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source: git/Singular/ipshell.cc @ 341696

spielwiese

Last change on this file since 341696 was 341696, checked in by Hans Schönemann <hannes@…>, 15 years ago
Adding Id property to all files git-svn-id: file:///usr/local/Singular/svn/trunk@12231 2c84dea3-7e68-4137-9b89-c4e89433aadc
Property mode set to `100644`
File size: 125.0 KB

Line
1	/****************************************
2	* Computer Algebra System SINGULAR *
3	****************************************/
4	/* $Id$ */
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	idhdl iiCurrProc=NULL;
62	int traceit = 0;
63	const char *lastreserved=NULL;
64
65	int myynest = -1;
66
67	static BOOLEAN iiNoKeepRing=TRUE;
68
69	/0 implementation/
70
71	const char * iiTwoOps(int t)
72	{
73	if (t<127)
74	{
75	static char ch[2];
76	switch (t)
77	{
78	case '&':
79	return "and";
80	case '\|':
81	return "or";
82	default:
83	ch[0]=t;
84	ch[1]='\0';
85	return ch;
86	}
87	}
88	switch (t)
89	{
90	case COLONCOLON: return "::";
91	case DOTDOT: return "..";
92	//case PLUSEQUAL: return "+=";
93	//case MINUSEQUAL: return "-=";
94	case MINUSMINUS: return "--";
95	case PLUSPLUS: return "++";
96	case EQUAL_EQUAL: return "==";
97	case LE: return "<=";
98	case GE: return ">=";
99	case NOTEQUAL: return "<>";
100	default: return Tok2Cmdname(t);
101	}
102	}
103
104	static void list1(const char* s, idhdl h,BOOLEAN c, BOOLEAN fullname)
105	{
106	char buffer[22];
107	int l;
108	char buf2[128];
109
110	if(fullname) sprintf(buf2, "%s::%s", "", IDID(h));
111	else sprintf(buf2, "%s", IDID(h));
112
113	Print("%s%-20.20s [%d] ",s,buf2,IDLEV(h));
114	if (h == currRingHdl) PrintS("*");
115	PrintS(Tok2Cmdname((int)IDTYP(h)));
116
117	ipListFlag(h);
118	switch(IDTYP(h))
119	{
120	case INT_CMD: Print(" %d",IDINT(h)); break;
121	case INTVEC_CMD:Print(" (%d)",IDINTVEC(h)->length()); break;
122	case INTMAT_CMD:Print(" %d x %d",IDINTVEC(h)->rows(),IDINTVEC(h)->cols());
123	break;
124	case POLY_CMD:
125	case VECTOR_CMD:if (c)
126	{
127	PrintS(" ");wrp(IDPOLY(h));
128	if(IDPOLY(h) != NULL)
129	{
130	Print(", %d monomial(s)",pLength(IDPOLY(h)));
131	}
132	}
133	break;
134	case MODUL_CMD: Print(", rk %d", (int)(IDIDEAL(h)->rank));
135	case IDEAL_CMD: Print(", %u generator(s)",
136	IDELEMS(IDIDEAL(h))); break;
137	case MAP_CMD:
138	Print(" from %s",IDMAP(h)->preimage); break;
139	case MATRIX_CMD:Print(" %u x %u"
140	,MATROWS(IDMATRIX(h))
141	,MATCOLS(IDMATRIX(h))
142	);
143	break;
144	case PACKAGE_CMD:
145	PrintS(" (");
146	switch (IDPACKAGE(h)->language)
147	{
148	case LANG_SINGULAR: PrintS("S"); break;
149	case LANG_C: PrintS("C"); break;
150	case LANG_TOP: PrintS("T"); break;
151	case LANG_NONE: PrintS("N"); break;
152	default: PrintS("U");
153	}
154	if(IDPACKAGE(h)->libname!=NULL)
155	Print(",%s", IDPACKAGE(h)->libname);
156	PrintS(")");
157	break;
158	case PROC_CMD: if(strlen(IDPROC(h)->libname)>0)
159	Print(" from %s",IDPROC(h)->libname);
160	if(IDPROC(h)->is_static)
161	PrintS(" (static)");
162	break;
163	case STRING_CMD:
164	{
165	char *s;
166	l=strlen(IDSTRING(h));
167	memset(buffer,0,22);
168	strncpy(buffer,IDSTRING(h),si_min(l,20));
169	if ((s=strchr(buffer,'\n'))!=NULL)
170	{
171	*s='\0';
172	}
173	PrintS(" ");
174	PrintS(buffer);
175	if((s!=NULL) \|\|(l>20))
176	{
177	Print("..., %d char(s)",l);
178	}
179	break;
180	}
181	case LIST_CMD: Print(", size: %d",IDLIST(h)->nr+1);
182	break;
183	case QRING_CMD:
184	case RING_CMD:
185	if ((IDRING(h)==currRing) && (currRingHdl!=h))
186	PrintS("()"); / this is an alias to currRing */
187	#ifdef RDEBUG
188	if (traceit &TRACE_SHOW_RINGS)
189	Print(" <%lx>",(long)(IDRING(h)));
