G = Gt; IntP = IntPt; Q = []; IntQ = [1]; C = 0;
594: continue;
595: } else C = C1;
596: T0 = time();
597: Ok = (*SIF)(C,G,IntQ,IntP,V,Ord|mod=Mod);
598: G1 = append(Ok,G);
599: Gt1 = incremental_gb(G1,V,Ord|mod=Mod);
600: T1 = time(); Tsep += T1[0]-T0[0]+T1[1]-T0[1]; Rsep += T1[3]-T0[3];
601: Gt = Gt1;
602: }
603: T0 = time();
604: if ( !NoSimp ) Q1 = qd_remove_redundant_comp(G0,Qi,Q0,V,Ord|mod=Mod);
605: else Q1 = Q0;
606: if ( Time ) {
607: T1 = time(); Tirred += T1[0]-T0[0]+T1[1]-T0[1]; Rirred += T1[3]-T0[3];
608: Tall = T1[0]-T00[0]+T1[1]-T00[1]; Rall += T1[3]-T00[3];
609: print(["total",Tall,"ass",Tass,"iso",Tiso, "colon",Tcolon,"sep",Tsep,"irred",Tirred]);
610: print(["Rtotal",Rall,"Rass",Rass,"Riso",Riso, "Rcolon",Rcolon,"Rsep",Rsep,"Rirred",Rirred]);
611: print(["iso",length(Qi),"emb",length(Q0),"->",length(Q1)]);
612: }
613: return [Qi,Q1];
614: }
615:
616: def syc0_dec(B,V)
617: {
618: T00 = time();
619: if ( type(SI=getopt(si)) == -1 ) SI = 1;
620: SIFList=[find_si0, find_si1,find_si2,find_ssi0,find_ssi1,find_ssi2]; SIF = SIFList[SI];
621: if ( !SIF ) error("syc0_dec : si should be 0,1,2");
622: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
623: if ( type(Lexdec=getopt(lexdec)) == -1 ) Lexdec = 0;
624: if ( type(NoSimp=getopt(nosimp)) == -1 ) NoSimp = 0;
625: if ( type(Time=getopt(time)) == -1 ) Time = 0;
626: Ord = 0;
627: G = fast_gb(B,V,Mod,Ord);
628: Q = []; IntQ = [1]; Gt = G; First = 1;
629: Tass = Tiso = Tcolon = Tsep = Tirred = 0;
630: Rass = Riso = Rcolon = Rsep = Rirred = 0;
631: while ( 1 ) {
632: if ( type(Gt[0])==1 ) break;
633: T0 = time();
634: PtR = prime_dec(Gt,V|indep=1,lexdec=Lexdec,mod=Mod,radical=1);
635: T1 = time(); Tass += T1[0]-T0[0]+T1[1]-T0[1]; Rass += T1[3]-T0[3];
636: Pt = PtR[0]; IntPt = PtR[1];
637: if ( gen_gb_comp(Gt,IntPt,Mod) ) {
638: /* Gt is radical and Gt = cap Pt */
639: for ( T = Pt, Qt = []; T != []; T = cdr(T) )
640: Qt = cons([car(T)[0],car(T)[0]],Qt);
641: if ( First )
642: return [Qt,[]];
643: else
644: Q = append(Qt,Q);
645: break;
646: }
647:
648: T0 = time();
649: Qt = iso_comp(Gt,Pt,V,Ord|mod=Mod,isgb=1);
650: T1 = time(); Tiso += T1[0]-T0[0]+T1[1]-T0[1]; Riso += T1[3]-T0[3];
651: IntQt = ideal_list_intersection(map(first,Qt),V,Ord|mod=Mod);
652: if ( First ) {
653: IntQ = IntQt; Qi = Qt; First = 0;
654: } else {
655: IntQ1 = ideal_intersection(IntQ,IntQt,V,Ord|mod=Mod);
656: if ( !gen_gb_comp(IntQ1,IntQ,Mod) )
657: Q = append(Qt,Q);
658: }
659: if ( gen_gb_comp(IntQ,G,Mod) || gen_gb_comp(IntQt,Gt,Mod) )
660: break;
661: T0 = time();
662: C = ideal_colon(Gt,IntQt,V|mod=Mod);
663: T1 = time(); Tcolon += T1[0]-T0[0]+T1[1]-T0[1]; Rcolon += T1[3]-T0[3];
664: T0 = time();
665: Ok = (*SIF)(C,Gt,IntQt,IntPt,V,Ord|mod=Mod);
666: G1 = append(Ok,Gt);
667: Gt = incremental_gb(G1,V,Ord|mod=Mod);
668: T1 = time(); Tsep += T1[0]-T0[0]+T1[1]-T0[1]; Rsep += T1[3]-T0[3];
669: }
670: T0 = time();
671: if ( !NoSimp ) Q1 = qd_remove_redundant_comp(G,Qi,Q,V,Ord|mod=Mod);
672: else Q1 = Q;
673: T1 = time(); Tirred += T1[0]-T0[0]+T1[1]-T0[1]; Rirred += T1[3]-T0[3];
674: Tall = T1[0]-T00[0]+T1[1]-T00[1]; Rall += T1[3]-T00[3];
675: if ( Time ) {
676: print(["total",Tall,"ass",Tass,"iso",Tiso, "colon",Tcolon,"sep",Tsep,"irred",Tirred]);
677: print(["Rtotal",Rall,"Rass",Rass,"Riso",Riso, "Rcolon",Rcolon,"Rsep",Rsep,"Rirred",Rirred]);
678: print(["iso",length(Qi),"emb",length(Q),"->",length(Q1)]);
679: }
680: return [Qi,Q1];
681: }
682:
683: def power(A,I) { return A^I; }
684:
685:
686: /* functions for computating a separing ideal */
687: /* C=G:Q, Rad=rad(Q), return J s.t. Q cap (G+J) = G */
688:
689: def find_si0(C,G,Q,Rad,V,Ord) {
690: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
691: for ( CI = C, I = 1; ; I++ ) {
692: for ( T = CI, S = []; T != []; T = cdr(T) )
693: if ( gen_nf(car(T),Q,V,Ord,Mod) ) S = cons(car(T),S);
694: if ( S == [] )
695: error("find_si0 : cannot happen");
696: G1 = append(S,G);
697: Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
698: /* check whether (Q cap (G+S)) = G */
699: if ( gen_gb_comp(Int,G,Mod) ) { print([0]); return reverse(S); }
700: CI = ideal_product(CI,C,V|mod=Mod);
701: }
702: }
703:
704: def find_si1(C,G,Q,Rad,V,Ord) {
705: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
706: for ( T = C, S = []; T != []; T = cdr(T) )
707: if ( gen_nf(car(T),Q,V,Ord,Mod) ) S = cons(car(T),S);
708: if ( S == [] )
709: error("find_si1 : cannot happen");
710: G1 = append(S,G);
711: Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
712: /* check whether (Q cap (G+S)) = G */
713: if ( gen_gb_comp(Int,G,Mod) ) { print([0]); return reverse(S); }
714:
1.9 ! ohara 715: C = qsort(C,noro_pd.comp_tdeg);
1.1 noro 716:
717: Tmp = ttttt; TV = cons(Tmp,V); Ord1 = [[0,1],[Ord,length(V)]];
718: Int0 = incremental_gb(append(vtol(ltov(G)*Tmp),vtol(ltov(Q)*(1-Tmp))),
719: TV,Ord1|gbblock=[[0,length(G)]],mod=Mod);
720: Dp = dp_gr_print(); dp_gr_print(0);
721: for ( T = C, S = []; T != []; T = cdr(T) ) {
722: if ( !gen_nf(car(T),Rad,V,Ord,Mod) ) continue;
723: Ui = U = car(T);
724: for ( I = 1; ; I++ ) {
725: G1 = cons(Ui,G);
726: Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
727: if ( gen_gb_comp(Int,G,Mod) ) break;
728: else
729: Ui = gen_nf(Ui*U,G,V,Ord,Mod);
730: }
731: print([length(T),I],2);
732: Int1 = incremental_gb(append(Int0,[Tmp*Ui]),TV,Ord1
733: |gbblock=[[0,length(Int0)]],mod=Mod);
734: Int = elimination(Int1,V);
735: if ( !gen_gb_comp(Int,G,Mod) ) {
736: break;
737: } else {
738: Int0 = Int1;
739: S = cons(Ui,S);
740: }
741: }
742: print("");
743: dp_gr_print(Dp);
744: return reverse(S);
745: }
746:
747: def find_si2(C,G,Q,Rad,V,Ord) {
748: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
749: for ( T = C, S = []; T != []; T = cdr(T) )
750: if ( gen_nf(car(T),Q,V,Ord,Mod) ) S = cons(car(T),S);
751: if ( S == [] )
752: error("find_si2 : cannot happen");
753: G1 = append(S,G);
754: Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
755: /* check whether (Q cap (G+S)) = G */
756: if ( gen_gb_comp(Int,G,Mod) ) { print([0]); return reverse(S); }
757:
1.9 ! ohara 758: C = qsort(C,noro_pd.comp_tdeg);
1.1 noro 759:
760: Dp = dp_gr_print(); dp_gr_print(0);
761: Tmp = ttttt; TV = cons(Tmp,V); Ord1 = [[0,1],[Ord,length(V)]];
762: Int0 = incremental_gb(append(vtol(ltov(G)*Tmp),vtol(ltov(Q)*(1-Tmp))),
763: TV,Ord1|gbblock=[[0,length(G)]],mod=Mod);
764: for ( T = C, S = []; T != []; T = cdr(T) ) {
765: if ( !gen_nf(car(T),Rad,V,Ord,Mod) ) continue;
766: Ui = U = car(T);
767: for ( I = 1; ; I++ ) {
768: Int1 = incremental_gb(append(Int0,[Tmp*Ui]),TV,Ord1
769: |gbblock=[[0,length(Int0)]],mod=Mod);
770: Int = elimination(Int1,V);
771: if ( gen_gb_comp(Int,G,Mod) ) break;
772: else
773: Ui = gen_nf(Ui*U,G,V,Ord,Mod);
774: }
775: print([length(T),I],2);
776: S = cons(Ui,S);
777: }
1.9 ! ohara 778: S = qsort(S,noro_pd.comp_tdeg);
1.1 noro 779: print("");
780: End = Len = length(S);
781:
782: Tmp = ttttt; TV = cons(Tmp,V); Ord1 = [[0,1],[Ord,length(V)]];
783: Prev = 1;
784: G1 = append(G,[S[0]]);
785: Int0 = incremental_gb(append(vtol(ltov(G1)*Tmp),vtol(ltov(Q)*(1-Tmp))),
786: TV,Ord1|gbblock=[[0,length(G)]],mod=Mod);
787: if ( End > 1 ) {
788: Cur = 2;
789: while ( Prev < Cur ) {
790: for ( St = [], I = Prev; I < Cur; I++ ) St = cons(Tmp*S[I],St);
791: Int1 = incremental_gb(append(Int0,St),TV,Ord1
792: |gbblock=[[0,length(Int0)]],mod=Mod);
793: Int = elimination(Int1,V);
794: if ( gen_gb_comp(Int,G,Mod) ) {
795: print([Cur],2);
796: Prev = Cur;
797: Cur = Cur+idiv(End-Cur+1,2);
798: Int0 = Int1;
799: } else {
800: End = Cur;
801: Cur = Prev + idiv(Cur-Prev,2);
802: }
803: }
804: for ( St = [], I = 0; I < Prev; I++ ) St = cons(S[I],St);
805: } else
806: St = [S[0]];
807: print("");
808: for ( I = Prev; I < Len; I++ ) {
809: Int1 = incremental_gb(append(Int0,[Tmp*S[I]]),TV,Ord1
810: |gbblock=[[0,length(Int0)]],mod=Mod);
811: Int = elimination(Int1,V);
812: if ( gen_gb_comp(Int,G,Mod) ) {
813: print([I],2);
814: St = cons(S[I],St);
815: Int0 = Int1;
816: }
817: }
818: Ok = reverse(St);
819: print("");
820: print([length(S),length(Ok)]);
821: dp_gr_print(Dp);
822: return Ok;
823: }
824:
825: /* functions for computing a saturated separating ideal */
826:
827: def find_ssi0(C,G,Q,Rad,V,Ord) {
828: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
829: if ( type(Reduce=getopt(red)) == -1 ) Reduce = 0;
830: for ( T = C, S = []; T != []; T = cdr(T) )
831: if ( gen_nf(car(T),Q,V,Ord,Mod) ) S = cons(car(T),S);
832: if ( S == [] )
833: error("find_ssi0 : cannot happen");
834: G1 = append(S,G);
835: Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
836: /* check whether (Q cap (G+S)) = G */
837: if ( gen_gb_comp(Int,G,Mod) ) { print([0]); return reverse(S); }
838:
839: if ( Reduce ) {
840: for ( T = C, U = []; T != []; T = cdr(T) )
841: if ( gen_nf(car(T),Rad,V,Ord,Mod) ) U = cons(car(T),U);
842: U = reverse(U);
843: } else
844: U = C;
845:
846: for ( I = 1; ; I++ ) {
847: print([I],2);
848: S = map(power,U,I);
849: G1 = append(S,G);
850: Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
851: /* check whether (Q cap (G+S)) = G */
