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source: git/Singular/ipshell.cc @ 8078c8

spielwiese

Last change on this file since 8078c8 was 8078c8, checked in by Hans Schönemann <hannes@…>, 16 years ago
hannes: better alg. for OrdSgn git-svn-id: file:///usr/local/Singular/svn/trunk@10593 2c84dea3-7e68-4137-9b89-c4e89433aadc
Property mode set to `100644`
File size: 117.2 KB

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1	/****************************************
2	* Computer Algebra System SINGULAR *
3	****************************************/
4	/* $Id: ipshell.cc,v 1.178 2008-02-22 11:14:16 Singular Exp $ */
5	/*
6	* ABSTRACT:
7	*/
8
9	//#include <stdlib.h>
10	#include <stdio.h>
11	#include <string.h>
12	#include <ctype.h>
13	#include <math.h>
14
15	#include "mod2.h"
16	#include "tok.h"
17	#include "ipid.h"
18	#include "intvec.h"
19	#include "omalloc.h"
20	#include "febase.h"
21	#include "polys.h"
22	#include "prCopy.h"
23	#include "ideals.h"
24	#include "matpol.h"
25	#include "kstd1.h"
26	#include "ring.h"
27	#include "subexpr.h"
28	#include "maps.h"
29	#include "syz.h"
30	#include "numbers.h"
31	#include "modulop.h"
32	#include "longalg.h"
33	#include "lists.h"
34	#include "attrib.h"
35	#include "ipconv.h"
36	#include "silink.h"
37	#include "stairc.h"
38	#include "weight.h"
39	#include "semic.h"
40	#include "splist.h"
41	#include "spectrum.h"
42	#include "gnumpfl.h"
43	#include "mpr_base.h"
44	#include "ffields.h"
45	#include "clapsing.h"
46	#include "hutil.h"
47	#include "ipshell.h"
48	#ifdef HAVE_FACTORY
49	#define SI_DONT_HAVE_GLOBAL_VARS
50	#include <factory.h>
51	#endif
52
53	// define this if you want to use the fast_map routine for mapping ideals
54	#define FAST_MAP
55
56	#ifdef FAST_MAP
57	#include "fast_maps.h"
58	#endif
59
60	leftv iiCurrArgs=NULL;
61	int traceit = 0;
62	char *lastreserved=NULL;
63
64	int myynest = -1;
65
66	static BOOLEAN iiNoKeepRing=TRUE;
67
68	/0 implementation/
69
70	char * iiTwoOps(int t)
71	{
72	if (t<127)
73	{
74	static char ch[2];
75	switch (t)
76	{
77	case '&':
78	return "and";
79	case '\|':
80	return "or";
81	default:
82	ch[0]=t;
83	ch[1]='\0';
84	return ch;
85	}
86	}
87	switch (t)
88	{
89	case COLONCOLON: return "::";
90	case DOTDOT: return "..";
91	//case PLUSEQUAL: return "+=";
92	//case MINUSEQUAL: return "-=";
93	case MINUSMINUS: return "--";
94	case PLUSPLUS: return "++";
95	case EQUAL_EQUAL: return "==";
96	case LE: return "<=";
97	case GE: return ">=";
98	case NOTEQUAL: return "<>";
99	default: return Tok2Cmdname(t);
100	}
101	}
102
103	static void list1(const char* s, idhdl h,BOOLEAN c, BOOLEAN fullname)
104	{
105	char buffer[22];
106	int l;
107	char buf2[128];
108
109	if(fullname) sprintf(buf2, "%s::%s", "", IDID(h));
110	else sprintf(buf2, "%s", IDID(h));
111
112	Print("%s%-20.20s [%d] ",s,buf2,IDLEV(h));
113	if (h == currRingHdl) PrintS("*");
114	PrintS(Tok2Cmdname((int)IDTYP(h)));
115
116	ipListFlag(h);
117	switch(IDTYP(h))
118	{
119	case INT_CMD: Print(" %d",IDINT(h)); break;
120	case INTVEC_CMD:Print(" (%d)",IDINTVEC(h)->length()); break;
121	case INTMAT_CMD:Print(" %d x %d",IDINTVEC(h)->rows(),IDINTVEC(h)->cols());
122	break;
123	case POLY_CMD:
124	case VECTOR_CMD:if (c)
125	{
126	PrintS(" ");wrp(IDPOLY(h));
127	if(IDPOLY(h) != NULL)
128	{
129	Print(", %d monomial(s)",pLength(IDPOLY(h)));
130	}
131	}
132	break;
133	case MODUL_CMD: Print(", rk %d", IDIDEAL(h)->rank);
134	case IDEAL_CMD: Print(", %u generator(s)",
135	IDELEMS(IDIDEAL(h)),IDIDEAL(h)->rank); break;
136	case MAP_CMD:
137	Print(" from %s",IDMAP(h)->preimage); break;
138	case MATRIX_CMD:Print(" %u x %u"
139	,MATROWS(IDMATRIX(h))
140	,MATCOLS(IDMATRIX(h))
141	);
142	break;
143	case PACKAGE_CMD:
144	PrintS(" (");
145	switch (IDPACKAGE(h)->language)
146	{
147	case LANG_SINGULAR: PrintS("S"); break;
148	case LANG_C: PrintS("C"); break;
149	case LANG_TOP: PrintS("T"); break;
150	case LANG_NONE: PrintS("N"); break;
151	default: PrintS("U");
152	}
153	if(IDPACKAGE(h)->libname!=NULL)
154	Print(",%s", IDPACKAGE(h)->libname);
155	PrintS(")");
156	break;
157	case PROC_CMD: if(strlen(IDPROC(h)->libname)>0)
158	Print(" from %s",IDPROC(h)->libname);
159	if(IDPROC(h)->is_static)
160	PrintS(" (static)");
161	break;
162	case STRING_CMD:
163	{
164	char *s;
165	l=strlen(IDSTRING(h));
166	memset(buffer,0,22);
167	strncpy(buffer,IDSTRING(h),si_min(l,20));
168	if ((s=strchr(buffer,'\n'))!=NULL)
169	{
170	*s='\0';
171	}
172	PrintS(" ");
173	PrintS(buffer);
174	if((s!=NULL) \|\|(l>20))
175	{
176	Print("..., %d char(s)",l);
177	}
178	break;
179	}
180	case LIST_CMD: Print(", size: %d",IDLIST(h)->nr+1);
181	break;
182	case QRING_CMD:
183	case RING_CMD:
184	if ((IDRING(h)==currRing) && (currRingHdl!=h))
185	PrintS("()"); / this is an alias to currRing */
186	#ifdef RDEBUG
187	if (traceit &TRACE_SHOW_RINGS)
188	Print(" <%x>",IDRING(h));
189	#endif
190	break;
191	/default: break;/
192	}
193	PrintLn();
194	}
195
196	void type_cmd(idhdl h)
197	{
198	BOOLEAN oldShortOut = FALSE;
199
200	if (currRing != NULL)
201	{
202	oldShortOut = currRing->ShortOut;
203	currRing->ShortOut = 1;
204	}
205	list1("// ",h,FALSE,FALSE);
206	if (IDTYP(h)!=INT_CMD)
207	{
208	sleftv expr;
209	memset(&expr,0,sizeof(expr));
210	expr.rtyp=IDHDL;
211	expr.name=IDID(h);
212	expr.data=(void *)h;
213	expr.Print();
214	}
215	if (currRing != NULL)
216	currRing->ShortOut = oldShortOut;
217	}
218
219	static void killlocals0(int v, idhdl * localhdl, const ring r)
220	{
221	idhdl h = *localhdl;
222	while (h!=NULL)
223	{
224	int vv;
225	//Print("consider %s, lev: %d:",IDID(h),IDLEV(h));
226	if ((vv=IDLEV(h))>0)
227	{
228	if (vv < v)
229	{
230	if (iiNoKeepRing)
231	{
232	//PrintS(" break\n");
233	return;
234	}
235	h = IDNEXT(h);
236	//PrintLn();
237	}
238	else if (vv >= v)
239	{
240	idhdl nexth = IDNEXT(h);
241	killhdl2(h,localhdl,r);
242	h = nexth;
243	//PrintS("kill\n");
244	}
245	}
246	else
247	{
248	h = IDNEXT(h);
249	//PrintLn();
250	}
251	}
252	}
253	#ifndef HAVE_NS
254	void killlocals(int v)
255	{
256	killlocals0(v,&IDROOT,currRing);
257
258	if ((iiRETURNEXPR_len > myynest)
259	&& ((iiRETURNEXPR[myynest].Typ()==RING_CMD)
260	\|\| (iiRETURNEXPR[myynest].Typ()==QRING_CMD)))
261	{
262	leftv h=&iiRETURNEXPR[myynest];
263	killlocals0(v,&(((ring)h->data)->idroot),(ring)h->data);
264	}
265
266	idhdl sh=currRingHdl;
267	ring sr=currRing;
268	BOOLEAN changed=FALSE;
269	idhdl h = IDROOT;
270
271	// Print("killlocals in %s\n",IDID(currPackHdl));
272	while (h!=NULL)
273	{
274	if (((IDTYP(h)==QRING_CMD) \|\| (IDTYP(h) == RING_CMD))
275	&& (IDRING(h)->idroot!=NULL))
276	{
277	if (IDRING(h)!=currRing) {changed=TRUE;rSetHdl(h);}
278	killlocals0(v,&(IDRING(h)->idroot),IDRING(h));
279	}
280	else if (IDTYP(h) == PACKAGE_CMD)
281	{
282	killlocals0(v,&(IDPACKAGE(h)->idroot),IDRING(h));
283	}
284	h = IDNEXT(h);
285	}
286	if (changed)
287	{
288	currRing=NULL;
289	currRingHdl=NULL;
290	if (sh!=NULL) rSetHdl(sh);
291	else if (sr!=NULL)
292	{
293	sh=rFindHdl(sr,NULL,NULL);
294	rSetHdl(sh);
295	}
296	}
297
298	if (myynest<=1) iiNoKeepRing=TRUE;
299	//Print("end killlocals >= %d\n",v);
300	//listall();
301	}
302	#endif
303	#ifdef HAVE_NS
304	void killlocals_rec(idhdl *root,int v, ring r)
305	{
306	idhdl h=*root;
307	while (h!=NULL)
308	{
309	if (IDLEV(h)>=v)
310	{
311	// Print("kill %s, lev %d for lev %d\n",IDID(h),IDLEV(h),v);
312	idhdl n=IDNEXT(h);
313	killhdl2(h,root,r);
314	h=n;
315	}
316	else if (IDTYP(h)==PACKAGE_CMD)
317	{
318	// Print("into pack %s, lev %d for lev %d\n",IDID(h),IDLEV(h),v);
319	if (IDPACKAGE(h)!=basePack)
320	killlocals_rec(&(IDRING(h)->idroot),v,r);
321	h=IDNEXT(h);
322	}
323	else if ((IDTYP(h)==RING_CMD)
324	\|\|(IDTYP(h)==QRING_CMD))
325	{
326	if (IDRING(h)->idroot!=NULL)
327	{
328	// Print("into ring %s, lev %d for lev %d\n",IDID(h),IDLEV(h),v);
329	killlocals_rec(&(IDRING(h)->idroot),v,IDRING(h));
330	}
331	h=IDNEXT(h);
332	}
333	else
334	{
335	// Print("skip %s lev %d for lev %d\n",IDID(h),IDLEV(h),v);
336	h=IDNEXT(h);
337	}
338	}
339	}
340	BOOLEAN killlocals_list(int v, lists L)
341	{
342	if (L==NULL) return FALSE;
343	BOOLEAN changed=FALSE;
344	int n=L->nr;
345	for(;n>=0;n--)
346	{
347	leftv h=&(L->m[n]);
348	void *d=h->data;
349	if (((h->rtyp==RING_CMD) \|\| (h->rtyp==QRING_CMD))
350	&& (((ring)d)->idroot!=NULL))
351	{
352	if (d!=currRing) {changed=TRUE;rChangeCurrRing((ring)d);}
353	killlocals0(v,&(((ring)h->data)->idroot),(ring)h->data);
354	}
355	else if (h->rtyp==LIST_CMD)
356	changed\|=killlocals_list(v,(lists)d);
357	}
358	return changed;
359	}
360	void killlocals(int v)
361	{
362	BOOLEAN changed=FALSE;
363	idhdl sh=currRingHdl;
364	ring cr=currRing;
365	if (sh!=NULL) changed=((IDLEV(sh)<v) \|\| (IDRING(sh)->ref>0));
366	//if (changed) Print("currRing=%s(%x), lev=%d,ref=%d\n",IDID(sh),IDRING(sh),IDLEV(sh),IDRING(sh)->ref);
367
368	killlocals_rec(&(basePack->idroot),v,currRing);
369
370	if (iiRETURNEXPR_len > myynest)
371	{
372	int t=iiRETURNEXPR[myynest].Typ();
373	if ((/iiRETURNEXPR[myynest].Typ()/ t==RING_CMD)
374	\|\| (/iiRETURNEXPR[myynest].Typ()/ t==QRING_CMD))
375	{
376	leftv h=&iiRETURNEXPR[myynest];
377	if (((ring)h->data)->idroot!=NULL)
378	killlocals0(v,&(((ring)h->data)->idroot),(ring)h->data);
379	}
380	else if (/iiRETURNEXPR[myynest].Typ()/ t==LIST_CMD)
381	{
382	leftv h=&iiRETURNEXPR[myynest];
383	changed \|=killlocals_list(v,(lists)h->data);
384	}
385	}
386	if (changed)
387	{
388	currRingHdl=rFindHdl(cr,NULL,NULL);
389	if (currRingHdl==NULL)
390	currRing=NULL;
391	else
392	rChangeCurrRing(cr);
393	}
394
395	if (myynest<=1) iiNoKeepRing=TRUE;
396	//Print("end killlocals >= %d\n",v);
397	//listall();
398	}
399	#endif
400
401	void list_cmd(int typ, const char* what, const char *prefix,BOOLEAN iterate, BOOLEAN fullname)
402	{
403	idhdl h,start;
404	BOOLEAN all = typ<0;
405	BOOLEAN really_all=FALSE;
406	BOOLEAN do_packages=FALSE;
407
408	if ( typ == -1 ) do_packages=TRUE;
409	if ( typ==0 )
410	{
411	if (strcmp(what,"all")==0)
412	{
413	really_all=TRUE;
414	#ifdef HAVE_NS
415	h=basePack->idroot;
416	#else
417	h=IDROOT;
418	#endif
419	}
420	else
421	{
422	h = ggetid(what);
423	if (h!=NULL)
424	{
425	if (iterate) list1(prefix,h,TRUE,fullname);
426	if ((IDTYP(h)==RING_CMD)
427	\|\| (IDTYP(h)==QRING_CMD)
428	#ifdef HAVE_NS
429	//\|\| (IDTYP(h)==PACKE_CMD)
430	#endif
431	)
432	{
433	h=IDRING(h)->idroot;
434	}
435	else if((IDTYP(h)==PACKAGE_CMD) \|\| (IDTYP(h)==POINTER_CMD))
436	{
437	//Print("list_cmd:package or pointer\n");
438	all=TRUE;typ=PROC_CMD;fullname=TRUE;really_all=TRUE;
439	h=IDPACKAGE(h)->idroot;
440	}
441	else
442	return;
443	}
444	else
445	{
446	Werror("%s is undefined",what);
447	return;
448	}
449	}
450	all=TRUE;
451	}
452	else if (RingDependend(typ))
453	{
454	h = currRing->idroot;
455	}
456	else
457	h = IDROOT;
458	start=h;
459	while (h!=NULL)
460	{
461	if ((all && (IDTYP(h)!=PROC_CMD) &&(IDTYP(h)!=PACKAGE_CMD))
462	\|\| (typ == IDTYP(h))
463	\|\| ((IDTYP(h)==QRING_CMD) && (typ==RING_CMD)))
464	{
465	list1(prefix,h,start==currRingHdl, fullname);
466	if (((IDTYP(h)==RING_CMD)\|\|(IDTYP(h)==QRING_CMD))
467	&& (really_all \|\| (all && (h==currRingHdl)))
468	&& ((IDLEV(h)==0)\|\|(IDLEV(h)==myynest)))
469	{
470	list_cmd(0,IDID(h),"// ",FALSE);
471	}
472	#ifdef HAVE_NS
473	if (IDTYP(h)==PACKAGE_CMD && really_all)
474	{
475	package save_p=currPack;
476	currPack=IDPACKAGE(h);
477	list_cmd(0,IDID(h),"// ",FALSE);
478	currPack=save_p;
479	}
480	#endif /* HAVE_NS */
481	}
482	h = IDNEXT(h);
483	}
484	}
485
486	void test_cmd(int i)
487	{
488	int ii=(char)i;
489
490	if (i == (-32))
491	{
492	test = 0;
493	}
494	else
495	{
496	if (i<0)
497	{
498	ii= -i;
499	if (Sy_bit(ii) & kOptions)
500	{
501	Warn("Gerhard, use the option command");
502	test &= ~Sy_bit(ii);
503	}
504	else if (Sy_bit(ii) & validOpts)
505	test &= ~Sy_bit(ii);
506	}
507	else if (i<32)
508	{
509	if (Sy_bit(ii) & kOptions)
510	{
511	Warn("Gerhard, use the option command");
512	test \|= Sy_bit(ii);
513	}
514	else if (Sy_bit(ii) & validOpts)
515	test \|= Sy_bit(ii);
516	}
517	}
518	}
519
520	int exprlist_length(leftv v)
521	{
522	int rc = 0;
523	while (v!=NULL)
524	{
525	switch (v->Typ())
526	{
527	case INT_CMD:
528	case POLY_CMD:
529	case VECTOR_CMD:
530	case NUMBER_CMD:
531	rc++;
532	break;
533	case INTVEC_CMD:
534	case INTMAT_CMD:
535	rc += ((intvec *)(v->Data()))->length();
536	break;
537	case MATRIX_CMD:
538	case IDEAL_CMD:
539	case MODUL_CMD:
540	{
541	matrix mm = (matrix)(v->Data());
542	rc += mm->rows() * mm->cols();
543	}
544	break;
545	case LIST_CMD:
546	rc+=((lists)v->Data())->nr+1;
547	break;
548	default:
549	rc++;
550	}
551	v = v->next;
552	}
553	return rc;
554	}
555
556	int IsPrime(int p) /* brute force !!!! */
557	{
558	int i,j;
559	if (p == 0) return 0;
560	else if (p == 1) return 1/1/;
561	else if (p == 2) return p;
562	else if (p < 0) return (-IsPrime(-p));
563	else if (!(p & 1)) return IsPrime(p-1);
564	#ifdef HAVE_FACTORY
565	else if (p<=32749) // max. small prime in factory
566	{
567	int a=0;
568	int e=cf_getNumSmallPrimes()-1;
569	i=e/2;
570	do
571	{
572	if (p==(j=cf_getSmallPrime(i))) return p;
573	if (p<j) e=i-1;
574	else a=i+1;
575	i=a+(e-a)/2;
576	} while ( a<= e);
577	if (p>j) return j;
578	else return cf_getSmallPrime(i-1);
579	}
580	#endif
581	#ifdef HAVE_FACTORY
582	int end_i=cf_getNumSmallPrimes()-1;
583	#else
584	int end_i=p/2;
585	#endif
586	int end_p=(int)sqrt((double)p);
587	restart:
588	for (i=0; i<end_i; i++)
589	{
590	#ifdef HAVE_FACTORY
591	j=cf_getSmallPrime(i);
592	#else
593	if (i==0) j=2;
594	else j=2*i-1;
595	#endif
596	if ((p%j) == 0)
597	{
598	#ifdef HAVE_FACTORY
599	if (p<=32751) return IsPrime(p-2);
600	#endif
601	p-=2;
602	goto restart;
603	}
604	if (j > end_p) return p;
605	}
606	return p;
607	}
608
609	BOOLEAN iiWRITE(leftv res,leftv v)
610	{
611	sleftv vf;
612	if (iiConvert(v->Typ(),LINK_CMD,iiTestConvert(v->Typ(),LINK_CMD),v,&vf))
613	{
614	WerrorS("link expected");
615	return TRUE;
616	}
617	si_link l=(si_link)vf.Data();
618	if (vf.next == NULL)
619	{
620	WerrorS("write: need at least two arguments");
621	return TRUE;
622	}
623
624	BOOLEAN b=slWrite(l,vf.next); /* iiConvert preserves next */
625	if (b)
626	{
627	const char *s;
628	if ((l!=NULL)&&(l->name!=NULL)) s=l->name;
629	else s=sNoName;
630	Werror("cannot write to %s",s);
631	}
632	vf.CleanUp();
633	return b;
634	}
635
636	leftv iiMap(map theMap, char * what)
637	{
638	idhdl w,r;
639	leftv v;
640	int i;
641	nMapFunc nMap;
642
643	r=IDROOT->get(theMap->preimage,myynest);
644	#ifdef HAVE_NS
645	if ((currPack!=basePack)
646	&&((r==NULL) \|\| ((r->typ != RING_CMD) && (r->typ != QRING_CMD))))
647	r=basePack->idroot->get(theMap->preimage,myynest);
648	if ((r==NULL) && (currRingHdl!=NULL)
649	&& (strcmp(theMap->preimage,IDID(currRingHdl))==0))
650	{
651	r=currRingHdl;
652	}
653	#endif /* HAVE_NS */
654	if ((r!=NULL) && ((r->typ == RING_CMD) \|\| (r->typ== QRING_CMD)))
655	{
656	//if ((nMap=nSetMap(rInternalChar(IDRING(r)),
657	// IDRING(r)->parameter,
658	// rPar(IDRING(r)),
659	// IDRING(r)->minpoly)))
660	if ((nMap=nSetMap(IDRING(r)))==NULL)
661	{
662	if (rEqual(IDRING(r),currRing))
663	{
664	nMap=nCopy;
665	}
666	else
667	{
668	Werror("can not map from ground field of %s to current ground field",
669	theMap->preimage);
670	return NULL;
671	}
672	}
673	if (IDELEMS(theMap)<IDRING(r)->N)
674	{
675	theMap->m=(polyset)omReallocSize((ADDRESS)theMap->m,
676	IDELEMS(theMap)*sizeof(poly),
677	(IDRING(r)->N)*sizeof(poly));
678	for(i=IDELEMS(theMap);i<IDRING(r)->N;i++)
679	theMap->m[i]=NULL;
680	IDELEMS(theMap)=IDRING(r)->N;
681	}
682	if (what==NULL)
683	{
684	WerrorS("argument of a map must have a name");
685	}
686	else if ((w=IDRING(r)->idroot->get(what,myynest))!=NULL)
687	{
688	char *save_r=NULL;
689	v=(leftv)omAlloc0Bin(sleftv_bin);
690	sleftv tmpW;
691	memset(&tmpW,0,sizeof(sleftv));
692	tmpW.rtyp=IDTYP(w);
693	if (tmpW.rtyp==MAP_CMD)