190	#endif
191	break;
192	/default: break;/
193	}
194	PrintLn();
195	}
196
197	void type_cmd(idhdl h)
198	{
199	BOOLEAN oldShortOut = FALSE;
200
201	if (currRing != NULL)
202	{
203	oldShortOut = currRing->ShortOut;
204	currRing->ShortOut = 1;
205	}
206	list1("// ",h,FALSE,FALSE);
207	if (IDTYP(h)!=INT_CMD)
208	{
209	sleftv expr;
210	memset(&expr,0,sizeof(expr));
211	expr.rtyp=IDHDL;
212	expr.name=IDID(h);
213	expr.data=(void *)h;
214	expr.Print();
215	}
216	if (currRing != NULL)
217	currRing->ShortOut = oldShortOut;
218	}
219
220	static void killlocals0(int v, idhdl * localhdl, const ring r)
221	{
222	idhdl h = *localhdl;
223	while (h!=NULL)
224	{
225	int vv;
226	//Print("consider %s, lev: %d:",IDID(h),IDLEV(h));
227	if ((vv=IDLEV(h))>0)
228	{
229	if (vv < v)
230	{
231	if (iiNoKeepRing)
232	{
233	//PrintS(" break\n");
234	return;
235	}
236	h = IDNEXT(h);
237	//PrintLn();
238	}
239	else //if (vv >= v)
240	{
241	idhdl nexth = IDNEXT(h);
242	killhdl2(h,localhdl,r);
243	h = nexth;
244	//PrintS("kill\n");
245	}
246	}
247	else
248	{
249	h = IDNEXT(h);
250	//PrintLn();
251	}
252	}
253	}
254	void killlocals_list(lists l,int v)
255	{
256	int i;
257	for(i=l->nr; i>=0; i--)
258	{
259	if (l->m[i].rtyp == LIST_CMD)
260	killlocals_list((lists)l->m[i].data,v);
261	else if ((l->m[i].rtyp == RING_CMD) \|\| (l->m[i].rtyp == QRING_CMD))
262	killlocals0(v,&(((ring)(l->m[i].data))->idroot),currRing);
263	}
264	}
265	void killlocals_rec(idhdl *root,int v, ring r)
266	{
267	idhdl h=*root;
268	while (h!=NULL)
269	{
270	if (IDLEV(h)>=v)
271	{
272	// Print("kill %s, lev %d for lev %d\n",IDID(h),IDLEV(h),v);
273	idhdl n=IDNEXT(h);
274	killhdl2(h,root,r);
275	h=n;
276	}
277	else if (IDTYP(h)==PACKAGE_CMD)
278	{
279	// Print("into pack %s, lev %d for lev %d\n",IDID(h),IDLEV(h),v);
280	if (IDPACKAGE(h)!=basePack)
281	killlocals_rec(&(IDRING(h)->idroot),v,r);
282	h=IDNEXT(h);
283	}
284	else if ((IDTYP(h)==RING_CMD)
285	\|\|(IDTYP(h)==QRING_CMD))
286	{
287	if ((IDRING(h)!=NULL) && (IDRING(h)->idroot!=NULL))
288	// we have to test IDRING(h)!=NULL: qring Q=groebner(...): killlocals
289	{
290	// Print("into ring %s, lev %d for lev %d\n",IDID(h),IDLEV(h),v);
291	killlocals_rec(&(IDRING(h)->idroot),v,IDRING(h));
292	}
293	h=IDNEXT(h);
294	}
295	else
296	{
297	// Print("skip %s lev %d for lev %d\n",IDID(h),IDLEV(h),v);
298	h=IDNEXT(h);
299	}
300	}
301	}
302	BOOLEAN killlocals_list(int v, lists L)
303	{
304	if (L==NULL) return FALSE;
305	BOOLEAN changed=FALSE;
306	int n=L->nr;
307	for(;n>=0;n--)
308	{
309	leftv h=&(L->m[n]);
310	void *d=h->data;
311	if (((h->rtyp==RING_CMD) \|\| (h->rtyp==QRING_CMD))
312	&& (((ring)d)->idroot!=NULL))
313	{
314	if (d!=currRing) {changed=TRUE;rChangeCurrRing((ring)d);}
315	killlocals0(v,&(((ring)h->data)->idroot),(ring)h->data);
316	}
317	else if (h->rtyp==LIST_CMD)
318	changed\|=killlocals_list(v,(lists)d);
319	}
320	return changed;
321	}
322	void killlocals(int v)
323	{
324	BOOLEAN changed=FALSE;
325	idhdl sh=currRingHdl;
326	ring cr=currRing;
327	if (sh!=NULL) changed=((IDLEV(sh)<v) \|\| (IDRING(sh)->ref>0));
328	//if (changed) Print("currRing=%s(%x), lev=%d,ref=%d\n",IDID(sh),IDRING(sh),IDLEV(sh),IDRING(sh)->ref);
329
330	killlocals_rec(&(basePack->idroot),v,currRing);
331
332	if (iiRETURNEXPR_len > myynest)
333	{
334	int t=iiRETURNEXPR[myynest].Typ();
335	if ((/iiRETURNEXPR[myynest].Typ()/ t==RING_CMD)
336	\|\| (/iiRETURNEXPR[myynest].Typ()/ t==QRING_CMD))
337	{
338	leftv h=&iiRETURNEXPR[myynest];
339	if (((ring)h->data)->idroot!=NULL)
340	killlocals0(v,&(((ring)h->data)->idroot),(ring)h->data);
341	}
342	else if (/iiRETURNEXPR[myynest].Typ()/ t==LIST_CMD)
343	{
344	leftv h=&iiRETURNEXPR[myynest];