852: if ( gen_gb_comp(Int,G,Mod) ) { print(""); return reverse(S); }
853: }
854: }
855:
856: def find_ssi1(C,G,Q,Rad,V,Ord) {
857: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
858: if ( type(Reduce=getopt(red)) == -1 ) Reduce = 0;
859: for ( T = C, S = []; T != []; T = cdr(T) )
860: if ( gen_nf(car(T),Q,V,Ord,Mod) ) S = cons(car(T),S);
861: if ( S == [] )
862: error("find_ssi1 : cannot happen");
863: G1 = append(S,G);
864: Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
865: /* check whether (Q cap (G+S)) = G */
866: if ( gen_gb_comp(Int,G,Mod) ) { print([0]); return reverse(S); }
867:
868: dp_ord(Ord); DC = map(dp_ptod,C,V);
1.9 ! ohara 869: DC = qsort(DC,noro_pd.comp_tord); C = map(dp_dtop,DC,V);
1.1 noro 870: print(length(C),2);
871: if ( Reduce ) {
872: SC = map(sq,C,Mod);
873: SC = reverse(SC); C = reverse(C);
874: for ( T = C, C1 = [], R1 = append(SC,Rad); T != []; T = cdr(T) ) {
875: R0 = car(R1); R1 = cdr(R1);
876: if ( !gen_nf(car(T),Rad,V,Ord,Mod) ) continue;
877: if ( radical_membership(R0,R1,V|mod=Mod) ) {
878: C1 = cons(car(T),C1);
879: R1 = append(R1,[R0]);
880: }
881: }
882: print("->",0); print(length(C1),2);
883: C = C1;
884: }
885: print(" ",2);
886:
887: Tmp = ttttt; TV = cons(Tmp,V); Ord1 = [[0,1],[Ord,length(V)]];
888: Int0 = incremental_gb(append(vtol(ltov(G)*Tmp),vtol(ltov(Q)*(1-Tmp))),
889: TV,Ord1|gbblock=[[0,length(G)]],mod=Mod);
890: Dp = dp_gr_print(); dp_gr_print(0);
891: for ( J = 0, T = C, S = [], GS = G; T != []; T = cdr(T), J++ ) {
892: if ( !gen_nf(car(T),Rad,V,Ord,Mod) ) continue;
893: Ui = U = car(T);
894: for ( I = 1; ; I++ ) {
895: Int1 = nd_gr(append(Int0,[Tmp*Ui]),TV,Mod,Ord1
896: |gbblock=[[0,length(Int0)]],newelim=1);
897: if ( Int1 ) {
898: Int = elimination(Int1,V);
899: if ( gen_gb_comp(Int,G,Mod) ) break;
900: }
901: print("x",2);
902: Ui = gen_nf(Ui*U,G,V,Ord,Mod);
903: }
904: print(J,2);
905: Int0 = Int1;
906: S = cons(Ui,S);
907: }
908: print("");
909: dp_gr_print(Dp);
910: return reverse(S);
911: }
912:
913: def find_ssi2(C,G,Q,Rad,V,Ord) {
914: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
915: if ( type(Reduce=getopt(red)) == -1 ) Reduce = 0;
916: for ( T = C, S = []; T != []; T = cdr(T) )
917: if ( gen_nf(car(T),Q,V,Ord,Mod) ) S = cons(car(T),S);
918: if ( S == [] )
919: error("find_ssi2 : cannot happen");
920: G1 = append(S,G);
921: Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
922: /* check whether (Q cap (G+S)) = G */
923: if ( gen_gb_comp(Int,G,Mod) ) { print([0]); return reverse(S); }
924:
925: #if 0
926: dp_ord(Ord); DC = map(dp_ptod,C,V);
1.9 ! ohara 927: DC = qsort(DC,noro_pd.comp_tord); C = map(dp_dtop,DC,V);
1.1 noro 928: #else
1.9 ! ohara 929: C = qsort(C,noro_pd.comp_tdeg);
1.1 noro 930: #endif
931: if ( Reduce ) {
932: for ( T = C, C1 = [], R1 = Rad; T != []; T = cdr(T) ) {
933: if ( !gen_nf(car(T),Rad,V,Ord,Mod) ) continue;
1.4 noro 934: if ( radical_membership(car(T),R1,V|mod=Mod) ) {
1.1 noro 935: C1 = cons(car(T),C1);
936: R1 = cons(sq(car(T),Mod),R1);
937: }
938: }
939: print(["C",length(C),"->",length(C1)]);
940: C = reverse(C1);
941: }
942: for ( T = C, S = []; T != []; T = cdr(T) ) {
943: if ( !gen_nf(car(T),Rad,V,Ord,Mod) ) continue;
944: Ui = U = car(T);
945: S = cons([Ui,U],S);
946: }
1.9 ! ohara 947: S = qsort(S,noro_pd.comp_tdeg_first);
1.1 noro 948: print("");
949:
950: Dp = dp_gr_print(); dp_gr_print(0);
951: Tmp = ttttt; TV = cons(Tmp,V); Ord1 = [[0,1],[Ord,length(V)]];
952: Int0 = incremental_gb(append(vtol(ltov(G)*Tmp),vtol(ltov(Q)*(1-Tmp))),
953: TV,Ord1|gbblock=[[0,length(G)]],mod=Mod);
954: OK = [];
955: while ( S != [] ) {
956: Len = length(S); print("remaining gens : ",0); print(Len);
957: S1 = [];
958: for ( Start = Prev = 0; Start < Len; Start = Prev ) {
959: Cur = Start+1;
960: print(Start,2);
961: while ( Prev < Len ) {
962: for ( St = [], I = Prev; I < Cur; I++ ) St = cons(Tmp*S[I][0],St);
963: Int1 = nd_gr(append(Int0,St),TV,Mod,Ord1|gbblock=[[0,length(Int0)]],newelim=1);
964: if ( !Int1 ) {
965: print("x",0); break;
966: }
967: Int = elimination(Int1,V);
968: if ( gen_gb_comp(Int,G,Mod) ) {
969: print([Prev,Cur-1],2);
970: Prev = Cur;
971: Cur += (Prev-Start)+1;
972: if ( Cur > Len ) Cur = Len;
973: Int0 = Int1;
974: } else
975: break;
976: }
977: for ( I = Start; I < Prev; I++ ) OK = cons(S[I][0],OK);
978: if ( Prev == Start ) {
979: Ui = S[I][0]; U = S[I][1];
980: Ui = gen_nf(Ui*U,G,V,Ord,Mod);
981: S1 = cons([Ui,U],S1);
982: Prev++;
983: }
984: }
985: S = reverse(S1);
986: print("");
987: }
988: print("");
989: OK = reverse(OK);
990: dp_gr_print(Dp);
991: return OK;
992: }
993:
994: /* SY primary decompsition */
995:
996: def sy_dec(B,V)
997: {
998: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
999: if ( type(Lexdec=getopt(lexdec)) == -1 ) Lexdec = 0;
1000: Ord = 0;
1001: G = fast_gb(B,V,Mod,Ord);
1002: Q = [];
1003: IntQ = [1];
1004: Gt = G;
1005: First = 1;
1006: while ( 1 ) {
1007: if ( type(Gt[0]) == 1 ) break;
1008: Pt = prime_dec(Gt,V|indep=1,lexdec=Lexdec,mod=Mod);
1009: L = pseudo_dec(Gt,Pt,V,Ord|mod=Mod);
1010: Qt = L[0]; Rt = L[1]; St = L[2];
1011: IntQt = ideal_list_intersection(map(first,Qt),V,Ord|mod=Mod);
1012: if ( First ) {
1013: IntQ = IntQt;
1014: Qi = Qt;
1015: First = 0;
1016: } else {
1017: IntQ = ideal_intersection(IntQ,IntQt,V,Ord|mod=Mod);
1018: Q = append(Qt,Q);
1019: }
1020: if ( gen_gb_comp(IntQ,G,Mod) ) break;
1021: for ( T = Rt; T != []; T = cdr(T) ) {
1022: if ( type(car(T)[0]) == 1 ) continue;
1023: U = sy_dec(car(T),V|lexdec=Lexdec,mod=Mod);
1024: IntQ = ideal_list_intersection(cons(IntQ,map(first,U)),
1025: V,Ord|mod=Mod);
1026: Q = append(U,Q);
1027: if ( gen_gb_comp(IntQ,G,Mod) ) break;
1028: }
1029: Gt = fast_gb(append(Gt,St),V,Mod,Ord);
1030: }
1031: Q = qd_remove_redundant_comp(G,Qi,Q,V,Ord|mod=Mod);
1032: return append(Qi,Q);
1033: }
1034:
1035: def pseudo_dec(G,L,V,Ord)
1036: {
1037: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1038: N = length(L);
1039: S = vector(N);
1040: Q = vector(N);
1041: R = vector(N);
1042: L0 = map(first,L);
1043: for ( I = 0; I < N; I++ ) {
1044: LI = setminus(L0,[L0[I]]);
1045: PI = ideal_list_intersection(LI,V,Ord|mod=Mod);
1.9 ! ohara 1046: PI = qsort(PI,noro_pd.comp_tdeg);
1.1 noro 1047: for ( T = PI; T != []; T = cdr(T) )
1048: if ( gen_nf(car(T),L0[I],V,Ord,Mod) ) break;
1049: if ( T == [] ) error("separator : cannot happen");
1050: SI = satind(G,car(T),V|mod=Mod);
1051: QI = SI[0];
1052: S[I] = car(T)^SI[1];
1053: PV = L[I][1];
1054: V0 = setminus(V,PV);
1055: #if 0
1056: GI = fast_gb(QI,append(V0,PV),Mod,
1057: [[Ord,length(V0)],[Ord,length(PV)]]);
1058: #else
1059: GI = fast_gb(QI,append(V0,PV),Mod,
1060: [[2,length(V0)],[Ord,length(PV)]]);
1061: #endif
1062: LCFI = lcfactor(GI,V0,Ord,Mod);
1063: for ( F = 1, T = LCFI, Gt = QI; T != []; T = cdr(T) ) {
1064: St = satind(Gt,T[0],V|mod=Mod);
1065: Gt = St[0]; F *= T[0]^St[1];
1066: }
1067: Q[I] = [Gt,L0[I]];
1068: R[I] = fast_gb(cons(F,QI),V,Mod,Ord);
1069: }
1070: return [vtol(Q),vtol(R),vtol(S)];
1071: }
1072:
1073: def iso_comp(G,L,V,Ord)
1074: {
1075: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1076: if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0;
1077: if ( type(Iso=getopt(iso)) == -1 ) Iso = 0;
1078: if ( type(Para=getopt(para)) == -1 ) Para = 0;
1079: if ( type(Q=getopt(intq)) == -1 ) Q = 0;
1.4 noro 1080: if ( type(S=getopt(sep)) == -1 ) S = 0;
1.1 noro 1081:
1.4 noro 1082: if ( !S ) S = separator(L,V|mod=Mod);
1.1 noro 1083: N = length(L);
1084: print("comps : ",2); print(N); print("",2);
1085: if ( Para ) {
1086: Task = [];
1087: for ( I = 0; I < N; I++ ) {
1088: T = ["noro_pd.locsat",G,V,L[I],S[I],Mod,IsGB,Iso,Q];
1089: Task = cons(T,Task);
1090: }
1091: Task = reverse(Task);
1092: R = para_exec(Para,Task);
1093: return R;
1094: } else {
1095: for ( I = 0, R = []; I < N; I++ ) {
1096: QI = locsat(G,V,L[I],S[I],Mod,IsGB,Iso,Q);
1097: if ( type(QI[0][0])==1 )
1098: error("iso_comp : cannot happen");
1099: print(".",2);
1100: R = cons(QI,R);
1101: }
1102: print("");
1103: return reverse(R);
1104: }
1105: }
1106:
1107: def locsat(G,V,L,S,Mod,IsGB,Iso,Q)
1108: {
1109: P = L[0]; PV = L[1]; V0 = setminus(V,PV);
1110: if ( Iso==1 ) {
1111: QI = sat(G,S,V|isgb=IsGB,mod=Mod);
1112: GI = elim_gb(QI,V0,PV,Mod,[[0,length(V0)],[0,length(PV)]]);
1.8 noro 1113: GI = nd_gr(contraction(GI,V0|mod=Mod,allv=V),V,Mod,0);
1.1 noro 1114: } else if ( Iso==0 ) {
1115: HI = elim_gb(G,V0,PV,Mod,[[0,length(V0)],[0,length(PV)]]);
1.8 noro 1116: GI = nd_gr(contraction(HI,V0|mod=Mod,allv=V),V,Mod,0);
1.1 noro 1117: GI = sat(GI,S,V|isgb=IsGB,mod=Mod);
1118: } else if ( Iso==2 ) {
1119: HI = elim_gb(G,V0,PV,Mod,[[0,length(V0)],[0,length(PV)]]);
1120: TV = ttttt;
1121: if ( Mod )
1122: GI = nd_gr(cons(TV*S-1,HI),cons(TV,V0),Mod,[[0,1],[0,length(V0)]]);
1123: else
1124: GI = nd_gr_trace(append(HI,[TV*S-1]),cons(TV,V0),
1125: 1,1,[[0,1],[0,length(V0)]]|gbblock=[[0,length(HI)]]);
1126: GI = elimination(GI,V);
1.8 noro 1127: GI = nd_gr(contraction(GI,V0|mod=Mod,allv=V),V,Mod,0);
1.4 noro 1128: } else if ( Iso==3 ) {
1129: GI = sat(G,S,V|isgb=IsGB,mod=Mod);
1.1 noro 1130: }