694	{
695	tmpW.rtyp=IDEAL_CMD;
696	save_r=IDMAP(w)->preimage;
697	IDMAP(w)->preimage=0;
698	}
699	tmpW.data=IDDATA(w);
700	#if 0
701	if (((tmpW.rtyp==IDEAL_CMD)\|\|(tmpW.rtyp==MODUL_CMD)) && idIs0(IDIDEAL(w)))
702	{
703	v->rtyp=tmpW.rtyp;
704	v->data=idInit(IDELEMS(IDIDEAL(w)),IDIDEAL(w)->rank);
705	}
706	else
707	#endif
708	{
709	#ifdef FAST_MAP
710	if ((tmpW.rtyp==IDEAL_CMD) && (nMap==nCopy)
711	#ifdef HAVE_PLURAL
712	&& (!rIsPluralRing(currRing))
713	#endif
714	)
715	{
716	v->rtyp=IDEAL_CMD;
717	v->data=fast_map(IDIDEAL(w), IDRING(r), (ideal)theMap, currRing);
718	}
719	else
720	#endif
721	if (maApplyFetch(MAP_CMD,theMap,v,&tmpW,IDRING(r),NULL,NULL,0,nMap))
722	{
723	Werror("cannot map %s(%d)",Tok2Cmdname(w->typ),w->typ);
724	omFreeBin((ADDRESS)v, sleftv_bin);
725	if (save_r!=NULL) IDMAP(w)->preimage=save_r;
726	return NULL;
727	}
728	}
729	if (save_r!=NULL)
730	{
731	IDMAP(w)->preimage=save_r;
732	IDMAP((idhdl)v)->preimage=omStrDup(save_r);
733	v->rtyp=MAP_CMD;
734	}
735	return v;
736	}
737	else
738	{
739	Werror("%s undefined in %s",what,theMap->preimage);
740	}
741	}
742	else
743	{
744	Werror("cannot find preimage %s",theMap->preimage);
745	}
746	return NULL;
747	}
748
749	#ifdef OLD_RES
750	void iiMakeResolv(resolvente r, int length, int rlen, char * name, int typ0,
751	intvec ** weights)
752	{
753	lists L=liMakeResolv(r,length,rlen,typ0,weights);
754	int i=0;
755	idhdl h;
756	char * s=(char *)omAlloc(strlen(name)+5);
757
758	while (i<=L->nr)
759	{
760	sprintf(s,"%s(%d)",name,i+1);
761	if (i==0)
762	h=enterid(s,myynest,typ0,&(currRing->idroot), FALSE);
763	else
764	h=enterid(s,myynest,MODUL_CMD,&(currRing->idroot), FALSE);
765	if (h!=NULL)
766	{
767	h->data.uideal=(ideal)L->m[i].data;
768	h->attribute=L->m[i].attribute;
769	if (BVERBOSE(V_DEF_RES))
770	Print("//defining: %s as %d-th syzygy module\n",s,i+1);
771	}
772	else
773	{
774	idDelete((ideal *)&(L->m[i].data));
775	Warn("cannot define %s",s);
776	}
777	//L->m[i].data=NULL;
778	//L->m[i].rtyp=0;
779	//L->m[i].attribute=NULL;
780	i++;
781	}
782	omFreeSize((ADDRESS)L->m,(L->nr+1)*sizeof(sleftv));
783	omFreeBin((ADDRESS)L, slists_bin);
784	omFreeSize((ADDRESS)s,strlen(name)+5);
785	}
786	#endif
787
788	//resolvente iiFindRes(char * name, int * len, int *typ0)
789	//{
790	// char s=(char )omAlloc(strlen(name)+5);
791	// int i=-1;
792	// resolvente r;
793	// idhdl h;
794	//
795	// do
796	// {
797	// i++;
798	// sprintf(s,"%s(%d)",name,i+1);
799	// h=currRing->idroot->get(s,myynest);
800	// } while (h!=NULL);
801	// *len=i-1;
802	// if (*len<=0)
803	// {
804	// Werror("no objects %s(1),.. found",name);
805	// omFreeSize((ADDRESS)s,strlen(name)+5);
806	// return NULL;
807	// }
808	// r=(ideal )omAlloc(/(len+1)/ isizeof(ideal));
809	// memset(r,0,(len)sizeof(ideal));
810	// i=-1;
811	// *typ0=MODUL_CMD;
812	// while (i<(*len))
813	// {
814	// i++;
815	// sprintf(s,"%s(%d)",name,i+1);
816	// h=currRing->idroot->get(s,myynest);
817	// if (h->typ != MODUL_CMD)
818	// {
819	// if ((i!=0) \|\| (h->typ!=IDEAL_CMD))
820	// {
821	// Werror("%s is not of type module",s);
822	// omFreeSize((ADDRESS)r,(len)sizeof(ideal));
823	// omFreeSize((ADDRESS)s,strlen(name)+5);
824	// return NULL;
825	// }
826	// *typ0=IDEAL_CMD;
827	// }
828	// if ((i>0) && (idIs0(r[i-1])))
829	// {
830	// *len=i-1;
831	// break;
832	// }
833	// r[i]=IDIDEAL(h);
834	// }
835	// omFreeSize((ADDRESS)s,strlen(name)+5);
836	// return r;
837	//}
838
839	static resolvente iiCopyRes(resolvente r, int l)
840	{
841	int i;
842	resolvente res=(ideal )omAlloc0((l+1)sizeof(ideal));
843
844	for (i=0; i<l; i++)
845	res[i]=idCopy(r[i]);
846	return res;
847	}
848
849	BOOLEAN jjMINRES(leftv res, leftv v)
850	{
851	int len=0;
852	int typ0;
853	lists L=(lists)v->Data();
854	intvec weights=(intvec)atGet(v,"isHomog",INTVEC_CMD);
855	int add_row_shift = 0;
856	if (weights==NULL)
857	weights=(intvec*)atGet(&(L->m[0]),"isHomog",INTVEC_CMD);
858	if (weights!=NULL) add_row_shift=weights->min_in();
859	resolvente rr=liFindRes(L,&len,&typ0);
860	if (rr==NULL) return TRUE;
861	resolvente r=iiCopyRes(rr,len);
862
863	syMinimizeResolvente(r,len,0);
864	omFreeSize((ADDRESS)rr,len*sizeof(ideal));
865	len++;
866	res->data=(char *)liMakeResolv(r,len,-1,typ0,NULL,add_row_shift);
867	return FALSE;
868	}
869
870	BOOLEAN jjBETTI(leftv res, leftv u)
871	{
872	sleftv tmp;
873	memset(&tmp,0,sizeof(tmp));
874	tmp.rtyp=INT_CMD;
875	tmp.data=(void *)1;
876	if ((u->Typ()==IDEAL_CMD)
877	\|\| (u->Typ()==MODUL_CMD))
878	return jjBETTI2_ID(res,u,&tmp);
879	else
880	return jjBETTI2(res,u,&tmp);
881	}
882
883	BOOLEAN jjBETTI2_ID(leftv res, leftv u, leftv v)
884	{
885	lists l=(lists) omAllocBin(slists_bin);
886	l->Init(1);
887	l->m[0].rtyp=u->Typ();
888	l->m[0].data=u->Data();
889	l->m[0].attribute=u->attribute;
890	sleftv tmp2;
891	memset(&tmp2,0,sizeof(tmp2));
892	tmp2.rtyp=LIST_CMD;
893	tmp2.data=(void *)l;
894	BOOLEAN r=jjBETTI2(res,&tmp2,v);
895	l->m[0].data=NULL;
896	l->m[0].attribute=NULL;
897	l->m[0].rtyp=DEF_CMD;
898	l->Clean();
899	return r;
900	}
901
902	BOOLEAN jjBETTI2(leftv res, leftv u, leftv v)
903	{
904	resolvente r;
905	int len;
906	int reg,typ0;
907	lists l=(lists)u->Data();
908
909	intvec *weights=NULL;
910	int add_row_shift=0;
911	intvec ww=(intvec )atGet(&(l->m[0]),"isHomog",INTVEC_CMD);
912	if (ww!=NULL)
913	{
914	weights=ivCopy(ww);
915	add_row_shift = ww->min_in();
916	(*weights) -= add_row_shift;
917	}
918	//Print("attr:%x\n",weights);
919
920	r=liFindRes(l,&len,&typ0);
921	if (r==NULL) return TRUE;
922	res->data=(char *)syBetti(r,len,&reg,weights,(int)(long)v->Data());
923	omFreeSize((ADDRESS)r,(len)*sizeof(ideal));
924	atSet(res,omStrDup("rowShift"),(void*)add_row_shift,INT_CMD);
925	if (weights!=NULL) delete weights;
926	return FALSE;
927	}
928
929	int iiRegularity(lists L)
930	{
931	int len,reg,typ0;
932
933	resolvente r=liFindRes(L,&len,&typ0);
934
935	if (r==NULL)
936	return -2;
937	intvec *weights=NULL;
938	int add_row_shift=0;
939	intvec ww=(intvec )atGet(&(L->m[0]),"isHomog",INTVEC_CMD);
940	if (ww!=NULL)
941	{
942	weights=ivCopy(ww);
943	add_row_shift = ww->min_in();
944	(*weights) -= add_row_shift;
945	}
946	//Print("attr:%x\n",weights);
947
948	intvec *dummy=syBetti(r,len,&reg,weights);
949	if (weights!=NULL) delete weights;
950	delete dummy;
951	omFreeSize((ADDRESS)r,len*sizeof(ideal));
952	return reg+1+add_row_shift;
953	}
954
955	BOOLEAN iiDebugMarker=TRUE;
956	#define BREAK_LINE_LENGTH 80
957	void iiDebug()
958	{
959	Print("\n-- break point in %s --\n",VoiceName());
960	if (iiDebugMarker) VoiceBackTrack();
961	char * s;
962	iiDebugMarker=FALSE;
963	s = (char *)omAlloc(BREAK_LINE_LENGTH+4);
964	loop
965	{
966	memset(s,0,80);
967	fe_fgets_stdin("",s,BREAK_LINE_LENGTH);
968	if (s[BREAK_LINE_LENGTH-1]!='\0')
969	{
970	Print("line too long, max is %d chars\n",BREAK_LINE_LENGTH);
971	}
972	else
973	break;
974	}
975	if (*s=='\n')
976	{
977	iiDebugMarker=TRUE;
978	}
979	#if MDEBUG
980	else if(strncmp(s,"cont;",5)==0)
981	{
982	iiDebugMarker=TRUE;
983	}
984	#endif /* MDEBUG */
985	else
986	{
987	strcat( s, "\n;~\n");
988	newBuffer(s,BT_execute);
989	}
990	}
991
992	lists scIndIndset(ideal S, BOOLEAN all, ideal Q)
993	{
994	int i;
995	indset save;
996	lists res=(lists)omAlloc0Bin(slists_bin);
997
998	hexist = hInit(S, Q, &hNexist);
999	if ((hNexist == 0) \|\| (hisModule!=0))
1000	{
1001	res->Init(0);
1002	return res;
1003	}
1004	save = ISet = (indset)omAlloc0Bin(indlist_bin);
1005	hMu = 0;
1006	hwork = (scfmon)omAlloc(hNexist * sizeof(scmon));
1007	hvar = (varset)omAlloc((pVariables + 1) * sizeof(int));
1008	hpure = (scmon)omAlloc((1 + (pVariables * pVariables)) * sizeof(Exponent_t));
1009	hrad = hexist;
1010	hNrad = hNexist;
1011	radmem = hCreate(pVariables - 1);
1012	hCo = pVariables + 1;
1013	hNvar = pVariables;
1014	hRadical(hrad, &hNrad, hNvar);
1015	hSupp(hrad, hNrad, hvar, &hNvar);
1016	if (hNvar)
1017	{
1018	hCo = hNvar;
1019	memset(hpure, 0, (pVariables + 1) * sizeof(Exponent_t));
1020	hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure);
1021	hLexR(hrad, hNrad, hvar, hNvar);
1022	hDimSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar);
1023	}
1024	if (hCo && (hCo < pVariables))
1025	{
1026	hIndMult(hpure, hNpure, hrad, hNrad, hvar, hNvar);
1027	}
1028	if (hMu!=0)
1029	{
1030	ISet = save;
1031	hMu2 = 0;
1032	if (all && (hCo+1 < pVariables))
1033	{
1034	JSet = (indset)omAlloc0Bin(indlist_bin);
1035	hIndAllMult(hpure, hNpure, hrad, hNrad, hvar, hNvar);
1036	i=hMu+hMu2;
1037	res->Init(i);
1038	if (hMu2 == 0)
1039	{
1040	omFreeBin((ADDRESS)JSet, indlist_bin);
1041	}
1042	}
1043	else
1044	{
1045	res->Init(hMu);
1046	}
1047	for (i=0;i<hMu;i++)
1048	{
1049	res->m[i].data = (void *)save->set;
1050	res->m[i].rtyp = INTVEC_CMD;
1051	ISet = save;
1052	save = save->nx;
1053	omFreeBin((ADDRESS)ISet, indlist_bin);
1054	}
1055	omFreeBin((ADDRESS)save, indlist_bin);
1056	if (hMu2 != 0)
1057	{
1058	save = JSet;
1059	for (i=hMu;i<hMu+hMu2;i++)
1060	{
1061	res->m[i].data = (void *)save->set;
1062	res->m[i].rtyp = INTVEC_CMD;
1063	JSet = save;
1064	save = save->nx;
1065	omFreeBin((ADDRESS)JSet, indlist_bin);
1066	}
1067	omFreeBin((ADDRESS)save, indlist_bin);
1068	}
1069	}
1070	else
1071	{
1072	res->Init(0);
1073	omFreeBin((ADDRESS)ISet, indlist_bin);
1074	}
1075	hKill(radmem, pVariables - 1);
1076	omFreeSize((ADDRESS)hpure, (1 + (pVariables * pVariables)) * sizeof(Exponent_t));
1077	omFreeSize((ADDRESS)hvar, (pVariables + 1) * sizeof(int));
1078	omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon));
1079	hDelete(hexist, hNexist);
1080	return res;
1081	}
1082
1083	int iiDeclCommand(leftv sy, leftv name, int lev,int t, idhdl* root,BOOLEAN isring, BOOLEAN init_b)
1084	{
1085	BOOLEAN res=FALSE;
1086	char *id = name->name;
1087
1088	memset(sy,0,sizeof(sleftv));
1089	if ((name->name==NULL)\|\|(isdigit(name->name[0])))
1090	{
1091	WerrorS("object to declare is not a name");
1092	res=TRUE;
1093	}
1094	else
1095	{
1096	//if (name->rtyp!=0)
1097	//{
1098	// Warn("`%s` is already in use",name->name);
1099	//}
1100	{
1101	sy->data = (char *)enterid(id,lev,t,root,init_b);
1102	}
1103	if (sy->data!=NULL)
1104	{
1105	sy->rtyp=IDHDL;
1106	currid=sy->name=IDID((idhdl)sy->data);
1107	// name->name=NULL; /* used in enterid */
1108	//sy->e = NULL;
1109	if (name->next!=NULL)
1110	{
1111	sy->next=(leftv)omAllocBin(sleftv_bin);
1112	res=iiDeclCommand(sy->next,name->next,lev,t,root, isring);
1113	}
1114	}
1115	else res=TRUE;
1116	}
1117	name->CleanUp();
1118	return res;
1119	}
1120
1121	BOOLEAN iiParameter(leftv p)
1122	{
1123	if (iiCurrArgs==NULL)
1124	{
1125	if (strcmp(p->name,"#")==0) return FALSE;
1126	Werror("not enough arguments for proc %s",VoiceName());
1127	p->CleanUp();
1128	return TRUE;
1129	}
1130	leftv h=iiCurrArgs;
1131	if (strcmp(p->name,"#")==0)
1132	{
1133	iiCurrArgs=NULL;
1134	}
1135	else
1136	{
1137	iiCurrArgs=h->next;
1138	h->next=NULL;
1139	}
1140	BOOLEAN res=iiAssign(p,h);
1141	h->CleanUp();
1142	omFreeBin((ADDRESS)h, sleftv_bin);
1143	return res;
1144	}
1145
1146	static BOOLEAN iiInternalExport (leftv v, int toLev)
1147	{
1148	idhdl h=(idhdl)v->data;
1149	//Print("iiInternalExport('%s',%d)%s\n", v->name, toLev,"");
1150	if (IDLEV(h)==0) Warn("`%s` is already global",IDID(h));
1151	else
1152	{
1153	h=IDROOT->get(v->name,toLev);
1154	idhdl *root=&IDROOT;
1155	if ((h==NULL)&&(currRing!=NULL))
1156	{
1157	h=currRing->idroot->get(v->name,toLev);
1158	root=&currRing->idroot;
1159	}
1160	BOOLEAN keepring=FALSE;
1161	if ((h!=NULL)&&(IDLEV(h)==toLev))
1162	{
1163	if (IDTYP(h)==v->Typ())
1164	{
1165	if (((IDTYP(h)==RING_CMD)\|\|(IDTYP(h)==QRING_CMD))
1166	&& (v->Data()==IDDATA(h)))
1167	{
1168	IDRING(h)->ref++;
1169	keepring=TRUE;
1170	IDLEV(h)=toLev;
1171	//WarnS("keepring");
1172	return FALSE;
1173	}
1174	if (BVERBOSE(V_REDEFINE))
1175	{
1176	Warn("redefining %s",IDID(h));
1177	}
1178	#ifdef USE_IILOCALRING
1179	if (iiLocalRing[0]==IDRING(h) && (!keepring)) iiLocalRing[0]=NULL;
1180	#else
1181	proclevel *p=procstack;
1182	while (p->next!=NULL) p=p->next;
1183	if ((p->cRing==IDRING(h)) && (!keepring))
1184	{
1185	p->cRing=NULL;
1186	p->cRingHdl=NULL;
1187	}
1188	#endif
1189	killhdl2(h,root,currRing);
1190	}
1191	else
1192	{
1193	return TRUE;
1194	}
1195	}
1196	h=(idhdl)v->data;
1197	IDLEV(h)=toLev;
1198	if (keepring) IDRING(h)->ref--;
1199	iiNoKeepRing=FALSE;
1200	//Print("export %s\n",IDID(h));
1201	}
1202	return FALSE;
1203	}
1204
1205	#ifdef HAVE_NS
1206	BOOLEAN iiInternalExport (leftv v, int toLev, idhdl roothdl)
1207	{
1208	idhdl h=(idhdl)v->data;
1209	if(h==NULL)
1210	{
1211	Warn("'%s': no such identifier\n", v->name);
1212	return FALSE;
1213	}
1214	package frompack=v->req_packhdl;
1215	if (frompack==NULL) frompack=currPack;
1216	package rootpack = IDPACKAGE(roothdl);
1217	// Print("iiInternalExport('%s',%d,%s->%s) typ:%d\n", v->name, toLev, IDID(currPackHdl),IDID(roothdl),v->Typ());
1218	if ((RingDependend(IDTYP(h)))
1219	\|\| ((IDTYP(h)==LIST_CMD)
1220	&& (lRingDependend(IDLIST(h)))
1221	)
1222	)
1223	{
1224	//Print("// ==> Ringdependent set nesting to 0\n");
1225	return (iiInternalExport(v, toLev));
1226	}
1227	else
1228	{
1229	IDLEV(h)=toLev;
1230	v->req_packhdl=rootpack;
1231	if (h==frompack->idroot)
1232	{
1233	frompack->idroot=h->next;
1234	}
1235	else
1236	{
1237	idhdl hh=frompack->idroot;
1238	while ((hh!=NULL) && (hh->next!=h))
1239	hh=hh->next;
1240	if ((hh!=NULL) && (hh->next==h))
1241	hh->next=h->next;
1242	else
1243	{
1244	Werror("`%s` not found",v->Name());
1245	return TRUE;
1246	}
1247	}
1248	h->next=rootpack->idroot;
1249	rootpack->idroot=h;
1250	}
1251	return FALSE;
1252	}
1253	#endif /* HAVE_NS */
1254
1255	BOOLEAN iiExport (leftv v, int toLev)
1256	{
1257	#ifdef HAVE_NS
1258	#ifndef NDEBUG
1259	checkall();
1260	#endif
1261	#endif
1262	BOOLEAN nok=FALSE;
1263	leftv r=v;
1264	while (v!=NULL)
1265	{
1266	if ((v->name==NULL)\|\|(v->rtyp==0)\|\|(v->e!=NULL))
1267	{
1268	WerrorS("cannot export");
1269	nok=TRUE;
1270	}
1271	else
1272	{
1273	if(iiInternalExport(v, toLev))
1274	{
1275	r->CleanUp();
1276	return TRUE;
1277	}
1278	}
1279	v=v->next;
1280	}
1281	r->CleanUp();
1282	#ifdef HAVE_NS
1283	#ifndef NDEBUG
1284	checkall();
1285	#endif
1286	#endif
1287	return nok;
1288	}
1289
1290	/assume root!=idroot/
1291	#ifdef HAVE_NS
1292	BOOLEAN iiExport (leftv v, int toLev, idhdl root)
1293	{
1294	#ifndef NDEBUG
1295	checkall();
1296	#endif
1297	// Print("iiExport1: pack=%s\n",IDID(root));
1298	package pack=IDPACKAGE(root);
1299	BOOLEAN nok=FALSE;
1300	leftv rv=v;
1301	while (v!=NULL)
1302	{
1303	if ((v->name==NULL)\|\|(v->rtyp==0)\|\|(v->e!=NULL)
1304	)
1305	{
1306	WerrorS("cannot export");
1307	nok=TRUE;
1308	}
1309	else
1310	{
1311	idhdl old=pack->idroot->get( v->name,toLev);
1312	if (old!=NULL)
1313	{
1314	if ((pack==currPack) && (old==(idhdl)v->data))
1315	{
1316	Warn("`%s` is already global",IDID(old));
1317	break;
1318	}
1319	else if (IDTYP(old)==v->Typ())
1320	{
1321	if (BVERBOSE(V_REDEFINE))
1322	{
1323	Warn("redefining %s",IDID(old));
1324	}
1325	v->name=omStrDup(v->name);
1326	killhdl2(old,&(pack->idroot),currRing);
1327	}
1328	else
1329	{
1330	rv->CleanUp();
1331	return TRUE;
1332	}
1333	}
1334	//Print("iiExport: pack=%s\n",IDID(root));
1335	if(iiInternalExport(v, toLev, root))
1336	{
1337	rv->CleanUp();
1338	return TRUE;
1339	}
1340	}
1341	v=v->next;
1342	}
1343	rv->CleanUp();
1344	#ifndef NDEBUG
1345	checkall();
1346	#endif
1347	return nok;
1348	}
1349	#endif
1350
1351	BOOLEAN iiCheckRing(int i)
1352	{
1353	if (currRingHdl==NULL)
1354	{
1355	#ifdef SIQ
1356	if (siq<=0)
1357	{
1358	#endif
1359	if (RingDependend(i))
1360	{
1361	WerrorS("no ring active");
1362	return TRUE;
1363	}
1364	#ifdef SIQ
1365	}
1366	#endif
1367	}
1368	return FALSE;
1369	}
1370
1371	poly iiHighCorner(ideal I, int ak)
1372	{
1373	int i;
1374	if(!idIsZeroDim(I)) return NULL; // not zero-dim.