345	changed \|=killlocals_list(v,(lists)h->data);
346	}
347	}
348	if (changed)
349	{
350	currRingHdl=rFindHdl(cr,NULL,NULL);
351	if (currRingHdl==NULL)
352	currRing=NULL;
353	else
354	rChangeCurrRing(cr);
355	}
356
357	if (myynest<=1) iiNoKeepRing=TRUE;
358	//Print("end killlocals >= %d\n",v);
359	//listall();
360	}
361
362	void list_cmd(int typ, const char* what, const char *prefix,BOOLEAN iterate, BOOLEAN fullname)
363	{
364	idhdl h,start;
365	BOOLEAN all = typ<0;
366	BOOLEAN really_all=FALSE;
367	BOOLEAN do_packages=FALSE;
368
369	if ( typ == -1 ) do_packages=TRUE;
370	if ( typ==0 )
371	{
372	if (strcmp(what,"all")==0)
373	{
374	really_all=TRUE;
375	h=basePack->idroot;
376	}
377	else
378	{
379	h = ggetid(what);
380	if (h!=NULL)
381	{
382	if (iterate) list1(prefix,h,TRUE,fullname);
383	if ((IDTYP(h)==RING_CMD)
384	\|\| (IDTYP(h)==QRING_CMD)
385	//\|\| (IDTYP(h)==PACKE_CMD)
386	)
387	{
388	h=IDRING(h)->idroot;
389	}
390	else if((IDTYP(h)==PACKAGE_CMD) \|\| (IDTYP(h)==POINTER_CMD))
391	{
392	//Print("list_cmd:package or pointer\n");
393	all=TRUE;typ=PROC_CMD;fullname=TRUE;really_all=TRUE;
394	h=IDPACKAGE(h)->idroot;
395	}
396	else
397	return;
398	}
399	else
400	{
401	Werror("%s is undefined",what);
402	return;
403	}
404	}
405	all=TRUE;
406	}
407	else if (RingDependend(typ))
408	{
409	h = currRing->idroot;
410	}
411	else
412	h = IDROOT;
413	start=h;
414	while (h!=NULL)
415	{
416	if ((all && (IDTYP(h)!=PROC_CMD) &&(IDTYP(h)!=PACKAGE_CMD))
417	\|\| (typ == IDTYP(h))
418	\|\| ((IDTYP(h)==QRING_CMD) && (typ==RING_CMD)))
419	{
420	list1(prefix,h,start==currRingHdl, fullname);
421	if (((IDTYP(h)==RING_CMD)\|\|(IDTYP(h)==QRING_CMD))
422	&& (really_all \|\| (all && (h==currRingHdl)))
423	&& ((IDLEV(h)==0)\|\|(IDLEV(h)==myynest)))
424	{
425	list_cmd(0,IDID(h),"// ",FALSE);
426	}
427	if (IDTYP(h)==PACKAGE_CMD && really_all)
428	{
429	package save_p=currPack;
430	currPack=IDPACKAGE(h);
431	list_cmd(0,IDID(h),"// ",FALSE);
432	currPack=save_p;
433	}
434	}
435	h = IDNEXT(h);
436	}
437	}
438
439	void test_cmd(int i)
440	{
441	int ii;
442
443	if (i<0)
444	{
445	ii= -i;
446	if (ii < 32)
447	{
448	test &= ~Sy_bit(ii);
449	}
450	else if (ii < 64)
451	{
452	verbose &= ~Sy_bit(ii-32);
453	}
454	else
455	WerrorS("out of bounds\n");
456	}
457	else if (i<32)
458	{
459	ii=i;
460	if (Sy_bit(ii) & kOptions)
461	{
462	Warn("Gerhard, use the option command");
463	test \|= Sy_bit(ii);
464	}
465	else if (Sy_bit(ii) & validOpts)
466	test \|= Sy_bit(ii);
467	}
468	else if (i<64)
469	{
470	ii=i-32;
471	verbose \|= Sy_bit(ii);
472	}
473	else
474	WerrorS("out of bounds\n");
475	}
476
477	int exprlist_length(leftv v)
478	{
479	int rc = 0;
480	while (v!=NULL)
481	{
482	switch (v->Typ())
483	{
484	case INT_CMD:
485	case POLY_CMD:
486	case VECTOR_CMD:
487	case NUMBER_CMD:
488	rc++;
489	break;
490	case INTVEC_CMD:
491	case INTMAT_CMD:
492	rc += ((intvec *)(v->Data()))->length();
493	break;
494	case MATRIX_CMD:
495	case IDEAL_CMD:
496	case MODUL_CMD:
497	{
498	matrix mm = (matrix)(v->Data());
499	rc += mm->rows() * mm->cols();
500	}
501	break;
502	case LIST_CMD:
503	rc+=((lists)v->Data())->nr+1;
504	break;
505	default:
506	rc++;
507	}
508	v = v->next;
509	}
510	return rc;
511	}
512
513	int iiIsPrime0(unsigned p) /* brute force !!!! */
514	{
515	unsigned i,j=0 /only to avoid compiler warnings/;
516	#ifdef HAVE_FACTORY
517	if (p<=32749) // max. small prime in factory
518	{
519	int a=0;
520	int e=cf_getNumSmallPrimes()-1;
521	i=e/2;
522	do
523	{
524	j=cf_getSmallPrime(i);
525	if (p==j) return p;
526	if (p<j) e=i-1;
527	else a=i+1;
528	i=a+(e-a)/2;
529	} while ( a<= e);
530	if (p>j) return j;
531	else return cf_getSmallPrime(i-1);