1131: if ( Q )
1132: GI = ideal_intersection(Q,GI,V,0|mod=Mod);
1133: return [GI,P,PV];
1134: }
1135:
1136: /* GTZ primary decompsition */
1137:
1138: def prima_dec(B,V)
1139: {
1140: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1141: if ( type(Ord=getopt(ord)) == -1 ) Ord = 0;
1142: G0 = fast_gb(B,V,Mod,0);
1143: G = fast_gb(G0,V,Mod,Ord);
1144: IntP = [1];
1145: QD = [];
1146: while ( 1 ) {
1147: if ( type(G[0])==1 || ideal_inclusion(IntP,G0,V,0|mod=Mod) )
1148: break;
1149: W = maxindep(G,V,Ord); NP = length(W);
1150: V0 = setminus(V,W); N = length(V0);
1151: V1 = append(V0,W);
1152: G1 = fast_gb(G,V1,Mod,[[Ord,N],[Ord,NP]]);
1153: LCF = lcfactor(G1,V0,Ord,Mod);
1154: L = zprimacomp(G,V0|mod=Mod);
1155: F = 1;
1156: for ( T = LCF, G2 = G; T != []; T = cdr(T) ) {
1157: S = satind(G2,T[0],V1|mod=Mod);
1158: G2 = S[0]; F *= T[0]^S[1];
1159: }
1160: for ( T = L, QL = []; T != []; T = cdr(T) )
1161: QL = cons(car(T)[0],QL);
1162: Int = ideal_list_intersection(QL,V,0|mod=Mod);
1163: IntP = ideal_intersection(IntP,Int,V,0|mod=Mod);
1164: QD = append(QD,L);
1165: F = gen_nf(F,G,V,0,Mod);
1166: G = fast_gb(cons(F,G),V,Mod,Ord);
1167: }
1168: QD = qd_remove_redundant_comp(G0,[],QD,V,0);
1169: return QD;
1170: }
1171:
1172: /* SL prime decomposition */
1173:
1174: def prime_dec(B,V)
1175: {
1176: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1177: if ( type(Indep=getopt(indep)) == -1 ) Indep = 0;
1.7 noro 1178: if ( type(LexDec=getopt(lexdec)) == -1 ) LexDec = 0;
1.1 noro 1179: if ( type(Rad=getopt(radical)) == -1 ) Rad = 0;
1180: B = map(sq,B,Mod);
1181: if ( LexDec )
1182: PD = lex_predec1(B,V|mod=Mod);
1183: else
1184: PD = [B];
1185: if ( length(PD) > 1 ) {
1186: G = ideal_list_intersection(PD,V,0|mod=Mod);
1187: PD = pd_remove_redundant_comp(G,PD,V,0|mod=Mod);
1188: }
1.8 noro 1189: R = []; RL = [];
1190: for ( T = PD; T != []; T = cdr(T) ) {
1191: PDT = prime_dec_main(car(T),V|indep=Indep,mod=Mod);
1192: R = append(R,PDT[0]);
1193: GT = nd_gr(PDT[1],V,Mod,0);
1194: RL = append(RL,[GT]);
1195: }
1196: if ( LexDec ) R = pd_simp_comp(R,V|first=Indep,mod=Mod);
1197: if ( Rad ) {
1198: G = ideal_list_intersection(RL,V,0|mod=Mod);
1199: return [R,G];
1200: } else return R;
1.7 noro 1201: }
1202:
1203: def prime_dec2(B,V)
1204: {
1205: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1206: if ( type(Indep=getopt(indep)) == -1 ) Indep = 0;
1207: if ( type(LexDec=getopt(lexdec)) == -1 ) LexDec = 0;
1208: if ( type(Rad=getopt(radical)) == -1 ) Rad = 0;
1209: if ( type(Para=getopt(para)) == -1 || type(Para) != 4 ) Para = [];
1210: B = map(sq,B,Mod);
1211: if ( LexDec )
1212: PD = lex_predec1(B,V|mod=Mod);
1213: else
1214: PD = [B];
1215: if ( length(PD) > 1 ) {
1216: G = ideal_list_intersection(PD,V,0|mod=Mod);
1217: PD = pd_remove_redundant_comp(G,PD,V,0|mod=Mod);
1218: }
1219: R = [];
1220: for ( T = PD; T != []; T = cdr(T) )
1221: R = append(prime_dec_main2(car(T),V|indep=Indep,mod=Mod,para=Para),R);
1222: if ( Indep ) {
1223: G = ideal_list_intersection(map(first,R),V,0|mod=Mod);
1224: R = pd_simp_comp(R,V|first=1,mod=Mod);
1225: } else {
1226: G = ideal_list_intersection(R,V,0|mod=Mod);
1227: R = pd_simp_comp(R,V|mod=Mod);
1.1 noro 1228: }
1229: return Rad ? [R,G] : R;
1230: }
1231:
1.8 noro 1232: /* returns [PD,rad(I)] */
1233:
1.1 noro 1234: def prime_dec_main(B,V)
1235: {
1.8 noro 1236: Tpint = RTpint = 0;
1.1 noro 1237: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1238: if ( type(Indep=getopt(indep)) == -1 ) Indep = 0;
1239: G = fast_gb(B,V,Mod,0);
1240: IntP = [1];
1241: PD = [];
1.4 noro 1242: DG = ltov(map(dp_ptod,G,V));
1243: for ( Ind = [], I = length(G)-1; I >= 0; I-- ) Ind = cons(I,Ind);
1244: if ( Mod ) DG = map(dp_mod,DG,Mod,[]);
1.1 noro 1245: while ( 1 ) {
1.8 noro 1246: print([length(PD)],2);
1.1 noro 1247: /* rad(G) subset IntP */
1248: /* check if IntP subset rad(G) */
1.4 noro 1249: /* print([length(PD),length(IntP)],2); */
1.7 noro 1250: for ( T = IntP; T != []; T = cdr(T) )
1.8 noro 1251: if ( (G0 = radical_membership_sat(car(T),G,V|mod=Mod,isgb=1,dg=[DG,Ind])) ) {
1.1 noro 1252: F = car(T);
1253: break;
1254: }
1.8 noro 1255: if ( T == [] ) {
1256: print(["pint",Tpint,"rpint",RTpint]);
1257: return [PD,IntP];
1258: }
1.1 noro 1259: PD0 = zprimecomp(G0,V,Indep|mod=Mod);
1.7 noro 1260: Int = ideal_list_intersection(Indep?map(first,PD0):PD0,V,0|mod=Mod);
1261: PD = append(PD,PD0);
1.8 noro 1262: #if 1
1263: T0=time();
1.4 noro 1264: IntP = ideal_intersection_m(IntP,Int,V,0|mod=Mod);
1.8 noro 1265: dp_ord(0); DC = map(dp_ptod,IntP,V);
1.9 ! ohara 1266: DC = qsort(DC,noro_pd.comp_tord); IntP = map(dp_dtop,DC,V);
1.8 noro 1267: ACCUM_TIME(Tpint,RTpint)
1.4 noro 1268: #else
1.7 noro 1269: IntP = ideal_intersection(IntP,Int,V,0|mod=Mod,gbblock=[[0,length(IntP)]]);
1.4 noro 1270: #endif
1.1 noro 1271: }
1272: }
1273:
1.8 noro 1274: localf callsat,callzcomp;
1275:
1276: def callsat(F,G,V,Mod,DG)
1277: {
1278: return radical_membership(F,G,V|mod=Mod,isgb=1,dg=DG,sat=1);
1279: }
1280:
1281: def callzcomp(F,V,Indep,Mod)
1282: {
1283: PD0 = zprimecomp(F,V,Indep|mod=Mod);
1284: Int = ideal_list_intersection(Indep?map(first,PD0):PD0,V,0|mod=Mod);
1285: return [PD0,Int];
1286: }
1287:
1.7 noro 1288: def prime_dec_main2(B,V)
1289: {
1290: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1291: if ( type(Indep=getopt(indep)) == -1 ) Indep = 0;
1292: if ( type(Para=getopt(para)) == -1 || type(Para) != 4 ) Para = [];
1293: NPara = length(Para);
1294:
1295: G = fast_gb(B,V,Mod,0);
1296: IntP = [1];
1297: PD = [];
1298: DG = ltov(map(dp_ptod,G,V));
1299: for ( Ind = [], I = length(G)-1; I >= 0; I-- ) Ind = cons(I,Ind);
1300: if ( Mod ) DG = map(dp_mod,DG,Mod,[]);
1.8 noro 1301: if ( NPara )
1302: while ( 1 ) {
1303: IntPM = mingen(IntP,V);
1304: for ( T = IntPM, CallSat = []; T != []; T = cdr(T) )
1305: CallSat = cons(["noro_pd.callsat",car(T),G,V,Mod,[DG,Ind]],CallSat);
1306: CallSat = reverse(CallSat);
1307: /* SatL = [[..],0,[...],...] */
1308: SatL = para_exec(Para,CallSat);
1309: for ( T = SatL, Sat = []; T != []; T = cdr(T) ) if ( car(T) ) Sat = cons(car(T),Sat);
1310: if ( Sat == [] ) return PD;
1311: print(length(Sat),2); print("->",2);
1312: Sat = remove_identical_comp(Sat|mod=Mod);
1313: print(length(Sat));
1314: for ( T = Sat, CallComp = []; T != []; T = cdr(T) )
1315: CallComp = cons(["noro_pd.callzcomp",car(T),V,Indep,Mod],CallComp);
1316: CallComp = reverse(CallComp);
1317: /* PDL = [[PD0,Int],...] */
1318: PDL = para_exec(Para,CallComp);
1319: for ( T = PDL; T != []; T = cdr(T) ) PD = append(PD,car(T)[0]);
1320: Int = ideal_list_intersection(map(second,PDL),V,0|mod=Mod);
1.7 noro 1321: IntP = ideal_intersection(IntP,Int,V,0|mod=Mod,gbblock=[[0,length(IntP)]]);
1322: }
1.8 noro 1323: else
1324: while ( 1 ) {
1325: /* rad(G) subset IntP */
1326: /* check if IntP subset rad(G) */
1327: /* print([length(PD),length(IntP)],2); */
1328: Sat = [];
1329: IntPM = mingen(IntP,V);
1330: for ( T = IntPM; T != [] && length(Sat) < 16; T = cdr(T) )
1331: if ( G0 = radical_membership(car(T),G,V|mod=Mod,isgb=1,dg=[DG,Ind],sat=1) )
1332: Sat = cons(G0,Sat);
1333: if ( Sat == [] ) return PD;
1334: print(length(Sat),2); print("->",2);
1335: Sat = remove_identical_comp(Sat|mod=Mod);
1336: print(length(Sat));
1337: for ( T = Sat; T != []; T = cdr(T) ) {
1338: PD0 = zprimecomp(car(T),V,Indep|mod=Mod); PD = append(PD,PD0);
1339: Int = ideal_list_intersection(Indep?map(first,PD0):PD0,V,0|mod=Mod);
1340: IntP = ideal_intersection(IntP,Int,V,0|mod=Mod,gbblock=[[0,length(IntP)]]);
1341: }
1342: }
1.7 noro 1343: }
1344:
1.1 noro 1345: /* pre-decomposition */
1346:
1347: def lex_predec1(B,V)
1348: {
1349: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1350: G = fast_gb(B,V,Mod,2);
1351: for ( T = G; T != []; T = cdr(T) ) {
1352: F = gen_fctr(car(T),Mod);
1353: if ( length(F) > 2 || length(F) == 2 && F[1][1] > 1 ) {
1354: for ( R = [], S = cdr(F); S != []; S = cdr(S) ) {
1355: Ft = car(S)[0];
1356: Gt = map(ptozp,map(gen_nf,G,[Ft],V,0,Mod));
1357: R1 = fast_gb(cons(Ft,Gt),V,Mod,0);
1358: R = cons(R1,R);
1359: }
1360: return R;
1361: }
1362: }
1363: return [G];
1364: }
1365:
1366: /* zero-dimensional prime/primary decomosition */
1367:
1368: def zprimedec(B,V,Mod)
1369: {
1370: L = partial_decomp(B,V,Mod);
1371: P = L[0]; NP = L[1];
1372: R = [];
1373: for ( ; P != []; P = cdr(P) ) R = cons(car(car(P)),R);
1374: for ( T = NP; T != []; T = cdr(T) ) {
1375: R1 = complete_decomp(car(T),V,Mod);
1376: R = append(R1,R);
1377: }
1378: return R;
1379: }
1380:
1381: def zprimadec(B,V,Mod)
1382: {
1383: L = partial_qdecomp(B,V,Mod);
1384: Q = L[0]; NQ = L[1];
1385: R = [];
1386: for ( ; Q != []; Q = cdr(Q) ) {
1387: T = car(Q); R = cons([T[0],T[1]],R);
1388: }
1389: for ( T = NQ; T != []; T = cdr(T) ) {
1390: R1 = complete_qdecomp(car(T),V,Mod);
1391: R = append(R1,R);
1392: }
1393: return R;
1394: }
1395:
1396: def complete_qdecomp(GD,V,Mod)
1397: {
1398: GQ = GD[0]; GP = GD[1]; D = GD[2];
1399: W = vars(GP);
1400: PV = setminus(W,V);
1401: N = length(V); PN = length(PV);
1402: U = find_npos([GP,D],V,PV,Mod);