1375	poly po=NULL;
1376	if (currRing->OrdSgn== -1)
1377	{
1378	scComputeHC(I,currQuotient,ak,po);
1379	if (po!=NULL)
1380	{
1381	pGetCoeff(po)=nInit(1);
1382	for (i=pVariables; i>0; i--)
1383	{
1384	if (pGetExp(po, i) > 0) pDecrExp(po,i);
1385	}
1386	pSetComp(po,ak);
1387	pSetm(po);
1388	}
1389	}
1390	else
1391	po=pOne();
1392	return po;
1393	}
1394
1395	#ifdef HAVE_NS
1396	void iiCheckPack(package &p)
1397	{
1398	if (p==basePack) return;
1399
1400	idhdl t=basePack->idroot;
1401
1402	while ((t!=NULL) && (IDTYP(t)!=PACKAGE_CMD) && (IDPACKAGE(t)!=p)) t=t->next;
1403
1404	if (t==NULL)
1405	{
1406	WarnS("package not found\n");
1407	p=basePack;
1408	}
1409	return;
1410	}
1411	#endif
1412
1413	idhdl rDefault(char *s)
1414	{
1415	idhdl tmp=NULL;
1416
1417	if (s!=NULL) tmp = enterid(s, myynest, RING_CMD, &IDROOT);
1418	if (tmp==NULL) return NULL;
1419
1420	if (ppNoether!=NULL) pDelete(&ppNoether);
1421	if (sLastPrinted.RingDependend())
1422	{
1423	sLastPrinted.CleanUp();
1424	memset(&sLastPrinted,0,sizeof(sleftv));
1425	}
1426
1427	ring r = IDRING(tmp);
1428
1429	r->ch = 32003;
1430	r->N = 3;
1431	/r->P = 0; Alloc0 in idhdl::set, ipid.cc/
1432	/names/
1433	r->names = (char *) omAlloc0(3 sizeof(char_ptr));
1434	r->names[0] = omStrDup("x");
1435	r->names[1] = omStrDup("y");
1436	r->names[2] = omStrDup("z");
1437	/weights: entries for 3 blocks: NULL/
1438	r->wvhdl = (int *)omAlloc0(3 sizeof(int_ptr));
1439	/order: dp,C,0/
1440	r->order = (int ) omAlloc(3 sizeof(int *));
1441	r->block0 = (int )omAlloc0(3 sizeof(int *));
1442	r->block1 = (int )omAlloc0(3 sizeof(int *));
1443	/* ringorder dp for the first block: var 1..3 */
1444	r->order[0] = ringorder_dp;
1445	r->block0[0] = 1;
1446	r->block1[0] = 3;
1447	/* ringorder C for the second block: no vars */
1448	r->order[1] = ringorder_C;
1449	/* the last block: everything is 0 */
1450	r->order[2] = 0;
1451	/polynomial ring/
1452	r->OrdSgn = 1;
1453
1454	/* complete ring intializations */
1455	rComplete(r);
1456	rSetHdl(tmp);
1457	return currRingHdl;
1458	}
1459
1460	idhdl rFindHdl(ring r, idhdl n, idhdl w)
1461	{
1462	idhdl h=rSimpleFindHdl(r,IDROOT,n);
1463	if (h!=NULL) return h;
1464	#ifdef HAVE_NS
1465	if (IDROOT!=basePack->idroot) h=rSimpleFindHdl(r,basePack->idroot,n);
1466	if (h!=NULL) return h;
1467	proclevel *p=procstack;
1468	while(p!=NULL)
1469	{
1470	if ((p->cPack!=basePack)
1471	&& (p->cPack!=currPack))
1472	h=rSimpleFindHdl(r,p->cPack->idroot,n);
1473	if (h!=NULL) return h;
1474	p=p->next;
1475	}
1476	idhdl tmp=basePack->idroot;
1477	while (tmp!=NULL)
1478	{
1479	if (IDTYP(tmp)==PACKAGE_CMD)
1480	h=rSimpleFindHdl(r,IDPACKAGE(tmp)->idroot,n);
1481	if (h!=NULL) return h;
1482	tmp=IDNEXT(tmp);
1483	}
1484	#endif
1485	return NULL;
1486	}
1487
1488	void rDecomposeCF(leftv h,const ring r,const ring R)
1489	{
1490	lists L=(lists)omAlloc0Bin(slists_bin);
1491	L->Init(4);
1492	h->rtyp=LIST_CMD;
1493	h->data=(void *)L;
1494	// 0: char/ cf - ring
1495	// 1: list (var)
1496	// 2: list (ord)
1497	// 3: qideal
1498	// ----------------------------------------
1499	// 0: char/ cf - ring
1500	L->m[0].rtyp=INT_CMD;
1501	L->m[0].data=(void *)r->ch;
1502	// ----------------------------------------
1503	// 1: list (var)
1504	lists LL=(lists)omAlloc0Bin(slists_bin);
1505	LL->Init(r->N);
1506	int i;
1507	for(i=0; i<r->N; i++)
1508	{
1509	LL->m[i].rtyp=STRING_CMD;
1510	LL->m[i].data=(void *)omStrDup(r->names[i]);
1511	}
1512	L->m[1].rtyp=LIST_CMD;
1513	L->m[1].data=(void *)LL;
1514	// ----------------------------------------
1515	// 2: list (ord)
1516	LL=(lists)omAlloc0Bin(slists_bin);
1517	i=rBlocks(r)-1;
1518	LL->Init(i);
1519	i--;
1520	lists LLL;
1521	for(; i>=0; i--)
1522	{
1523	intvec *iv;
1524	int j;
1525	LL->m[i].rtyp=LIST_CMD;
1526	LLL=(lists)omAlloc0Bin(slists_bin);
1527	LLL->Init(2);
1528	LLL->m[0].rtyp=STRING_CMD;
1529	LLL->m[0].data=(void *)omStrDup(rSimpleOrdStr(r->order[i]));
1530	if (r->block1[i]-r->block0[i] >=0 )
1531	{
1532	j=r->block1[i]-r->block0[i];
1533	if(r->order[i]==ringorder_M) j=(j+1)*(j+1)-1;
1534	iv=new intvec(j+1);
1535	if ((r->wvhdl!=NULL) && (r->wvhdl[i]!=NULL))
1536	{
1537	for(;j>=0; j--) (*iv)[j]=r->wvhdl[i][j];
1538	}
1539	else switch (r->order[i])
1540	{
1541	case ringorder_dp:
1542	case ringorder_Dp:
1543	case ringorder_ds:
1544	case ringorder_Ds:
1545	case ringorder_lp:
1546	for(;j>=0; j--) (*iv)[j]=1;
1547	break;
1548	default: /* do nothing */;
1549	}
1550	}
1551	else
1552	{
1553	iv=new intvec(1);
1554	}
1555	LLL->m[1].rtyp=INTVEC_CMD;
1556	LLL->m[1].data=(void *)iv;
1557	LL->m[i].data=(void *)LLL;
1558	}
1559	L->m[2].rtyp=LIST_CMD;
1560	L->m[2].data=(void *)LL;
1561	// ----------------------------------------
1562	// 3: qideal
1563	L->m[3].rtyp=IDEAL_CMD;
1564	if (R->minpoly==NULL)
1565	L->m[3].data=(void *)idInit(1,1);
1566	else
1567	{
1568	ideal I=idInit(1,1);
1569	L->m[3].data=(void *)I;
1570	I->m[0]=pOne();
1571	pSetCoeff(I->m[0],R->minpoly);
1572	}
1573	// ----------------------------------------
1574	}
1575	void rDecomposeC(leftv h,const ring R)
1576	/* field is R or C */
1577	{
1578	lists L=(lists)omAlloc0Bin(slists_bin);
1579	if (rField_is_long_C(R)) L->Init(3);
1580	else L->Init(2);
1581	h->rtyp=LIST_CMD;
1582	h->data=(void *)L;
1583	// 0: char/ cf - ring
1584	// 1: list (var)
1585	// 2: list (ord)
1586	// ----------------------------------------
1587	// 0: char/ cf - ring
1588	L->m[0].rtyp=INT_CMD;
1589	L->m[0].data=(void *)0;
1590	// ----------------------------------------
1591	// 1:
1592	lists LL=(lists)omAlloc0Bin(slists_bin);
1593	LL->Init(2);
1594	LL->m[0].rtyp=INT_CMD;
1595	LL->m[0].data=(void *)si_max(R->float_len,SHORT_REAL_LENGTH/2);
1596	LL->m[1].rtyp=INT_CMD;
1597	LL->m[1].data=(void *)si_max(R->float_len2,SHORT_REAL_LENGTH);
1598	L->m[1].rtyp=LIST_CMD;
1599	L->m[1].data=(void *)LL;
1600	// ----------------------------------------
1601	// 2: list (par)
1602	if (rField_is_long_C(R))
1603	{
1604	L->m[2].rtyp=STRING_CMD;
1605	L->m[2].data=(void *)omStrDup(R->parameter[0]);
1606	}
1607	// ----------------------------------------
1608	}
1609
1610	lists rDecompose(const ring r)
1611	{
1612	// sanity check: require currRing==r for rings with polynomial data
1613	if ((r!=currRing)
1614	&& ((r->minpoly!=NULL) \|\| (r->qideal!=NULL) \|\| (r->minideal!=NULL)
1615	#ifdef HAVE_PLURAL
1616	\|\| (rIsPluralRing(r))
1617	#endif
1618	))
1619	{
1620	WerrorS("ring with polynomial data must be the base ring or compatible");
1621	return NULL;
1622	}
1623	// 0: char/ cf - ring
1624	// 1: list (var)
1625	// 2: list (ord)
1626	// 3: qideal
1627	// possibly:
1628	// 4: C
1629	// 5: D
1630	lists L=(lists)omAlloc0Bin(slists_bin);
1631	if (rIsPluralRing(r))
1632	L->Init(6);
1633	else
1634	L->Init(4);
1635	// ----------------------------------------
1636	// 0: char/ cf - ring
1637	#if 1 /* TODO */
1638	if (rField_is_numeric(r))
1639	{
1640	rDecomposeC(&(L->m[0]),r);
1641	}
1642	else if (rIsExtension(r))
1643	{
1644	if (r->algring!=NULL)
1645	rDecomposeCF(&(L->m[0]),r->algring,r);
1646	if (L->m[0].rtyp==0)
1647	{
1648	//omFreeBin(slists_bin,(void *)L);
1649	return NULL;
1650	}
1651	}
1652	else
1653	#endif
1654	{
1655	L->m[0].rtyp=INT_CMD;
1656	L->m[0].data=(void *)r->ch;
1657	}
1658	// ----------------------------------------
1659	// 1: list (var)
1660	lists LL=(lists)omAlloc0Bin(slists_bin);
1661	LL->Init(r->N);
1662	int i;
1663	for(i=0; i<r->N; i++)
1664	{
1665	LL->m[i].rtyp=STRING_CMD;
1666	LL->m[i].data=(void *)omStrDup(r->names[i]);
1667	}
1668	L->m[1].rtyp=LIST_CMD;
1669	L->m[1].data=(void *)LL;
1670	// ----------------------------------------
1671	// 2: list (ord)
1672	LL=(lists)omAlloc0Bin(slists_bin);
1673	i=rBlocks(r)-1;
1674	LL->Init(i);
1675	i--;
1676	lists LLL;
1677	for(; i>=0; i--)
1678	{
1679	intvec *iv;
1680	int j;
1681	LL->m[i].rtyp=LIST_CMD;
1682	LLL=(lists)omAlloc0Bin(slists_bin);
1683	LLL->Init(2);
1684	LLL->m[0].rtyp=STRING_CMD;
1685	LLL->m[0].data=(void *)omStrDup(rSimpleOrdStr(r->order[i]));
1686	if (r->block1[i]-r->block0[i] >=0 )
1687	{
1688	j=r->block1[i]-r->block0[i];
1689	if (r->order[i]==ringorder_M) j=(j+1)*(j+1)-1;
1690	iv=new intvec(j+1);
1691	if ((r->wvhdl!=NULL) && (r->wvhdl[i]!=NULL))
1692	{
1693	for(;j>=0; j--) (*iv)[j]=r->wvhdl[i][j];
1694	}
1695	else switch (r->order[i])
1696	{
1697	case ringorder_dp:
1698	case ringorder_Dp:
1699	case ringorder_ds:
1700	case ringorder_Ds:
1701	case ringorder_lp:
1702	for(;j>=0; j--) (*iv)[j]=1;
1703	break;
1704	default: /* do nothing */;
1705	}
1706	}
1707	else
1708	{
1709	iv=new intvec(1);
1710	}
1711	LLL->m[1].rtyp=INTVEC_CMD;
1712	LLL->m[1].data=(void *)iv;
1713	LL->m[i].data=(void *)LLL;
1714	}
1715	L->m[2].rtyp=LIST_CMD;
1716	L->m[2].data=(void *)LL;
1717	// ----------------------------------------
1718	// 3: qideal
1719	L->m[3].rtyp=IDEAL_CMD;
1720	if (r->qideal==NULL)
1721	L->m[3].data=(void *)idInit(1,1);
1722	else
1723	L->m[3].data=(void *)idCopy(r->qideal);
1724	// ----------------------------------------
1725	#ifdef HAVE_PLURAL
1726	if (rIsPluralRing(r))
1727	{
1728	L->m[4].rtyp=MATRIX_CMD;
1729	L->m[4].data=(void *)mpCopy(r->nc->C);
1730	L->m[5].rtyp=MATRIX_CMD;
1731	L->m[5].data=(void *)mpCopy(r->nc->D);
1732	}
1733	#endif
1734	return L;
1735	}
1736
1737	void rComposeC(lists L, ring R)
1738	/* field is R or C */
1739	{
1740	// ----------------------------------------
1741	// 0: char/ cf - ring
1742	if ((L->m[0].rtyp!=INT_CMD) \|\| (L->m[0].data!=(char *)0))
1743	{
1744	Werror("invald coeff. field description, expecting 0");
1745	return;
1746	}
1747	R->ch=-1;
1748	// ----------------------------------------
1749	// 1:
1750	if (L->m[1].rtyp!=LIST_CMD)
1751	Werror("invald coeff. field description, expecting precision list");
1752	lists LL=(lists)L->m[1].data;
1753	int r1=(int)(long)LL->m[0].data;
1754	int r2=(int)(long)LL->m[1].data;
1755	if ((r1<=SHORT_REAL_LENGTH)
1756	&& (r2=SHORT_REAL_LENGTH))
1757	{
1758	R->float_len=SHORT_REAL_LENGTH/2;
1759	R->float_len2=SHORT_REAL_LENGTH;
1760	}
1761	else
1762	{
1763	R->float_len=si_min(r1,32767);
1764	R->float_len2=si_min(r2,32767);
1765	}
1766	// ----------------------------------------
1767	// 2: list (par)
1768	if (L->nr==2)
1769	{
1770	R->P=1;
1771	if (L->m[2].rtyp!=STRING_CMD)
1772	{
1773	Werror("invald coeff. field description, expecting parameter name");
1774	return;
1775	}
1776	R->parameter=(char*)omAlloc0(R->Psizeof(char_ptr));
1777	R->parameter[0]=omStrDup((char *)L->m[2].data);
1778	}
1779	// ----------------------------------------
1780	}
1781	ring rCompose(const lists L)
1782	{
1783	if ((L->nr!=3)
1784	#ifdef HAVE_PLURAL
1785	&&(L->nr!=5)
1786	#endif
1787	)
1788	return NULL;
1789	// 0: char/ cf - ring
1790	// 1: list (var)
1791	// 2: list (ord)
1792	// 3: qideal
1793	// possibly:
1794	// 4: C
1795	// 5: D
1796	ring R=(ring) omAlloc0Bin(sip_sring_bin);
1797	// ------------------------- VARS ---------------------------
1798	if (L->m[1].Typ()==LIST_CMD)
1799	{
1800	lists v=(lists)L->m[1].Data();
1801	R->N = v->nr+1;
1802	R->names = (char *)omAlloc0(R->N sizeof(char_ptr));
1803	int i;
1804	for(i=0;i<R->N;i++)
1805	{
1806	if (v->m[i].Typ()==STRING_CMD)
1807	R->names[i]=omStrDup((char *)v->m[i].Data());
1808	else if (v->m[i].Typ()==POLY_CMD)
1809	{
1810	poly p=(poly)v->m[i].Data();
1811	int nr=pIsPurePower(p);
1812	if (nr>0)
1813	R->names[i]=omStrDup(currRing->names[nr-1]);
1814	else
1815	{
1816	Werror("var name %d must be a string or a ring variable",i+1);
1817	goto rCompose_err;
1818	}
1819	}
1820	else
1821	{
1822	Werror("var name %d must be `string`",i+1);
1823	goto rCompose_err;
1824	}
1825	}
1826	}
1827	else
1828	{
1829	WerrorS("variable must be given as `list`");
1830	goto rCompose_err;
1831	}
1832	rNameCheck(R);
1833	// ------------------------ ORDER ------------------------------
1834	if (L->m[2].Typ()==LIST_CMD)
1835	{
1836	lists v=(lists)L->m[2].Data();
1837	int n= v->nr+2;
1838	int j;
1839	// initialize fields of R
1840	R->order=(int )omAlloc0(nsizeof(int));
1841	R->block0=(int )omAlloc0(nsizeof(int));
1842	R->block1=(int )omAlloc0(nsizeof(int));
1843	R->wvhdl=(int*)omAlloc0(nsizeof(int_ptr));
1844	// init order, so that rBlocks works correctly
1845	for (j=0; j < n-1; j++)
1846	R->order[j] = (int) ringorder_unspec;
1847	// orderings
1848	R->OrdSgn=1;
1849	for(j=0;j<n-1;j++)
1850	{
1851	// todo: a(..), M
1852	if (v->m[j].Typ()!=LIST_CMD)
1853	{
1854	WerrorS("ordering must be list of lists");
1855	goto rCompose_err;
1856	}
1857	lists vv=(lists)v->m[j].Data();
1858	if ((vv->nr!=1)
1859	\|\| (vv->m[0].Typ()!=STRING_CMD)
1860	\|\| ((vv->m[1].Typ()!=INTVEC_CMD) && (vv->m[1].Typ()!=INT_CMD)))
1861	{
1862	WerrorS("ordering name must be a (string,intvec)");
1863	goto rCompose_err;
1864	}
1865	R->order[j]=rOrderName(omStrDup((char*)vv->m[0].Data())); // assume STRING
1866	if (j==0) R->block0[0]=1;
1867	else
1868	{
1869	int jj=j-1;
1870	while((jj>=0)
1871	&& ((R->order[jj]== ringorder_a)
1872	\|\| (R->order[jj]== ringorder_aa)
1873	\|\| (R->order[jj]== ringorder_c)
1874	\|\| (R->order[jj]== ringorder_C)
1875	))
1876	{
1877	//Print("jj=%, skip %s\n",rSimpleOrdStr(R->order[jj]));
1878	jj--;
1879	}
1880	if (jj<0) R->block0[j]=1;
1881	else R->block0[j]=R->block1[jj]+1;
1882	}
1883	intvec *iv;
1884	if (vv->m[1].Typ()==INT_CMD)
1885	iv=new intvec((int)(long)vv->m[1].Data(),(int)(long)vv->m[1].Data());
1886	else
1887	iv=ivCopy((intvec*)vv->m[1].Data()); //assume INTVEC
1888	R->block1[j]=si_max(R->block0[j],R->block0[j]+iv->length()-1);
1889	//Print("block %d from %d to %d\n",j,R->block0[j], R->block1[j]);
1890	int i;
1891	switch (R->order[j])
1892	{
1893	case ringorder_ws:
1894	case ringorder_Ws:
1895	R->OrdSgn=-1;
1896	case ringorder_aa:
1897	case ringorder_a:
1898	case ringorder_wp:
1899	case ringorder_Wp:
1900	R->wvhdl[j] =( int )omAlloc((iv->length())sizeof(int));
1901	for (i=0; i<iv->length();i++)
1902	{
1903	R->wvhdl[j][i]=(*iv)[i];
1904	}
1905	break;
1906	case ringorder_M:
1907	R->wvhdl[j] =( int )omAlloc((iv->length())sizeof(int));
1908	for (i=0; i<iv->length();i++) R->wvhdl[j][i]=(*iv)[i];
1909	R->block1[j]=si_max(R->block0[j],R->block0[j]+(int)sqrt((double)(iv->length()-1)));
1910	break;
1911	case ringorder_ls:
1912	case ringorder_ds:
1913	case ringorder_Ds:
1914	case ringorder_rs:
1915	R->OrdSgn=-1;
1916	case ringorder_lp:
1917	case ringorder_dp:
1918	case ringorder_Dp:
1919	case ringorder_rp:
1920	break;
1921	case ringorder_S:
1922	break;
1923	case ringorder_c:
1924	case ringorder_C:
1925	R->block1[j]=R->block0[j]=0;
1926	break;
1927	case 0:
1928	case ringorder_unspec:
1929	break;
1930	}
1931	}
1932	// sanity check
1933	j=n-2;
1934	if ((R->order[j]==ringorder_c)
1935	\|\| (R->order[j]==ringorder_C)
1936	\|\| (R->order[j]==ringorder_unspec)) j--;
1937	if (R->block1[j] != R->N)
1938	{
1939	if (((R->order[j]==ringorder_dp) \|\|