532	}
533	#endif
534	#ifdef HAVE_FACTORY
535	unsigned end_i=cf_getNumSmallPrimes()-1;
536	#else
537	unsigned end_i=p/2;
538	#endif
539	unsigned end_p=(unsigned)sqrt((double)p);
540	restart:
541	for (i=0; i<end_i; i++)
542	{
543	#ifdef HAVE_FACTORY
544	j=cf_getSmallPrime(i);
545	#else
546	if (i==0) j=2;
547	else j=2*i-1;
548	#endif
549	if ((p%j) == 0)
550	{
551	#ifdef HAVE_FACTORY
552	if (p<=32751) return iiIsPrime0(p-2);
553	#endif
554	p-=2;
555	goto restart;
556	}
557	if (j > end_p) return p;
558	}
559	#ifdef HAVE_FACTORY
560	if (i>=end_i)
561	{
562	while(j<=end_p)
563	{
564	j+=2;
565	if ((p%j) == 0)
566	{
567	if (p<=32751) return iiIsPrime0(p-2);
568	p-=2;
569	goto restart;
570	}
571	}
572	}
573	#endif
574	return p;
575	}
576	int IsPrime(int p) /* brute force !!!! */
577	{
578	int i,j;
579	if (p == 0) return 0;
580	else if (p == 1) return 1/1/;
581	else if ((p == 2)\|\|(p==3)) return p;
582	else if (p < 0) return 2; //(iiIsPrime0((unsigned)(-p)));
583	else if ((p & 1)==0) return iiIsPrime0((unsigned)(p-1));
584	return iiIsPrime0((unsigned)(p));
585	}
586
587	BOOLEAN iiWRITE(leftv res,leftv v)
588	{
589	sleftv vf;
590	if (iiConvert(v->Typ(),LINK_CMD,iiTestConvert(v->Typ(),LINK_CMD),v,&vf))
591	{
592	WerrorS("link expected");
593	return TRUE;
594	}
595	si_link l=(si_link)vf.Data();
596	if (vf.next == NULL)
597	{
598	WerrorS("write: need at least two arguments");
599	return TRUE;
600	}
601
602	BOOLEAN b=slWrite(l,vf.next); /* iiConvert preserves next */
603	if (b)
604	{
605	const char *s;
606	if ((l!=NULL)&&(l->name!=NULL)) s=l->name;
607	else s=sNoName;
608	Werror("cannot write to %s",s);
609	}
610	vf.CleanUp();
611	return b;
612	}
613
614	leftv iiMap(map theMap, const char * what)
615	{
616	idhdl w,r;
617	leftv v;
618	int i;
619	nMapFunc nMap;
620
621	r=IDROOT->get(theMap->preimage,myynest);
622	if ((currPack!=basePack)
623	&&((r==NULL) \|\| ((r->typ != RING_CMD) && (r->typ != QRING_CMD))))
624	r=basePack->idroot->get(theMap->preimage,myynest);
625	if ((r==NULL) && (currRingHdl!=NULL)
626	&& (strcmp(theMap->preimage,IDID(currRingHdl))==0))
627	{
628	r=currRingHdl;
629	}
630	if ((r!=NULL) && ((r->typ == RING_CMD) \|\| (r->typ== QRING_CMD)))
631	{
632	//if ((nMap=nSetMap(rInternalChar(IDRING(r)),
633	// IDRING(r)->parameter,
634	// rPar(IDRING(r)),
635	// IDRING(r)->minpoly)))
636	if ((nMap=nSetMap(IDRING(r)))==NULL)
637	{
638	if (rEqual(IDRING(r),currRing))
639	{
640	nMap=nCopy;
641	}
642	else
643	{
644	Werror("can not map from ground field of %s to current ground field",
645	theMap->preimage);
646	return NULL;
647	}
648	}
649	if (IDELEMS(theMap)<IDRING(r)->N)
650	{
651	theMap->m=(polyset)omReallocSize((ADDRESS)theMap->m,
652	IDELEMS(theMap)*sizeof(poly),
653	(IDRING(r)->N)*sizeof(poly));
654	for(i=IDELEMS(theMap);i<IDRING(r)->N;i++)
655	theMap->m[i]=NULL;
656	IDELEMS(theMap)=IDRING(r)->N;
657	}
658	if (what==NULL)
659	{
660	WerrorS("argument of a map must have a name");
661	}
662	else if ((w=IDRING(r)->idroot->get(what,myynest))!=NULL)
663	{
664	char *save_r=NULL;
665	v=(leftv)omAlloc0Bin(sleftv_bin);
666	sleftv tmpW;
667	memset(&tmpW,0,sizeof(sleftv));
668	tmpW.rtyp=IDTYP(w);
669	if (tmpW.rtyp==MAP_CMD)
670	{
671	tmpW.rtyp=IDEAL_CMD;
672	save_r=IDMAP(w)->preimage;
673	IDMAP(w)->preimage=0;
674	}
675	tmpW.data=IDDATA(w);
676	#if 0
677	if (((tmpW.rtyp==IDEAL_CMD)\|\|(tmpW.rtyp==MODUL_CMD)) && idIs0(IDIDEAL(w)))
678	{
679	v->rtyp=tmpW.rtyp;
680	v->data=idInit(IDELEMS(IDIDEAL(w)),IDIDEAL(w)->rank);
681	}
682	else
683	#endif
684	{
685	#ifdef FAST_MAP
686	if ((tmpW.rtyp==IDEAL_CMD) && (nMap==nCopy)
687	#ifdef HAVE_PLURAL
688	&& (!rIsPluralRing(currRing))
689	#endif
