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1.3 noro 1: /*
2: * Copyright (c) 1994-2000 FUJITSU LABORATORIES LIMITED
3: * All rights reserved.
4: *
5: * FUJITSU LABORATORIES LIMITED ("FLL") hereby grants you a limited,
6: * non-exclusive and royalty-free license to use, copy, modify and
7: * redistribute, solely for non-commercial and non-profit purposes, the
8: * computer program, "Risa/Asir" ("SOFTWARE"), subject to the terms and
9: * conditions of this Agreement. For the avoidance of doubt, you acquire
10: * only a limited right to use the SOFTWARE hereunder, and FLL or any
11: * third party developer retains all rights, including but not limited to
12: * copyrights, in and to the SOFTWARE.
13: *
14: * (1) FLL does not grant you a license in any way for commercial
15: * purposes. You may use the SOFTWARE only for non-commercial and
16: * non-profit purposes only, such as academic, research and internal
17: * business use.
18: * (2) The SOFTWARE is protected by the Copyright Law of Japan and
19: * international copyright treaties. If you make copies of the SOFTWARE,
20: * with or without modification, as permitted hereunder, you shall affix
21: * to all such copies of the SOFTWARE the above copyright notice.
22: * (3) An explicit reference to this SOFTWARE and its copyright owner
23: * shall be made on your publication or presentation in any form of the
24: * results obtained by use of the SOFTWARE.
25: * (4) In the event that you modify the SOFTWARE, you shall notify FLL by
1.4 noro 26: * e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification
1.3 noro 27: * for such modification or the source code of the modified part of the
28: * SOFTWARE.
29: *
30: * THE SOFTWARE IS PROVIDED AS IS WITHOUT ANY WARRANTY OF ANY KIND. FLL
31: * MAKES ABSOLUTELY NO WARRANTIES, EXPRESSED, IMPLIED OR STATUTORY, AND
32: * EXPRESSLY DISCLAIMS ANY IMPLIED WARRANTY OF MERCHANTABILITY, FITNESS
33: * FOR A PARTICULAR PURPOSE OR NONINFRINGEMENT OF THIRD PARTIES'
34: * RIGHTS. NO FLL DEALER, AGENT, EMPLOYEES IS AUTHORIZED TO MAKE ANY
35: * MODIFICATIONS, EXTENSIONS, OR ADDITIONS TO THIS WARRANTY.
36: * UNDER NO CIRCUMSTANCES AND UNDER NO LEGAL THEORY, TORT, CONTRACT,
37: * OR OTHERWISE, SHALL FLL BE LIABLE TO YOU OR ANY OTHER PERSON FOR ANY
38: * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, PUNITIVE OR CONSEQUENTIAL
39: * DAMAGES OF ANY CHARACTER, INCLUDING, WITHOUT LIMITATION, DAMAGES
40: * ARISING OUT OF OR RELATING TO THE SOFTWARE OR THIS AGREEMENT, DAMAGES
41: * FOR LOSS OF GOODWILL, WORK STOPPAGE, OR LOSS OF DATA, OR FOR ANY
42: * DAMAGES, EVEN IF FLL SHALL HAVE BEEN INFORMED OF THE POSSIBILITY OF
43: * SUCH DAMAGES, OR FOR ANY CLAIM BY ANY OTHER PARTY. EVEN IF A PART
44: * OF THE SOFTWARE HAS BEEN DEVELOPED BY A THIRD PARTY, THE THIRD PARTY
45: * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE,
46: * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE.
47: *
1.10 ! noro 48: * $OpenXM: OpenXM_contrib2/asir2000/engine/F.c,v 1.9 2001/07/04 07:19:19 noro Exp $
1.3 noro 49: */
1.1 noro 50: #include "ca.h"
51: #include <math.h>
52:
1.9 noro 53: int use_new_hensel;
54:
1.10 ! noro 55: void fctrp(VL vl,P f,DCP *dcp)
1.1 noro 56: {
57: VL nvl;
58: DCP dc;
59:
60: if ( !f || NUM(f) ) {
61: NEWDC(dc); COEF(dc) = f; DEG(dc) = ONE;
62: NEXT(dc) = 0; *dcp = dc;
63: return;
64: } else if ( !qpcheck((Obj)f) )
65: error("fctrp : invalid argument");
66: else {
67: clctv(vl,f,&nvl);
68: if ( !NEXT(nvl) )
69: ufctr(f,1,dcp);
70: else
71: mfctr(nvl,f,dcp);
72: }
73: }
74:
1.10 ! noro 75: void fctr_wrt_v_p(VL vl,P f,V v,DCP *dcp)
1.8 noro 76: {
77: VL nvl;
78: DCP dc;
79:
80: if ( !f || NUM(f) ) {
81: NEWDC(dc); COEF(dc) = f; DEG(dc) = ONE;
82: NEXT(dc) = 0; *dcp = dc;
83: return;
84: } else if ( !qpcheck((Obj)f) )
85: error("fctrp : invalid argument");
86: else {
87: clctv(vl,f,&nvl);
88: if ( !NEXT(nvl) )
89: ufctr(f,1,dcp);
90: else
91: mfctr_wrt_v(nvl,f,v,dcp);
92: }
93: }
94:
1.10 ! noro 95: void homfctr(VL vl,P g,DCP *dcp)
1.1 noro 96: {
97: P s,t,u,f,h,x;
98: Q e;
99: int d,d0;
100: DCP dc,dct;
101:
102: substp(vl,g,vl->v,(P)ONE,&t); fctrp(vl,t,&dc); MKV(vl->v,x);
103: for ( dct = dc; dct; dct = NEXT(dct) )
104: if ( !NUM(dc->c) ) {