1940	(R->order[j]==ringorder_ds) \|\|
1941	(R->order[j]==ringorder_Dp) \|\|
1942	(R->order[j]==ringorder_Ds) \|\|
1943	(R->order[j]==ringorder_rp) \|\|
1944	(R->order[j]==ringorder_rs) \|\|
1945	(R->order[j]==ringorder_lp) \|\|
1946	(R->order[j]==ringorder_ls))
1947	&&
1948	R->block0[j] <= R->N)
1949	{
1950	R->block1[j] = R->N;
1951	}
1952	else
1953	{
1954	Werror("ordering incomplete: size (%d) should be %d",R->block1[j],R->N);
1955	goto rCompose_err;
1956	}
1957	}
1958	}
1959	else
1960	{
1961	WerrorS("ordering must be given as `list`");
1962	goto rCompose_err;
1963	}
1964	// ------------------------------------------------------------------
1965	// 0: char:
1966	if (L->m[0].Typ()==INT_CMD)
1967	{
1968	R->ch=(int)(long)L->m[0].Data();
1969	if (R->ch!=-1)
1970	{
1971	int l;
1972	if (((R->ch!=0) && (R->ch<2))
1973	#ifndef NV_OPS
1974	\|\| (R->ch > 32003)
1975	#endif
1976	\|\| ((l=IsPrime(R->ch))!=R->ch)
1977	)
1978	{
1979	Warn("%d is invalid characteristic of ground field. %d is used.", R->ch,l);
1980	R->ch=l;
1981	}
1982	}
1983	}
1984	else if (L->m[0].Typ()==LIST_CMD)
1985	{
1986	lists LL=(lists)L->m[0].Data();
1987	if (LL->nr<3)
1988	rComposeC(LL,R); /* R, long_R, long_C */
1989	else
1990	{
1991	R->algring=rCompose((lists)L->m[0].Data());
1992	if (R->algring==NULL)
1993	{
1994	WerrorS("could not create rational function coefficient field");
1995	goto rCompose_err;
1996	}
1997	if (R->algring->ch>0)
1998	R->ch= -R->algring->ch;
1999	else
2000	R->ch=1;
2001	R->P=R->algring->N;
2002	R->parameter=(char*)omAlloc0(R->Psizeof(char_ptr));
2003	int i;
2004	for(i=R->P-1;i>=0;i--)
2005	R->parameter[i]=omStrDup(R->algring->names[i]);
2006	if (R->algring->qideal!=NULL)
2007	{
2008	if (IDELEMS(R->algring->qideal)==1)
2009	{
2010	R->minpoly=naInit(1);
2011	lnumber n=(lnumber)R->minpoly;
2012	n->z=R->algring->qideal->m[0];
2013	R->algring->qideal->m[0]=NULL;
2014	idDelete(&(R->algring->qideal));
2015	}
2016	else
2017	{
2018	WerrorS("not implemented yet.");
2019	}
2020	}
2021	}
2022	}
2023	else
2024	{
2025	WerrorS("coefficient field must be described by `int` or `list`");
2026	goto rCompose_err;
2027	}
2028	// ------------------------ Q-IDEAL ------------------------
2029	rComplete(R);
2030
2031	if (L->m[3].Typ()==IDEAL_CMD)
2032	{
2033	ideal q=(ideal)L->m[3].Data();
2034	if (q->m[0]!=NULL)
2035	{
2036	if (R->ch!=currRing->ch)
2037	{
2038	#if 0
2039	WerrorS("coefficient fields must be equal if q-ideal !=0");
2040	goto rCompose_err;
2041	#else
2042	ring orig_ring=currRing;
2043	rChangeCurrRing(R);
2044	int *perm=NULL;
2045	int *par_perm=NULL;
2046	int par_perm_size=0;
2047	nMapFunc nMap;
2048	BOOLEAN bo;
2049
2050	if ((nMap=nSetMap(orig_ring))==NULL)
2051	{
2052	if (rEqual(orig_ring,currRing))
2053	{
2054	nMap=nCopy;
2055	}
2056	else
2057	// Allow imap/fetch to be make an exception only for:
2058	if ( (rField_is_Q_a(orig_ring) && // Q(a..) -> Q(a..) \|\| Q \|\| Zp \|\| Zp(a)
2059	(rField_is_Q() \|\| rField_is_Q_a() \|\|
2060	(rField_is_Zp() \|\| rField_is_Zp_a())))
2061	\|\|
2062	(rField_is_Zp_a(orig_ring) && // Zp(a..) -> Zp(a..) \|\| Zp
2063	(rField_is_Zp(currRing, rInternalChar(orig_ring)) \|\|
2064	rField_is_Zp_a(currRing, rInternalChar(orig_ring)))) )
2065	{
2066	par_perm_size=rPar(orig_ring);
2067	BITSET save_test=test;
2068	naSetChar(rInternalChar(orig_ring),orig_ring);
2069	nSetChar(currRing);
2070	test=save_test;
2071	}
2072	else
2073	{
2074	WerrorS("coefficient fields must be equal if q-ideal !=0");
2075	goto rCompose_err;
2076	}
2077	}
2078	perm=(int )omAlloc0((orig_ring->N+1)sizeof(int));
2079	if (par_perm_size!=0)
2080	par_perm=(int )omAlloc0(par_perm_sizesizeof(int));
2081	int i;
2082	#if 0
2083	// use imap:
2084	maFindPerm(orig_ring->names,orig_ring->N,orig_ring->parameter,orig_ring->P,
2085	currRing->names,currRing->N,currRing->parameter, currRing->P,
2086	perm,par_perm, currRing->ch);
2087	#else
2088	// use fetch
2089	if ((rPar(orig_ring)>0) && (rPar(currRing)==0))
2090	{
2091	for(i=si_min(rPar(orig_ring),rVar(currRing))-1;i>=0;i--) par_perm[i]=i+1;
2092	}
2093	else if (par_perm_size!=0)
2094	for(i=si_min(rPar(orig_ring),rPar(currRing))-1;i>=0;i--) par_perm[i]=-(i+1);
2095	for(i=si_min(orig_ring->N,pVariables);i>0;i--) perm[i]=i;
2096	#endif
2097	ideal dest_id=idInit(IDELEMS(q),1);
2098	for(i=IDELEMS(q)-1; i>=0; i--)
2099	{
2100	dest_id->m[i]=pPermPoly(q->m[i],perm,orig_ring,nMap,
2101	par_perm,par_perm_size);
2102	// PrintS("map:");pWrite(dest_id->m[i]);PrintLn();
2103	pTest(dest_id->m[i]);
2104	}
2105	R->qideal=dest_id;
2106	if (perm!=NULL)
2107	omFreeSize((ADDRESS)perm,(orig_ring->N+1)*sizeof(int));
2108	if (par_perm!=NULL)
2109	omFreeSize((ADDRESS)par_perm,par_perm_size*sizeof(int));
2110	rChangeCurrRing(orig_ring);
2111	#endif
2112	}
2113	else
2114	R->qideal=idrCopyR(q,currRing,R);
2115	}
2116	}
2117	else
2118	{
2119	WerrorS("q-ideal must be given as `ideal`");
2120	goto rCompose_err;
2121	}
2122
2123
2124	// ---------------------------------------------------------------
2125	#ifdef HAVE_PLURAL
2126	if (L->nr==5)
2127	{
2128	if (nc_CallPlural((matrix)L->m[4].Data(),(matrix)L->m[5].Data(),
2129	NULL,NULL,R))
2130	goto rCompose_err;
2131	}
2132	#endif
2133	return R;
2134
2135	rCompose_err:
2136	if (R->N>0)
2137	{
2138	int i;
2139	if (R->names!=NULL)
2140	{
2141	i=R->N-1;
2142	while (i>=0) { if (R->names[i]!=NULL) omFree(R->names[i]); i--; }
2143	omFree(R->names);
2144	}
2145	}
2146	if (R->order!=NULL) omFree(R->order);
2147	if (R->block0!=NULL) omFree(R->block0);
2148	if (R->block1!=NULL) omFree(R->block1);
2149	if (R->wvhdl!=NULL) omFree(R->wvhdl);
2150	omFree(R);
2151	return NULL;
2152	}
2153
2154	// from matpol.cc
2155
2156	/*2
2157	* compute the jacobi matrix of an ideal
2158	*/
2159	BOOLEAN mpJacobi(leftv res,leftv a)
2160	{
2161	int i,j;
2162	matrix result;
2163	ideal id=(ideal)a->Data();
2164
2165	result =mpNew(IDELEMS(id),pVariables);
2166	for (i=1; i<=IDELEMS(id); i++)
2167	{
2168	for (j=1; j<=pVariables; j++)
2169	{
2170	MATELEM(result,i,j) = pDiff(id->m[i-1],j);
2171	}
2172	}
2173	res->data=(char *)result;
2174	return FALSE;
2175	}
2176
2177	/*2
2178	* returns the Koszul-matrix of degree d of a vectorspace with dimension n
2179	* uses the first n entrees of id, if id <> NULL
2180	*/
2181	BOOLEAN mpKoszul(leftv res,leftv c/ip/, leftv b/in/, leftv id)
2182	{
2183	int n=(int)(long)b->Data();
2184	int d=(int)(long)c->Data();
2185	int k,l,sign,row,col;
2186	matrix result;
2187	ideal temp;
2188	BOOLEAN bo;
2189	poly p;
2190
2191	if ((d>n) \|\| (d<1) \|\| (n<1))
2192	{
2193	res->data=(char *)mpNew(1,1);
2194	return FALSE;
2195	}
2196	int choise = (int)omAlloc(d*sizeof(int));
2197	if (id==NULL)
2198	temp=idMaxIdeal(1);
2199	else
2200	temp=(ideal)id->Data();
2201
2202	k = binom(n,d);
2203	l = k*d;
2204	l /= n-d+1;
2205	result =mpNew(l,k);
2206	col = 1;
2207	idInitChoise(d,1,n,&bo,choise);
2208	while (!bo)
2209	{
2210	sign = 1;
2211	for (l=1;l<=d;l++)
2212	{
2213	if (choise[l-1]<=IDELEMS(temp))
2214	{
2215	p = pCopy(temp->m[choise[l-1]-1]);
2216	if (sign == -1) p = pNeg(p);
2217	sign *= -1;
2218	row = idGetNumberOfChoise(l-1,d,1,n,choise);
2219	MATELEM(result,row,col) = p;
2220	}
2221	}
2222	col++;
2223	idGetNextChoise(d,n,&bo,choise);
2224	}
2225	if (id==NULL) idDelete(&temp);
2226
2227	res->data=(char *)result;
2228	return FALSE;
2229	}
2230
2231	// from syz1.cc
2232	/*2
2233	* read out the Betti numbers from resolution
2234	* (interpreter interface)
2235	*/
2236	BOOLEAN syBetti2(leftv res, leftv u, leftv w)
2237	{
2238	syStrategy syzstr=(syStrategy)u->Data();
2239	BOOLEAN minim=(int)(long)w->Data();
2240	int row_shift=0;
2241	int add_row_shift=0;
2242	intvec *weights=NULL;
2243	intvec ww=(intvec )atGet(u,"isHomog",INTVEC_CMD);
2244	if (ww!=NULL)
2245	{
2246	weights=ivCopy(ww);
2247	add_row_shift = ww->min_in();
2248	(*weights) -= add_row_shift;
2249	}
2250	res->data=(void *)syBettiOfComputation(syzstr,minim,&row_shift,weights);
2251	//row_shift += add_row_shift;
2252	//Print("row_shift=%d, add_row_shift=%d\n",row_shift,add_row_shift);
2253	atSet(res,omStrDup("rowShift"),(void*)add_row_shift,INT_CMD);
2254	return FALSE;
2255	}
2256	BOOLEAN syBetti1(leftv res, leftv u)
2257	{
2258	sleftv tmp;
2259	memset(&tmp,0,sizeof(tmp));
2260	tmp.rtyp=INT_CMD;
2261	tmp.data=(void *)1;
2262	return syBetti2(res,u,&tmp);
2263	}
2264
2265	/*3
2266	* converts a resolution into a list of modules
2267	*/
2268	lists syConvRes(syStrategy syzstr,BOOLEAN toDel,int add_row_shift)
2269	{
2270	if ((syzstr->fullres==NULL) && (syzstr->minres==NULL))
2271	{
2272	if (syzstr->hilb_coeffs==NULL)
2273	{
2274	syzstr->fullres = syReorder(syzstr->res,syzstr->length,syzstr);
2275	}
2276	else
2277	{
2278	syzstr->minres = syReorder(syzstr->orderedRes,syzstr->length,syzstr);
2279	syKillEmptyEntres(syzstr->minres,syzstr->length);
2280	}
2281	}
2282	resolvente tr;
2283	int typ0=IDEAL_CMD;
2284	if (syzstr->minres!=NULL)
2285	tr = syzstr->minres;
2286	else
2287	tr = syzstr->fullres;
2288	resolvente trueres=NULL;
2289	intvec ** w=NULL;
2290	if (syzstr->length>0)
2291	{
2292	trueres=(resolvente)omAlloc0((syzstr->length)*sizeof(ideal));
2293	for (int i=(syzstr->length)-1;i>=0;i--)
2294	{
2295	if (tr[i]!=NULL)
2296	{
2297	trueres[i] = idCopy(tr[i]);
2298	}
2299	}
2300	if (idRankFreeModule(trueres[0]) > 0)
2301	typ0 = MODUL_CMD;
2302	if (syzstr->weights!=NULL)
2303	{
2304	w = (intvec*)omAlloc0((syzstr->length)sizeof(intvec*));
2305	for (int i=(syzstr->length)-1;i>=0;i--)
2306	{
2307	if (syzstr->weights[i]!=NULL) w[i] = ivCopy(syzstr->weights[i]);
2308	}
2309	}
2310	}
2311	lists li = liMakeResolv(trueres,syzstr->length,syzstr->list_length,typ0,
2312	w,add_row_shift);
2313	if (w != NULL) omFreeSize(w, (syzstr->length)sizeof(intvec));
2314	if (toDel) syKillComputation(syzstr);
2315	return li;
2316	}
2317
2318	/*3
2319	* converts a list of modules into a resolution
2320	*/
2321	syStrategy syConvList(lists li,BOOLEAN toDel)
2322	{
2323	int typ0;
2324	syStrategy result=(syStrategy)omAlloc0(sizeof(ssyStrategy));
2325
2326	resolvente fr = liFindRes(li,&(result->length),&typ0,&(result->weights));
2327	if (fr != NULL)
2328	{
2329
2330	result->fullres = (resolvente)omAlloc0((result->length+1)*sizeof(ideal));
2331	for (int i=result->length-1;i>=0;i--)
2332	{
2333	if (fr[i]!=NULL)
2334	result->fullres[i] = idCopy(fr[i]);
2335	}
2336	result->list_length=result->length;
2337	omFreeSize((ADDRESS)fr,(result->length)*sizeof(ideal));
2338	}
2339	else
2340	{
2341	omFreeSize(result, sizeof(ssyStrategy));
2342	result = NULL;
2343	}
2344	if (toDel) li->Clean();
2345	return result;
2346	}
2347
2348	/*3
2349	* converts a list of modules into a minimal resolution
2350	*/
2351	syStrategy syForceMin(lists li)
2352	{
2353	int typ0;
2354	syStrategy result=(syStrategy)omAlloc0(sizeof(ssyStrategy));
2355
2356	resolvente fr = liFindRes(li,&(result->length),&typ0);
2357	result->minres = (resolvente)omAlloc0((result->length+1)*sizeof(ideal));
2358	for (int i=result->length-1;i>=0;i--)
2359	{
2360	if (fr[i]!=NULL)
2361	result->minres[i] = idCopy(fr[i]);
2362	}
2363	omFreeSize((ADDRESS)fr,(result->length)*sizeof(ideal));
2364	return result;
2365	}
2366	// from weight.cc
2367	BOOLEAN kWeight(leftv res,leftv id)
2368	{
2369	ideal F=(ideal)id->Data();
2370	intvec * iv = new intvec(pVariables);
2371	polyset s;
2372	int sl, n, i;
2373	int *x;
2374
2375	res->data=(char *)iv;
2376	s = F->m;
2377	sl = IDELEMS(F) - 1;
2378	n = pVariables;
2379	double wNsqr = (double)2.0 / (double)n;
2380	wFunctional = wFunctionalBuch;
2381	x = (int * )omAlloc(2 * (n + 1) * sizeof(int));
2382	wCall(s, sl, x, wNsqr);
2383	for (i = n; i!=0; i--)
2384	(*iv)[i-1] = x[i + n + 1];
2385	omFreeSize((ADDRESS)x, 2 * (n + 1) * sizeof(int));
2386	return FALSE;
2387	}
2388
2389	BOOLEAN kQHWeight(leftv res,leftv v)
2390	{
2391	res->data=(char *)idQHomWeight((ideal)v->Data());
2392	if (res->data==NULL)
2393	res->data=(char *)new intvec(pVariables);
2394	return FALSE;
2395	}
2396	/==============================================================/
2397	// from clapsing.cc
2398	#if 0
2399	BOOLEAN jjIS_SQR_FREE(leftv res, leftv u)
2400	{
2401	BOOLEAN b=singclap_factorize((poly)(u->CopyD()), &v, 0);
2402	res->data=(void *)b;
2403	}
2404	#endif
2405
2406	BOOLEAN jjRESULTANT(leftv res, leftv u, leftv v, leftv w)
2407	{
2408	res->data=singclap_resultant((poly)u->Data(),(poly)v->Data(), (poly)w->Data());
2409	return errorreported;
2410	}
2411	BOOLEAN jjCHARSERIES(leftv res, leftv u)
2412	{
2413	res->data=singclap_irrCharSeries((ideal)u->Data());
2414	return (res->data==NULL);
2415	}
2416
2417	// from semic.cc
2418	#ifdef HAVE_SPECTRUM
2419
2420	// ----------------------------------------------------------------------------
2421	// Initialize a spectrum deep from another spectrum
2422	// ----------------------------------------------------------------------------
2423
2424	void spectrum::copy_deep( const spectrum &spec )
2425	{
2426	mu = spec.mu;
2427	pg = spec.pg;
2428	n = spec.n;
2429
2430	copy_new( n );
2431
2432	for( int i=0; i<n; i++ )
2433	{
2434	s[i] = spec.s[i];
2435	w[i] = spec.w[i];
2436	}
2437	}
2438
2439	// ----------------------------------------------------------------------------
2440	// Initialize a spectrum deep from a singular lists
2441	// ----------------------------------------------------------------------------
2442
2443	void spectrum::copy_deep( lists l )
2444	{
2445	mu = (int)(long)(l->m[0].Data( ));
2446	pg = (int)(long)(l->m[1].Data( ));
2447	n = (int)(long)(l->m[2].Data( ));
2448
2449	copy_new( n );
2450
2451	intvec num = (intvec)l->m[3].Data( );
2452	intvec den = (intvec)l->m[4].Data( );
2453	intvec mul = (intvec)l->m[5].Data( );
2454
2455	for( int i=0; i<n; i++ )
2456	{
2457	s[i] = (Rational)((num)[i])/(Rational)((den)[i]);
2458	w[i] = (*mul)[i];
2459	}
2460	}
2461
2462	// ----------------------------------------------------------------------------
2463	// singular lists constructor for spectrum
2464	// ----------------------------------------------------------------------------
2465
2466	spectrum::spectrum( lists l )
2467	{
2468	copy_deep( l );
2469	}
2470
2471	// ----------------------------------------------------------------------------
2472	// generate a Singular lists from a spectrum
2473	// ----------------------------------------------------------------------------
2474
2475	lists spectrum::thelist( void )
2476	{
2477	lists L = (lists)omAllocBin( slists_bin);
2478
2479	L->Init( 6 );
2480
2481	intvec *num = new intvec( n );
2482	intvec *den = new intvec( n );
2483	intvec *mult = new intvec( n );
2484
2485	for( int i=0; i<n; i++ )
2486	{
2487	(*num) [i] = s[i].get_num_si( );
2488	(*den) [i] = s[i].get_den_si( );
2489	(*mult)[i] = w[i];
2490	}
2491
2492	L->m[0].rtyp = INT_CMD; // milnor number