1403: NV = ttttt;
1404: M = gen_minipoly(cons(NV-U,GQ),cons(NV,V),PV,0,NV,Mod);
1405: M = ppart(M,NV,Mod);
1.6 noro 1406: MF = Mod ? modfctr(M,Mod) : fctr(M);
1.1 noro 1407: R = [];
1408: for ( T = cdr(MF); T != []; T = cdr(T) ) {
1409: S = car(T);
1410: Mt = subst(S[0],NV,U);
1411: GP1 = fast_gb(cons(Mt,GP),W,Mod,0);
1412: GQ1 = fast_gb(cons(Mt^S[1],GQ),W,Mod,0);
1413: if ( PV != [] ) {
1414: GP1 = elim_gb(GP1,V,PV,Mod,[[0,N],[0,PN]]);
1415: GQ1 = elim_gb(GQ1,V,PV,Mod,[[0,N],[0,PN]]);
1416: }
1417: R = cons([GQ1,GP1],R);
1418: }
1419: return R;
1420: }
1421:
1422: def partial_qdecomp(B,V,Mod)
1423: {
1424: Elim = (Elim=getopt(elim))&&type(Elim)!=-1 ? 1 : 0;
1425: N = length(V);
1426: W = vars(B);
1427: PV = setminus(W,V);
1428: NP = length(PV);
1429: W = append(V,PV);
1430: if ( Elim && PV != [] ) Ord = [[0,N],[0,NP]];
1431: else Ord = 0;
1432: if ( Mod )
1433: B = nd_f4(B,W,Mod,Ord);
1434: else
1435: B = nd_gr_trace(B,W,1,GBCheck,Ord);
1436: Q = []; NQ = [[B,B,vector(N+1)]];
1437: for ( I = length(V)-1; I >= 0; I-- ) {
1438: NQ1 = [];
1439: for ( T = NQ; T != []; T = cdr(T) ) {
1440: L = partial_qdecomp0(car(T),V,PV,Ord,I,Mod);
1441: Q = append(L[0],Q);
1442: NQ1 = append(L[1],NQ1);
1443: }
1444: NQ = NQ1;
1445: }
1446: return [Q,NQ];
1447: }
1448:
1449: def partial_qdecomp0(GD,V,PV,Ord,I,Mod)
1450: {
1451: GQ = GD[0]; GP = GD[1]; D = GD[2];
1452: N = length(V); PN = length(PV);
1453: W = append(V,PV);
1454: VI = V[I];
1455: M = gen_minipoly(GQ,V,PV,Ord,VI,Mod);
1456: M = ppart(M,VI,Mod);
1457: if ( Mod )
1458: MF = modfctr(M,Mod);
1459: else
1460: MF = fctr(M);
1461: Q = []; NQ = [];
1462: if ( length(MF) == 2 && MF[1][1] == 1 ) {
1463: D1 = D*1; D1[I] = M;
1464: GQelim = elim_gb(GQ,V,PV,Mod,Ord);
1465: GPelim = elim_gb(GP,V,PV,Mod,Ord);
1466: LD = ldim(GQelim,V);
1467: if ( deg(M,VI) == LD )
1468: Q = cons([GQelim,GPelim,D1],Q);
1469: else
1470: NQ = cons([GQelim,GPelim,D1],NQ);
1471: return [Q,NQ];
1472: }
1473: for ( T = cdr(MF); T != []; T = cdr(T) ) {
1474: S = car(T); Mt = S[0]; D1 = D*1; D1[I] = Mt;
1475:
1476: GQ1 = fast_gb(cons(Mt^S[1],GQ),W,Mod,Ord);
1477: GQelim = elim_gb(GQ1,V,PV,Mod,Ord);
1478: GP1 = fast_gb(cons(Mt,GP),W,Mod,Ord);
1479: GPelim = elim_gb(GP1,V,PV,Mod,Ord);
1480:
1481: D1[N] = LD = ldim(GPelim,V);
1482:
1483: for ( J = 0; J < N; J++ )
1484: if ( D1[J] && deg(D1[J],V[J]) == LD ) break;
1485: if ( J < N )
1486: Q = cons([GQelim,GPelim,D1],Q);
1487: else
1488: NQ = cons([GQelim,GPelim,D1],NQ);
1489: }
1490: return [Q,NQ];
1491: }
1492:
1493: def complete_decomp(GD,V,Mod)
1494: {
1495: G = GD[0]; D = GD[1];
1496: W = vars(G);
1497: PV = setminus(W,V);
1498: N = length(V); PN = length(PV);
1499: U = find_npos(GD,V,PV,Mod);
1500: NV = ttttt;
1501: M = gen_minipoly(cons(NV-U,G),cons(NV,V),PV,0,NV,Mod);
1502: M = ppart(M,NV,Mod);
1.6 noro 1503: MF = Mod ? modfctr(M,Mod) : fctr(M);
1.1 noro 1504: if ( length(MF) == 2 ) return [G];
1505: R = [];
1506: for ( T = cdr(MF); T != []; T = cdr(T) ) {
1507: Mt = subst(car(car(T)),NV,U);
1508: G1 = fast_gb(cons(Mt,G),W,Mod,0);
1509: if ( PV != [] ) G1 = elim_gb(G1,V,PV,Mod,[[0,N],[0,PN]]);
1510: R = cons(G1,R);
1511: }
1512: return R;
1513: }
1514:
1515: def partial_decomp(B,V,Mod)
1516: {
1517: Elim = (Elim=getopt(elim))&&type(Elim)!=-1 ? 1 : 0;
1518: N = length(V);
1519: W = vars(B);
1520: PV = setminus(W,V);
1521: NP = length(PV);
1522: W = append(V,PV);
1523: if ( Elim && PV != [] ) Ord = [[0,N],[0,NP]];
1524: else Ord = 0;
1525: if ( Mod )
1526: B = nd_f4(B,W,Mod,Ord);
1527: else
1528: B = nd_gr_trace(B,W,1,GBCheck,Ord);
1529: P = []; NP = [[B,vector(N+1)]];
1530: for ( I = length(V)-1; I >= 0; I-- ) {
1531: NP1 = [];
1532: for ( T = NP; T != []; T = cdr(T) ) {
1533: L = partial_decomp0(car(T),V,PV,Ord,I,Mod);
1534: P = append(L[0],P);
1535: NP1 = append(L[1],NP1);
1536: }
1537: NP = NP1;
1538: }
1539: return [P,NP];
1540: }
1541:
1542: def partial_decomp0(GD,V,PV,Ord,I,Mod)
1543: {
1544: G = GD[0]; D = GD[1];
1545: N = length(V); PN = length(PV);
1546: W = append(V,PV);
1547: VI = V[I];
1548: M = gen_minipoly(G,V,PV,Ord,VI,Mod);
1549: M = ppart(M,VI,Mod);
1550: if ( Mod )
1551: MF = modfctr(M,Mod);
1552: else
1553: MF = fctr(M);
1554: if ( length(MF) == 2 && MF[1][1] == 1 ) {
1555: D1 = D*1;
1556: D1[I] = M;
1557: Gelim = elim_gb(G,V,PV,Mod,Ord);
1558: D1[N] = LD = ldim(Gelim,V);
1559: GD1 = [Gelim,D1];
1560: for ( J = 0; J < N; J++ )
1561: if ( D1[J] && deg(D1[J],V[J]) == LD )
1562: return [[GD1],[]];
1563: return [[],[GD1]];
1564: }
1565: P = []; NP = [];
1566: GI = elim_gb(G,V,PV,Mod,Ord);
1567: for ( T = cdr(MF); T != []; T = cdr(T) ) {
1568: Mt = car(car(T));
1569: D1 = D*1;
1570: D1[I] = Mt;
1571: GIt = map(gen_nf,GI,[Mt],V,Ord,Mod);
1572: G1 = cons(Mt,GIt);
1573: Gelim = elim_gb(G1,V,PV,Mod,Ord);
1574: D1[N] = LD = ldim(Gelim,V);
1575: for ( J = 0; J < N; J++ )
1576: if ( D1[J] && deg(D1[J],V[J]) == LD ) break;
1577: if ( J < N )
1578: P = cons([Gelim,D1],P);
1579: else
1580: NP = cons([Gelim,D1],NP);
1581: }
1582: return [P,NP];
1583: }
1584:
1585: /* prime/primary components over rational function field */
1586:
1587: def zprimacomp(G,V) {
1588: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1589: L = zprimadec(G,V,0|mod=Mod);
1590: R = [];
1591: dp_ord(0);
1592: for ( T = L; T != []; T = cdr(T) ) {
1593: S = car(T);
1594: UQ = contraction(S[0],V|mod=Mod);
1595: UP = contraction(S[1],V|mod=Mod);
1596: R = cons([UQ,UP],R);
1597: }
1598: return R;
1599: }
1600:
1601: def zprimecomp(G,V,Indep) {
1602: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1603: W = maxindep(G,V,0|mod=Mod);
1604: V0 = setminus(V,W);
1605: V1 = append(V0,W);
1606: #if 0
1607: O1 = [[0,length(V0)],[0,length(W)]];
1608: G1 = fast_gb(G,V1,Mod,O1);
1609: dp_ord(0);
1610: #else
1611: G1 = G;
1612: #endif
1613: PD = zprimedec(G1,V0,Mod);
1614: dp_ord(0);
1615: R = [];
1616: for ( T = PD; T != []; T = cdr(T) ) {
1617: U = contraction(car(T),V0|mod=Mod);
1618: U = nd_gr(U,V,Mod,0);
1.7 noro 1619: R = cons(Indep?[U,W]:U,R);
1.1 noro 1620: }
1.7 noro 1621: return R;
1.1 noro 1622: }
1623:
1624: def fast_gb(B,V,Mod,Ord)
1625: {
1626: if ( type(Block=getopt(gbblock)) == -1 ) Block = 0;
1627: if ( type(NoRA=getopt(nora)) == -1 ) NoRA = 0;
1628: if ( type(Trace=getopt(trace)) == -1 ) Trace = 0;
1629: if ( Mod )
1630: G = nd_f4(B,V,Mod,Ord|nora=NoRA);
1631: else if ( F4 )
1632: G = map(ptozp,f4_chrem(B,V,Ord));
1633: else if ( Trace ) {
1634: if ( Block )
1635: G = nd_gr_trace(B,V,1,1,Ord|nora=NoRA,gbblock=Block);
1636: else
1637: G = nd_gr_trace(B,V,1,1,Ord|nora=NoRA);
1638: } else {
1639: if ( Block )
1640: G = nd_gr(B,V,0,Ord|nora=NoRA,gbblock=Block);
1641: else
1642: G = nd_gr(B,V,0,Ord|nora=NoRA);
1643: }
1644: return G;
1645: }
1646:
1647: def incremental_gb(A,V,Ord)
1648: {
1649: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1650: if ( type(Block=getopt(gbblock)) == -1 ) Block = 0;
1651: if ( Mod ) {
1652: if ( Block )
1653: G = nd_gr(A,V,Mod,Ord|gbblock=Block);
1654: else
1655: G = nd_gr(A,V,Mod,Ord);
1656: } else if ( Procs ) {
1657: Arg0 = ["nd_gr",A,V,0,Ord];
1658: Arg1 = ["nd_gr_trace",A,V,1,GBCheck,Ord];
1659: G = competitive_exec(Procs,Arg0,Arg1);
1660: } else if ( Block )
1661: G = nd_gr(A,V,0,Ord|gbblock=Block);
1662: else
1663: G = nd_gr(A,V,0,Ord);
1664: return G;
1665: }
1666:
1667: def elim_gb(G,V,PV,Mod,Ord)
1668: {
1669: N = length(V); PN = length(PV);
1670: O1 = [[0,N],[0,PN]];
1671: if ( Ord == O1 )
1672: Ord = Ord[0][0];
1673: if ( Mod ) /* XXX */ {
1674: for ( T = G, H = []; T != []; T = cdr(T) )
1675: if ( car(T) ) H = cons(car(T),H);
1676: G = reverse(H);
1677: G = dp_gr_mod_main(G,V,0,Mod,Ord);
1678: } else if ( EProcs ) {
1679: #if 1
1680: Arg0 = ["dp_gr_main",G,V,0,0,Ord];
1681: #else
1682: Arg0 = ["nd_gr",G,V,0,Ord];
1683: #endif
1684: Arg1 = ["noro_pd.nd_gr_rat",G,V,PV,O1,Ord];
1685: G = competitive_exec(EProcs,Arg0,Arg1);
1686: } else if ( GBRat ) {
1687: G1 = nd_gr(G,append(V,PV),0,O1);
1.8 noro 1688: if ( GBRat == 1 )
1689: G1 = nd_gr_postproc(G1,V,0,Ord,0|nora=1);
1.1 noro 1690: return G1;
1691: } else
1692: #if 1
1.2 noro 1693: #if 0
1.1 noro 1694: G = dp_gr_main(G,V,0,0,Ord);
1695: #else
1696: G = nd_gr_trace(G,V,1,1,Ord);
1697: #endif
1698: #else
1699: G = nd_gr(G,V,0,Ord);
1700: #endif
1701: return G;
1702: }
1703:
1704: def ldim(G,V)
1705: {
1706: O0 = dp_ord(); dp_ord(0);
1707: D = length(dp_mbase(map(dp_ptod,G,V)));
1708: dp_ord(O0);
1709: return D;
1710: }
1711:
1712: /* over Q only */
1713:
1714: def make_mod_subst(GD,V,PV,HC)
1715: {
1716: N = length(V);
1717: PN = length(PV);
1718: G = GD[0]; D = GD[1];
1719: for ( I = 0; ; I = (I+1)%100 ) {
1720: Mod = lprime(I);
1721: S = [];
1722: for ( J = PN-1; J >= 0; J-- )
1723: S = append([PV[J],random()%Mod],S);
1724: for ( T = HC; T != []; T = cdr(T) )
1725: if ( !(subst(car(T),S)%Mod) ) break;
1726: if ( T != [] ) continue;
1727: for ( J = 0; J < N; J++ ) {
1728: M = subst(D[J],S);
1729: F = modsqfr(M,Mod);
1730: if ( length(F) != 2 || F[1][1] != 1 ) break;
1731: }
1732: if ( J < N ) continue;
1733: G0 = map(subst,G,S);
1734: return [G0,Mod];
1735: }
1736: }
1737:
1738: def rsgn()
1739: {
1740: return random()%2 ? 1 : -1;
1741: }
1742:
1743: def find_npos(GD,V,PV,Mod)
1744: {
1745: N = length(V); PN = length(PV);
1746: G = GD[0]; D = GD[1]; LD = D[N];
1.5 noro 1747: DH = map(dp_dtop,map(dp_ht,map(dp_ptod,D,V)),V);
1.1 noro 1748: Ord0 = dp_ord(); dp_ord(0);
1749: HC = map(dp_hc,map(dp_ptod,G,V));
1750: dp_ord(Ord0);
1751: if ( !Mod ) {
1752: W = append(V,PV);
1753: G1 = nd_gr_trace(G,W,1,GBCheck,[[0,N],[0,PN]]);
1754: L = make_mod_subst([G1,D],V,PV,HC);
1755: return find_npos([L[0],D],V,[],L[1]);
1756: }
1757: N = length(V);
1758: NV = ttttt;
1759: for ( B = 2; ; B++ ) {
1760: for ( J = N-2; J >= 0; J-- ) {
1.5 noro 1761: for ( U = 0, K = J; K < N; K++ ) {
1762: if ( DH[K] == V[K] ) continue;
1.1 noro 1763: U += rsgn()*((random()%B+1))*V[K];
1.5 noro 1764: }
1.6 noro 1765: #if 0
1.1 noro 1766: M = minipolym(G,V,0,U,NV,Mod);
1.6 noro 1767: #else
1768: M = gen_minipoly(cons(NV-U,G),cons(NV,V),PV,0,NV,Mod);
1769: #endif
1.1 noro 1770: if ( deg(M,NV) == LD ) return U;
1771: }
1772: }
1773: }
1774:
1775: def gen_minipoly(G,V,PV,Ord,VI,Mod)
1776: {
1.6 noro 1777: O0 = dp_ord();
1.1 noro 1778: if ( PV == [] ) {
1779: NV = sssss;
1780: if ( Mod )
1781: M = minipolym(G,V,Ord,VI,NV,Mod);
1782: else
1783: M = minipoly(G,V,Ord,VI,NV);
1.6 noro 1784: dp_ord(O0);
1.1 noro 1785: return subst(M,NV,VI);
1786: }
1787: W = setminus(V,[VI]);
1788: PV1 = cons(VI,PV);
1789: #if 0
1790: while ( 1 ) {
1791: V1 = append(W,PV1);
1792: if ( Mod )
1793: G = nd_gr(G,V1,Mod,[[0,1],[0,length(V1)-1]]|nora=1);
1794: else
1795: G = nd_gr_trace(G,V1,1,GBCheck,[[0,1],[0,length(V1)-1]]|nora=1);
1796: if ( W == [] ) break;
1797: else {
1798: W = cdr(W);
1799: G = elimination(G,cdr(V1));
1800: }
1801: }
1.8 noro 1802: #elif 1
1.1 noro 1803: if ( Mod ) {
1804: V1 = append(W,PV1);
1805: G = nd_gr(G,V1,Mod,[[0,length(W)],[0,length(PV1)]]);
1806: G = elimination(G,PV1);
1807: } else {
1808: PV2 = setminus(PV1,[PV1[length(PV1)-1]]);
1809: V2 = append(W,PV2);
1810: G = nd_gr_trace(G,V2,1,GBCheck,[[0,length(W)],[0,length(PV2)]]|nora=1);
1811: G = elimination(G,PV1);
1812: }
1813: #else
1814: V1 = append(W,PV1);
1815: if ( Mod )
1816: G = nd_gr(G,V1,Mod,[[0,length(W)],[0,length(PV1)]]|nora=1);
1817: else
1818: G = nd_gr_trace(G,V1,1,GBCheck,[[0,length(W)],[0,length(PV1)]]|nora=1);
1819: G = elimination(G,PV1);
1820: #endif
1821: if ( Mod )
1822: G = nd_gr(G,PV1,Mod,[[0,1],[0,length(PV)]]|nora=1);
1823: else
1824: G = nd_gr_trace(G,PV1,1,GBCheck,[[0,1],[0,length(PV)]]|nora=1);
1825: for ( M = car(G), T = cdr(G); T != []; T = cdr(T) )
1826: if ( deg(car(T),VI) < deg(M,VI) ) M = car(T);
1.6 noro 1827: dp_ord(O0);
1.1 noro 1828: return M;
1829: }
1830:
1831: def indepset(V,H)
1832: {
1833: if ( H == [] ) return V;
1834: N = -1;
1835: for ( T = V; T != []; T = cdr(T) ) {
1836: VI = car(T);
1837: HI = [];
1838: for ( S = H; S != []; S = cdr(S) )
1839: if ( !tdiv(car(S),VI) ) HI = cons(car(S),HI);
1840: RI = indepset(setminus(V,[VI]),HI);
1841: if ( length(RI) > N ) {
1842: R = RI; N = length(RI);
1843: }
1844: }
1845: return R;
1846: }
1847:
1848: def maxindep(B,V,O)
1849: {
1850: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1851: G = fast_gb(B,V,Mod,O);
1852: Old = dp_ord();
1853: dp_ord(O);
1854: H = map(dp_dtop,map(dp_ht,map(dp_ptod,G,V)),V);
1855: H = map(sq,H,0);
1856: H = nd_gr(H,V,0,0);
1857: H = monodec0(H,V);
1858: N = length(V);
1859: Dep = [];
1860: for ( T = H, Len = N+1; T != []; T = cdr(T) ) {
1861: M = length(car(T));
1862: if ( M < Len ) {
1863: Dep = [car(T)];
1864: Len = M;
1865: } else if ( M == Len )
1866: Dep = cons(car(T),Dep);
1867: }
1868: R = setminus(V,Dep[0]);
1869: dp_ord(Old);
1870: return R;
1871: }
1872:
1.7 noro 1873: def maxindep2(B,V,O)
1874: {
1875: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1876: G = fast_gb(B,V,Mod,O);
1877: Old = dp_ord();
1878: dp_ord(O);
1879: H = map(dp_dtop,map(dp_ht,map(dp_ptod,G,V)),V);
1880: H = map(sq,H,0);
1881: H = nd_gr(H,V,0,0);
1882: H = monodec0(H,V);
1883: N = length(V);
1884: Dep = [];
1885: for ( T = H, Len = N+1; T != []; T = cdr(T) ) {
1886: M = length(car(T));
1887: if ( M < Len ) {
1888: Dep = [car(T)];
1889: Len = M;
1890: } else if ( M == Len )
1891: Dep = cons(car(T),Dep);
1892: }
1893: R = [];
1894: for ( T = Dep; T != []; T = cdr(T) )
1895: R = cons(setminus(V,car(T)),R);
1896: dp_ord(Old);
1897: return reverse(R);
1898: }
1899:
1900:
1.1 noro 1901: /* ideal operations */
1902: def contraction(G,V)
1903: {
1.8 noro 1904: if ( type(AllV=getopt(allv)) == -1 ) AllV = 0;
1.1 noro 1905: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1.8 noro 1906:
1907: if ( RepColon ) return contraction_m(G,V|allv=AllV,mod=Mod);
1908:
1.1 noro 1909: C = [];
1910: for ( T = G; T != []; T = cdr(T) ) {
1911: C1 = dp_hc(dp_ptod(car(T),V));
1912: S = gen_fctr(C1,Mod);
1913: for ( S = cdr(S); S != []; S = cdr(S) )
1914: if ( !member(S[0][0],C) ) C = cons(S[0][0],C);
1915: }
1916: W = vars(G);
1917: PV = setminus(W,V);
1.8 noro 1918: if ( AllV ) W = AllV;
1919: else W = append(V,PV);
1.1 noro 1920: NV = ttttt;
1.8 noro 1921: if ( SuccSat ) {
1922: W1 = cons(NV,W);
1923: O1 = [[0,1],[0,length(W)]];
1924: Block = [];
1925: for ( T = C; T != []; T = cdr(T) ) {
1926: G1 = nd_gr(append(G,[NV*car(T)-1]),W1,Mod,O1|gbblock=Block);
1927: G = elimination(G1,W);
1928: Block = [[0,length(G)]];
1929: }
1930: } else {
1931: for ( T = C, S = 1; T != []; T = cdr(T) )
1932: S *= car(T);
1933: G = saturation([G,NV],S,W|mod=Mod);
1934: }
1.1 noro 1935: return G;
1936: }
1937:
1.8 noro 1938: def contraction_m(G,V)
1939: {
1940: if ( type(AllV=getopt(allv)) == -1 ) AllV = 0;
1941: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1942: C = [];
1943: for ( T = G; T != []; T = cdr(T) ) {
1944: C1 = dp_hc(dp_ptod(car(T),V));
1945: S = gen_fctr(C1,Mod);
1946: for ( S = cdr(S); S != []; S = cdr(S) )
1947: if ( !member(S[0][0],C) ) C = cons(S[0][0],C);
1948: }
1949: W = vars(G);
1950: PV = setminus(W,V);
1951: if ( AllV ) W = AllV;
1952: else W = append(V,PV);
1953: H = H0 = G;
1954: while ( 1 ) {
1955: for ( T = C; T != []; T = cdr(T) )
1956: H = map(sdiv,ideal_intersection_m([car(T)],H,W,0),car(T));
1957: H = nd_gr(H,W,0,0);
1958: if ( gb_comp(H0,H) ) break;
1959: else H0 = H;
1960: }
1961: return H;
1962: }
1963:
1.1 noro 1964: def ideal_list_intersection(L,V,Ord)
1965: {
1966: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1.4 noro 1967: if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0;
1.1 noro 1968: N = length(L);
1969: if ( N == 0 ) return [1];
1.4 noro 1970: if ( N == 1 )
1971: return IsGB ? L[0] : fast_gb(L[0],V,Mod,Ord);
1.8 noro 1972: else {
1.4 noro 1973: for ( I = 0, T = [1]; I < N; I++ )
1974: T = ideal_intersection_m(T,L[I],V,Ord|mod=Mod);
1975: T = nd_gr(T,V,Mod,Ord);
1976: return T;
1.1 noro 1977: }
1978: }
1979:
1.4 noro 1980: def call_ideal_list_intersection(L,V,Mod,Ord,IsGB)
1.1 noro 1981: {
1.4 noro 1982: return ideal_list_intersection(L,V,Ord|mod=Mod,isgb=IsGB);
1.1 noro 1983: }
1984:
1985: def ideal_intersection(A,B,V,Ord)
1986: {
1987: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1988: if ( type(Block=getopt(gbblock)) == -1 ) Block = 0;
1989: T = ttttt;
1990: if ( Mod ) {
1991: if ( Block )
1992: G = nd_gr(append(vtol(ltov(A)*T),vtol(ltov(B)*(1-T))),
1993: cons(T,V),Mod,[[0,1],[Ord,length(V)]]|gbblock=Block,nora=0);
1994: else
1995: G = nd_gr(append(vtol(ltov(A)*T),vtol(ltov(B)*(1-T))),
1996: cons(T,V),Mod,[[0,1],[Ord,length(V)]]|nora=0);
1997: } else
1998: if ( Procs ) {
1999: Arg0 = ["nd_gr",
2000: append(vtol(ltov(A)*T),vtol(ltov(B)*(1-T))),
2001: cons(T,V),0,[[0,1],[Ord,length(V)]]];
2002: Arg1 = ["nd_gr_trace",
2003: append(vtol(ltov(A)*T),vtol(ltov(B)*(1-T))),
2004: cons(T,V),1,GBCheck,[[0,1],[Ord,length(V)]]];
2005: G = competitive_exec(Procs,Arg0,Arg1);
2006: } else {
2007: if ( Block )
2008: G = nd_gr(append(vtol(ltov(A)*T),vtol(ltov(B)*(1-T))),
2009: cons(T,V),0,[[0,1],[Ord,length(V)]]|gbblock=Block,nora=0);
2010: else
2011: G = nd_gr(append(vtol(ltov(A)*T),vtol(ltov(B)*(1-T))),
2012: cons(T,V),0,[[0,1],[Ord,length(V)]]|nora=0);
2013: }
2014: G0 = elimination(G,V);
2015: if ( 0 && !Procs )
2016: G0 = nd_gr_postproc(G0,V,Mod,Ord,0);
2017: return G0;
2018: }
2019:
1.4 noro 2020:
2021: def aa(A) { return [A,A]; }
2022:
2023: def ideal_intersection_m(A,B,V,Ord)
2024: {
2025: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2026:
2027: dp_ord(Ord);
2028: DA = map(dp_ptod,A,V); DB = ltov(map(dp_ptod,B,V));
2029: if ( Mod ) {
2030: DA = map(dp_mod,DA,Mod,[]); DB = map(dp_mod,DB,Mod,[]);
2031: setmod(Mod);
2032: }
2033: N = length(B);
2034: for ( Ind = [], I = N-1; I >= 0; I-- ) Ind = cons(I,Ind);
2035: for ( T = DA, C = []; T != []; T = cdr(T) ) {
2036: L = Mod?dp_true_nf_mod(Ind,car(T),DB,1,Mod):dp_true_nf(Ind,car(T),DB,1);
2037: R = dp_dtop(L[0],V); Q = dp_dtop(car(T)*L[1]-L[0],V);
2038: C = cons([R,-Q],C);
2039: }
2040: G = nd_gr(append(C,map(aa,B)),V,Mod,[1,Ord]|intersect=1);
2041: G = map(second,G);
2042: return G;
2043: }
2044:
1.1 noro 2045: /* returns GB if F notin rad(G) */
2046:
2047: def radical_membership(F,G,V) {