105: for ( s = 0, f = dc->c, d = d0 = homdeg(f); f; d = homdeg(f) ) {
106: exthp(vl,f,d,&h); STOQ(d0-d,e); pwrp(vl,x,e,&t);
107: mulp(vl,t,h,&u); addp(vl,s,u,&t); s = t;
108: subp(vl,f,h,&u); f = u;
109: }
110: dc->c = s;
111: }
112: *dcp = dc;
113: }
114:
1.10 ! noro 115: void mfctr(VL vl,P f,DCP *dcp)
1.1 noro 116: {
117: DCP dc,dc0,dct,dcs,dcr;
118: P p,pmin,ppmin,cmin,t;
119: VL mvl;
120: Q c;
121:
122: ptozp(f,1,&c,&p);
123: NEWDC(dc0); dc = dc0; COEF(dc) = (P)c; DEG(dc) = ONE; NEXT(dc) = 0;
124: msqfr(vl,p,&dct);
125: for ( ; dct; dct = NEXT(dct) ) {
126: mindegp(vl,COEF(dct),&mvl,&pmin);
127: #if 0
128: minlcdegp(vl,COEF(dct),&mvl,&pmin);
129: min_common_vars_in_coefp(vl,COEF(dct),&mvl,&pmin);
130: #endif
1.8 noro 131: pcp(mvl,pmin,&ppmin,&cmin);
132: if ( !NUM(cmin) ) {
133: mfctrmain(mvl,cmin,&dcs);
134: for ( dcr = dcs; dcr; dcr = NEXT(dcr) ) {
135: DEG(dcr) = DEG(dct);
136: reorderp(vl,mvl,COEF(dcr),&t); COEF(dcr) = t;
137: }
138: for ( ; NEXT(dc); dc = NEXT(dc) );
139: NEXT(dc) = dcs;
140: }
141: mfctrmain(mvl,ppmin,&dcs);
142: for ( dcr = dcs; dcr; dcr = NEXT(dcr) ) {
143: DEG(dcr) = DEG(dct);
144: reorderp(vl,mvl,COEF(dcr),&t); COEF(dcr) = t;
145: }
146: for ( ; NEXT(dc); dc = NEXT(dc) );
147: NEXT(dc) = dcs;
148: }
149: adjsgn(f,dc0); *dcp = dc0;
150: }
151:
1.10 ! noro 152: void mfctr_wrt_v(VL vl,P f,V v,DCP *dcp)
1.8 noro 153: {
154: DCP dc,dc0,dct,dcs,dcr;
155: P p,pmin,ppmin,cmin,t;
156: VL nvl,mvl;
157: Q c;
158:
159: ptozp(f,1,&c,&p);
160: NEWDC(dc0); dc = dc0; COEF(dc) = (P)c; DEG(dc) = ONE; NEXT(dc) = 0;
161: msqfr(vl,p,&dct);
162: for ( ; dct; dct = NEXT(dct) ) {
163: clctv(vl,f,&nvl);
164: reordvar(nvl,v,&mvl);
165: reorderp(mvl,vl,f,&pmin);
1.1 noro 166: pcp(mvl,pmin,&ppmin,&cmin);
167: if ( !NUM(cmin) ) {
168: mfctrmain(mvl,cmin,&dcs);
169: for ( dcr = dcs; dcr; dcr = NEXT(dcr) ) {
170: DEG(dcr) = DEG(dct);
171: reorderp(vl,mvl,COEF(dcr),&t); COEF(dcr) = t;
172: }
173: for ( ; NEXT(dc); dc = NEXT(dc) );
174: NEXT(dc) = dcs;
175: }
176: mfctrmain(mvl,ppmin,&dcs);
177: for ( dcr = dcs; dcr; dcr = NEXT(dcr) ) {
178: DEG(dcr) = DEG(dct);
179: reorderp(vl,mvl,COEF(dcr),&t); COEF(dcr) = t;
180: }
181: for ( ; NEXT(dc); dc = NEXT(dc) );
182: NEXT(dc) = dcs;
183: }
184: adjsgn(f,dc0); *dcp = dc0;
185: }
186:
1.2 noro 187: #if 0
1.10 ! noro 188: void adjsgn(P p,DCP dc)
1.1 noro 189: {
190: int sgn;
191: DCP dct;
192: P c;
193:
194: for ( dct = dc, sgn = headsgn(p); dct; dct = NEXT(dct) )
195: if ( !EVENN(NM(dct->d)) )
196: sgn *= headsgn(COEF(dct));
197: if ( sgn < 0 ) {
198: chsgnp(COEF(dc),&c); COEF(dc) = c;
199: }
200: }
1.2 noro 201: #else
1.10 ! noro 202: void adjsgn(P p,DCP dc)
1.2 noro 203: {
204: DCP dct;
205: P c;
206:
207: if ( headsgn(COEF(dc)) != headsgn(p) ) {
208: chsgnp(COEF(dc),&c); COEF(dc) = c;
209: }
210: for ( dct = NEXT(dc); dct; dct = NEXT(dct) )
211: if ( headsgn(COEF(dct)) < 0 ) {
212: chsgnp(COEF(dct),&c); COEF(dct) = c;
213: }
214: }
215: #endif
1.1 noro 216:
1.10 ! noro 217: int headsgn(P p)
1.1 noro 218: {
219: if ( !p )
220: return 0;
221: else {
222: while ( !NUM(p) )
223: p = COEF(DC(p));
224: return SGN((Q)p);
225: }
226: }
227:
1.10 ! noro 228: void fctrwithmvp(VL vl,P f,V v,DCP *dcp)
1.1 noro 229: {
230: VL nvl;
231: DCP dc;
232:
233: if ( NUM(f) ) {
234: NEWDC(dc); COEF(dc) = f; DEG(dc) = ONE;
235: NEXT(dc) = 0; *dcp = dc;
236: return;
237: }
238:
239: clctv(vl,f,&nvl);
240: if ( !NEXT(nvl) )
241: ufctr(f,1,dcp);
242: else
243: mfctrwithmv(nvl,f,v,dcp);
244: }
245:
1.10 ! noro 246: void mfctrwithmv(VL vl,P f,V v,DCP *dcp)
1.1 noro 247: {
248: DCP dc,dc0,dct,dcs,dcr;
249: P p,pmin,ppmin,cmin,t;
250: VL mvl;
251: Q c;
252:
253: ptozp(f,1,&c,&p);
254: NEWDC(dc0); dc = dc0; COEF(dc) = (P)c; DEG(dc) = ONE; NEXT(dc) = 0;
255: msqfr(vl,p,&dct);
256: for ( ; dct; dct = NEXT(dct) ) {
257: if ( !v )
258: mindegp(vl,COEF(dct),&mvl,&pmin);
259: else {
260: reordvar(vl,v,&mvl); reorderp(mvl,vl,COEF(dct),&pmin);
261: }
262: pcp(mvl,pmin,&ppmin,&cmin);
263: if ( !NUM(cmin) ) {
264: mfctrmain(mvl,cmin,&dcs);
265: for ( dcr = dcs; dcr; dcr = NEXT(dcr) ) {
266: DEG(dcr) = DEG(dct);
267: reorderp(vl,mvl,COEF(dcr),&t); COEF(dcr) = t;
268: }
269: for ( ; NEXT(dc); dc = NEXT(dc) );
270: NEXT(dc) = dcs;
271: }
272: mfctrmain(mvl,ppmin,&dcs);