690	)
691	{
692	v->rtyp=IDEAL_CMD;
693	v->data=fast_map(IDIDEAL(w), IDRING(r), (ideal)theMap, currRing);
694	}
695	else
696	#endif
697	if (maApplyFetch(MAP_CMD,theMap,v,&tmpW,IDRING(r),NULL,NULL,0,nMap))
698	{
699	Werror("cannot map %s(%d)",Tok2Cmdname(w->typ),w->typ);
700	omFreeBin((ADDRESS)v, sleftv_bin);
701	if (save_r!=NULL) IDMAP(w)->preimage=save_r;
702	return NULL;
703	}
704	}
705	if (save_r!=NULL)
706	{
707	IDMAP(w)->preimage=save_r;
708	IDMAP((idhdl)v)->preimage=omStrDup(save_r);
709	v->rtyp=MAP_CMD;
710	}
711	return v;
712	}
713	else
714	{
715	Werror("%s undefined in %s",what,theMap->preimage);
716	}
717	}
718	else
719	{
720	Werror("cannot find preimage %s",theMap->preimage);
721	}
722	return NULL;
723	}
724
725	#ifdef OLD_RES
726	void iiMakeResolv(resolvente r, int length, int rlen, char * name, int typ0,
727	intvec ** weights)
728	{
729	lists L=liMakeResolv(r,length,rlen,typ0,weights);
730	int i=0;
731	idhdl h;
732	char * s=(char *)omAlloc(strlen(name)+5);
733
734	while (i<=L->nr)
735	{
736	sprintf(s,"%s(%d)",name,i+1);
737	if (i==0)
738	h=enterid(s,myynest,typ0,&(currRing->idroot), FALSE);
739	else
740	h=enterid(s,myynest,MODUL_CMD,&(currRing->idroot), FALSE);
741	if (h!=NULL)
742	{
743	h->data.uideal=(ideal)L->m[i].data;
744	h->attribute=L->m[i].attribute;
745	if (BVERBOSE(V_DEF_RES))
746	Print("//defining: %s as %d-th syzygy module\n",s,i+1);
747	}
748	else
749	{
750	idDelete((ideal *)&(L->m[i].data));
751	Warn("cannot define %s",s);
752	}
753	//L->m[i].data=NULL;
754	//L->m[i].rtyp=0;
755	//L->m[i].attribute=NULL;
756	i++;
757	}
758	omFreeSize((ADDRESS)L->m,(L->nr+1)*sizeof(sleftv));
759	omFreeBin((ADDRESS)L, slists_bin);
760	omFreeSize((ADDRESS)s,strlen(name)+5);
761	}
762	#endif
763
764	//resolvente iiFindRes(char * name, int * len, int *typ0)
765	//{
766	// char s=(char )omAlloc(strlen(name)+5);
767	// int i=-1;
768	// resolvente r;
769	// idhdl h;
770	//
771	// do
772	// {
773	// i++;
774	// sprintf(s,"%s(%d)",name,i+1);
775	// h=currRing->idroot->get(s,myynest);
776	// } while (h!=NULL);
777	// *len=i-1;
778	// if (*len<=0)
779	// {
780	// Werror("no objects %s(1),.. found",name);
781	// omFreeSize((ADDRESS)s,strlen(name)+5);
782	// return NULL;
783	// }
784	// r=(ideal )omAlloc(/(len+1)/ isizeof(ideal));
785	// memset(r,0,(len)sizeof(ideal));
786	// i=-1;
787	// *typ0=MODUL_CMD;
788	// while (i<(*len))
789	// {
790	// i++;
791	// sprintf(s,"%s(%d)",name,i+1);
792	// h=currRing->idroot->get(s,myynest);
793	// if (h->typ != MODUL_CMD)
794	// {
795	// if ((i!=0) \|\| (h->typ!=IDEAL_CMD))
796	// {
797	// Werror("%s is not of type module",s);
798	// omFreeSize((ADDRESS)r,(len)sizeof(ideal));
799	// omFreeSize((ADDRESS)s,strlen(name)+5);
800	// return NULL;
801	// }
802	// *typ0=IDEAL_CMD;
803	// }
804	// if ((i>0) && (idIs0(r[i-1])))
805	// {
806	// *len=i-1;
807	// break;
808	// }
809	// r[i]=IDIDEAL(h);
810	// }
811	// omFreeSize((ADDRESS)s,strlen(name)+5);
812	// return r;
813	//}
814
815	static resolvente iiCopyRes(resolvente r, int l)
816	{
817	int i;
818	resolvente res=(ideal )omAlloc0((l+1)sizeof(ideal));
819
820	for (i=0; i<l; i++)
821	res[i]=idCopy(r[i]);
822	return res;
823	}
824
825	BOOLEAN jjMINRES(leftv res, leftv v)
826	{
827	int len=0;
828	int typ0;
829	lists L=(lists)v->Data();
830	intvec weights=(intvec)atGet(v,"isHomog",INTVEC_CMD);
831	int add_row_shift = 0;
832	if (weights==NULL)
833	weights=(intvec*)atGet(&(L->m[0]),"isHomog",INTVEC_CMD);
834	if (weights!=NULL) add_row_shift=weights->min_in();
835	resolvente rr=liFindRes(L,&len,&typ0);
836	if (rr==NULL) return TRUE;
837	resolvente r=iiCopyRes(rr,len);
838
839	syMinimizeResolvente(r,len,0);