2048: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2049: if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0;
1.4 noro 2050: if ( type(L=getopt(dg)) == -1 ) L = 0;
1.7 noro 2051: if ( type(Sat=getopt(sat)) == -1 ) Sat = 0;
1.4 noro 2052: dp_ord(0);
2053: if ( L ) { DG = L[0]; Ind = L[1]; }
2054: else {
2055: DG = ltov(map(dp_ptod,G,V));
2056: if ( Mod ) DG = map(dp_mod,DG,Mod,[]);
2057: for ( Ind = [], I = length(G)-1; I >= 0; I-- ) Ind = cons(I,Ind);
2058: }
2059: DF = dp_ptod(F,V); DFI = dp_ptod(1,V);
2060: if ( Mod ) {
2061: DF = dp_mod(DF,Mod,[]); DFI = dp_mod(DFI,Mod,[]);
2062: setmod(Mod);
2063: }
2064: for ( I = 0; I < 3; I++ ) {
2065: DFI = Mod?dp_nf_mod(Ind,DF*DFI,DG,0,Mod):dp_nf(Ind,DF*DFI,DG,0);
2066: if ( !DFI ) return 0;
2067: }
1.1 noro 2068: NV = ttttt;
2069: if ( IsGB )
2070: T = nd_gr(append(G,[NV*F-1]),cons(NV,V),Mod,0
2071: |gbblock=[[0,length(G)]]);
2072: else
2073: T = nd_gr(append(G,[NV*F-1]),cons(NV,V),Mod,0);
1.7 noro 2074: if ( type(car(T)) == 1 ) return 0;
2075: else if ( Sat ) {
2076: G1 = fast_gb(T,cons(NV,V),Mod,[[0,1],[0,length(V)]]);
2077: G0 = elimination(G1,V);
2078: return G0;
2079: } else return [T,NV];
1.1 noro 2080: }
2081:
1.8 noro 2082: def radical_membership_sat(F,G,V) {
2083: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2084: if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0;
2085: if ( type(L=getopt(dg)) == -1 ) L = 0;
2086: dp_ord(0);
2087: if ( L ) { DG = L[0]; Ind = L[1]; }
2088: else {
2089: DG = ltov(map(dp_ptod,G,V));
2090: if ( Mod ) DG = map(dp_mod,DG,Mod,[]);
2091: for ( Ind = [], I = length(G)-1; I >= 0; I-- ) Ind = cons(I,Ind);
2092: }
2093: DF = dp_ptod(F,V); DFI = dp_ptod(1,V);
2094: if ( Mod ) {
2095: DF = dp_mod(DF,Mod,[]); DFI = dp_mod(DFI,Mod,[]);
2096: setmod(Mod);
2097: }
2098: for ( I = 0; I < 3; I++ ) {
2099: DFI = Mod?dp_nf_mod(Ind,DF*DFI,DG,0,Mod):dp_nf(Ind,DF*DFI,DG,0);
2100: if ( !DFI ) return 0;
2101: }
2102: NV = ttttt;
2103: if ( IsGB )
2104: T = nd_gr(append(G,[NV*F-1]),cons(NV,V),Mod,[[0,1],[0,length(V)]]
2105: |gbblock=[[0,length(G)]]);
2106: else
2107: T = nd_gr(append(G,[NV*F-1]),cons(NV,V),Mod,[[0,1],[0,length(V)]]);
2108: if ( type(car(T)) == 1 ) return 0;
2109: G0 = elimination(T,V);
2110: return G0;
2111: }
2112:
1.1 noro 2113: def modular_radical_membership(F,G,V) {
2114: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2115: if ( Mod )
2116: return radical_membership(F,G,V|mod=Mod);
2117:
2118: F = gen_nf(F,G,V,0,0);
2119: if ( !F ) return 0;
2120: NV = ttttt;
2121: for ( J = 0; ; J++ ) {
2122: Mod = lprime(J);
2123: H = map(dp_hc,map(dp_ptod,G,V));
2124: for ( ; H != []; H = cdr(H) ) if ( !(car(H)%Mod) ) break;
2125: if ( H != [] ) continue;
2126:
2127: T = nd_f4(cons(NV*F-1,G),cons(NV,V),Mod,0);
2128: if ( type(car(T)) == 1 ) {
2129: I = radical_membership_rep(F,G,V,-1,0,Mod);
2130: I1 = radical_membership_rep(F,G,V,I,0,0);
2131: if ( I1 > 0 ) return 0;
2132: }
2133: return radical_membership(F,G,V);
2134: }
2135: }
2136:
2137: def radical_membership_rep(F,G,V,Max,Ord,Mod) {
2138: Ft = F;
2139: I = 1;
2140: while ( Max < 0 || I <= Max ) {
2141: Ft = gen_nf(Ft,G,V,Ord,Mod);
2142: if ( !Ft ) return I;
2143: Ft *= F;
2144: I++;
2145: }
2146: return -1;
2147: }
2148:
2149: def ideal_product(A,B,V)
2150: {
2151: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2152: dp_ord(0);
2153: DA = map(dp_ptod,A,V);
2154: DB = map(dp_ptod,B,V);
2155: DegA = map(dp_td,DA);
2156: DegB = map(dp_td,DB);
2157: for ( PA = [], T = A, DT = DegA; T != []; T = cdr(T), DT = cdr(DT) )
2158: PA = cons([car(T),car(DT)],PA);
2159: PA = reverse(PA);
2160: for ( PB = [], T = B, DT = DegB; T != []; T = cdr(T), DT = cdr(DT) )
2161: PB = cons([car(T),car(DT)],PB);
2162: PB = reverse(PB);
2163: R = [];
2164: for ( T = PA; T != []; T = cdr(T) )
2165: for ( S = PB; S != []; S = cdr(S) )
2166: R = cons([car(T)[0]*car(S)[0],car(T)[1]+car(S)[1]],R);
1.9 ! ohara 2167: T = qsort(R,noro_pd.comp_by_second);
1.1 noro 2168: T = map(first,T);
2169: Len = length(A)>length(B)?length(A):length(B);
2170: Len *= 2;
2171: L = sep_list(T,Len); B0 = L[0]; B1 = L[1];
2172: R = fast_gb(B0,V,Mod,0);
2173: while ( B1 != [] ) {
2174: print(length(B1));
2175: L = sep_list(B1,Len);
2176: B0 = L[0]; B1 = L[1];
2177: R = fast_gb(append(R,B0),V,Mod,0|gbblock=[[0,length(R)]],nora=1);
2178: }
2179: return R;
2180: }
2181:
2182: def saturation(GNV,F,V)
2183: {
2184: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2185: G = GNV[0]; NV = GNV[1];
2186: if ( Mod )
2187: G1 = nd_gr(cons(NV*F-1,G),cons(NV,V),Mod,[[0,1],[0,length(V)]]);
2188: else if ( Procs ) {
2189: Arg0 = ["nd_gr_trace",
2190: cons(NV*F-1,G),cons(NV,V),0,GBCheck,[[0,1],[0,length(V)]]];
2191: Arg1 = ["nd_gr_trace",
2192: cons(NV*F-1,G),cons(NV,V),1,GBCheck,[[0,1],[0,length(V)]]];
2193: G1 = competitive_exec(Procs,Arg0,Arg1);
2194: } else
2195: G1 = nd_gr(cons(NV*F-1,G),cons(NV,V),0,[[0,1],[0,length(V)]]);
2196: return elimination(G1,V);
2197: }
2198:
2199: def sat(G,F,V)
2200: {
2201: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2202: if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0;
2203: NV = ttttt;
2204: if ( Mod )
2205: G1 = nd_gr(cons(NV*F-1,G),cons(NV,V),Mod,[[0,1],[0,length(V)]]);
2206: else if ( Procs ) {
2207: Arg0 = ["nd_gr_trace",
2208: cons(NV*F-1,G),cons(NV,V),0,GBCheck,[[0,1],[0,length(V)]]];
2209: Arg1 = ["nd_gr_trace",
2210: cons(NV*F-1,G),cons(NV,V),1,GBCheck,[[0,1],[0,length(V)]]];
2211: G1 = competitive_exec(Procs,Arg0,Arg1);
2212: } else {
2213: B1 = append(G,[NV*F-1]);
2214: V1 = cons(NV,V);
2215: Ord1 = [[0,1],[0,length(V)]];
2216: if ( IsGB )
2217: G1 = nd_gr(B1,V1,0,Ord1|gbblock=[[0,length(G)]]);
2218: else
2219: G1 = nd_gr(B1,V1,0,Ord1);
2220: }
2221: return elimination(G1,V);
2222: }
2223:
1.4 noro 2224: def isat(B,S,V)
2225: {
2226: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2227: if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0;
2228: F = cdr(fctr(S));
2229: R = B;
2230: for ( T = F; T != []; T = cdr(T) )
2231: R = sat(R,car(T)[0],V|mod=Mod,isgb=IsGB);
2232: return R;
2233: }
2234:
1.1 noro 2235: def satind(G,F,V)
2236: {
2237: if ( type(Block=getopt(gbblock)) == -1 ) Block = 0;
2238: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2239: NV = ttttt;
2240: N = length(V);
2241: B = append(G,[NV*F-1]);
2242: V1 = cons(NV,V);
2243: Ord1 = [[0,1],[0,N]];
2244: if ( Mod )
2245: if ( Block )
2246: D = nd_gr(B,V1,Mod,Ord1|nora=1,gentrace=1,gbblock=Block);
2247: else
2248: D = nd_gr(B,V1,Mod,Ord1|nora=1,gentrace=1);
2249: else
2250: if ( Block )
2251: D = nd_gr_trace(B,V1,SatHomo,GBCheck,Ord1
2252: |nora=1,gentrace=1,gbblock=Block);
2253: else
2254: D = nd_gr_trace(B,V1,SatHomo,GBCheck,Ord1
2255: |nora=1,gentrace=1);
2256: G1 = D[0];
2257: Len = length(G1);
2258: Deg = compute_deg(B,V1,NV,D);
2259: D1 = 0;
2260: R = [];
2261: M = length(B);
2262: for ( I = 0; I < Len; I++ ) {
2263: if ( !member(NV,vars(G1[I])) ) {
2264: for ( J = 1; J < M; J++ )
2265: D1 = MAX(D1,Deg[I][J]);
2266: R = cons(G1[I],R);
2267: }
2268: }
2269: return [reverse(R),D1];
2270: }
2271:
2272: def sat_ind(G,F,V)
2273: {
2274: if ( type(Ord=getopt(ord)) == -1 ) Ord = 0;
2275: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2276: NV = ttttt;
2277: F = gen_nf(F,G,V,Ord,Mod);
2278: for ( I = 0, GI = G; ; I++ ) {
2279: G1 = colon(GI,F,V|mod=Mod,ord=Ord);
2280: if ( ideal_inclusion(G1,GI,V,Ord|mod=Mod) ) {
2281: return [GI,I];
2282: }
2283: else GI = G1;
2284: }
2285: }
2286:
2287: def colon(G,F,V)
2288: {
2289: if ( type(Ord=getopt(ord)) == -1 ) Ord = 0;
2290: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2291: if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0;
2292: F = gen_nf(F,G,V,Ord,Mod);
2293: if ( !F ) return [1];
2294: if ( IsGB )
2295: T = ideal_intersection(G,[F],V,Ord|gbblock=[[0,length(G)]],mod=Mod);
2296: else
2297: T = ideal_intersection(G,[F],V,Ord|mod=Mod);
1.4 noro 2298: Gen = Mod?map(sdivm,T,F,Mod):map(ptozp,map(sdiv,T,F));
2299: return nd_gr(Gen,V,Mod,Ord);
1.1 noro 2300: }
2301:
2302: #if 1
2303: def ideal_colon(G,F,V)
2304: {
2305: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2306: G = nd_gr(G,V,Mod,0);
2307: C = [1];
2308: TV = ttttt;
1.9 ! ohara 2309: F = qsort(F,noro_pd.comp_tdeg);
1.1 noro 2310: for ( T = F; T != []; T = cdr(T) ) {
2311: S = colon(G,car(T),V|isgb=1,mod=Mod);
2312: if ( type(S[0])!= 1 ) {
2313: C = nd_gr(append(vtol(ltov(C)*TV),vtol(ltov(S)*(1-TV))),
2314: cons(TV,V),Mod,[[0,1],[Ord,length(V)]]|gbblock=[[0,length(C)]]);
2315: C = elimination(C,V);
2316: }
2317: }
2318: return C;
2319: }
2320: #else
2321: def ideal_colon(G,F,V)
2322: {
2323: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2324: G = nd_gr(G,V,Mod,0);
2325: for ( T = F, L = []; T != []; T = cdr(T) ) {
2326: C = colon(G,car(T),V|isgb=1,mod=Mod);
2327: if ( type(C[0]) != 1 ) L = cons(C,L);
2328: }
2329: L = reverse(L);
2330: return ideal_list_intersection(L,V,0|mod=Mod);
2331: }
2332:
2333: #endif
2334:
2335: def member(A,L)
2336: {
2337: for ( ; L != []; L = cdr(L) )
2338: if ( car(L) == A ) return 1;
2339: return 0;
2340: }
2341:
2342: def mingen(B,V) {