273: for ( dcr = dcs; dcr; dcr = NEXT(dcr) ) {
274: DEG(dcr) = DEG(dct);
275: reorderp(vl,mvl,COEF(dcr),&t); COEF(dcr) = t;
276: }
277: for ( ; NEXT(dc); dc = NEXT(dc) );
278: NEXT(dc) = dcs;
279: }
280: *dcp = dc0;
281: }
282:
1.10 ! noro 283: void ufctr(P f,int hint,DCP *dcp)
1.1 noro 284: {
285: P p,c;
286: DCP dc,dct,dcs,dcr;
287:
288: ptozp(f,SGN((Q)UCOEF(f)),(Q *)&c,&p);
289: NEWDC(dc); COEF(dc) = c; DEG(dc) = ONE; NEXT(dc) = 0;
290: usqp(p,&dct);
291: for ( *dcp = dc; dct; dct = NEXT(dct) ) {
292: ufctrmain(COEF(dct),hint,&dcs);
293: for ( dcr = dcs; dcr; dcr = NEXT(dcr) )
294: DEG(dcr) = DEG(dct);
295: for ( ; NEXT(dc); dc = NEXT(dc) );
296: NEXT(dc) = dcs;
297: }
298: }
299:
1.10 ! noro 300: void mfctrmain(VL vl,P p,DCP *dcp)
1.1 noro 301: {
1.5 noro 302: int i,j,k,*win,np,x;
1.1 noro 303: VL nvl,tvl;
304: VN vn,vnt,vn1;
305: P p0,f,g,f0,g0,s,t,lp,m;
306: P *fp0,*fpt,*l,*tl;
307: DCP dc,dc0,dcl;
308: int count,nv;
1.5 noro 309: int *nonzero;
1.1 noro 310:
311: if ( !cmpq(DEG(DC(p)),ONE) ) {
312: NEWDC(dc); DEG(dc) = ONE; COEF(dc) = p; NEXT(dc) = 0;
313: *dcp = dc; return;
314: }
315: lp = LC(p); fctrp(vl,lp,&dcl); clctv(vl,p,&nvl);
316: for ( nv = 0, tvl = nvl; tvl; tvl = NEXT(tvl), nv++);
317: W_CALLOC(nv,struct oVN,vn); W_CALLOC(nv,struct oVN,vnt);
318: W_CALLOC(nv,struct oVN,vn1);
1.5 noro 319: W_CALLOC(nv,int,nonzero);
320:
1.1 noro 321: for ( i = 0, tvl = NEXT(nvl); tvl; tvl = NEXT(tvl), i++ )
322: vn1[i].v = vn[i].v = tvl->v;
323: vn1[i].v = vn[i].v = 0;
1.5 noro 324:
325: /* determine a heuristic bound of deg(GCD(p,p')) */
326: while ( 1 ) {
327: for ( i = 0; vn1[i].v; i++ )
328: vn1[i].n = ((unsigned int)random())%256+1;
329: substvp(nvl,LC(p),vn1,&p0);
330: if ( p0 ) {
331: substvp(nvl,p,vn1,&p0);
332: if ( sqfrchk(p0) ) {
333: ufctr(p0,1,&dc0);
334: if ( NEXT(NEXT(dc0)) == 0 ) {
335: NEWDC(dc); DEG(dc) = ONE; COEF(dc) = p; NEXT(dc) = 0;
336: *dcp = dc;
337: return;
338: } else {
339: for ( dc0 = NEXT(dc0), np = 0; dc0; dc0 = NEXT(dc0), np++ );
340: break;
341: }
342: }
343: }
344: }
345:
1.6 noro 346: /* determine the position of variables which is not allowed to
347: be set to 0 */
1.5 noro 348: for ( i = 0; vn1[i].v; i++ ) {
349: x = vn1[i].n; vn1[i].n = 0;
350: substvp(nvl,LC(p),vn1,&p0);
351: if ( !p0 )
352: vn1[i].n = x;
353: else {
354: substvp(nvl,p,vn1,&p0);
355: if ( !sqfrchk(p0) )
356: vn1[i].n = x;
357: else {
358: ufctr(p0,1,&dc0);
359: for ( dc0 = NEXT(dc0), j = 0; dc0; dc0 = NEXT(dc0), j++ );
360: if ( j > np )
361: vn1[i].n = x;
362: }
363: }
364: }
365: for ( i = 0; vn1[i].v; i++ )
366: if (vn1[i].n )
367: nonzero[i] = 1;
368:
1.1 noro 369: count = 0;
370: while ( 1 ) {
371: while ( 1 ) {
372: count++;
373: for ( i = 0, j = 0; vn[i].v; i++ )
374: if ( vn[i].n )
375: vnt[j++].v = (V)i;
376: vnt[j].n = 0; mulsgn(vn,vnt,j,vn1);
377: for ( i = 0; vn1[i].v; i++ )
378: if ( vn1[i].n ) {
379: if ( vn1[i].n > 0 )
380: vn1[i].n = sprime[vn1[i].n];
381: else
382: vn1[i].n = -sprime[-vn1[i].n];
383: }
384: if ( valideval(nvl,dcl,vn1) ) {
385: substvp(nvl,p,vn1,&p0);
386: if ( sqfrchk(p0) ) {
387: ufctr(p0,1,&dc0);
388: if ( NEXT(NEXT(dc0)) == 0 ) {
389: NEWDC(dc); DEG(dc) = ONE; COEF(dc) = p; NEXT(dc) = 0;
390: *dcp = dc;
391: return;
1.5 noro 392: } else {
393: for ( dc = NEXT(dc0), i = 0; dc; dc = NEXT(dc), i++ );
394: if ( i <= np )
395: goto MAIN;
396: if ( i < np )
397: np = i;
398: }
399: }
1.1 noro 400: }
401: if ( nextbin(vnt,j) )
402: break;
403: }
1.5 noro 404: while ( 1 ) {
405: next(vn);
406: for ( i = 0; vn[i].v; i++ )
407: if ( nonzero[i] && !vn[i].n )
408: break;
409: if ( !vn[i].v )
410: break;
411: }
1.1 noro 412: }
413: MAIN :
414: #if 0
415: for ( i = 0; vn1[i].v; i++ )
416: fprintf(stderr,"%d ",vn1[i].n);
417: fprintf(stderr,"\n");
418: #endif
419: for ( np = 0, dc = NEXT(dc0); dc; dc = NEXT(dc), np++ );
420: fp0 = (P *)ALLOCA((np + 1)*sizeof(P));
421: fpt = (P *)ALLOCA((np + 1)*sizeof(P));
422: l = tl = (P *)ALLOCA((np + 1)*sizeof(P));
423: for ( i = 1, dc = NEXT(dc0); dc; i++, dc = NEXT(dc) )
424: fp0[i-1] = COEF(dc);
425: #if 0
426: sort_by_deg(np,fp0,fpt);
427: sort_by_deg_rev(np-1,fpt+1,fp0+1);
428: #endif
429: #if 0
430: sort_by_deg_rev(np,fp0,fpt); fp0[0] = fpt[0];
431: sort_by_deg(np-1,fpt+1,fp0+1); fp0[np] = 0;