840	omFreeSize((ADDRESS)rr,len*sizeof(ideal));
841	len++;
842	res->data=(char *)liMakeResolv(r,len,-1,typ0,NULL,add_row_shift);
843	return FALSE;
844	}
845
846	BOOLEAN jjBETTI(leftv res, leftv u)
847	{
848	sleftv tmp;
849	memset(&tmp,0,sizeof(tmp));
850	tmp.rtyp=INT_CMD;
851	tmp.data=(void *)1;
852	if ((u->Typ()==IDEAL_CMD)
853	\|\| (u->Typ()==MODUL_CMD))
854	return jjBETTI2_ID(res,u,&tmp);
855	else
856	return jjBETTI2(res,u,&tmp);
857	}
858
859	BOOLEAN jjBETTI2_ID(leftv res, leftv u, leftv v)
860	{
861	lists l=(lists) omAllocBin(slists_bin);
862	l->Init(1);
863	l->m[0].rtyp=u->Typ();
864	l->m[0].data=u->Data();
865	l->m[0].attribute=u->attribute;
866	sleftv tmp2;
867	memset(&tmp2,0,sizeof(tmp2));
868	tmp2.rtyp=LIST_CMD;
869	tmp2.data=(void *)l;
870	BOOLEAN r=jjBETTI2(res,&tmp2,v);
871	l->m[0].data=NULL;
872	l->m[0].attribute=NULL;
873	l->m[0].rtyp=DEF_CMD;
874	l->Clean();
875	return r;
876	}
877
878	BOOLEAN jjBETTI2(leftv res, leftv u, leftv v)
879	{
880	resolvente r;
881	int len;
882	int reg,typ0;
883	lists l=(lists)u->Data();
884
885	intvec *weights=NULL;
886	int add_row_shift=0;
887	intvec ww=(intvec )atGet(&(l->m[0]),"isHomog",INTVEC_CMD);
888	if (ww!=NULL)
889	{
890	weights=ivCopy(ww);
891	add_row_shift = ww->min_in();
892	(*weights) -= add_row_shift;
893	}
894	//Print("attr:%x\n",weights);
895
896	r=liFindRes(l,&len,&typ0);
897	if (r==NULL) return TRUE;
898	res->data=(char *)syBetti(r,len,&reg,weights,(int)(long)v->Data());
899	omFreeSize((ADDRESS)r,(len)*sizeof(ideal));
900	atSet(res,omStrDup("rowShift"),(void*)add_row_shift,INT_CMD);
901	if (weights!=NULL) delete weights;
902	return FALSE;
903	}
904
905	int iiRegularity(lists L)
906	{
907	int len,reg,typ0;
908
909	resolvente r=liFindRes(L,&len,&typ0);
910
911	if (r==NULL)
912	return -2;
913	intvec *weights=NULL;
914	int add_row_shift=0;
915	intvec ww=(intvec )atGet(&(L->m[0]),"isHomog",INTVEC_CMD);
916	if (ww!=NULL)
917	{
918	weights=ivCopy(ww);
919	add_row_shift = ww->min_in();
920	(*weights) -= add_row_shift;
921	}
922	//Print("attr:%x\n",weights);
923
924	intvec *dummy=syBetti(r,len,&reg,weights);
925	if (weights!=NULL) delete weights;
926	delete dummy;
927	omFreeSize((ADDRESS)r,len*sizeof(ideal));
928	return reg+1+add_row_shift;
929	}
930
931	BOOLEAN iiDebugMarker=TRUE;
932	#define BREAK_LINE_LENGTH 80
933	void iiDebug()
934	{
935	Print("\n-- break point in %s --\n",VoiceName());
936	if (iiDebugMarker) VoiceBackTrack();
937	char * s;
938	iiDebugMarker=FALSE;
939	s = (char *)omAlloc(BREAK_LINE_LENGTH+4);
940	loop
941	{
942	memset(s,0,80);
943	fe_fgets_stdin("",s,BREAK_LINE_LENGTH);
944	if (s[BREAK_LINE_LENGTH-1]!='\0')
945	{
946	Print("line too long, max is %d chars\n",BREAK_LINE_LENGTH);
947	}
948	else
949	break;
950	}
951	if (*s=='\n')
952	{
953	iiDebugMarker=TRUE;
954	}
955	#if MDEBUG
956	else if(strncmp(s,"cont;",5)==0)
957	{
958	iiDebugMarker=TRUE;
959	}
960	#endif /* MDEBUG */
961	else
962	{
963	strcat( s, "\n;~\n");
964	newBuffer(s,BT_execute);
965	}
966	}
967
968	lists scIndIndset(ideal S, BOOLEAN all, ideal Q)
969	{
970	int i;
971	indset save;
972	lists res=(lists)omAlloc0Bin(slists_bin);
973
974	hexist = hInit(S, Q, &hNexist);
975	if ((hNexist == 0) \|\| (hisModule!=0))
976	{
977	res->Init(0);
978	return res;
979	}
980	save = ISet = (indset)omAlloc0Bin(indlist_bin);
981	hMu = 0;
982	hwork = (scfmon)omAlloc(hNexist * sizeof(scmon));
983	hvar = (varset)omAlloc((pVariables + 1) * sizeof(int));
984	hpure = (scmon)omAlloc((1 + (pVariables * pVariables)) * sizeof(Exponent_t));
985	hrad = hexist;
986	hNrad = hNexist;
987	radmem = hCreate(pVariables - 1);
988	hCo = pVariables + 1;
989	hNvar = pVariables;