2493	L->m[1].rtyp = INT_CMD; // geometrical genus
2494	L->m[2].rtyp = INT_CMD; // # of spectrum numbers
2495	L->m[3].rtyp = INTVEC_CMD; // numerators
2496	L->m[4].rtyp = INTVEC_CMD; // denomiantors
2497	L->m[5].rtyp = INTVEC_CMD; // multiplicities
2498
2499	L->m[0].data = (void*)mu;
2500	L->m[1].data = (void*)pg;
2501	L->m[2].data = (void*)n;
2502	L->m[3].data = (void*)num;
2503	L->m[4].data = (void*)den;
2504	L->m[5].data = (void*)mult;
2505
2506	return L;
2507	}
2508	// from spectrum.cc
2509	// ----------------------------------------------------------------------------
2510	// print out an error message for a spectrum list
2511	// ----------------------------------------------------------------------------
2512
2513	void list_error( semicState state )
2514	{
2515	switch( state )
2516	{
2517	case semicListTooShort:
2518	WerrorS( "the list is too short" );
2519	break;
2520	case semicListTooLong:
2521	WerrorS( "the list is too long" );
2522	break;
2523
2524	case semicListFirstElementWrongType:
2525	WerrorS( "first element of the list should be int" );
2526	break;
2527	case semicListSecondElementWrongType:
2528	WerrorS( "second element of the list should be int" );
2529	break;
2530	case semicListThirdElementWrongType:
2531	WerrorS( "third element of the list should be int" );
2532	break;
2533	case semicListFourthElementWrongType:
2534	WerrorS( "fourth element of the list should be intvec" );
2535	break;
2536	case semicListFifthElementWrongType:
2537	WerrorS( "fifth element of the list should be intvec" );
2538	break;
2539	case semicListSixthElementWrongType:
2540	WerrorS( "sixth element of the list should be intvec" );
2541	break;
2542
2543	case semicListNNegative:
2544	WerrorS( "first element of the list should be positive" );
2545	break;
2546	case semicListWrongNumberOfNumerators:
2547	WerrorS( "wrong number of numerators" );
2548	break;
2549	case semicListWrongNumberOfDenominators:
2550	WerrorS( "wrong number of denominators" );
2551	break;
2552	case semicListWrongNumberOfMultiplicities:
2553	WerrorS( "wrong number of multiplicities" );
2554	break;
2555
2556	case semicListMuNegative:
2557	WerrorS( "the Milnor number should be positive" );
2558	break;
2559	case semicListPgNegative:
2560	WerrorS( "the geometrical genus should be nonnegative" );
2561	break;
2562	case semicListNumNegative:
2563	WerrorS( "all numerators should be positive" );
2564	break;
2565	case semicListDenNegative:
2566	WerrorS( "all denominators should be positive" );
2567	break;
2568	case semicListMulNegative:
2569	WerrorS( "all multiplicities should be positive" );
2570	break;
2571
2572	case semicListNotSymmetric:
2573	WerrorS( "it is not symmetric" );
2574	break;
2575	case semicListNotMonotonous:
2576	WerrorS( "it is not monotonous" );
2577	break;
2578
2579	case semicListMilnorWrong:
2580	WerrorS( "the Milnor number is wrong" );
2581	break;
2582	case semicListPGWrong:
2583	WerrorS( "the geometrical genus is wrong" );
2584	break;
2585
2586	default:
2587	WerrorS( "unspecific error" );
2588	break;
2589	}
2590	}
2591	// ----------------------------------------------------------------------------
2592	// this is the main spectrum computation function
2593	// ----------------------------------------------------------------------------
2594
2595	spectrumState spectrumCompute( poly h,lists *L,int fast )
2596	{
2597	int i,j;
2598
2599	#ifdef SPECTRUM_DEBUG
2600	#ifdef SPECTRUM_PRINT
2601	#ifdef SPECTRUM_IOSTREAM
2602	cout << "spectrumCompute\n";
2603	if( fast==0 ) cout << " no optimization" << endl;
2604	if( fast==1 ) cout << " weight optimization" << endl;
2605	if( fast==2 ) cout << " symmetry optimization" << endl;
2606	#else
2607	fprintf( stdout,"spectrumCompute\n" );
2608	if( fast==0 ) fprintf( stdout," no optimization\n" );
2609	if( fast==1 ) fprintf( stdout," weight optimization\n" );
2610	if( fast==2 ) fprintf( stdout," symmetry optimization\n" );
2611	#endif
2612	#endif
2613	#endif
2614
2615	// ----------------------
2616	// check if h is zero
2617	// ----------------------
2618
2619	if( h==(poly)NULL )
2620	{
2621	return spectrumZero;
2622	}
2623
2624	// ----------------------------------
2625	// check if h has a constant term
2626	// ----------------------------------
2627
2628	if( hasConstTerm( h ) )
2629	{
2630	return spectrumBadPoly;
2631	}
2632
2633	// --------------------------------
2634	// check if h has a linear term
2635	// --------------------------------
2636
2637	if( hasLinearTerm( h ) )
2638	{
2639	*L = (lists)omAllocBin( slists_bin);
2640	(*L)->Init( 1 );
2641	(*L)->m[0].rtyp = INT_CMD; // milnor number
2642	/* (L)->m[0].data = (void)0;a -- done by Init */
2643
2644	return spectrumNoSingularity;
2645	}
2646
2647	// ----------------------------------
2648	// compute the jacobi ideal of (h)
2649	// ----------------------------------
2650
2651	ideal J = NULL;
2652	J = idInit( pVariables,1 );
2653
2654	#ifdef SPECTRUM_DEBUG
2655	#ifdef SPECTRUM_PRINT
2656	#ifdef SPECTRUM_IOSTREAM
2657	cout << "\n computing the Jacobi ideal...\n";
2658	#else
2659	fprintf( stdout,"\n computing the Jacobi ideal...\n" );
2660	#endif
2661	#endif
2662	#endif
2663
2664	for( i=0; i<pVariables; i++ )
2665	{
2666	J->m[i] = pDiff( h,i+1); //j );
2667
2668	#ifdef SPECTRUM_DEBUG
2669	#ifdef SPECTRUM_PRINT
2670	#ifdef SPECTRUM_IOSTREAM
2671	cout << " ";
2672	#else
2673	fprintf( stdout," " );
2674	#endif
2675	pWrite( J->m[i] );
2676	#endif
2677	#endif
2678	}
2679
2680	// --------------------------------------------
2681	// compute a standard basis stdJ of jac(h)
2682	// --------------------------------------------
2683
2684	#ifdef SPECTRUM_DEBUG
2685	#ifdef SPECTRUM_PRINT
2686	#ifdef SPECTRUM_IOSTREAM
2687	cout << endl;
2688	cout << " computing a standard basis..." << endl;
2689	#else
2690	fprintf( stdout,"\n" );
2691	fprintf( stdout," computing a standard basis...\n" );
2692	#endif
2693	#endif
2694	#endif
2695
2696	ideal stdJ = kStd(J,currQuotient,isNotHomog,NULL);
2697	idSkipZeroes( stdJ );
2698
2699	#ifdef SPECTRUM_DEBUG
2700	#ifdef SPECTRUM_PRINT
2701	for( i=0; i<IDELEMS(stdJ); i++ )
2702	{
2703	#ifdef SPECTRUM_IOSTREAM
2704	cout << " ";
2705	#else
2706	fprintf( stdout," " );
2707	#endif
2708
2709	pWrite( stdJ->m[i] );
2710	}
2711	#endif
2712	#endif
2713
2714	idDelete( &J );
2715
2716	// ------------------------------------------
2717	// check if the h has a singularity
2718	// ------------------------------------------
2719
2720	if( hasOne( stdJ ) )
2721	{
2722	// -------------------------------
2723	// h is smooth in the origin
2724	// return only the Milnor number
2725	// -------------------------------
2726
2727	*L = (lists)omAllocBin( slists_bin);
2728	(*L)->Init( 1 );
2729	(*L)->m[0].rtyp = INT_CMD; // milnor number
2730	/* (L)->m[0].data = (void)0;a -- done by Init */
2731
2732	return spectrumNoSingularity;
2733	}
2734
2735	// ------------------------------------------
2736	// check if the singularity h is isolated
2737	// ------------------------------------------
2738
2739	for( i=pVariables; i>0; i-- )
2740	{
2741	if( hasAxis( stdJ,i )==FALSE )
2742	{
2743	return spectrumNotIsolated;
2744	}
2745	}
2746
2747	// ------------------------------------------
2748	// compute the highest corner hc of stdJ
2749	// ------------------------------------------
2750
2751	#ifdef SPECTRUM_DEBUG
2752	#ifdef SPECTRUM_PRINT
2753	#ifdef SPECTRUM_IOSTREAM
2754	cout << "\n computing the highest corner...\n";
2755	#else
2756	fprintf( stdout,"\n computing the highest corner...\n" );
2757	#endif
2758	#endif
2759	#endif
2760
2761	poly hc = (poly)NULL;
2762
2763	scComputeHC( stdJ,currQuotient, 0,hc );
2764
2765	if( hc!=(poly)NULL )
2766	{
2767	pGetCoeff(hc) = nInit(1);
2768
2769	for( i=pVariables; i>0; i-- )
2770	{
2771	if( pGetExp( hc,i )>0 ) pDecrExp( hc,i );
2772	}
2773	pSetm( hc );
2774	}
2775	else
2776	{
2777	return spectrumNoHC;
2778	}
2779
2780	#ifdef SPECTRUM_DEBUG
2781	#ifdef SPECTRUM_PRINT
2782	#ifdef SPECTRUM_IOSTREAM
2783	cout << " ";
2784	#else
2785	fprintf( stdout," " );
2786	#endif
2787	pWrite( hc );
2788	#endif
2789	#endif
2790
2791	// ----------------------------------------
2792	// compute the Newton polygon nph of h
2793	// ----------------------------------------
2794
2795	#ifdef SPECTRUM_DEBUG
2796	#ifdef SPECTRUM_PRINT
2797	#ifdef SPECTRUM_IOSTREAM
2798	cout << "\n computing the newton polygon...\n";
2799	#else
2800	fprintf( stdout,"\n computing the newton polygon...\n" );
2801	#endif
2802	#endif
2803	#endif
2804
2805	newtonPolygon nph( h );
2806
2807	#ifdef SPECTRUM_DEBUG
2808	#ifdef SPECTRUM_PRINT
2809	cout << nph;
2810	#endif
2811	#endif
2812
2813	// -----------------------------------------------
2814	// compute the weight corner wc of (stdj,nph)
2815	// -----------------------------------------------
2816
2817	#ifdef SPECTRUM_DEBUG
2818	#ifdef SPECTRUM_PRINT
2819	#ifdef SPECTRUM_IOSTREAM
2820	cout << "\n computing the weight corner...\n";
2821	#else
2822	fprintf( stdout,"\n computing the weight corner...\n" );
2823	#endif
2824	#endif
2825	#endif
2826
2827	poly wc = ( fast==0 ? pCopy( hc ) :
2828	( fast==1 ? computeWC( nph,(Rational)pVariables ) :
2829	/* fast==2 */computeWC( nph,((Rational)pVariables)/(Rational)2 ) ) );
2830
2831	#ifdef SPECTRUM_DEBUG
2832	#ifdef SPECTRUM_PRINT
2833	#ifdef SPECTRUM_IOSTREAM
2834	cout << " ";
2835	#else
2836	fprintf( stdout," " );
2837	#endif
2838	pWrite( wc );
2839	#endif
2840	#endif
2841
2842	// -------------
2843	// compute NF
2844	// -------------
2845
2846	#ifdef SPECTRUM_DEBUG
2847	#ifdef SPECTRUM_PRINT
2848	#ifdef SPECTRUM_IOSTREAM
2849	cout << "\n computing NF...\n" << endl;
2850	#else
2851	fprintf( stdout,"\n computing NF...\n" );
2852	#endif
2853	#endif
2854	#endif
2855
2856	spectrumPolyList NF( &nph );
2857
2858	computeNF( stdJ,hc,wc,&NF );
2859
2860	#ifdef SPECTRUM_DEBUG
2861	#ifdef SPECTRUM_PRINT
2862	cout << NF;
2863	#ifdef SPECTRUM_IOSTREAM
2864	cout << endl;
2865	#else
2866	fprintf( stdout,"\n" );
2867	#endif
2868	#endif
2869	#endif
2870
2871	// ----------------------------
2872	// compute the spectrum of h
2873	// ----------------------------
2874
2875	return NF.spectrum( L,fast );
2876	}
2877
2878	// ----------------------------------------------------------------------------
2879	// this procedure is called from the interpreter
2880	// ----------------------------------------------------------------------------
2881	// first = polynomial
2882	// result = list of spectrum numbers
2883	// ----------------------------------------------------------------------------
2884
2885	BOOLEAN spectrumProc( leftv result,leftv first )
2886	{
2887	spectrumState state = spectrumOK;
2888
2889	// -------------------
2890	// check consistency
2891	// -------------------
2892
2893	// check for a local ring
2894
2895	if( !ringIsLocal( ) )
2896	{
2897	WerrorS( "only works for local orderings" );
2898	state = spectrumWrongRing;
2899	}
2900
2901	// no quotient rings are allowed
2902
2903	else if( currRing->qideal != NULL )
2904	{
2905	WerrorS( "does not work in quotient rings" );
2906	state = spectrumWrongRing;
2907	}
2908	else
2909	{
2910	lists L = (lists)NULL;
2911	int flag = 1; // weight corner optimization is safe
2912
2913	state = spectrumCompute( (poly)first->Data( ),&L,flag );
2914
2915	if( state==spectrumOK )
2916	{
2917	result->rtyp = LIST_CMD;
2918	result->data = (char*)L;
2919	}
2920	else
2921	{
2922	spectrumPrintError(state);
2923	}
2924	}
2925
2926	return (state!=spectrumOK);
2927	}
2928
2929	// ----------------------------------------------------------------------------
2930	// this procedure is called from the interpreter
2931	// ----------------------------------------------------------------------------
2932	// first = polynomial
2933	// result = list of spectrum numbers
2934	// ----------------------------------------------------------------------------
2935
2936	BOOLEAN spectrumfProc( leftv result,leftv first )
2937	{
2938	spectrumState state = spectrumOK;
2939
2940	// -------------------
2941	// check consistency
2942	// -------------------
2943
2944	// check for a local polynomial ring
2945
2946	if( currRing->OrdSgn != -1 )
2947	// ?? HS: the test above is also true for k[x][[y]], k[[x]][y]
2948	// or should we use:
2949	//if( !ringIsLocal( ) )
2950	{
2951	WerrorS( "only works for local orderings" );
2952	state = spectrumWrongRing;
2953	}
2954	else if( currRing->qideal != NULL )
2955	{
2956	WerrorS( "does not work in quotient rings" );
2957	state = spectrumWrongRing;
2958	}
2959	else
2960	{
2961	lists L = (lists)NULL;
2962	int flag = 2; // symmetric optimization
2963
2964	state = spectrumCompute( (poly)first->Data( ),&L,flag );
2965
2966	if( state==spectrumOK )
2967	{
2968	result->rtyp = LIST_CMD;
2969	result->data = (char*)L;
2970	}
2971	else
2972	{
2973	spectrumPrintError(state);
2974	}
2975	}
2976
2977	return (state!=spectrumOK);
2978	}
2979
2980	// ----------------------------------------------------------------------------
2981	// check if a list is a spectrum
2982	// check for:
2983	// list has 6 elements
2984	// 1st element is int (mu=Milnor number)
2985	// 2nd element is int (pg=geometrical genus)
2986	// 3rd element is int (n =number of different spectrum numbers)
2987	// 4th element is intvec (num=numerators)
2988	// 5th element is intvec (den=denomiantors)
2989	// 6th element is intvec (mul=multiplicities)
2990	// exactly n numerators
2991	// exactly n denominators
2992	// exactly n multiplicities
2993	// mu>0
2994	// pg>=0
2995	// n>0
2996	// num>0
2997	// den>0
2998	// mul>0
2999	// symmetriy with respect to numberofvariables/2
3000	// monotony
3001	// mu = sum of all multiplicities
3002	// pg = sum of all multiplicities where num/den<=1
3003	// ----------------------------------------------------------------------------
3004
3005	semicState list_is_spectrum( lists l )
3006	{
3007	// -------------------
3008	// check list length
3009	// -------------------
3010
3011	if( l->nr < 5 )
3012	{
3013	return semicListTooShort;
3014	}
3015	else if( l->nr > 5 )
3016	{
3017	return semicListTooLong;
3018	}
3019
3020	// -------------
3021	// check types
3022	// -------------
3023
3024	if( l->m[0].rtyp != INT_CMD )
3025	{
3026	return semicListFirstElementWrongType;
3027	}
3028	else if( l->m[1].rtyp != INT_CMD )
3029	{
3030	return semicListSecondElementWrongType;
3031	}
3032	else if( l->m[2].rtyp != INT_CMD )
3033	{
3034	return semicListThirdElementWrongType;
3035	}
3036	else if( l->m[3].rtyp != INTVEC_CMD )
3037	{
3038	return semicListFourthElementWrongType;
3039	}
3040	else if( l->m[4].rtyp != INTVEC_CMD )
3041	{
3042	return semicListFifthElementWrongType;
3043	}
3044	else if( l->m[5].rtyp != INTVEC_CMD )
3045	{
3046	return semicListSixthElementWrongType;
3047	}