432: #endif
433: fp0[np] = 0;
434: win = W_ALLOC(np + 1); f = p; divsp(vl,p0,COEF(dc0),&f0);
435: for ( k = 1, win[0] = 1, --np; ; ) {
436: P h0,lcg,lch;
437: Q c;
438:
439: g0 = fp0[win[0]];
440: for ( i = 1; i < k; i++ ) {
441: mulp(vl,g0,fp0[win[i]],&m); g0 = m;
442: }
443: mulq((Q)LC(g0),(Q)COEF(dc0),&c); estimatelc(nvl,c,dcl,vn1,&lcg);
444: divsp(nvl,f0,g0,&h0);
445: mulq((Q)LC(h0),(Q)COEF(dc0),&c); estimatelc(nvl,c,dcl,vn1,&lch);
446: mfctrhen2(nvl,vn1,f,f0,g0,h0,lcg,lch,&g);
447: if ( g ) {
448: *tl++ = g; divsp(vl,f,g,&t);
449: f = t; divsp(vl,f0,g0,&t); ptozp(t,1,(Q *)&s,&f0);
450: for ( i = 0; i < k - 1; i++ )
451: for ( j = win[i] + 1; j < win[i + 1]; j++ )
452: fp0[j - i - 1] = fp0[j];
453: for ( j = win[k - 1] + 1; j <= np; j++ )
454: fp0[j - k] = fp0[j];
455: if ( ( np -= k ) < k ) break;
456: if ( np - win[0] + 1 < k )
457: if ( ++k <= np ) {
458: for ( i = 0; i < k; i++ ) win[i] = i + 1;
459: continue;
460: } else
461: break;
462: else for ( i = 1; i < k; i++ ) win[i] = win[0] + i;
463: } else {
464: if ( ncombi(1,np,k,win) == 0 )
465: if ( k == np ) break;
466: else for ( i = 0, ++k; i < k; i++ ) win[i] = i + 1;
467: }
468: }
469: *tl++ = f; *tl = 0;
470: for ( dc0 = 0; *l; l++ ) {
471: NEXTDC(dc0,dc); DEG(dc) = ONE; COEF(dc) = *l;
472: }
473: NEXT(dc) = 0; *dcp = dc0;
474: }
475:
1.10 ! noro 476: void ufctrmain(P p,int hint,DCP *dcp)
1.1 noro 477: {
478: ML list;
479: DCP dc;
480:
481: if ( NUM(p) || (UDEG(p) == 1) ) {
482: NEWDC(dc); DEG(dc) = ONE; COEF(dc) = p; NEXT(dc) = 0;
483: *dcp = dc;
484: } else if ( iscycm(p) )
485: cycm(VR(p),UDEG(p),dcp);
486: else if ( iscycp(p) )
487: cycp(VR(p),UDEG(p),dcp);
488: else {
1.9 noro 489: if ( use_new_hensel )
490: hensel2(5,5,p,&list);
491: else
492: hensel(5,5,p,&list);
1.1 noro 493: if ( list->n == 1 ) {
494: NEWDC(dc); DEG(dc) = ONE; COEF(dc) = p; NEXT(dc) = 0;
495: *dcp = dc;
496: } else
497: dtest(p,list,hint,dcp);
498: }
499: }
500:
1.10 ! noro 501: void cycm(V v,int n,DCP *dcp)
1.1 noro 502: {
503: register int i,j;
504: struct oMF *mfp;
505: DCP dc,dc0;
506:
507: if ( n == 1 ) {
508: NEWDC(dc); mkssum(v,1,1,-1,&COEF(dc)); DEG(dc) = ONE;
509: } else {
510: mfp = (struct oMF *) ALLOCA((n+1)*sizeof(struct oMF));
511: bzero((char *)mfp,(int)(sizeof(struct oMF)*(n+1)));
512: for ( i = 1, j = 0; i <= n; i++ )
513: if ( !(n%i) ) mfp[j++].m = i;
514: mkssum(v,1,1,-1,&mfp[0].f);
515: for ( i = 1; i < j; i++ )
516: calcphi(v,i,mfp);
517: for ( dc0 = 0, i = 0; i < j; i++ ) {
518: NEXTDC(dc0,dc); COEF(dc) = mfp[i].f; DEG(dc) = ONE;
519: }
520: }
521: NEXT(dc) = 0; *dcp = dc0;
522: }
523:
1.10 ! noro 524: void cycp(V v,int n,DCP *dcp)
1.1 noro 525: {
526: register int i,j;
527: int n0;
528: struct oMF *mfp;
529: DCP dc,dc0;
530:
531: if ( n == 1 ) {
532: NEWDC(dc); mkssum(v,1,1,1,&COEF(dc)); DEG(dc) = ONE;
533: } else {
534: n0 = n; n *= 2;
535: mfp = (struct oMF *) ALLOCA((n+1)*sizeof(struct oMF));
536: bzero((char *)mfp,(int)(sizeof(struct oMF)*(n+1)));
537: for ( i = 1, j = 0; i <= n; i++ )
538: if ( !(n%i) ) mfp[j++].m = i;
539: mkssum(v,1,1,-1,&mfp[0].f);
540: for ( i = 1; i < j; i++ )
541: calcphi(v,i,mfp);
542: for ( dc0 = 0, i = 0; i < j; i++ )
543: if ( n0 % mfp[i].m ) {
544: NEXTDC(dc0,dc); COEF(dc) = mfp[i].f; DEG(dc) = ONE;
545: }
546: }
547: NEXT(dc) = 0; *dcp = dc0;
548: }
549:
1.10 ! noro 550: void calcphi(V v,int n,struct oMF *mfp)
1.1 noro 551: {
552: register int i,m;
553: P t,s,tmp;
554:
555: for ( t = (P)ONE, i = 0, m = mfp[n].m; i < n; i++ )
556: if ( !(m%mfp[i].m) ) {
557: mulp(CO,t,mfp[i].f,&s); t = s;
558: }
559: mkssum(v,m,1,-1,&s); udivpz(s,t,&mfp[n].f,&tmp);
560: if ( tmp )
561: error("calcphi: cannot happen");
562: }
563:
1.10 ! noro 564: void mkssum(V v,int e,int s,int sgn,P *r)
1.1 noro 565: {
566: register int i,sgnt;
567: DCP dc,dc0;
568: Q q;
569:
570: for ( dc0 = 0, i = s, sgnt = 1; i >= 0; i--, sgnt *= sgn ) {
571: if ( !dc0 ) {
572: NEWDC(dc0); dc = dc0;
573: } else {
574: NEWDC(NEXT(dc)); dc = NEXT(dc);
575: }
576: STOQ(i*e,DEG(dc)); STOQ(sgnt,q),COEF(dc) = (P)q;
577: }
578: NEXT(dc) = 0; MKP(v,dc0,*r);
579: }
580:
1.10 ! noro 581: int iscycp(P f)
1.1 noro 582: {
583: DCP dc;
584: dc = DC(f);
585:
586: if ( !UNIQ((Q)COEF(dc)) )
587: return ( 0 );
588: dc = NEXT(dc);