990	hRadical(hrad, &hNrad, hNvar);
991	hSupp(hrad, hNrad, hvar, &hNvar);
992	if (hNvar)
993	{
994	hCo = hNvar;
995	memset(hpure, 0, (pVariables + 1) * sizeof(Exponent_t));
996	hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure);
997	hLexR(hrad, hNrad, hvar, hNvar);
998	hDimSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar);
999	}
1000	if (hCo && (hCo < pVariables))
1001	{
1002	hIndMult(hpure, hNpure, hrad, hNrad, hvar, hNvar);
1003	}
1004	if (hMu!=0)
1005	{
1006	ISet = save;
1007	hMu2 = 0;
1008	if (all && (hCo+1 < pVariables))
1009	{
1010	JSet = (indset)omAlloc0Bin(indlist_bin);
1011	hIndAllMult(hpure, hNpure, hrad, hNrad, hvar, hNvar);
1012	i=hMu+hMu2;
1013	res->Init(i);
1014	if (hMu2 == 0)
1015	{
1016	omFreeBin((ADDRESS)JSet, indlist_bin);
1017	}
1018	}
1019	else
1020	{
1021	res->Init(hMu);
1022	}
1023	for (i=0;i<hMu;i++)
1024	{
1025	res->m[i].data = (void *)save->set;
1026	res->m[i].rtyp = INTVEC_CMD;
1027	ISet = save;
1028	save = save->nx;
1029	omFreeBin((ADDRESS)ISet, indlist_bin);
1030	}
1031	omFreeBin((ADDRESS)save, indlist_bin);
1032	if (hMu2 != 0)
1033	{
1034	save = JSet;
1035	for (i=hMu;i<hMu+hMu2;i++)
1036	{
1037	res->m[i].data = (void *)save->set;
1038	res->m[i].rtyp = INTVEC_CMD;
1039	JSet = save;
1040	save = save->nx;
1041	omFreeBin((ADDRESS)JSet, indlist_bin);
1042	}
1043	omFreeBin((ADDRESS)save, indlist_bin);
1044	}
1045	}
1046	else
1047	{
1048	res->Init(0);
1049	omFreeBin((ADDRESS)ISet, indlist_bin);
1050	}
1051	hKill(radmem, pVariables - 1);
1052	omFreeSize((ADDRESS)hpure, (1 + (pVariables * pVariables)) * sizeof(Exponent_t));
1053	omFreeSize((ADDRESS)hvar, (pVariables + 1) * sizeof(int));
1054	omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon));
1055	hDelete(hexist, hNexist);
1056	return res;
1057	}
1058
1059	int iiDeclCommand(leftv sy, leftv name, int lev,int t, idhdl* root,BOOLEAN isring, BOOLEAN init_b)
1060	{
1061	BOOLEAN res=FALSE;
1062	const char *id = name->name;
1063
1064	memset(sy,0,sizeof(sleftv));
1065	if ((name->name==NULL)\|\|(isdigit(name->name[0])))
1066	{
1067	WerrorS("object to declare is not a name");
1068	res=TRUE;
1069	}
1070	else
1071	{
1072	//if (name->rtyp!=0)
1073	//{
1074	// Warn("`%s` is already in use",name->name);
1075	//}
1076	{
1077	sy->data = (char *)enterid(id,lev,t,root,init_b);
1078	}
1079	if (sy->data!=NULL)
1080	{
1081	sy->rtyp=IDHDL;
1082	currid=sy->name=IDID((idhdl)sy->data);
1083	// name->name=NULL; /* used in enterid */
1084	//sy->e = NULL;
1085	if (name->next!=NULL)
1086	{
1087	sy->next=(leftv)omAllocBin(sleftv_bin);
1088	res=iiDeclCommand(sy->next,name->next,lev,t,root, isring);
1089	}
1090	}
1091	else res=TRUE;
1092	}
1093	name->CleanUp();
1094	return res;
1095	}
1096
1097	BOOLEAN iiDefaultParameter(leftv p)
1098	{
1099	attr at=NULL;
1100	if (iiCurrProc!=NULL)
1101	at=iiCurrProc->attribute->get("default_arg");
1102	if (at==NULL)
1103	return FALSE;
1104	sleftv tmp;
1105	memset(&tmp,0,sizeof(sleftv));
1106	tmp.rtyp=at->atyp;
1107	tmp.data=at->CopyA();
1108	return iiAssign(p,&tmp);
1109	}
1110	BOOLEAN iiParameter(leftv p)
1111	{
1112	if (iiCurrArgs==NULL)
1113	{
1114	if (strcmp(p->name,"#")==0)
1115	return iiDefaultParameter(p);
1116	Werror("not enough arguments for proc %s",VoiceName());
1117	p->CleanUp();
1118	return TRUE;
1119	}
1120	leftv h=iiCurrArgs;
1121	if (strcmp(p->name,"#")==0)
1122	{
1123	iiCurrArgs=NULL;
1124	}
1125	else
1126	{
1127	iiCurrArgs=h->next;
1128	h->next=NULL;
1129	}
1130	BOOLEAN res=iiAssign(p,h);
1131	h->CleanUp();
1132	omFreeBin((ADDRESS)h, sleftv_bin);
1133	return res;
1134	}
1135
1136	static BOOLEAN iiInternalExport (leftv v, int toLev)
1137	{
1138	idhdl h=(idhdl)v->data;