2343: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2344: Data = nd_gr(B,V,Mod,O|gentrace=1,gensyz=1);
1.4 noro 2345: G = Data[0]; STrace = Data[6];
1.1 noro 2346: N = length(G);
1.4 noro 2347: S = compute_gbsyz(N,V,STrace,Mod);
2348: for ( T = S, R = []; T != []; T = cdr(T) ) {
2349: for ( A = car(T); A1 = dp_rest(A); A = A1);
2350: if ( type(dp_hc(A)) ==1 ) R = cons(dp_etov(A)[0],R);
2351: }
2352: for ( I = 0, U = []; I < N; I++ ) if ( !member(I,R) ) U = cons(G[I],U);
1.1 noro 2353: return U;
2354: }
2355:
1.4 noro 2356: def compute_gbsyz(N,V,Trace,Mod)
1.1 noro 2357: {
2358: P = vector(N);
1.4 noro 2359: for ( I = 0; I < N; I++ ) P[I] = dp_ptod(x^I,[x]);
2360: for ( U = [], T = Trace; T != []; T = cdr(T) ) {
1.1 noro 2361: Ti = car(T);
2362: if ( Ti[0] != -1 ) error("Input is not a GB");
1.4 noro 2363: R = recompute_trace(Ti[1],P,V,Mod);
2364: U = cons(R,U);
1.1 noro 2365: }
2366: return reverse(U);
2367: }
2368:
1.4 noro 2369: def recompute_trace(Ti,P,V,Mod)
1.1 noro 2370: {
2371: for ( Num = 0, Den = 1; Ti != []; Ti = cdr(Ti) ) {
1.4 noro 2372: Sj = car(Ti); Dj = Sj[0]; Ij =Sj[1]; Mj = dp_dtop(Sj[2],V); Cj = Sj[3];
1.1 noro 2373: /* Num/Den <- (Dj*Num+Den*Mj*P[Ij])/(Den*Cj) */
1.4 noro 2374: if ( Dj ) Num = (Dj*Num+Den*Mj*P[Ij]);
1.1 noro 2375: Den *= Cj;
2376: }
1.4 noro 2377: return Num;
1.1 noro 2378: }
2379:
2380: def ideal_sat(G,F,V)
2381: {
2382: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2383: G = nd_gr(G,V,Mod,0);
2384: for ( T = F, L = []; T != []; T = cdr(T) )
2385: L = cons(sat(G,car(T),V|mod=Mod),L);
2386: L = reverse(L);
2387: return ideal_list_intersection(L,V,0|mod=Mod);
2388: }
2389:
2390: def ideal_inclusion(F,G,V,O)
2391: {
2392: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2393: for ( T = F; T != []; T = cdr(T) )
2394: if ( gen_nf(car(T),G,V,O,Mod) ) return 0;
2395: return 1;
2396: }
2397:
2398: /* remove redundant components */
2399:
2400: def qd_simp_comp(QP,V)
2401: {
2402: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2403: R = ltov(QP);
2404: N = length(R);
2405: for ( I = 0; I < N; I++ ) {
2406: if ( R[I] ) {
2407: QI = R[I][0]; PI = R[I][1];
2408: for ( J = I+1; J < N; J++ )
2409: if ( R[J] && gen_gb_comp(PI,R[J][1],Mod) ) {
2410: QI = ideal_intersection(QI,R[J][0],V,0|mod=Mod);
2411: R[J] = 0;
2412: }
2413: R[I] = [QI,PI];
2414: }
2415: }
2416: for ( I = N-1, S = []; I >= 0; I-- )
2417: if ( R[I] ) S = cons(R[I],S);
2418: return S;
2419: }
2420:
2421: def qd_remove_redundant_comp(G,Iso,Emb,V,Ord)
2422: {
2423: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2424: IsoInt = ideal_list_intersection(map(first,Iso),V,Ord|mod=Mod);
2425: Emb = qd_simp_comp(Emb,V|mod=Mod);
2426: Emb = reverse(qsort(Emb));
2427: A = ltov(Emb); N = length(A);
2428: Pre = IsoInt; Post = vector(N+1);
2429: for ( Post[N] = IsoInt, I = N-1; I >= 1; I-- )
2430: Post[I] = ideal_intersection(Post[I+1],A[I][0],V,Ord|mod=Mod);
2431: for ( I = 0; I < N; I++ ) {
2432: print(".",2);
2433: Int = ideal_intersection(Pre,Post[I+1],V,Ord|mod=Mod);
2434: if ( gen_gb_comp(Int,G,Mod) ) A[I] = 0;
2435: else
2436: Pre = ideal_intersection(Pre,A[I][0],V,Ord|mod=Mod);
2437: }
2438: for ( T = [], I = 0; I < N; I++ )
2439: if ( A[I] ) T = cons(A[I],T);
2440: return reverse(T);
2441: }
2442:
2443: def pd_simp_comp(PL,V)
2444: {
2445: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2446: if ( type(First=getopt(first)) == -1 ) First = 0;
2447: A = ltov(PL); N = length(A);
2448: if ( N == 1 ) return PL;
2449: for ( I = 0; I < N; I++ ) {
2450: if ( !A[I] ) continue;
2451: AI = First?A[I][0]:A[I];
2452: for ( J = 0; J < N; J++ ) {
2453: if ( J == I || !A[J] ) continue;
2454: AJ = First?A[J][0]:A[J];
2455: if ( gen_gb_comp(AI,AJ,Mod) || ideal_inclusion(AI,AJ,V,Ord|mod=Mod) )
2456: A[J] = 0;
2457: }
2458: }
2459: for ( I = 0, T = []; I < N; I++ ) if ( A[I] ) T = cons(A[I],T);
2460: return reverse(T);
2461: }
2462:
2463: def pd_remove_redundant_comp(G,P,V,Ord)
2464: {
2465: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2466: if ( type(First=getopt(first)) == -1 ) First = 0;
2467: if ( length(P) == 1 ) return P;
2468:
2469: A = ltov(P); N = length(A);
2470: for ( I = 0; I < N; I++ ) {
2471: if ( !A[I] ) continue;
2472: for ( J = I+1; J < N; J++ )
2473: if ( A[J] &&
2474: gen_gb_comp(First?A[I][0]:A[I],First?A[J][0]:A[J],Mod) ) A[J] = 0;
2475: }
2476: for ( I = 0, T = []; I < N; I++ ) if ( A[I] ) T = cons(A[I],T);
2477: A = ltov(reverse(T)); N = length(A);
2478: Pre = [1]; Post = vector(N+1);
2479: for ( Post[N] = [1], I = N-1; I >= 1; I-- )
2480: Post[I] = ideal_intersection(Post[I+1],First?A[I][0]:A[I],V,Ord|mod=Mod);
2481: for ( I = 0; I < N; I++ ) {
2482: Int = ideal_intersection(Pre,Post[I+1],V,Ord|mod=Mod);
2483: if ( gen_gb_comp(Int,G,Mod) ) A[I] = 0;
2484: else
2485: Pre = ideal_intersection(Pre,First?A[I][0]:A[I],V,Ord|mod=Mod);
2486: }
2487: for ( T = [], I = 0; I < N; I++ ) if ( A[I] ) T = cons(A[I],T);
2488: return reverse(T);
2489: }
2490:
1.7 noro 2491: def remove_identical_comp(L)
2492: {
2493: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2494: if ( length(L) == 1 ) return L;
2495:
2496: A = ltov(L); N = length(A);
2497: for ( I = 0; I < N; I++ ) {
2498: if ( !A[I] ) continue;
2499: for ( J = I+1; J < N; J++ )
2500: if ( A[J] &&
2501: gen_gb_comp(A[I],A[J],Mod) ) A[J] = 0;
2502: }
2503: for ( I = 0, T = []; I < N; I++ ) if ( A[I] ) T = cons(A[I],T);
2504: return reverse(T);
2505: }
2506:
1.1 noro 2507: /* polynomial operations */
2508:
2509: def ppart(F,V,Mod)
2510: {
2511: if ( !Mod )
2512: G = nd_gr([F],[V],0,0);
2513: else
2514: G = dp_gr_mod_main([F],[V],0,Mod,0);
2515: return G[0];
2516: }
2517:
2518:
2519: def sq(F,Mod)
2520: {
2521: if ( !F ) return 0;
2522: A = cdr(gen_fctr(F,Mod));
2523: for ( R = 1; A != []; A = cdr(A) )
2524: R *= car(car(A));
2525: return R;
2526: }
2527:
2528: def lcfactor(G,V,O,Mod)
2529: {
2530: O0 = dp_ord(); dp_ord(O);
2531: C = [];
2532: for ( T = G; T != []; T = cdr(T) ) {
2533: C1 = dp_hc(dp_ptod(car(T),V));
2534: S = gen_fctr(C1,Mod);
2535: for ( S = cdr(S); S != []; S = cdr(S) )
2536: if ( !member(S[0][0],C) ) C = cons(S[0][0],C);
2537: }
2538: dp_ord(O0);
2539: return C;
2540: }
2541:
2542: def gen_fctr(F,Mod)
2543: {
2544: if ( Mod ) return modfctr(F,Mod);
2545: else return fctr(F);
2546: }
2547:
2548: def gen_mptop(F)
2549: {
2550: if ( !F ) return F;
2551: else if ( type(F)==1 )
2552: if ( ntype(F)==5 ) return mptop(F);
2553: else return F;
2554: else {
2555: V = var(F);
2556: D = deg(F,V);
2557: for ( R = 0, I = 0; I <= D; I++ )
2558: if ( C = coef(F,I,V) ) R += gen_mptop(C)*V^I;
2559: return R;
2560: }
2561: }
2562:
2563: def gen_nf(F,G,V,Ord,Mod)
2564: {
2565: if ( !Mod ) return p_nf(F,G,V,Ord);
2566:
2567: setmod(Mod);
2568: dp_ord(Ord); DF = dp_mod(dp_ptod(F,V),Mod,[]);
2569: N = length(G); DG = newvect(N);
2570: for ( I = N-1, IL = []; I >= 0; I-- ) {
2571: DG[I] = dp_mod(dp_ptod(G[I],V),Mod,[]);
2572: IL = cons(I,IL);
2573: }
2574: T = dp_nf_mod(IL,DF,DG,1,Mod);
2575: for ( R = 0; T; T = dp_rest(T) )
2576: R += gen_mptop(dp_hc(T))*dp_dtop(dp_ht(T),V);
2577: return R;
2578: }
2579:
2580: /* Ti = [D,I,M,C] */
2581:
2582: def compute_deg0(Ti,P,V,TV)
2583: {
2584: N = length(P[0]);
2585: Num = vector(N);
2586: for ( I = 0; I < N; I++ ) Num[I] = -1;
2587: for ( ; Ti != []; Ti = cdr(Ti) ) {
2588: Sj = car(Ti);
2589: Dj = Sj[0];
2590: Ij =Sj[1];
2591: Mj = deg(type(Sj[2])==9?dp_dtop(Sj[2],V):Sj[2],TV);
2592: Pj = P[Ij];
2593: if ( Dj )
2594: for ( I = 0; I < N; I++ )
2595: if ( Pj[I] >= 0 ) {
2596: T = Mj+Pj[I];
2597: Num[I] = MAX(Num[I],T);
2598: }
2599: }
2600: return Num;
2601: }
2602:
2603: def compute_deg(B,V,TV,Data)
2604: {
2605: GB = Data[0];
2606: Homo = Data[1];
2607: Trace = Data[2];
2608: IntRed = Data[3];
2609: Ind = Data[4];
2610: DB = map(dp_ptod,B,V);
2611: if ( Homo ) {
2612: DB = map(dp_homo,DB);
2613: V0 = append(V,[hhh]);
2614: } else
2615: V0 = V;
2616: Perm = Trace[0]; Trace = cdr(Trace);
2617: for ( I = length(Perm)-1, T = Trace; T != []; T = cdr(T) )
2618: if ( (J=car(T)[0]) > I ) I = J;
2619: N = I+1;
2620: N0 = length(B);
2621: P = vector(N);
2622: for ( T = Perm, I = 0; T != []; T = cdr(T), I++ ) {
2623: Pi = car(T);
2624: C = vector(N0);
2625: for ( J = 0; J < N0; J++ ) C[J] = -1;
2626: C[Pi[1]] = 0;
2627: P[Pi[0]] = C;
2628: }
2629: for ( T = Trace; T != []; T = cdr(T) ) {
2630: Ti = car(T); P[Ti[0]] = compute_deg0(Ti[1],P,V0,TV);
2631: }
2632: M = length(Ind);
2633: for ( T = IntRed; T != []; T = cdr(T) ) {
2634: Ti = car(T); P[Ti[0]] = compute_deg0(Ti[1],P,V,TV);
2635: }
2636: R = [];
2637: for ( J = 0; J < M; J++ ) {
2638: U = P[Ind[J]];
2639: R = cons(U,R);
2640: }
2641: return reverse(R);
2642: }
2643:
2644: /* set theoretic functions */
2645:
2646: def member(A,S)
2647: {
2648: for ( ; S != []; S = cdr(S) )
2649: if ( car(S) == A ) return 1;
2650: return 0;
2651: }
2652:
2653: def elimination(G,V) {
2654: for ( R = [], T = G; T != []; T = cdr(T) )
2655: if ( setminus(vars(car(T)),V) == [] ) R =cons(car(T),R);
2656: return R;
2657: }
2658:
2659: def setintersection(A,B)
2660: {
2661: for ( L = []; A != []; A = cdr(A) )