589: if ( NEXT(dc) || DEG(dc) || !UNIQ((Q)COEF(dc)) )
590: return ( 0 );
591: return ( 1 );
592: }
593:
1.10 ! noro 594: int iscycm(P f)
1.1 noro 595: {
596: DCP dc;
597:
598: dc = DC(f);
599: if ( !UNIQ((Q)COEF(dc)) )
600: return ( 0 );
601: dc = NEXT(dc);
602: if ( NEXT(dc) || DEG(dc) || !MUNIQ((Q)COEF(dc)) )
603: return ( 0 );
604: return ( 1 );
605: }
606:
1.10 ! noro 607: void sortfs(DCP *dcp)
1.1 noro 608: {
609: int i,k,n,k0,d;
610: DCP dc,dct,t;
611: DCP *a;
612:
613: dc = *dcp;
614: for ( n = 0, dct = dc; dct; dct = NEXT(dct), n++ );
615: a = (DCP *)ALLOCA((n+1)*(sizeof(DCP)));
616: for ( i = 0, dct = dc; dct; dct = NEXT(dct), i++ )
617: a[i] = dct;
618: a[n] = 0;
619:
620: for ( i = 0; i < n; i++ ) {
621: for ( k0 = k = i, d = UDEG(COEF(a[i])); k < n; k++ )
622: if ( (int)UDEG(COEF(a[k])) < d ) {
623: k0 = k;
624: d = UDEG(COEF(a[k]));
625: }
626: if ( i != k0 ) {
627: t = a[i]; a[i] = a[k0]; a[k0] = t;
628: }
629: }
630: for ( *dcp = dct = a[0], i = 1; i < n; i++ )
631: dct = NEXT(dct) = a[i];
632: NEXT(dct) = 0;
633: }
634:
1.10 ! noro 635: void sortfsrev(DCP *dcp)
1.1 noro 636: {
637: int i,k,n,k0,d;
638: DCP dc,dct,t;
639: DCP *a;
640:
641: dc = *dcp;
642: for ( n = 0, dct = dc; dct; dct = NEXT(dct), n++ );
643: a = (DCP *)ALLOCA((n+1)*(sizeof(DCP)));
644: for ( i = 0, dct = dc; dct; dct = NEXT(dct), i++ )
645: a[i] = dct;
646: a[n] = 0;
647:
648: for ( i = 0; i < n; i++ ) {
649: for ( k0 = k = i, d = UDEG(COEF(a[i])); k < n; k++ )
650: if ( (int)UDEG(COEF(a[k])) > d ) {
651: k0 = k;
652: d = UDEG(COEF(a[k]));
653: }
654: if ( i != k0 ) {
655: t = a[i]; a[i] = a[k0]; a[k0] = t;
656: }
657: }
658: for ( *dcp = dct = a[0], i = 1; i < n; i++ )
659: dct = NEXT(dct) = a[i];
660: NEXT(dct) = 0;
661: }
662:
1.10 ! noro 663: void nthrootchk(P f,struct oDUM *dc,ML fp,DCP *dcp)
1.1 noro 664: {
665: register int i,k;
666: int e,n,dr,tmp,t;
667: int *tmpp,**tmppp;
668: int **pp,**wpp;
669: LUM fpa,tpa,f0l;
670: UM wt,wq,ws,dvr,f0,fe;
671: N lc;
672: int lcm;
673: int m,b;
674:
675: m = fp->mod; b = fp->bound; fe = *((UM *)fp->c);
676: e = dc->n; f0 = dc->f; nthrootn(NM((Q)COEF(DC(f))),e,&lc);
677: if ( !lc ) {
678: *dcp = 0;
679: return;
680: }
681: lcm = rem(lc,m); W_LUMALLOC(DEG(f0),b,f0l);
682: for ( i = DEG(f0), tmppp = COEF(f0l), tmpp = COEF(f0);
683: i >= 0; i-- )
684: *(tmppp[i]) = dmb(m,tmpp[i],lcm,&tmp);
685: dtestroot(m,1,f,f0l,dc,dcp);
686: if ( *dcp )
687: return;
688: n = UDEG(f); W_LUMALLOC(n,b,fpa); W_LUMALLOC(n,b,tpa);
689: ptolum(m,b,f,fpa);
690: dvr = W_UMALLOC(n); wq = W_UMALLOC(n);
691: wt = W_UMALLOC(n); ws = W_UMALLOC(n);
692: cpyum(fe,dvr); divum(m,dvr,f0,wq);
693: t = dmb(m,pwrm(m,lcm,e-1),e,&tmp); DEG(dvr) = DEG(wq);
694: for ( k = 0; k <= DEG(wq); k++ )
695: COEF(dvr)[k] = dmb(m,COEF(wq)[k],t,&tmp);
696: for ( i = 1; i < b; i++ ) {
697: pwrlum(m,i+1,f0l,e,tpa);
698: for ( k = 0, pp = COEF(fpa), wpp = COEF(tpa);
699: k <= n; k++ )
700: COEF(wt)[k] = (pp[k][i]-wpp[k][i]+m)%m;
701: degum(wt,n); dr = divum(m,wt,dvr,ws);
702: if ( dr >= 0 ) {
703: *dcp = 0;
704: return;
705: }
706: for ( k = 0, pp = COEF(f0l); k <= DEG(ws); k++ )
707: pp[k][i] = COEF(ws)[k];
708: dtestroot(m,i+1,f,f0l,dc,dcp);
709: if ( *dcp )
710: return;
711: }
712: }
713:
1.10 ! noro 714: void sqfrp(VL vl,P f,DCP *dcp)
1.1 noro 715: {
716: P c,p;
717: DCP dc,dc0;
718:
719: if ( !f || NUM(f) ) {
720: NEWDC(dc0); *dcp = dc0; DEG(dc0) = ONE;
721: COEF(dc0) = f; NEXT(dc0) = 0;
722: } else if ( !qpcheck((Obj)f) )
723: error("sqfrp : invalid argument");
724: else {
725: NEWDC(dc0); *dcp = dc0; DEG(dc0) = ONE;
726: ptozp(f,1,(Q *)&c,&p); msqfr(vl,p,&dc);
727: COEF(dc0) = c; NEXT(dc0) = dc;
728: adjsgn(f,dc0);
729: }
730: }
731:
732: /*
733: * f : must be a poly with int coef, ignore int content
734: */
1.10 ! noro 735: void msqfr(VL vl,P f,DCP *dcp)
1.1 noro 736: {
737: DCP dc,dct,dcs;
738: P c,p,t,s,pc;
739: VL mvl;
740:
741: ptozp(f,1,(Q *)&c,&t); monomialfctr(vl,t,&p,&dc);
742: if ( NUM(p) ) {
743: *dcp = dc;
744: return;
745: }
746: mindegp(vl,p,&mvl,&s);
747: #if 0
748: minlcdegp(vl,p,&mvl,&s);
749: min_common_vars_in_coefp(vl,p,&mvl,&s);
750: #endif
751: pcp(mvl,s,&p,&pc);
752: if ( !NUM(pc) ) {
753: msqfr(mvl,pc,&dcs);
754: if ( !dc )
755: dc = dcs;
756: else {