3048
3049	// -------------------------
3050	// check number of entries
3051	// -------------------------
3052
3053	int mu = (int)(long)(l->m[0].Data( ));
3054	int pg = (int)(long)(l->m[1].Data( ));
3055	int n = (int)(long)(l->m[2].Data( ));
3056
3057	if( n <= 0 )
3058	{
3059	return semicListNNegative;
3060	}
3061
3062	intvec num = (intvec)l->m[3].Data( );
3063	intvec den = (intvec)l->m[4].Data( );
3064	intvec mul = (intvec)l->m[5].Data( );
3065
3066	if( n != num->length( ) )
3067	{
3068	return semicListWrongNumberOfNumerators;
3069	}
3070	else if( n != den->length( ) )
3071	{
3072	return semicListWrongNumberOfDenominators;
3073	}
3074	else if( n != mul->length( ) )
3075	{
3076	return semicListWrongNumberOfMultiplicities;
3077	}
3078
3079	// --------
3080	// values
3081	// --------
3082
3083	if( mu <= 0 )
3084	{
3085	return semicListMuNegative;
3086	}
3087	if( pg < 0 )
3088	{
3089	return semicListPgNegative;
3090	}
3091
3092	int i;
3093
3094	for( i=0; i<n; i++ )
3095	{
3096	if( (*num)[i] <= 0 )
3097	{
3098	return semicListNumNegative;
3099	}
3100	if( (*den)[i] <= 0 )
3101	{
3102	return semicListDenNegative;
3103	}
3104	if( (*mul)[i] <= 0 )
3105	{
3106	return semicListMulNegative;
3107	}
3108	}
3109
3110	// ----------------
3111	// check symmetry
3112	// ----------------
3113
3114	int j;
3115
3116	for( i=0, j=n-1; i<=j; i++,j-- )
3117	{
3118	if( (num)[i] != pVariables((den)[i]) - (num)[j] \|\|
3119	(den)[i] != (den)[j] \|\|
3120	(mul)[i] != (mul)[j] )
3121	{
3122	return semicListNotSymmetric;
3123	}
3124	}
3125
3126	// ----------------
3127	// check monotony
3128	// ----------------
3129
3130	for( i=0, j=1; i<n/2; i++,j++ )
3131	{
3132	if( (num)[i](den)[j] >= (num)[j](den)[i] )
3133	{
3134	return semicListNotMonotonous;
3135	}
3136	}
3137
3138	// ---------------------
3139	// check Milnor number
3140	// ---------------------
3141
3142	for( mu=0, i=0; i<n; i++ )
3143	{
3144	mu += (*mul)[i];
3145	}
3146
3147	if( mu != (int)(long)(l->m[0].Data( )) )
3148	{
3149	return semicListMilnorWrong;
3150	}
3151
3152	// -------------------------
3153	// check geometrical genus
3154	// -------------------------
3155
3156	for( pg=0, i=0; i<n; i++ )
3157	{
3158	if( (num)[i]<=(den)[i] )
3159	{
3160	pg += (*mul)[i];
3161	}
3162	}
3163
3164	if( pg != (int)(long)(l->m[1].Data( )) )
3165	{
3166	return semicListPGWrong;
3167	}
3168
3169	return semicOK;
3170	}
3171
3172	// ----------------------------------------------------------------------------
3173	// this procedure is called from the interpreter
3174	// ----------------------------------------------------------------------------
3175	// first = list of spectrum numbers
3176	// second = list of spectrum numbers
3177	// result = sum of the two lists
3178	// ----------------------------------------------------------------------------
3179
3180	BOOLEAN spaddProc( leftv result,leftv first,leftv second )
3181	{
3182	semicState state;
3183
3184	// -----------------
3185	// check arguments
3186	// -----------------
3187
3188	lists l1 = (lists)first->Data( );
3189	lists l2 = (lists)second->Data( );
3190
3191	if( (state=list_is_spectrum( l1 )) != semicOK )
3192	{
3193	WerrorS( "first argument is not a spectrum:" );
3194	list_error( state );
3195	}
3196	else if( (state=list_is_spectrum( l2 )) != semicOK )
3197	{
3198	WerrorS( "second argument is not a spectrum:" );
3199	list_error( state );
3200	}
3201	else
3202	{
3203	spectrum s1( l1 );
3204	spectrum s2( l2 );
3205	spectrum sum( s1+s2 );
3206
3207	result->rtyp = LIST_CMD;
3208	result->data = (char*)(sum.thelist( ));
3209	}
3210
3211	return (state!=semicOK);
3212	}
3213
3214	// ----------------------------------------------------------------------------
3215	// this procedure is called from the interpreter
3216	// ----------------------------------------------------------------------------
3217	// first = list of spectrum numbers
3218	// second = integer
3219	// result = the multiple of the first list by the second factor
3220	// ----------------------------------------------------------------------------
3221
3222	BOOLEAN spmulProc( leftv result,leftv first,leftv second )
3223	{
3224	semicState state;
3225
3226	// -----------------
3227	// check arguments
3228	// -----------------
3229
3230	lists l = (lists)first->Data( );
3231	int k = (int)(long)second->Data( );
3232
3233	if( (state=list_is_spectrum( l ))!=semicOK )
3234	{
3235	WerrorS( "first argument is not a spectrum" );
3236	list_error( state );
3237	}
3238	else if( k < 0 )
3239	{
3240	WerrorS( "second argument should be positive" );
3241	state = semicMulNegative;
3242	}
3243	else
3244	{
3245	spectrum s( l );
3246	spectrum product( k*s );
3247
3248	result->rtyp = LIST_CMD;
3249	result->data = (char*)product.thelist( );
3250	}
3251
3252	return (state!=semicOK);
3253	}
3254
3255	// ----------------------------------------------------------------------------
3256	// this procedure is called from the interpreter
3257	// ----------------------------------------------------------------------------
3258	// first = list of spectrum numbers
3259	// second = list of spectrum numbers
3260	// result = semicontinuity index
3261	// ----------------------------------------------------------------------------
3262
3263	BOOLEAN semicProc3 ( leftv res,leftv u,leftv v,leftv w )
3264	{
3265	semicState state;
3266	BOOLEAN qh=(((int)(long)w->Data())==1);
3267
3268	// -----------------
3269	// check arguments
3270	// -----------------
3271
3272	lists l1 = (lists)u->Data( );
3273	lists l2 = (lists)v->Data( );
3274
3275	if( (state=list_is_spectrum( l1 ))!=semicOK )
3276	{
3277	WerrorS( "first argument is not a spectrum" );
3278	list_error( state );
3279	}
3280	else if( (state=list_is_spectrum( l2 ))!=semicOK )
3281	{
3282	WerrorS( "second argument is not a spectrum" );
3283	list_error( state );
3284	}
3285	else
3286	{
3287	spectrum s1( l1 );
3288	spectrum s2( l2 );
3289
3290	res->rtyp = INT_CMD;
3291	if (qh)
3292	res->data = (void*)(s1.mult_spectrumh( s2 ));
3293	else
3294	res->data = (void*)(s1.mult_spectrum( s2 ));
3295	}
3296
3297	// -----------------
3298	// check status
3299	// -----------------
3300
3301	return (state!=semicOK);
3302	}
3303	BOOLEAN semicProc ( leftv res,leftv u,leftv v )
3304	{
3305	sleftv tmp;
3306	memset(&tmp,0,sizeof(tmp));
3307	tmp.rtyp=INT_CMD;
3308	/* tmp.data = (void )0; -- done by memset /
3309
3310	return semicProc3(res,u,v,&tmp);
3311	}
3312	// from splist.cc
3313	// ----------------------------------------------------------------------------
3314	// Compute the spectrum of a spectrumPolyList
3315	// ----------------------------------------------------------------------------
3316
3317	spectrumState spectrumPolyList::spectrum( lists *L,int fast )
3318	{
3319	spectrumPolyNode **node = &root;
3320	spectrumPolyNode *search;
3321
3322	poly f,tmp;
3323	int found,cmp;
3324
3325	Rational smax( ( fast==0 ? 0 : pVariables ),
3326	( fast==2 ? 2 : 1 ) );
3327
3328	Rational weight_prev( 0,1 );
3329
3330	int mu = 0; // the milnor number
3331	int pg = 0; // the geometrical genus
3332	int n = 0; // number of different spectral numbers
3333	int z = 0; // number of spectral number equal to smax
3334
3335	int k = 0;
3336
3337	while( (node)!=(spectrumPolyNode)NULL &&
3338	( fast==0 \|\| (*node)->weight<=smax ) )
3339	{
3340	// ---------------------------------------
3341	// determine the first normal form which
3342	// contains the monomial node->mon
3343	// ---------------------------------------
3344
3345	found = FALSE;
3346	search = *node;
3347
3348	while( search!=(spectrumPolyNode*)NULL && found==FALSE )
3349	{
3350	if( search->nf!=(poly)NULL )
3351	{
3352	f = search->nf;
3353
3354	do
3355	{
3356	// --------------------------------
3357	// look for (*node)->mon in f
3358	// --------------------------------
3359
3360	cmp = pCmp( (*node)->mon,f );
3361
3362	if( cmp<0 )
3363	{
3364	f = pNext( f );
3365	}
3366	else if( cmp==0 )
3367	{
3368	// -----------------------------
3369	// we have found a normal form
3370	// -----------------------------
3371
3372	found = TRUE;
3373
3374	// normalize coefficient
3375
3376	number inv = nInvers( pGetCoeff( f ) );
3377	pMult_nn( search->nf,inv );
3378	nDelete( &inv );
3379
3380	// exchange normal forms
3381
3382	tmp = (*node)->nf;
3383	(*node)->nf = search->nf;
3384	search->nf = tmp;
3385	}
3386	}
3387	while( cmp<0 && f!=(poly)NULL );
3388	}
3389	search = search->next;
3390	}
3391
3392	if( found==FALSE )
3393	{
3394	// ------------------------------------------------
3395	// the weight of node->mon is a spectrum number
3396	// ------------------------------------------------
3397
3398	mu++;
3399
3400	if( (*node)->weight<=(Rational)1 ) pg++;
3401	if( (*node)->weight==smax ) z++;
3402	if( (*node)->weight>weight_prev ) n++;
3403
3404	weight_prev = (*node)->weight;
3405	node = &((*node)->next);
3406	}
3407	else
3408	{
3409	// -----------------------------------------------
3410	// determine all other normal form which contain
3411	// the monomial node->mon
3412	// replace for node->mon its normal form
3413	// -----------------------------------------------
3414
3415	while( search!=(spectrumPolyNode*)NULL )
3416	{
3417	if( search->nf!=(poly)NULL )
3418	{
3419	f = search->nf;
3420
3421	do
3422	{
3423	// --------------------------------
3424	// look for (*node)->mon in f
3425	// --------------------------------
3426
3427	cmp = pCmp( (*node)->mon,f );
3428
3429	if( cmp<0 )
3430	{
3431	f = pNext( f );
3432	}
3433	else if( cmp==0 )
3434	{
3435	search->nf = pSub( search->nf,
3436	ppMult_nn( (*node)->nf,pGetCoeff( f ) ) );
3437	pNorm( search->nf );
3438	}
3439	}
3440	while( cmp<0 && f!=(poly)NULL );
3441	}
3442	search = search->next;
3443	}
3444	delete_node( node );
3445	}
3446
3447	}
3448
3449	// --------------------------------------------------------
3450	// fast computation exploits the symmetry of the spectrum
3451	// --------------------------------------------------------
3452
3453	if( fast==2 )
3454	{
3455	mu = 2*mu - z;
3456	n = ( z > 0 ? 2n - 1 : 2n );
3457	}
3458
3459	// --------------------------------------------------------
3460	// compute the spectrum numbers with their multiplicities
3461	// --------------------------------------------------------
3462
3463	intvec *nom = new intvec( n );
3464	intvec *den = new intvec( n );
3465	intvec *mult = new intvec( n );
3466
3467	int count = 0;
3468	int multiplicity = 1;
3469
3470	for( search=root; search!=(spectrumPolyNode*)NULL &&
3471	( fast==0 \|\| search->weight<=smax );
3472	search=search->next )
3473	{
3474	if( search->next==(spectrumPolyNode*)NULL \|\|
3475	search->weight<search->next->weight )
3476	{
3477	(*nom) [count] = search->weight.get_num_si( );
3478	(*den) [count] = search->weight.get_den_si( );
3479	(*mult)[count] = multiplicity;
3480
3481	multiplicity=1;
3482	count++;
3483	}
3484	else
3485	{
3486	multiplicity++;
3487	}
3488	}
3489
3490	// --------------------------------------------------------
3491	// fast computation exploits the symmetry of the spectrum
3492	// --------------------------------------------------------
3493
3494	if( fast==2 )
3495	{
3496	int n1,n2;
3497	for( n1=0, n2=n-1; n1<n2; n1++, n2-- )
3498	{
3499	(nom) [n2] = pVariables(den)[n1]-(nom)[n1];
3500	(den) [n2] = (den)[n1];
3501	(mult)[n2] = (mult)[n1];
3502	}
3503	}
3504
3505	// -----------------------------------
3506	// test if the spectrum is symmetric
3507	// -----------------------------------
3508
3509	if( fast==0 \|\| fast==1 )
3510	{
3511	int symmetric=TRUE;
3512
3513	for( int n1=0, n2=n-1 ; n1<n2 && symmetric==TRUE; n1++, n2-- )
3514	{
3515	if( (mult)[n1]!=(mult)[n2] \|\|
3516	(den) [n1]!= (den)[n2] \|\|
3517	(nom)[n1]+(nom)[n2]!=pVariables(den) [n1] )
3518	{
3519	symmetric = FALSE;
3520	}
3521	}
3522
3523	if( symmetric==FALSE )
3524	{
3525	// ---------------------------------------------
3526	// the spectrum is not symmetric => degenerate
3527	// principal part
3528	// ---------------------------------------------
3529
3530	*L = (lists)omAllocBin( slists_bin);
3531	(*L)->Init( 1 );
3532	(*L)->m[0].rtyp = INT_CMD; // milnor number
3533	(L)->m[0].data = (void)mu;
3534
3535	return spectrumDegenerate;
3536	}
3537	}
3538
3539	*L = (lists)omAllocBin( slists_bin);
3540
3541	(*L)->Init( 6 );
3542
3543	(*L)->m[0].rtyp = INT_CMD; // milnor number
3544	(*L)->m[1].rtyp = INT_CMD; // geometrical genus
3545	(*L)->m[2].rtyp = INT_CMD; // number of spectrum values
3546	(*L)->m[3].rtyp = INTVEC_CMD; // nominators
3547	(*L)->m[4].rtyp = INTVEC_CMD; // denomiantors
3548	(*L)->m[5].rtyp = INTVEC_CMD; // multiplicities
3549
3550	(L)->m[0].data = (void)mu;
3551	(L)->m[1].data = (void)pg;
3552	(L)->m[2].data = (void)n;
3553	(L)->m[3].data = (void)nom;
3554	(L)->m[4].data = (void)den;
3555	(L)->m[5].data = (void)mult;
3556
3557	return spectrumOK;
3558	}
3559
3560	#endif
3561
3562	//from mpr_inout.cc
3563	extern void nPrint(number n);
3564
3565	BOOLEAN loNewtonP( leftv res, leftv arg1 )
3566	{
3567	res->data= (void*)loNewtonPolytope( (ideal)arg1->Data() );
3568	return FALSE;
3569	}
3570
3571	BOOLEAN loSimplex( leftv res, leftv args )
3572	{
3573	if ( !(rField_is_long_R()) )
3574	{
3575	WerrorS("Ground field not implemented!");
3576	return TRUE;
3577	}
3578
3579	simplex * LP;
3580	matrix m;
3581
3582	leftv v= args;
3583	if ( v->Typ() != MATRIX_CMD ) // 1: matrix
3584	return TRUE;
3585	else
3586	m= (matrix)(v->CopyD());
3587
3588	LP = new simplex(MATROWS(m),MATCOLS(m));
3589	LP->mapFromMatrix(m);
3590
3591	v= v->next;
3592	if ( v->Typ() != INT_CMD ) // 2: m = number of constraints
3593	return TRUE;
3594	else
3595	LP->m= (int)(long)(v->Data());
3596
3597	v= v->next;
3598	if ( v->Typ() != INT_CMD ) // 3: n = number of variables
3599	return TRUE;
3600	else
3601	LP->n= (int)(long)(v->Data());
3602
3603	v= v->next;
3604	if ( v->Typ() != INT_CMD ) // 4: m1 = number of <= constraints
3605	return TRUE;
3606	else
3607	LP->m1= (int)(long)(v->Data());
3608
3609	v= v->next;
3610	if ( v->Typ() != INT_CMD ) // 5: m2 = number of >= constraints
3611	return TRUE;
3612	else
3613	LP->m2= (int)(long)(v->Data());
3614
3615	v= v->next;
3616	if ( v->Typ() != INT_CMD ) // 6: m3 = number of == constraints
3617	return TRUE;
3618	else
3619	LP->m3= (int)(long)(v->Data());
3620
3621	#ifdef mprDEBUG_PROT
3622	Print("m (constraints) %d\n",LP->m);
3623	Print("n (columns) %d\n",LP->n);
3624	Print("m1 (<=) %d\n",LP->m1);
3625	Print("m2 (>=) %d\n",LP->m2);
3626	Print("m3 (==) %d\n",LP->m3);
3627	#endif
3628
3629	LP->compute();
3630
3631	lists lres= (lists)omAlloc( sizeof(slists) );
3632	lres->Init( 6 );
3633
3634	lres->m[0].rtyp= MATRIX_CMD; // output matrix
3635	lres->m[0].data=(void*)LP->mapToMatrix(m);
3636
3637	lres->m[1].rtyp= INT_CMD; // found a solution?