2662: if ( member(car(A),B) )
2663: L = cons(car(A),L);
2664: return L;
2665: }
2666:
2667: def setminus(A,B) {
2668: for ( T = reverse(A), R = []; T != []; T = cdr(T) ) {
2669: for ( S = B, M = car(T); S != []; S = cdr(S) )
2670: if ( car(S) == M ) break;
2671: if ( S == [] ) R = cons(M,R);
2672: }
2673: return R;
2674: }
2675:
2676: def sep_list(L,N)
2677: {
2678: if ( length(L) <= N ) return [L,[]];
2679: R = [];
2680: for ( T = L, I = 0; I < N; I++, T = cdr(T) )
2681: R = cons(car(T),R);
2682: return [reverse(R),T];
2683: }
2684:
2685: def first(L)
2686: {
2687: return L[0];
2688: }
2689:
2690: def second(L)
2691: {
2692: return L[1];
2693: }
2694:
2695: def third(L)
2696: {
2697: return L[2];
2698: }
2699:
2700: def first_second(L)
2701: {
2702: return [L[0],L[1]];
2703: }
2704:
2705: def comp_tord(A,B)
2706: {
2707: DA = dp_ht(A);
2708: DB = dp_ht(B);
2709: if ( DA > DB ) return 1;
2710: else if ( DA < DB ) return -1;
2711: else return 0;
2712: }
2713:
2714: def comp_tdeg(A,B)
2715: {
2716: DA = tdeg(A);
2717: DB = tdeg(B);
2718: if ( DA > DB ) return 1;
2719: else if ( DA < DB ) return -1;
2720: else return 0;
2721: }
2722:
2723: def comp_tdeg_first(A,B)
2724: {
2725: DA = tdeg(A[0]);
2726: DB = tdeg(B[0]);
2727: if ( DA > DB ) return 1;
2728: else if ( DA < DB ) return -1;
2729: else return 0;
2730: }
2731:
2732: def comp_third_tdeg(A,B)
2733: {
2734: if ( A[2] > B[2] ) return 1;
2735: if ( A[2] < B[2] ) return -1;
2736: DA = tdeg(A[0]);
2737: DB = tdeg(B[0]);
2738: if ( DA > DB ) return 1;
2739: else if ( DA < DB ) return -1;
2740: else return 0;
2741: }
2742:
2743: def tdeg(P)
2744: {
2745: dp_ord(0);
2746: return dp_td(dp_ptod(P,vars(P)));
2747: }
2748:
2749: def comp_by_ord(A,B)
2750: {
2751: if ( dp_ht(A) > dp_ht(B) ) return 1;
2752: else if ( dp_ht(A) < dp_ht(B) ) return -1;
2753: else return 0;
2754: }
2755:
2756: def comp_by_second(A,B)
2757: {
2758: if ( A[1] > B[1] ) return 1;
2759: else if ( A[1] < B[1] ) return -1;
2760: else return 0;
2761: }
2762:
2763: def get_lc(F)
2764: {
2765: if ( type(F)==1 ) return F;
2766: V = var(F);
2767: D = deg(F,V);
2768: return get_lc(coef(F,D,V));
2769: }
2770:
2771: def tomonic(F,Mod)
2772: {
2773: C = get_lc(F);
2774: IC = inv(C,Mod);
2775: return (IC*F)%Mod;
2776: }
2777:
2778: def gen_gb_comp(A,B,Mod)
2779: {
2780: if ( !Mod ) return gb_comp(A,B);
2781: LA = length(A); LB = length(B);
2782: if ( LA != LB ) return 0;
2783: A = map(tomonic,A,Mod);
2784: B = map(tomonic,B,Mod);
2785: A = qsort(A); B = qsort(B);
2786: if ( A != B ) return 0;
2787: return 1;
2788: }
2789:
2790: def prod(L)
2791: {
2792: for ( R = 1; L != []; L = cdr(L) )
2793: R *= car(L);
2794: return R;
2795: }
2796:
2797: def monodec0(B,V)
2798: {
2799: M = monodec(B,V);
2800: return map(vars,M);
2801: }
2802:
2803: def monodec(B,V)
2804: {
2805: B = map(sq,B,0);
2806: G = nd_gr_postproc(B,V,0,0,0);
2807: V = vars(G);
2808: N = length(V);
2809: if ( N == 0 ) return G == [] ? [[]] : [];
2810: if ( N == 1 ) return G;
2811: if ( N < 20 ) {
2812: T = dp_mono_raddec(G,V);
2813: return map(prod,T);
2814: }
2815: X = car(V); W = cdr(V);
2816: D0 = monodec(map(subst,B,X,0),W);
2817: T0 = map(dp_ptod,D0,W);
2818: D1 = monodec(map(subst,B,X,1),W);
2819: T1 = map(dp_ptod,D1,W);
1.4 noro 2820: #if 0
1.1 noro 2821: for ( T = T1; T != []; T = cdr(T) ) {
2822: for ( M = car(T), S1 = [], S = T0; S != []; S = cdr(S) )
2823: if ( !dp_redble(car(S),M) ) S1= cons(car(S),S1);
2824: T0 = S1;
2825: }
1.4 noro 2826: #else
2827: T0 = dp_mono_reduce(T0,T1);
2828: #endif
1.1 noro 2829: D0 = map(dp_dtop,T0,W);
2830: D0 = vtol(X*ltov(D0));
2831: return append(D0,D1);
2832: }
2833:
2834: def separator(P,V)
2835: {
2836: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2837: N = length(P);
1.4 noro 2838: dp_ord(0);
2839: DP = vector(N);
1.9 ! ohara 2840: for ( I = 0; I < N; I++ ) DP[I] = qsort(ltov(map(dp_ptod,P[I][0],V)),noro_pd.comp_tord);
1.4 noro 2841: if ( Mod )
2842: for ( I = 0; I < N; I++ ) DP[I] = map(dp_mod,DP[I],Mod,[]);
2843: Ind = vector(N);
2844: for ( I = 0; I < N; I++ ) {
2845: for ( K = [], J = length(DP[I])-1; J >= 0; J-- ) K = cons(J,K);
2846: Ind[I] = K;
2847: }
2848: S = vector(N);
2849: for ( I = 0; I < N; I++ ) S[I] = 1;
1.1 noro 2850: for ( I = 0; I < N; I++ ) {
1.4 noro 2851: print(".",2);
1.1 noro 2852: for ( J = 0; J < N; J++ ) {
2853: if ( J == I ) continue;
1.4 noro 2854: T = DP[I]; L = length(T);
2855: if ( Mod ) {
2856: for ( K = 0; K < L; K++ )
2857: if ( dp_nf_mod(Ind[J],T[K],DP[J],0,Mod) ) break;
2858: } else {
2859: for ( K = 0; K < L; K++ )
2860: if ( dp_nf(Ind[J],T[K],DP[J],0) ) break;
2861: }
2862: S[J] = lcm(S[J],dp_dtop(T[K],V));
1.1 noro 2863: }
2864: }
1.4 noro 2865: print("");
1.1 noro 2866: return S;
2867: }
2868:
2869: def prepost(PL,V)
1.4 noro 2870: {
2871: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1.1 noro 2872: A = ltov(PL); N = length(A);
2873: Pre = vector(N);
2874: Post = vector(N);
2875: R = vector(N);
2876: Pre[0] = [1];
2877: print("pre ",2);
2878: for ( I = 1; I < N; I++, print(".",2) )
1.4 noro 2879: Pre[I] = ideal_intersection_m(Pre[I-1],A[I-1],V,0|mod=Mod);
1.1 noro 2880: print("done");
2881: print("post ",2);
2882: Post[N-1] = [1];
2883: for ( I = N-2; I >= 0; I--, print(".",2) )
1.4 noro 2884: Post[I] = ideal_intersection_m(Post[I+1],A[I+1],V,0|mod=Mod);
1.1 noro 2885: print("done");
2886: print("int ",2);
2887: for ( I = 0; I < N; I++, print(".",2) )
1.4 noro 2888: R[I] = ideal_intersection_m(Pre[I],Post[I],V,0|mod=Mod);
1.1 noro 2889: print("done");
2890: return R;
2891: }
2892:
2893: /* XXX */
2894:
2895: def call_func(Arg)
2896: {
2897: F = car(Arg);
2898: return call(strtov(F),cdr(Arg));
2899: }
2900:
1.8 noro 2901: def call_func_serial(Arg,Serial)
2902: {
2903: F = car(Arg);
2904: return [call(strtov(F),cdr(Arg)),Serial];
2905: }
2906:
1.1 noro 2907: def competitive_exec(P,Arg0,Arg1)
2908: {
2909: P0 = P[0]; P1 = P[1];
2910: ox_cmo_rpc(P0,"noro_pd.call_func",Arg0|sync=1);
2911: ox_cmo_rpc(P1,"noro_pd.call_func",Arg1|sync=1);
2912: F = ox_select(P);
2913: R = ox_get(F[0]);
2914: if ( length(F) == 2 ) {
2915: ox_get(F[1]);
2916: } else {
2917: U = setminus(P,F);
2918: ox_reset(U[0]);
2919: }
2920: return R;
2921: }
2922:
2923:
2924: def nd_gr_rat(B,V,PV,Ord1,Ord)
2925: {
2926: G = nd_gr(B,append(V,PV),0,Ord1);
2927: G1 = nd_gr_postproc(G,V,0,Ord,0);
2928: return G1;
2929: }
2930:
2931: /* Task[i] = [fname,[arg0,...,argn]] */
2932:
2933: def para_exec(Proc,Task) {
2934: Free = Proc;
2935: N = length(Task);
2936: R = [];
1.8 noro 2937: print([N],2); print("->",2);
2938: Serial = 0;
1.1 noro 2939: while ( N ) {
2940: while ( Task != [] && Free != [] ) {
2941: T = car(Task); Task = cdr(Task);
1.8 noro 2942: ox_rpc(car(Free),"noro_pd.call_func_serial",T,Serial++);
1.1 noro 2943: ox_push_cmd(car(Free),258); Free = cdr(Free);
2944: }
2945: Finish0 = Finish = ox_select(Proc);
2946: for ( ; Finish != []; Finish = cdr(Finish) ) {
2947: print(".",2);
2948: L = ox_get(car(Finish));
2949: R = cons(L,R);
2950: N--;
2951: }
1.8 noro 2952: print([N],2);
1.1 noro 2953: Free = append(Free,Finish0);
2954: }
2955: print("");
1.9 ! ohara 2956: R = qsort(R,noro_pd.comp_by_second);
1.8 noro 2957: R = map(first,R);
2958: return R;
1.1 noro 2959: }
1.4 noro 2960:
2961: def redbase(B,V,Mod,Ord)
2962: {
2963: M = nd_gr_postproc(B,V,Mod,Ord,0);
2964: dp_ord(Ord);
2965: DM = ltov(map(dp_ptod,M,V));
2966: if ( Mod ) DM = map(dp_mod,DM,Mod,[]);
2967: N = length(DM);
2968: for ( Ind = [], I = N-1; I >= 0; I-- ) Ind = cons(I,Ind);
2969: for ( T = B, R = vtol(DM); T != []; T = cdr(T) ) {
2970: D = dp_ptod(car(T),V);
2971: if ( Mod ) D = dp_mod(D,Mod,[]);
2972: D = Mod?dp_nf_mod(Ind,D,DM,1,Mod):dp_nf(Ind,D,DM,1);
2973: if ( D ) R = cons(D,R);
2974: }
1.9 ! ohara 2975: D = qsort(R,noro_pd.comp_tord);
1.4 noro 2976: return map(dp_dtop,D,V);
2977: }
2978:
2979: def witness(A,B,V)
2980: {
2981: G = nd_gr(B,V,0,Mod);
2982: L = length(A);
2983: QL = []; PL = [];
2984: for ( I = L-1; I >= 0; I-- ) {
2985: QL = append(map(first,A[I]),QL);
2986: PL = append(map(second,A[I]),PL);
2987: }
2988: N = length(QL);
2989: Qhat = prepost(QL,V);
2990: for ( I = 0, W = []; I < N; I++ ) {
2991: for ( T = Qhat[I]; T != []; T = cdr(T) )
2992: if ( gen_nf(car(T),QL[I],V,0,Mod) ) break;
2993: Ai = car(T);
2994: Ji = colon(G,Ai,V|isgb=1,mod=Mod);
2995: Ji = nd_gr(Ji,V,Mod,0);
2996: if ( gen_gb_comp(Ji,PL[I],Mod) ) Bi = 1;
2997: else {
2998: Ki = ideal_colon(Ji,PL[I],V|mod=Mod);
2999: for ( T = Ki; T != []; T = cdr(T) )
3000: if ( gen_nf(car(T),Ji,V,0,Mod) ) break;
3001: Bi = car(T);
3002: }
3003: W = cons(Ai*Bi,W);
3004: Li = colon(G,W[0],V|isgb=1,mod=Mod);
3005: Li = nd_gr(Li,V,Mod,0);
3006: if ( !gen_gb_comp(Li,PL[I],Mod) )
3007: error("afo");
3008: }
3009: return reverse(W);
3010: }
1.1 noro 3011: endmodule$
3012: end$
FreeBSD-CVSweb <freebsd-cvsweb@FreeBSD.org>
![[BACK]](/icons/cvsweb/back.gif){kind=icon}
Return to new_pd.rr CVS log ![[TXT]](/icons/cvsweb/text.gif){kind=icon}
![[DIR]](/icons/cvsweb/dir.gif){kind=icon}
Up to [local] / OpenXM / src / asir-contrib / testing / noro