757: for ( dct = dc; NEXT(dct); dct = NEXT(dct) );
758: NEXT(dct) = dcs;
759: }
760: }
761: msqfrmain(mvl,p,&dcs);
762: for ( dct = dcs; dct; dct = NEXT(dct) ) {
763: reorderp(vl,mvl,COEF(dct),&t); COEF(dct) = t;
764: }
765: if ( !dc )
766: *dcp = dcs;
767: else {
768: for ( dct = dc; NEXT(dct); dct = NEXT(dct) );
769: NEXT(dct) = dcs; *dcp = dc;
770: }
771: }
772:
1.10 ! noro 773: void usqp(P f,DCP *dcp)
1.1 noro 774: {
775: int index,nindex;
776: P g,c,h;
777: DCP dc;
778:
779: ptozp(f,1,(Q *)&c,&h);
780: if ( SGN((Q)LC(h)) < 0 )
781: chsgnp(h,&g);
782: else
783: g = h;
784: for ( index = 0, dc = 0; !dc; index = nindex )
785: hsq(index,5,g,&nindex,&dc);
786: *dcp = dc;
787: }
788:
1.10 ! noro 789: void msqfrmain(VL vl,P p,DCP *dcp)
1.1 noro 790: {
791: int i,j;
792: VL nvl,tvl;
793: VN vn,vnt,vn1;
794: P gg,tmp,p0,g;
795: DCP dc,dc0,dcr,dcr0;
796: int nv,d,d1;
797: int found;
798: VN svn1;
799: P sp0;
800: DCP sdc0;
801:
802: if ( deg(VR(p),p) == 1 ) {
803: NEWDC(dc); DEG(dc) = ONE; COEF(dc) = p; NEXT(dc) = 0;
804: *dcp = dc;
805: return;
806: }
807: clctv(vl,p,&nvl);
808: for ( nv = 0, tvl = nvl; tvl; tvl = NEXT(tvl), nv++);
809: if ( nv == 1 ) {
810: usqp(p,dcp);
811: return;
812: }
813: #if 0
814: if ( heusqfrchk(nvl,p) ) {
815: NEWDC(dc); DEG(dc) = ONE; COEF(dc) = p; NEXT(dc) = 0;
816: *dcp = dc;
817: return;
818: }
819: #endif
820: W_CALLOC(nv,struct oVN,vn);
821: W_CALLOC(nv,struct oVN,vnt);
822: W_CALLOC(nv,struct oVN,vn1);
823: W_CALLOC(nv,struct oVN,svn1);
824: for ( i = 0, tvl = NEXT(nvl); tvl; tvl = NEXT(tvl), i++ )
825: vn1[i].v = vn[i].v = tvl->v;
826: vn1[i].v = vn[i].v = 0;
1.5 noro 827:
828: /* determine a heuristic bound of deg(GCD(p,p')) */
829: while ( 1 ) {
830: for ( i = 0; vn1[i].v; i++ )
831: vn1[i].n = ((unsigned int)random())%256+1;
832: substvp(nvl,LC(p),vn1,&tmp);
833: if ( tmp ) {
834: substvp(nvl,p,vn1,&p0);
835: usqp(p0,&dc0);
836: for ( d1 = 0, dc = dc0; dc; dc = NEXT(dc) )
837: if ( DEG(dc) )
838: d1 += (QTOS(DEG(dc))-1)*UDEG(COEF(dc));
839: if ( d1 == 0 ) {
840: /* p is squarefree */
841: NEWDC(dc); DEG(dc) = ONE; COEF(dc) = p; NEXT(dc) = 0;
842: *dcp = dc;
843: return;
844: } else {
1.7 noro 845: d = d1+1; /* XXX : try searching better evaluation */
846: found = 0;
1.5 noro 847: break;
848: }
849: }
850: }
1.1 noro 851:
1.6 noro 852: for ( dcr0 = 0, g = p; ; ) {
1.1 noro 853: while ( 1 ) {
854: for ( i = 0, j = 0; vn[i].v; i++ )
855: if ( vn[i].n ) vnt[j++].v = (V)i;
856: vnt[j].n = 0;
857:
858: mulsgn(vn,vnt,j,vn1);
859: substvp(nvl,LC(g),vn1,&tmp);
860: if ( tmp ) {
861: substvp(nvl,g,vn1,&p0);
862: usqp(p0,&dc0);
863: for ( d1 = 0, dc = dc0; dc; dc = NEXT(dc) )
864: if ( DEG(dc) )
865: d1 += (QTOS(DEG(dc))-1)*UDEG(COEF(dc));
866:
867: if ( d1 == 0 ) {
868: NEWDC(dc); DEG(dc) = ONE; COEF(dc) = g; NEXT(dc) = 0;
869: if ( !dcr0 )
870: dcr0 = dc;
871: else
872: NEXT(dcr) = dc;
873: *dcp = dcr0;
874: return;
875: }
876:
877: if ( d < d1 )
878: goto END;
879: if ( d > d1 ) {
880: d = d1;
881: found = 1;
882: bcopy((char *)vn1,(char *)svn1,(int)(sizeof(struct oVN)*nv));
883: sp0 = p0; sdc0 = dc0;
884: goto END;
885: }
886: /* d1 == d */
887: if ( found ) {
888: found = 0;
889: #if 0
890: if ( d > d1 ) {
891: d = d1;
892: /*} */
893: #endif
894: msqfrmainmain(nvl,g,svn1,sp0,sdc0,&dc,&gg); g = gg;
895: if ( dc ) {
896: if ( !dcr0 )
897: dcr0 = dc;
898: else
899: NEXT(dcr) = dc;
900: for ( dcr = dc; NEXT(dcr); dcr = NEXT(dcr) );
901: if ( NUM(g) ) {
902: NEXT(dcr) = 0; *dcp = dcr0;
903: return;
904: }
905: d = deg(VR(g),g);
906: }
907: }
908: }
909: END:
910: if ( nextbin(vnt,j) )
911: break;
912: }
913: next(vn);
914: }
915: }
916:
1.10 ! noro 917: void msqfrmainmain(VL vl,P p,VN vn,P p0,DCP dc0,DCP *dcp,P *pp)
1.1 noro 918: {
919: int i,j,k,np;
920: DCP *a;
921: DCP dc,dcr,dcr0,dct;
922: P g,t,s,u,t0,f,f0,d,d0,g0,h0,x,xx;
923: Q q;
924: V v;
925:
926: for ( np = 0, dc = dc0; dc; dc = NEXT(dc), np++ );
927: a = (DCP *)ALLOCA((np + 1)*sizeof(DCP));
928: for ( i = 0, dc = dc0; dc; i++, dc = NEXT(dc) )
929: a[np-i-1] = dc;
930:
931: for ( i = 0, dcr0 = 0, f = p, f0 = p0, v = VR(p);
932: i < np; i++ ) {
933: if ( (i == (np-1))&&UNIQ(DEG(a[i])) ) {
934: NEXTDC(dcr0,dcr);
935: DEG(dcr) = DEG(a[i]);
936: COEF(dcr) = f;
937: f = (P)ONE;