3638	lres->m[1].data=(void*)LP->icase;
3639
3640	lres->m[2].rtyp= INTVEC_CMD;
3641	lres->m[2].data=(void*)LP->posvToIV();
3642
3643	lres->m[3].rtyp= INTVEC_CMD;
3644	lres->m[3].data=(void*)LP->zrovToIV();
3645
3646	lres->m[4].rtyp= INT_CMD;
3647	lres->m[4].data=(void*)LP->m;
3648
3649	lres->m[5].rtyp= INT_CMD;
3650	lres->m[5].data=(void*)LP->n;
3651
3652	res->data= (void*)lres;
3653
3654	return FALSE;
3655	}
3656
3657	BOOLEAN nuMPResMat( leftv res, leftv arg1, leftv arg2 )
3658	{
3659	ideal gls = (ideal)(arg1->Data());
3660	int imtype= (int)(long)arg2->Data();
3661
3662	uResultant::resMatType mtype= determineMType( imtype );
3663
3664	// check input ideal ( = polynomial system )
3665	if ( mprIdealCheck( gls, arg1->Name(), mtype, true ) != mprOk )
3666	{
3667	return TRUE;
3668	}
3669
3670	uResultant *resMat= new uResultant( gls, mtype, false );
3671	if (resMat!=NULL)
3672	{
3673	res->rtyp = MODUL_CMD;
3674	res->data= (void*)resMat->accessResMat()->getMatrix();
3675	if (!errorreported) delete resMat;
3676	}
3677	return errorreported;
3678	}
3679
3680	BOOLEAN nuLagSolve( leftv res, leftv arg1, leftv arg2, leftv arg3 )
3681	{
3682
3683	poly gls;
3684	gls= (poly)(arg1->Data());
3685	int howclean= (int)(long)arg3->Data();
3686
3687	if ( !(rField_is_R() \|\|
3688	rField_is_Q() \|\|
3689	rField_is_long_R() \|\|
3690	rField_is_long_C()) )
3691	{
3692	WerrorS("Ground field not implemented!");
3693	return TRUE;
3694	}
3695
3696	if ( !(rField_is_R()\|\|rField_is_long_R()\|\|rField_is_long_C()) )
3697	{
3698	unsigned long int ii = (unsigned long int)arg2->Data();
3699	setGMPFloatDigits( ii, ii );
3700	}
3701
3702	if ( gls == NULL \|\| pIsConstant( gls ) )
3703	{
3704	WerrorS("Input polynomial is constant!");
3705	return TRUE;
3706	}
3707
3708	int ldummy;
3709	int deg= pLDeg( gls, &ldummy, currRing );
3710	// int deg= pDeg( gls );
3711	int len= pLength( gls );
3712	int i,vpos;
3713	poly piter;
3714	lists elist;
3715	lists rlist;
3716
3717	elist= (lists)omAlloc( sizeof(slists) );
3718	elist->Init( 0 );
3719
3720	if ( pVariables > 1 )
3721	{
3722	piter= gls;
3723	for ( i= 1; i <= pVariables; i++ )
3724	if ( pGetExp( piter, i ) )
3725	{
3726	vpos= i;
3727	break;
3728	}
3729	while ( piter )
3730	{
3731	for ( i= 1; i <= pVariables; i++ )
3732	if ( (vpos != i) && (pGetExp( piter, i ) != 0) )
3733	{
3734	WerrorS("The input polynomial must be univariate!");
3735	return TRUE;
3736	}
3737	pIter( piter );
3738	}
3739	}
3740
3741	rootContainer * roots= new rootContainer();
3742	number * pcoeffs= (number )omAlloc( (deg+1) sizeof( number ) );
3743	piter= gls;
3744	for ( i= deg; i >= 0; i-- )
3745	{
3746	//if ( piter ) Print("deg %d, pDeg(piter) %d\n",i,pTotaldegree(piter));
3747	if ( piter && pTotaldegree(piter) == i )
3748	{
3749	pcoeffs[i]= nCopy( pGetCoeff( piter ) );
3750	//nPrint( pcoeffs[i] );PrintS(" ");
3751	pIter( piter );
3752	}
3753	else
3754	{
3755	pcoeffs[i]= nInit(0);
3756	}
3757	}
3758
3759	#ifdef mprDEBUG_PROT
3760	for (i=deg; i >= 0; i--)
3761	{
3762	nPrint( pcoeffs[i] );PrintS(" ");
3763	}
3764	PrintLn();
3765	#endif
3766
3767	roots->fillContainer( pcoeffs, NULL, 1, deg, rootContainer::onepoly, 1 );
3768	roots->solver( howclean );
3769
3770	int elem= roots->getAnzRoots();
3771	char *out;
3772	char *dummy;
3773	int j;
3774
3775	rlist= (lists)omAlloc( sizeof(slists) );
3776	rlist->Init( elem );
3777
3778	if (rField_is_long_C())
3779	{
3780	for ( j= 0; j < elem; j++ )
3781	{
3782	rlist->m[j].rtyp=NUMBER_CMD;
3783	rlist->m[j].data=(void *)nCopy((number)(roots->getRoot(j)));
3784	//rlist->m[j].data=(void *)(number)(roots->getRoot(j));
3785	}
3786	}
3787	else
3788	{
3789	for ( j= 0; j < elem; j++ )
3790	{
3791	dummy = complexToStr( (*roots)[j], gmp_output_digits );
3792	rlist->m[j].rtyp=STRING_CMD;
3793	rlist->m[j].data=(void *)dummy;
3794	}
3795	}
3796
3797	elist->Clean();
3798	//omFreeSize( (ADDRESS) elist, sizeof(slists) );
3799
3800	// this is (via fillContainer) the same data as in root
3801	//for ( i= deg; i >= 0; i-- ) nDelete( &pcoeffs[i] );
3802	//omFreeSize( (ADDRESS) pcoeffs, (deg+1) * sizeof( number ) );
3803
3804	delete roots;
3805
3806	res->rtyp= LIST_CMD;
3807	res->data= (void*)rlist;
3808
3809	return FALSE;
3810	}
3811
3812	BOOLEAN nuVanderSys( leftv res, leftv arg1, leftv arg2, leftv arg3)
3813	{
3814	int i;
3815	ideal p,w;
3816	p= (ideal)arg1->Data();
3817	w= (ideal)arg2->Data();
3818
3819	// w[0] = f(p^0)
3820	// w[1] = f(p^1)
3821	// ...
3822	// p can be a vector of numbers (multivariate polynom)
3823	// or one number (univariate polynom)
3824	// tdg = deg(f)
3825
3826	int n= IDELEMS( p );
3827	int m= IDELEMS( w );
3828	int tdg= (int)(long)arg3->Data();
3829
3830	res->data= (void*)NULL;
3831
3832	// check the input
3833	if ( tdg < 1 )
3834	{
3835	WerrorS("Last input parameter must be > 0!");
3836	return TRUE;
3837	}
3838	if ( n != pVariables )
3839	{
3840	Werror("Size of first input ideal must be equal to %d!",pVariables);
3841	return TRUE;
3842	}
3843	if ( m != (int)pow((double)tdg+1,(double)n) )
3844	{
3845	Werror("Size of second input ideal must be equal to %d!",
3846	(int)pow((double)tdg+1,(double)n));
3847	return TRUE;
3848	}
3849	if ( !(rField_is_Q() /* \|\|
3850	rField_is_R() \|\| rField_is_long_R() \|\|
3851	rField_is_long_C()*/ ) )
3852	{
3853	WerrorS("Ground field not implemented!");
3854	return TRUE;
3855	}
3856
3857	number tmp;
3858	number pevpoint= (number )omAlloc( n * sizeof( number ) );
3859	for ( i= 0; i < n; i++ )
3860	{
3861	pevpoint[i]=nInit(0);
3862	if ( (p->m)[i] )
3863	{
3864	tmp = pGetCoeff( (p->m)[i] );
3865	if ( nIsZero(tmp) \|\| nIsOne(tmp) \|\| nIsMOne(tmp) )
3866	{
3867	omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
3868	WerrorS("Elements of first input ideal must not be equal to -1, 0, 1!");
3869	return TRUE;
3870	}
3871	} else tmp= NULL;
3872	if ( !nIsZero(tmp) )
3873	{
3874	if ( !pIsConstant((p->m)[i]))
3875	{
3876	omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
3877	WerrorS("Elements of first input ideal must be numbers!");
3878	return TRUE;
3879	}
3880	pevpoint[i]= nCopy( tmp );
3881	}
3882	}
3883
3884	number wresults= (number )omAlloc( m * sizeof( number ) );
3885	for ( i= 0; i < m; i++ )
3886	{
3887	wresults[i]= nInit(0);
3888	if ( (w->m)[i] && !nIsZero(pGetCoeff((w->m)[i])) )
3889	{
3890	if ( !pIsConstant((w->m)[i]))
3891	{
3892	omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
3893	omFreeSize( (ADDRESS)wresults, m * sizeof( number ) );
3894	WerrorS("Elements of second input ideal must be numbers!");
3895	return TRUE;
3896	}
3897	wresults[i]= nCopy(pGetCoeff((w->m)[i]));
3898	}
3899	}
3900
3901	vandermonde vm( m, n, tdg, pevpoint, FALSE );
3902	number *ncpoly= vm.interpolateDense( wresults );
3903	// do not free ncpoly[]!!
3904	poly rpoly= vm.numvec2poly( ncpoly );
3905
3906	omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
3907	omFreeSize( (ADDRESS)wresults, m * sizeof( number ) );
3908
3909	res->data= (void*)rpoly;
3910	return FALSE;
3911	}
3912
3913	BOOLEAN nuUResSolve( leftv res, leftv args )
3914	{
3915	leftv v= args;
3916
3917	ideal gls;
3918	int imtype;
3919	int howclean;
3920
3921	// get ideal
3922	if ( v->Typ() != IDEAL_CMD )
3923	return TRUE;
3924	else gls= (ideal)(v->Data());
3925	v= v->next;
3926
3927	// get resultant matrix type to use (0,1)
3928	if ( v->Typ() != INT_CMD )
3929	return TRUE;
3930	else imtype= (int)(long)v->Data();
3931	v= v->next;
3932
3933	if (imtype==0)
3934	{
3935	ideal test_id=idInit(1,1);
3936	int j;
3937	for(j=IDELEMS(gls)-1;j>=0;j--)
3938	{
3939	if (gls->m[j]!=NULL)
3940	{
3941	test_id->m[0]=gls->m[j];
3942	intvec *dummy_w=idQHomWeight(test_id);
3943	if (dummy_w!=NULL)
3944	{
3945	WerrorS("Newton polytope not of expected dimension");
3946	delete dummy_w;
3947	return TRUE;
3948	}
3949	}
3950	}
3951	}
3952
3953	// get and set precision in digits ( > 0 )
3954	if ( v->Typ() != INT_CMD )
3955	return TRUE;
3956	else if ( !(rField_is_R()\|\|rField_is_long_R()\|\|rField_is_long_C()) )
3957	{
3958	unsigned long int ii=(unsigned long int)v->Data();
3959	setGMPFloatDigits( ii, ii );
3960	}
3961	v= v->next;
3962
3963	// get interpolation steps (0,1,2)
3964	if ( v->Typ() != INT_CMD )
3965	return TRUE;
3966	else howclean= (int)(long)v->Data();
3967
3968	uResultant::resMatType mtype= determineMType( imtype );
3969	int i,c,count;
3970	lists listofroots= NULL;
3971	lists emptylist;
3972	number smv= NULL;
3973	BOOLEAN interpolate_det= (mtype==uResultant::denseResMat)?TRUE:FALSE;
3974
3975	//emptylist= (lists)omAlloc( sizeof(slists) );
3976	//emptylist->Init( 0 );
3977
3978	//res->rtyp = LIST_CMD;
3979	//res->data= (void *)emptylist;
3980
3981	// check input ideal ( = polynomial system )
3982	if ( mprIdealCheck( gls, args->Name(), mtype ) != mprOk )
3983	{
3984	return TRUE;
3985	}
3986
3987	uResultant * ures;
3988	rootContainer ** iproots;
3989	rootContainer ** muiproots;
3990	rootArranger * arranger;
3991
3992	// main task 1: setup of resultant matrix
3993	ures= new uResultant( gls, mtype );
3994	if ( ures->accessResMat()->initState() != resMatrixBase::ready )
3995	{
3996	WerrorS("Error occurred during matrix setup!");
3997	return TRUE;
3998	}
3999
4000	// if dense resultant, check if minor nonsingular
4001	if ( mtype == uResultant::denseResMat )
4002	{
4003	smv= ures->accessResMat()->getSubDet();
4004	#ifdef mprDEBUG_PROT
4005	PrintS("// Determinant of submatrix: ");nPrint(smv);PrintLn();
4006	#endif
4007	if ( nIsZero(smv) )
4008	{
4009	WerrorS("Unsuitable input ideal: Minor of resultant matrix is singular!");
4010	return TRUE;
4011	}
4012	}
4013
4014	// main task 2: Interpolate specialized resultant polynomials
4015	if ( interpolate_det )
4016	iproots= ures->interpolateDenseSP( false, smv );
4017	else
4018	iproots= ures->specializeInU( false, smv );
4019
4020	// main task 3: Interpolate specialized resultant polynomials
4021	if ( interpolate_det )
4022	muiproots= ures->interpolateDenseSP( true, smv );
4023	else
4024	muiproots= ures->specializeInU( true, smv );
4025
4026	#ifdef mprDEBUG_PROT
4027	c= iproots[0]->getAnzElems();
4028	for (i=0; i < c; i++) pWrite(iproots[i]->getPoly());
4029	c= muiproots[0]->getAnzElems();
4030	for (i=0; i < c; i++) pWrite(muiproots[i]->getPoly());
4031	#endif
4032
4033	// main task 4: Compute roots of specialized polys and match them up
4034	arranger= new rootArranger( iproots, muiproots, howclean );
4035	arranger->solve_all();
4036
4037	// get list of roots
4038	if ( arranger->success() )
4039	{
4040	arranger->arrange();
4041	listofroots= arranger->listOfRoots( gmp_output_digits );
4042	}
4043	else
4044	{
4045	WerrorS("Solver was unable to find any roots!");
4046	return TRUE;
4047	}
4048
4049	// free everything
4050	count= iproots[0]->getAnzElems();
4051	for (i=0; i < count; i++) delete iproots[i];
4052	omFreeSize( (ADDRESS) iproots, count * sizeof(rootContainer*) );
4053	count= muiproots[0]->getAnzElems();
4054	for (i=0; i < count; i++) delete muiproots[i];
4055	omFreeSize( (ADDRESS) muiproots, count * sizeof(rootContainer*) );
4056
4057	delete ures;
4058	delete arranger;
4059	nDelete( &smv );
4060
4061	res->data= (void *)listofroots;
4062
4063	//emptylist->Clean();
4064	// omFreeSize( (ADDRESS) emptylist, sizeof(slists) );
4065
4066	return FALSE;
4067	}
4068
4069	// from mpr_numeric.cc
4070	lists rootArranger::listOfRoots( const unsigned int oprec )
4071	{
4072	int i,j,tr;
4073	int count= roots[0]->getAnzRoots(); // number of roots
4074	int elem= roots[0]->getAnzElems(); // number of koordinates per root
4075
4076	lists listofroots= (lists)omAlloc( sizeof(slists) ); // must be done this way!
4077
4078	if ( found_roots )
4079	{
4080	listofroots->Init( count );
4081
4082	for (i=0; i < count; i++)
4083	{
4084	lists onepoint= (lists)omAlloc(sizeof(slists)); // must be done this way!
4085	onepoint->Init(elem);
4086	for ( j= 0; j < elem; j++ )
4087	{
4088	if ( !rField_is_long_C() )
4089	{
4090	onepoint->m[j].rtyp=STRING_CMD;
4091	onepoint->m[j].data=(void )complexToStr((roots[j])[i],oprec);
4092	}
4093	else
4094	{
4095	onepoint->m[j].rtyp=NUMBER_CMD;
4096	onepoint->m[j].data=(void *)nCopy((number)(roots[j]->getRoot(i)));
4097	}
4098	onepoint->m[j].next= NULL;
4099	onepoint->m[j].name= NULL;
4100	}
4101	listofroots->m[i].rtyp=LIST_CMD;
4102	listofroots->m[i].data=(void *)onepoint;
4103	listofroots->m[j].next= NULL;
4104	listofroots->m[j].name= NULL;
4105	}
4106
4107	}
4108	else
4109	{
4110	listofroots->Init( 0 );
4111	}
4112
4113	return listofroots;
4114	}
4115
4116	// from ring.cc
4117	void rSetHdl(idhdl h)
4118	{
4119	int i;
4120	ring rg = NULL;
4121	if (h!=NULL)
4122	{
4123	// Print(" new ring:%s (l:%d)\n",IDID(h),IDLEV(h));
4124	rg = IDRING(h);
4125	omCheckAddrSize((ADDRESS)h,sizeof(idrec));
4126	if (IDID(h)) // OB: ????
4127	omCheckAddr((ADDRESS)IDID(h));
4128	rTest(rg);
4129	}
4130
4131	// clean up history
4132	if (sLastPrinted.RingDependend())
4133	{
4134	sLastPrinted.CleanUp();
4135	memset(&sLastPrinted,0,sizeof(sleftv));
4136	}
4137
4138	// test for valid "currRing":
4139	if ((rg!=NULL) && (rg->idroot==NULL))
4140	{
4141	ring old=rg;
4142	rg=rAssure_HasComp(rg);
4143	if (old!=rg)
4144	{
4145	rKill(old);
4146	IDRING(h)=rg;
4147	}
4148	}
4149	/------------ change the global ring -----------------------/
4150	rChangeCurrRing(rg);
4151	currRingHdl = h;
4152	}
4153
4154	BOOLEAN rSleftvOrdering2Ordering(sleftv *ord, ring R)
4155	{
4156	int last = 0, o=0, n = 1, i=0, typ = 1, j;
4157	sleftv *sl = ord;
4158
4159	// determine nBlocks
4160	while (sl!=NULL)
4161	{
4162	intvec iv = (intvec )(sl->data);
4163	if (((iv)[1]==ringorder_c)\|\|((iv)[1]==ringorder_C))
4164	i++;
4165	else if ((*iv)[1]==ringorder_L)
4166	{
4167	R->bitmask=(*iv)[2];
4168	n--;
4169	}
4170	else if (((*iv)[1]!=ringorder_a)
4171	&& ((*iv)[1]!=ringorder_a64))
4172	o++;
4173	n++;
4174	sl=sl->next;
4175	}
4176	// check whether at least one real ordering
4177	if (o==0)
4178	{
4179	WerrorS("invalid combination of orderings");
4180	return TRUE;
4181	}
4182	// if no c/C ordering is given, increment n
4183	if (i==0) n++;
4184	else if (i != 1)
4185	{
4186	// throw error if more than one is given
4187	WerrorS("more than one ordering c/C specified");
4188	return TRUE;
4189	}
4190
4191	// initialize fields of R
4192	R->order=(int )omAlloc0(nsizeof(int));
4193	R->block0=(int )omAlloc0(nsizeof(int));
4194	R->block1=(int )omAlloc0(nsizeof(int));
4195	R->wvhdl=(int*)omAlloc0(nsizeof(int_ptr));
4196
4197	int weights=(int)omAlloc0((R->N+1)*sizeof(int));
4198
4199	// init order, so that rBlocks works correctly
4200	for (j=0; j < n-1; j++)
4201	R->order[j] = (int) ringorder_unspec;
4202	// set last _C order, if no c/C order was given
4203	if (i == 0) R->order[n-2] = ringorder_C;
4204
4205	/* init orders */
4206	sl=ord;
4207	n=-1;
4208	while (sl!=NULL)
4209	{
4210	intvec *iv;
4211	iv = (intvec *)(sl->data);
4212	if ((*iv)[1]!=ringorder_L)
4213	{
4214	n++;
4215
4216	/* the format of an ordering:
4217	* iv[0]: factor
4218	* iv[1]: ordering
4219	* iv[2..end]: weights
4220	*/
4221	R->order[n] = (*iv)[1];
4222	typ=1;
4223	switch ((*iv)[1])
4224	{
4225	case ringorder_ws:
4226	case ringorder_Ws:
4227	typ=-1;
4228	case ringorder_wp:
4229	case ringorder_Wp:
4230	R->wvhdl[n]=(int)omAlloc((iv->length()-1)sizeof(int));
4231	R->block0[n] = last+1;
4232	for (i=2; i<iv->length(); i++)
4233	{
4234	R->wvhdl[n][i-2] = (*iv)[i];
4235	last++;
4236	if (weights[last]==0) weights[last]=(iv)[i]typ;
4237	}
4238	R->block1[n] = last;
4239	break;
4240	case ringorder_ls:
4241	case ringorder_ds:
4242	case ringorder_Ds:
4243	case ringorder_rs:
4244	typ=-1;
4245	case ringorder_lp:
4246	case ringorder_dp:
4247	case ringorder_Dp:
4248	case ringorder_rp:
4249	R->block0[n] = last+1;
4250	if (iv->length() == 3) last+=(*iv)[2];
4251	else last += (*iv)[0];
4252	R->block1[n] = last;
4253	if (R->block0[n]>R->block1[n]) return TRUE;
4254	if (rCheckIV(iv)) return TRUE;
4255	for(i=R->block0[n];i<=R->block1[n];i++)
4256	{
4257	if (weights[i]==0) weights[i]=typ;
4258	}
4259	break;
4260	case ringorder_S:
4261	case ringorder_c:
4262	case ringorder_C:
4263	if (rCheckIV(iv)) return TRUE;
4264	break;
4265	case ringorder_aa:
4266	case ringorder_a:
4267	R->block0[n] = last+1;
4268	R->block1[n] = si_min(last+iv->length()-2 , R->N);
4269	R->wvhdl[n] = (int)omAlloc((iv->length()-1)sizeof(int));
4270	for (i=2; i<iv->length(); i++)
4271	{
4272	R->wvhdl[n][i-2]=(*iv)[i];
4273	last++;
4274	if (weights[last]==0) weights[last]=(iv)[i]typ;
4275	}
4276	last=R->block0[n]-1;
4277	break;
4278	case ringorder_a64:
4279	{
4280	R->block0[n] = last+1;
4281	R->block1[n] = si_min(last+iv->length()-2 , R->N);
4282	R->wvhdl[n] = (int)omAlloc((iv->length()-1)sizeof(int64));
4283	int64 w=(int64 )R->wvhdl[n];
4284	for (i=2; i<iv->length(); i++)
4285	{
4286	w[i-2]=(*iv)[i];
4287	last++;
4288	if (weights[last]==0) weights[last]=(iv)[i]typ;
4289	}
4290	last=R->block0[n]-1;
4291	break;
4292	}
4293	case ringorder_M:
4294	{
4295	int Mtyp=rTypeOfMatrixOrder(iv);
4296	if (Mtyp==0) return TRUE;
4297	if (Mtyp==-1) typ = -1;
4298	for(i=R->block0[n];i<=R->block1[n];i++)
4299	{
4300	if (weights[i]==0) weights[i]=typ;
4301	}
4302
4303	R->wvhdl[n] =( int )omAlloc((iv->length()-1)sizeof(int));
4304	for (i=2; i<iv->length();i++)
4305	R->wvhdl[n][i-2]=(*iv)[i];
4306
4307	R->block0[n] = last+1;
4308	last += (int)sqrt((double)(iv->length()-2));
4309	R->block1[n] = last;
4310	break;
4311	}
4312
4313	case ringorder_no:
4314	R->order[n] = ringorder_unspec;
4315	return TRUE;
4316
4317	default:
4318	Werror("Internal Error: Unknown ordering %d", (*iv)[1]);
4319	R->order[n] = ringorder_unspec;
4320	return TRUE;
4321	}
4322	}
4323	sl=sl->next;
4324	}
4325
4326	// check for complete coverage
4327	if ((R->order[n]==ringorder_c) \|\| (R->order[n]==ringorder_C)) n--;
4328	if (R->block1[n] != R->N)
4329	{
4330	if (((R->order[n]==ringorder_dp) \|\|
4331	(R->order[n]==ringorder_ds) \|\|
4332	(R->order[n]==ringorder_Dp) \|\|
4333	(R->order[n]==ringorder_Ds) \|\|
4334	(R->order[n]==ringorder_rp) \|\|
4335	(R->order[n]==ringorder_rs) \|\|
4336	(R->order[n]==ringorder_lp) \|\|
4337	(R->order[n]==ringorder_ls))
4338	&&
4339	R->block0[n] <= R->N)
4340	{
4341	R->block1[n] = R->N;
4342	}
4343	else
4344	{
4345	Werror("mismatch of number of vars (%d) and ordering (%d vars)",
4346	R->N,R->block1[n]);
4347	return TRUE;
4348	}
4349	}
4350	// find OrdSgn:
4351	R->OrdSgn = 1;
4352	for(i=1;i<=R->N;i++)
4353	{ if (weights[i]<0) { R->OrdSgn=-1;break; }}
4354	omFree(weights);
4355	return FALSE;
4356	}
4357
4358	BOOLEAN rSleftvList2StringArray(sleftv* sl, char** p)
4359	{
4360
4361	while(sl!=NULL)
4362	{
4363	if (sl->Name() == sNoName)
4364	{
4365	if (sl->Typ()==POLY_CMD)
4366	{
4367	sleftv s_sl;
4368	iiConvert(POLY_CMD,ANY_TYPE,-1,sl,&s_sl);
4369	if (s_sl.Name() != sNoName)
4370	*p = omStrDup(s_sl.Name());
4371	else
4372	*p = NULL;
4373	sl->next = s_sl.next;
4374	s_sl.next = NULL;
4375	s_sl.CleanUp();
4376	if (*p == NULL) return TRUE;
4377	}
4378	else
4379	return TRUE;
4380	}
4381	else
4382	*p = omStrDup(sl->Name());
4383	p++;
4384	sl=sl->next;
4385	}
4386	return FALSE;
4387	}
4388
4389	////////////////////
4390	//
4391	// rInit itself:
4392	//
4393	// INPUT: s: name, pn: ch & parameter (names), rv: variable (names)
4394	// ord: ordering
4395	// RETURN: currRingHdl on success
4396	// NULL on error
4397	// NOTE: * makes new ring to current ring, on success
4398	// * considers input sleftv's as read-only
4399	//idhdl rInit(char s, sleftv pn, sleftv* rv, sleftv* ord)
4400	ring rInit(sleftv* pn, sleftv* rv, sleftv* ord)
4401	{
4402	int ch;
4403	#ifdef HAVE_RINGS
4404	unsigned int ringtype = 0;
4405	unsigned long long ringflaga = 0;
4406	unsigned int ringflagb = 0;
4407	#endif
4408	int float_len=0;
4409	int float_len2=0;
4410	ring R = NULL;
4411	idhdl tmp = NULL;
4412	BOOLEAN ffChar=FALSE;
4413	int typ = 1;
4414
4415	/* ch -------------------------------------------------------*/
4416	// get ch of ground field
4417	int numberOfAllocatedBlocks;
4418
4419	if (pn->Typ()==INT_CMD)
4420	{
4421	ch=(int)(long)pn->Data();
4422	}
4423	else if ((pn->name != NULL)
4424	&& ((strcmp(pn->name,"real")==0) \|\| (strcmp(pn->name,"complex")==0)))
4425	{
4426	BOOLEAN complex_flag=(strcmp(pn->name,"complex")==0);
4427	ch=-1;
4428	if ((pn->next!=NULL) && (pn->next->Typ()==INT_CMD))
4429	{
4430	float_len=(int)(long)pn->next->Data();
4431	float_len2=float_len;
4432	pn=pn->next;
4433	if ((pn->next!=NULL) && (pn->next->Typ()==INT_CMD))
4434	{
4435	float_len2=(int)(long)pn->next->Data();
4436	pn=pn->next;
4437	}
4438	}
4439	if ((pn->next==NULL) && complex_flag)
4440	{
4441	pn->next=(leftv)omAlloc0Bin(sleftv_bin);
4442	pn->next->name=omStrDup("i");
4443	}
4444	}
4445	#ifdef HAVE_RINGZ
4446	else if ((pn->name != NULL)
4447	&& (strcmp(pn->name,"integers")==0))
4448	{
4449	ch = 0;
4450	ringtype = 4;
4451	}
4452	#endif
4453	#ifdef HAVE_RINGMODN
4454	else if ((pn->name != NULL)
4455	&& (strcmp(pn->name,"modnat")==0))
4456	{
4457	unsigned long long module = 1;
4458	while ((pn->next!=NULL) && (pn->next->Typ()==INT_CMD))
4459	{
4460	module *= (unsigned long long) pn->next->Data();
4461	pn=pn->next;
4462	}
4463	if ((module < 2))
4464	{
4465	Werror("Wrong ground ring specification (modnat)");
4466	goto rInitError;
4467	}
4468	ch = module;
4469	ringtype = 2;
4470	ringflaga = module;
4471	ringflagb = 1;
4472	}
4473	#endif
4474	#ifdef HAVE_RING2TOM
4475	else if ((pn->name != NULL)
4476	&& (strcmp(pn->name,"modpow")==0))
4477	{
4478	unsigned long base = 0;
4479	unsigned int exp = 0;
4480	if ((pn->next!=NULL) && (pn->next->Typ()==INT_CMD))
4481	{
4482	base =(unsigned long) pn->next->Data();
4483	pn=pn->next;
4484	if ((pn->next!=NULL) && (pn->next->Typ()==INT_CMD))
4485	{
4486	exp = (unsigned int) (unsigned long) pn->next->Data();
4487	pn=pn->next;
4488	}
4489	}
4490	if ((base < 2) \|\| (exp < 1))
4491	{
4492	Werror("Wrong ground ring specification");
4493	goto rInitError;
4494	}
4495	ch = exp;
4496	if ((base == 2) && (exp + 2 <= 8*sizeof(NATNUMBER)))
4497	{
4498	ringtype = 1; // Use Z/2^ch
4499	ringflaga = 2;
4500	ringflagb = exp;
4501	WarnS("Z/2^n not yet fully tested");
4502	}
4503	else
4504	{
4505	if ((base == 2) && (exp + 2 > 8*sizeof(NATNUMBER)))
4506	{
4507	Print("// exponent+2 is larger then number of bits in 'NATNUMBER' (%d bits)\n", 8*sizeof(NATNUMBER));
4508	WarnS("==> using generic gmp implementation (restriction from design and NTL)");
4509	}
4510	ringtype = 3;
4511	ringflaga = base;
4512	ringflagb = exp;
4513	}
4514	}
4515	#endif
4516	else
4517	{
4518	Werror("Wrong ground field specification");
4519	goto rInitError;
4520	}
4521	pn=pn->next;
4522
4523	#ifdef HAVE_RINGS
4524	if (ringtype > 0)
4525	{
4526	WarnS("You are using a preview implementation of coefficients rings.");
4527	WarnS("Please note that only the following commands are meant to work:");
4528	WarnS("- basic polynomial arithmetic");
4529	WarnS("- std");
4530	WarnS("- reduce");
4531	}
4532	#endif
4533
4534	int l, last;
4535	sleftv * sl;
4536	/every entry in the new ring is initialized to 0/
4537
4538	/* characteristic -----------------------------------------------*/
4539	/* input: 0 ch=0 : Q parameter=NULL ffChar=FALSE float_len
4540	* 0 1 : Q(a,...) *names FALSE
4541	* 0 -1 : R NULL FALSE 0
4542	* 0 -1 : R NULL FALSE prec. >6
4543	* 0 -1 : C *names FALSE prec. 0..?
4544	* p p : Fp NULL FALSE
4545	* p -p : Fp(a) *names FALSE
4546	* q q : GF(q=p^n) *names TRUE
4547	*/
4548	if ((ch!=-1)
4549	#ifdef HAVE_RINGS
4550	&& (ringtype == 0)
4551	#endif
4552	)
4553	{
4554	int l = 0;
4555
4556	if (((ch!=0) && (ch<2))
4557	#ifndef NV_OPS
4558	\|\| (ch > 32003)
4559	#endif
4560	)
4561	{
4562	Warn("%d is invalid characteristic of ground field. 32003 is used.", ch);
4563	ch=32003;
4564	}
4565	// load fftable, if necessary
4566	if (pn!=NULL)
4567	{
4568	while ((ch!=fftable[l]) && (fftable[l])) l++;
4569	if (fftable[l]==0) ch = IsPrime(ch);
4570	else
4571	{
4572	char m[1]={(char )sNoName};
4573	nfSetChar(ch,m);
4574	if (errorreported) goto rInitError;
4575	else ffChar=TRUE;
4576	}
4577	}
4578	else
4579	{
4580	ch = IsPrime(ch);
4581	}
4582	}
4583	// allocated ring and set ch
4584	R = (ring) omAlloc0Bin(sip_sring_bin);
4585	R->ch = ch;
4586	#ifdef HAVE_RINGS
4587	R->ringtype = ringtype;
4588	R->ringflaga = ringflaga;
4589	R->ringflagb = ringflagb;
4590	#endif
4591	if (ch == -1)
4592	{
4593	R->float_len= si_min(float_len,32767);
4594	R->float_len2= si_min(float_len2,32767);
4595	}
4596
4597	/* parameter -------------------------------------------------------*/
4598	if (pn!=NULL)
4599	{
4600	R->P=pn->listLength();
4601	//if ((ffChar\|\| (ch == 1)) && (R->P > 1))
4602	if ((R->P > 1) && (ffChar \|\| (ch == -1)))
4603	{
4604	WerrorS("too many parameters");
4605	goto rInitError;
4606	}
4607	R->parameter=(char*)omAlloc0(R->Psizeof(char_ptr));
4608	if (rSleftvList2StringArray(pn, R->parameter))
4609	{
4610	WerrorS("parameter expected");
4611	goto rInitError;
4612	}
4613	if (ch>1 && !ffChar) R->ch=-ch;
4614	else if (ch==0) R->ch=1;
4615	}
4616	else if (ffChar)
4617	{
4618	WerrorS("need one parameter");
4619	goto rInitError;
4620	}
4621	/* post-processing of field description */
4622	// we have short reals, but no short complex
4623	if ((R->ch == - 1)
4624	&& (R->parameter !=NULL)
4625	&& (R->float_len < SHORT_REAL_LENGTH))
4626	{
4627	R->float_len = SHORT_REAL_LENGTH;
4628	R->float_len2 = SHORT_REAL_LENGTH;
4629	}
4630
4631	/* names and number of variables-------------------------------------*/
4632	{
4633	int l=rv->listLength();
4634	#if SIZEOF_SHORT == 2
4635	#define MAX_SHORT 0x7fff
4636	#endif
4637	if (l>MAX_SHORT)
4638	{
4639	Werror("too many ring variables(%d), max is %d",l,MAX_SHORT);
4640	goto rInitError;
4641	}
4642	R->N = l; /rv->listLength();/
4643	}
4644	R->names = (char *)omAlloc0(R->N sizeof(char_ptr));
4645	if (rSleftvList2StringArray(rv, R->names))
4646	{
4647	WerrorS("name of ring variable expected");
4648	goto rInitError;
4649	}
4650
4651	/* check names and parameters for conflicts ------------------------- */
4652	{
4653	int i,j;
4654	for(i=0;i<R->P; i++)
4655	{
4656	for(j=0;j<R->N;j++)
4657	{
4658	if (strcmp(R->parameter[i],R->names[j])==0)
4659	{
4660	Werror("parameter %d conflicts with variable %d",i+1,j+1);
4661	goto rInitError;
4662	}
4663	}
4664	}
4665	}
4666	rNameCheck(R);
4667	/* ordering -------------------------------------------------------------*/
4668	if (rSleftvOrdering2Ordering(ord, R))
4669	goto rInitError;
4670
4671	// Complete the initialization
4672	if (rComplete(R,1))
4673	goto rInitError;
4674
4675	rTest(R);
4676
4677	// try to enter the ring into the name list
4678	// need to clean up sleftv here, before this ring can be set to
4679	// new currRing or currRing can be killed beacuse new ring has
4680	// same name
4681	if (pn != NULL) pn->CleanUp();
4682	if (rv != NULL) rv->CleanUp();
4683	if (ord != NULL) ord->CleanUp();
4684	//if ((tmp = enterid(s, myynest, RING_CMD, &IDROOT))==NULL)
4685	// goto rInitError;
4686
4687	//memcpy(IDRING(tmp),R,sizeof(*R));
4688	// set current ring
4689	//omFreeBin(R, ip_sring_bin);
4690	//return tmp;
4691	return R;
4692
4693	// error case:
4694	rInitError:
4695	if (R != NULL) rDelete(R);
4696	if (pn != NULL) pn->CleanUp();
4697	if (rv != NULL) rv->CleanUp();
4698	if (ord != NULL) ord->CleanUp();
4699	return NULL;
4700	}
4701
4702	void rKill(ring r)
4703	{
4704	if ((r->ref<=0)&&(r->order!=NULL))
4705	{
4706	#ifdef RDEBUG
4707	if (traceit &TRACE_SHOW_RINGS) Print("kill ring %x\n",r);
4708	#endif
4709	if (r==currRing)
4710	{
4711	if (r->qideal!=NULL)
4712	{
4713	currQuotient=NULL;
4714	}
4715	if (ppNoether!=NULL) pDelete(&ppNoether);
4716	if (sLastPrinted.RingDependend())
4717	{
4718	sLastPrinted.CleanUp();
4719	}
4720	if ((myynest>0) && (iiRETURNEXPR[myynest].RingDependend()))
4721	{
4722	WerrorS("return value depends on local ring variable (export missing ?)");
4723	iiRETURNEXPR[myynest].CleanUp();
4724	}
4725	currRing=NULL;
4726	currRingHdl=NULL;
4727	}
4728	if (r->qideal!=NULL)
4729	{
4730	id_Delete(&r->qideal, r);
4731	r->qideal = NULL;
4732	}
4733	int i=1;
4734	int j;
4735	int *pi=r->order;
4736	#ifdef USE_IILOCALRING
4737	for (j=0;j<iiRETURNEXPR_len;j++)
4738	{
4739	if (iiLocalRing[j]==r)
4740	{
4741	if (j<myynest) Warn("killing the basering for level %d",j);
4742	iiLocalRing[j]=NULL;
4743	}
4744	}
4745	#else /* USE_IILOCALRING */
4746	//#endif /* USE_IILOCALRING */
4747	{
4748	proclevel * nshdl = procstack;
4749	int lev=myynest-1;
4750
4751	for(; nshdl != NULL; nshdl = nshdl->next)
4752	{
4753	if (nshdl->cRing==r)
4754	{
4755	Warn("killing the basering for level %d",lev);
4756	nshdl->cRing=NULL;
4757	nshdl->cRingHdl=NULL;
4758	}
4759	}
4760	}
4761	#endif /* USE_IILOCALRING */
4762	// any variables depending on r ?
4763	while (r->idroot!=NULL)
4764	{
4765	killhdl2(r->idroot,&(r->idroot),r);
4766	}
4767
4768	/* nKillChar(r); will be called from inside of rDelete */
4769	rDelete(r);
4770	return;
4771	}
4772	r->ref--;
4773	}
4774
4775	void rKill(idhdl h)
4776	{
4777	ring r = IDRING(h);
4778	int ref=0;
4779	if (r!=NULL)
4780	{
4781	ref=r->ref;
4782	rKill(r);
4783	}
4784	if (h==currRingHdl)
4785	{
4786	if (ref<=0) { currRing=NULL; currRingHdl=NULL;}
4787	else
4788	{
4789	currRingHdl=rFindHdl(r,currRingHdl,NULL);
4790	}
4791	}
4792	}
4793
4794	idhdl rSimpleFindHdl(ring r, idhdl root, idhdl n=NULL)
4795	{
4796	//idhdl next_best=NULL;
4797	idhdl h=root;
4798	while (h!=NULL)
4799	{
4800	if (((IDTYP(h)==RING_CMD)\|\|(IDTYP(h)==QRING_CMD))
4801	&& (h!=n)
4802	&& (IDRING(h)==r)
4803	)
4804	{
4805	// if (IDLEV(h)==myynest)
4806	// return h;
4807	// if ((IDLEV(h)==0) \|\| (next_best==NULL))
4808	// next_best=h;
4809	// else if (IDLEV(next_best)<IDLEV(h))
4810	// next_best=h;
4811	return h;
4812	}
4813	h=IDNEXT(h);
4814	}
4815	//return next_best;
4816	return NULL;
4817	}
4818
4819	extern BOOLEAN jjPROC(leftv res, leftv u, leftv v);
4820	ideal kGroebner(ideal F, ideal Q)
4821	{
4822	//test\|=Sy_bit(OPT_PROT);
4823	idhdl save_ringhdl=currRingHdl;
4824	ideal resid;
4825	idhdl new_ring=NULL;
4826	if ((currRingHdl==NULL) \|\| (IDRING(currRingHdl)!=currRing))
4827	{
4828	currRingHdl=enterid(omStrDup(" GROEBNERring"),0,RING_CMD,&IDROOT,FALSE);
4829	new_ring=currRingHdl;
4830	IDRING(currRingHdl)=currRing;
4831	}
4832	sleftv v; memset(&v,0,sizeof(v)); v.rtyp=IDEAL_CMD; v.data=(char *) F;
4833	idhdl h=ggetid("groebner",FALSE);
4834	sleftv u; memset(&u,0,sizeof(u)); u.rtyp=IDHDL; u.data=(char *) h;
4835	u.name=IDID(h);
4836
4837	sleftv res; memset(&res,0,sizeof(res));
4838	if(jjPROC(&res,&u,&v))
4839	{
4840	resid=kStd(F,Q,testHomog,NULL);
4841	}
4842	else
4843	{
4844	//printf("typ:%d\n",res.rtyp);
4845	resid=(ideal)(res.data);
4846	}
4847	// cleanup GROEBNERring, save_ringhdl, u,v,(res )
4848	if (new_ring!=NULL)
4849	{
4850	idhdl h=IDROOT;
4851	if (h==new_ring) IDROOT=h->next;
4852	else
4853	{
4854	while ((h!=NULL) &&(h->next!=new_ring)) h=h->next;
4855	if (h!=NULL) h->next=h->next->next;
4856	}
4857	if (h!=NULL) omFreeSize(h,sizeof(*h));
4858	}
4859	currRingHdl=save_ringhdl;
4860	u.CleanUp();
4861	v.CleanUp();
4862	return resid;
4863	}
4864
4865	void jjINT_S_TO_LIST(int n,int *e, leftv res)
4866	{
4867	lists l=(lists)omAlloc0Bin(slists_bin);
4868	l->Init(n);
4869	int i;
4870	poly p;
4871	for(i=pVariables;i>0;i--)
4872	{
4873	if (e[i]>0)
4874	{
4875	n--;
4876	l->m[n].rtyp=POLY_CMD;
4877	p=pOne();
4878	pSetExp(p,i,1);
4879	pSetm(p);
4880	l->m[n].data=(char *)p;
4881	if (n==0) break;
4882	}
4883	}
4884	res->data=(char*)l;
4885	omFreeSize((ADDRESS)e,(pVariables+1)*sizeof(int));
4886	}
4887	BOOLEAN jjVARIABLES_P(leftv res, leftv u)
4888	{
4889	int e=(int )omAlloc0((pVariables+1)*sizeof(int));
4890	int n=pGetVariables((poly)u->Data(),e);
4891	jjINT_S_TO_LIST(n,e,res);
4892	return FALSE;
4893	}
4894
4895	BOOLEAN jjVARIABLES_ID(leftv res, leftv u)
4896	{
4897	int e=(int )omAlloc0((pVariables+1)*sizeof(int));
4898	ideal I=(ideal)u->Data();
4899	int i;
4900	int n=0;
4901	for(i=I->nrows*I->ncols-1;i>=0;i--)
4902	{
4903	n=pGetVariables(I->m[i],e);
4904	}
4905	jjINT_S_TO_LIST(n,e,res);
4906	return FALSE;
4907	}

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