938: } else if ( (i == (np-1))&&UNIQ(DEG(DC(COEF(a[i])))) ) {
939: diffp(vl,f,v,&s); pcp(vl,s,&t,&u);
940: if ( divtpz(vl,f,t,&s) ) {
941: NEXTDC(dcr0,dcr);
942: DEG(dcr) = DEG(a[i]);
943: COEF(dcr) = s;
944: f = (P)ONE;
945: } else
946: break;
947: } else {
948: for ( t = f, t0 = f0,
949: j = 0, k = QTOS(DEG(a[i]))-1; j < k; j++ ) {
950: diffp(vl,t,v,&s); t = s;
951: diffp(vl,t0,v,&s); t0 = s;
952: }
953: factorial(k,&q);
954: divsp(vl,t,(P)q,&s);
955: for ( dct = DC(s); NEXT(dct); dct = NEXT(dct) );
956: if ( DEG(dct) ) {
957: MKV(VR(s),x); pwrp(vl,x,DEG(dct),&xx);
958: divsp(vl,s,xx,&d);
959: } else {
960: xx = (P)ONE; d = s;
961: }
962: divsp(vl,t0,xx,&t);
963: divsp(vl,t,(P)q,&s);
964: ptozp(s,1,(Q *)&t,&d0);
965:
966: for ( dct = DC(COEF(a[i])); NEXT(dct); dct = NEXT(dct) );
967: if ( DEG(dct) )
968: divsp(vl,COEF(a[i]),xx,&g0);
969: else {
970: xx = (P)ONE; g0 = COEF(a[i]);
971: }
972:
973: pcp(vl,d,&t,&u); d = t;
974: ptozp(g0,1,(Q *)&u,&t); g0 = t;
975:
976: {
977: DCP dca,dcb;
978:
979: fctrp(vl,LC(d),&dca);
980: for ( dcb = dca, u = (P)ONE; dcb; dcb = NEXT(dcb) ) {
981: if ( NUM(COEF(dcb)) ) {
982: mulp(vl,u,COEF(dcb),&t); u = t;
983: } else {
984: Q qq;
985: P tt;
986:
987: pwrp(vl,COEF(dcb),DEG(a[i]),&s);
988: for ( t = LC(f), j = 0; divtpz(vl,t,s,&tt); j++, t = tt );
989: STOQ(j,qq);
990: if ( cmpq(qq,DEG(dcb)) > 0 )
991: qq = DEG(dcb);
992: pwrp(vl,COEF(dcb),qq,&t); mulp(vl,u,t,&s); u = s;
993: }
994: }
995: divsp(vl,d0,g0,&h0);
996: }
997: mfctrhen2(vl,vn,d,d0,g0,h0,u,LC(d),&s);
998: if ( s ) {
999: mulp(vl,s,xx,&g);
1000: pwrp(vl,g,DEG(a[i]),&t);
1001: if ( divtpz(vl,f,t,&s) ) {
1002: NEXTDC(dcr0,dcr);
1003: DEG(dcr) = DEG(a[i]); COEF(dcr) = g;
1004: f = s; substvp(vl,f,vn,&f0);
1005: } else
1006: break;
1007: } else
1008: break;
1009: }
1010: }
1011: *pp = f;
1012: if ( dcr0 )
1013: NEXT(dcr) = 0;
1014: *dcp = dcr0;
1015: }
1016:
1.10 ! noro 1017: void mfctrhen2(VL vl,VN vn,P f,P f0,P g0,P h0,P lcg,P lch,P *gp)
1.1 noro 1018: {
1019: V v;
1020: P f1,lc,lc0,lcg0,lch0;
1021: P m,ff0,gg0,hh0,gk,hk,ggg,gggr,hhh,ak,bk,tmp;
1022: Q bb,qk,s;
1023: Q cbd;
1024: int dbd;
1025: int d;
1026:
1027: if ( NUM(g0) ) {
1028: *gp = (P)ONE;
1029: return;
1030: }
1031:
1032: v = VR(f); d = deg(v,f);
1033: if ( d == deg(v,g0) ) {
1034: pcp(vl,f,gp,&tmp);
1035: return;
1036: }
1037:
1038: mulp(vl,lcg,lch,&lc);
1039: if ( !divtpz(vl,lc,LC(f),(P *)&s) ) {
1040: *gp = 0;
1041: return;
1042: }
1043: mulp(vl,(P)s,f,&f1);
1044: dbd = dbound(VR(f1),f1) + 1; cbound(vl,f1,&cbd);
1045:
1046: substvp(vl,lc,vn,&lc0);
1047: divq((Q)lc0,(Q)LC(f0),(Q *)&m); mulp(vl,f0,m,&ff0);
1048: substvp(vl,lcg,vn,&lcg0);
1049: divq((Q)lcg0,(Q)LC(g0),(Q *)&m); mulp(vl,g0,m,&gg0);
1050: substvp(vl,lch,vn,&lch0);
1051: divq((Q)lch0,(Q)LC(h0),(Q *)&m); mulp(vl,h0,m,&hh0);
1052: addq(cbd,cbd,&bb);
1053: henzq1(gg0,hh0,bb,&bk,&ak,&qk); gk = gg0; hk = hh0;
1054: henmv(vl,vn,f1,gk,hk,ak,bk,
1055: lcg,lch,lcg0,lch0,qk,dbd,&ggg,&hhh);
1056:
1057: if ( divtpz(vl,f1,ggg,&gggr) )
1058: pcp(vl,ggg,gp,&tmp);
1059: else
1060: *gp = 0;
1061: }
1062:
1.10 ! noro 1063: int sqfrchk(P p)
1.1 noro 1064: {
1065: Q c;
1066: P f;
1067: DCP dc;
1068:
1069: ptozp(p,SGN((Q)UCOEF(p)),&c,&f); usqp(f,&dc);
1070: if ( NEXT(dc) || !UNIQ(DEG(dc)) )
1071: return ( 0 );
1072: else
1073: return ( 1 );
1074: }
1075:
1.10 ! noro 1076: int cycchk(P p)
1.1 noro 1077: {
1078: Q c;
1079: P f;
1080:
1081: ptozp(p,SGN((Q)UCOEF(p)),&c,&f);
1082: if ( iscycp(f) || iscycm(f) )
1083: return 0;
1084: else
1085: return 1;
1086: }
1087:
1.10 ! noro 1088: int zerovpchk(VL vl,P p,VN vn)
1.1 noro 1089: {
1090: P t;
1091:
1092: substvp(vl,p,vn,&t);
1093: if ( t )
1094: return ( 0 );
1095: else
1096: return ( 1 );
1097: }
1098:
1.10 ! noro 1099: int valideval(VL vl,DCP dc,VN vn)
1.1 noro 1100: {
1101: DCP dct;
1102: Q *a;
1103: int i,j,n;
1104: N q,r;
1105:
1106: for ( dct = NEXT(dc), n = 0; dct; dct = NEXT(dct), n++ );
1107: W_CALLOC(n,Q,a);
1108: for ( dct = NEXT(dc), i = 0; dct; dct = NEXT(dct), i++ ) {
1109: substvp(vl,COEF(dct),vn,(P *)&a[i]);
1110: if ( !a[i] )
1111: return ( 0 );
1112:
1113: for ( j = 0; j < i; j++ ) {
1114: divn(NM(a[j]),NM(a[i]),&q,&r);
1115: if ( !r )
1116: return ( 0 );
1117: divn(NM(a[i]),NM(a[j]),&q,&r);
1118: if ( !r )
1119: return ( 0 );
1120: }
1121: }
1122: return ( 1 );
1123: }
1124:
1.10 ! noro 1125: void estimatelc(VL vl,Q c,DCP dc,VN vn,P *lcp)
1.1 noro 1126: {
1127: int i;
1128: DCP dct;
1129: P r,s,t;
1130: Q c0,c1,c2;
1131:
1132: for ( dct = dc, r = (P)ONE; dct; dct = NEXT(dct) ) {
1133: if ( NUM(COEF(dct)) ) {
1134: mulp(vl,r,COEF(dct),&s); r = s;
1135: } else {
1136: substvp(vl,COEF(dct),vn,(P *)&c0);
1137: for ( i = 0, c1 = c; i < (int)QTOS(DEG(dct)); i++ ) {
1138: divq(c1,c0,&c2);
1139: if ( !INT(c2) )
1140: break;
1141: else
1142: c1 = c2;
1143: }
1144: if ( i ) {
1145: STOQ(i,c1);
1146: pwrp(vl,COEF(dct),c1,&s); mulp(vl,r,s,&t); r = t;
1147: }
1148: }
1149: }
1150: *lcp = r;
1151: }
1152:
1.10 ! noro 1153: void monomialfctr(VL vl,P p,P *pr,DCP *dcp)
1.1 noro 1154: {
1155: VL nvl,avl;
1156: Q d;
1157: P f,t,s;
1158: DCP dc0,dc;
1159:
1160: clctv(vl,p,&nvl);
1161: for ( dc0 = 0, avl = nvl, f = p; avl; avl = NEXT(avl) ) {
1162: getmindeg(avl->v,f,&d);
1163: if ( d ) {
1164: MKV(avl->v,t); NEXTDC(dc0,dc); DEG(dc) = d; COEF(dc) = t;
1165: pwrp(vl,t,d,&s); divsp(vl,f,s,&t); f = t;
1166: }
1167: }
1168: if ( dc0 )
1169: NEXT(dc) = 0;
1170: *pr = f; *dcp = dc0;
1171: }
1172:
1.10 ! noro 1173: void afctr(VL vl,P p0,P p,DCP *dcp)
1.1 noro 1174: {
1175: DCP dc,dc0,dcr,dct,dcs;
1176: P t;
1177: VL nvl;
1178:
1179: if ( VR(p) == VR(p0) ) {
1180: NEWDC(dc);
1181: DEG(dc) = ONE;
1182: COEF(dc) = p;
1183: NEXT(dc) = 0;
1184: *dcp = dc;
1185: return;
1186: }
1187:
1188: clctv(vl,p,&nvl);
1189: if ( !NEXT(nvl) )
1190: ufctr(p,1,&dc);
1191: else {
1192: sqa(vl,p0,p,&dc);
1193: for ( dct = dc; dct; dct = NEXT(dct) ) {
1194: pmonic(vl,p0,COEF(dct),&t); COEF(dct) = t;
1195: }
1196: }
1197: if ( NUM(COEF(dc)) )
1198: dcr = NEXT(dc);
1199: else
1200: dcr = dc;
1201: for ( dc0 = 0; dcr; dcr = NEXT(dcr) ) {
1202: afctrmain(vl,p0,COEF(dcr),1,&dcs);
1203:
1204: for ( dct = dcs; dct; dct = NEXT(dct) )
1205: DEG(dct) = DEG(dcr);
1206: if ( !dc0 )
1207: dc0 = dcs;
1208: else {
1209: for ( dct = dc0; NEXT(dct); dct = NEXT(dct) );
1210: NEXT(dct) = dcs;
1211: }
1212: }
1213: *dcp = dc0;
1214: }
1215:
1.10 ! noro 1216: void afctrmain(VL vl,P p0,P p,int init,DCP *dcp)
1.1 noro 1217: {
1218: P x,y,s,m,a,t,u,pt,pt1,res,g;
1219: Q q;
1220: DCP dc,dc0,dcsq0,dcr0,dcr,dct,dcs;
1221: V v,v0;
1222:
1223: if ( !cmpq(DEG(DC(p)),ONE) ) {
1224: NEWDC(dc); DEG(dc) = ONE; NEXT(dc) = 0;
1225: pmonic(vl,p0,p,&COEF(dc)); *dcp = dc;
1226: return;
1227: }
1228:
1229: v = VR(p); MKV(v,x);
1230: v0 = VR(p0); MKV(v0,y);
1231: STOQ(init,q),s = (P)q;
1232: mulp(vl,s,y,&m); subp(vl,x,m,&t); addp(vl,x,m,&a);
1233: substp(vl,p,v,t,&pt);
1234: remsdcp(vl,pt,p0,&pt1);
1235:
1236: /*
1237: if ( ( deg(v0,p0) <= 3 ) || ( TCPQ(p0) <= 2 ) )
1238: resultp(vl,v0,p0,pt1,&res);
1239: else
1240: srcrnorm(vl,v0,pt1,p0,&res);
1241: */
1242: #if 0
1243: srcr(vl,v0,pt1,p0,&res);
1244: #endif
1245: resultp(vl,v0,p0,pt1,&res);
1246: usqp(res,&dcsq0);
1247: for ( dc0 = 0, dct = dcsq0; dct; dct = NEXT(dct) ) {
1248: if ( UNIQ(DEG(dct)) )
1249: ufctr(COEF(dct),deg(v0,p0),&dcs);
1250: else
1251: ufctr(COEF(dct),1,&dcs);
1252: for ( dcr = dcs; dcr; dcr = NEXT(dcr) )
1253: DEG(dcr) = DEG(dct);
1254: if ( !dc0 ) {
1255: dc0 = NEXT(dcs);
1256: dc = dc0;
1257: } else {
1258: for ( ; NEXT(dc); dc = NEXT(dc) );
1259: NEXT(dc) = NEXT(dcs);
1260: }
1261: }
1262: sortfs(&dc0);
1263:
1264: for ( g = p, dcr = dcr0 = 0, dc = dc0; dc; dc = NEXT(dc) ) {
1265: if ( !UNIQ(DEG(dc)) ) {
1266: substp(vl,COEF(dc),v,a,&pt); remsdcp(vl,pt,p0,&s);
1267: gcda(vl,p0,s,g,&u);
1268: if ( !NUM(u) && (VR(u) == v)) {
1269: afctrmain(vl,p0,u,init+1,&dct);
1270: for ( dcs = dct, t = (P)ONE; dcs; dcs = NEXT(dcs) ) {
1271: mulp(vl,t,COEF(dcs),&s); remsdcp(vl,s,p0,&t);
1272: }
1273: pdiva(vl,p0,g,t,&s); g = s;
1274: if ( !dcr0 )
1275: dcr0 = dct;
1276: else
1277: NEXT(dcr) = dct;
1278: for ( dcr = dct; NEXT(dcr); dcr = NEXT(dcr) );
1279: }
1280: } else {
1281: substp(vl,COEF(dc),v,a,&pt); remsdcp(vl,pt,p0,&s);
1282: gcda(vl,p0,s,g,&u);
1283: if ( !NUM(u) && (VR(u) == v)) {
1284: NEXTDC(dcr0,dcr);
1285: DEG(dcr) = ONE;
1286: COEF(dcr) = u;
1287: pdiva(vl,p0,g,u,&t); g = t;
1288: }
1289: }
1290: }
1291: if ( dcr0 )
1292: NEXT(dcr) = 0;
1293: *dcp = dcr0;
1294: }