1139	//Print("iiInternalExport('%s',%d)%s\n", v->name, toLev,"");
1140	if (IDLEV(h)==0) Warn("`%s` is already global",IDID(h));
1141	else
1142	{
1143	h=IDROOT->get(v->name,toLev);
1144	idhdl *root=&IDROOT;
1145	if ((h==NULL)&&(currRing!=NULL))
1146	{
1147	h=currRing->idroot->get(v->name,toLev);
1148	root=&currRing->idroot;
1149	}
1150	BOOLEAN keepring=FALSE;
1151	if ((h!=NULL)&&(IDLEV(h)==toLev))
1152	{
1153	if (IDTYP(h)==v->Typ())
1154	{
1155	if (((IDTYP(h)==RING_CMD)\|\|(IDTYP(h)==QRING_CMD))
1156	&& (v->Data()==IDDATA(h)))
1157	{
1158	IDRING(h)->ref++;
1159	keepring=TRUE;
1160	IDLEV(h)=toLev;
1161	//WarnS("keepring");
1162	return FALSE;
1163	}
1164	if (BVERBOSE(V_REDEFINE))
1165	{
1166	Warn("redefining %s",IDID(h));
1167	}
1168	#ifdef USE_IILOCALRING
1169	if (iiLocalRing[0]==IDRING(h) && (!keepring)) iiLocalRing[0]=NULL;
1170	#else
1171	proclevel *p=procstack;
1172	while (p->next!=NULL) p=p->next;
1173	if ((p->cRing==IDRING(h)) && (!keepring))
1174	{
1175	p->cRing=NULL;
1176	p->cRingHdl=NULL;
1177	}
1178	#endif
1179	killhdl2(h,root,currRing);
1180	}
1181	else
1182	{
1183	return TRUE;
1184	}
1185	}
1186	h=(idhdl)v->data;
1187	IDLEV(h)=toLev;
1188	if (keepring) IDRING(h)->ref--;
1189	iiNoKeepRing=FALSE;
1190	//Print("export %s\n",IDID(h));
1191	}
1192	return FALSE;
1193	}
1194
1195	BOOLEAN iiInternalExport (leftv v, int toLev, idhdl roothdl)
1196	{
1197	idhdl h=(idhdl)v->data;
1198	if(h==NULL)
1199	{
1200	Warn("'%s': no such identifier\n", v->name);
1201	return FALSE;
1202	}
1203	package frompack=v->req_packhdl;
1204	if (frompack==NULL) frompack=currPack;
1205	package rootpack = IDPACKAGE(roothdl);
1206	// Print("iiInternalExport('%s',%d,%s->%s) typ:%d\n", v->name, toLev, IDID(currPackHdl),IDID(roothdl),v->Typ());
1207	if ((RingDependend(IDTYP(h)))
1208	\|\| ((IDTYP(h)==LIST_CMD)
1209	&& (lRingDependend(IDLIST(h)))
1210	)
1211	)
1212	{
1213	//Print("// ==> Ringdependent set nesting to 0\n");
1214	return (iiInternalExport(v, toLev));
1215	}
1216	else
1217	{
1218	IDLEV(h)=toLev;
1219	v->req_packhdl=rootpack;
1220	if (h==frompack->idroot)
1221	{
1222	frompack->idroot=h->next;
1223	}
1224	else
1225	{
1226	idhdl hh=frompack->idroot;
1227	while ((hh!=NULL) && (hh->next!=h))
1228	hh=hh->next;
1229	if ((hh!=NULL) && (hh->next==h))
1230	hh->next=h->next;
1231	else
1232	{
1233	Werror("`%s` not found",v->Name());
1234	return TRUE;
1235	}
1236	}
1237	h->next=rootpack->idroot;
1238	rootpack->idroot=h;
1239	}
1240	return FALSE;
1241	}
1242
1243	BOOLEAN iiExport (leftv v, int toLev)
1244	{
1245	#ifndef NDEBUG
1246	checkall();
1247	#endif
1248	BOOLEAN nok=FALSE;
1249	leftv r=v;
1250	while (v!=NULL)
1251	{
1252	if ((v->name==NULL)\|\|(v->rtyp==0)\|\|(v->e!=NULL))
1253	{
1254	WerrorS("cannot export");
1255	nok=TRUE;
1256	}
1257	else
1258	{
1259	if(iiInternalExport(v, toLev))
1260	{
1261	r->CleanUp();
1262	return TRUE;
1263	}
1264	}
1265	v=v->next;
1266	}
1267	r->CleanUp();
1268	#ifndef NDEBUG
1269	checkall();
1270	#endif
1271	return nok;
1272	}
1273
1274	/assume root!=idroot/
1275	BOOLEAN iiExport (leftv v, int toLev, idhdl root)
1276	{
1277	#ifndef NDEBUG
1278	checkall();
1279	#endif
1280	// Print("iiExport1: pack=%s\n",IDID(root));
1281	package pack=IDPACKAGE(root);
1282	BOOLEAN nok=FALSE;
1283	leftv rv=v;
1284	while (v!=NULL)
1285	{
1286	if ((v->name==NULL)\|\|(v->rtyp==0)\|\|(v->e!=NULL)
1287	)
1288	{
1289	WerrorS("cannot export");
1290	nok=TRUE;
1291	}
1292	else
1293	{
1294	idhdl old=pack->idroot->get( v->name,toLev);
1295	if (old!=NULL)
1296	{
1297	if ((pack==currPack) && (old==(idhdl)v->data))
1298	{
1299	Warn("`%s` is already global",IDID(old));
1300	break;
1301	}
1302	else if (IDTYP(old)==v->Typ())
1303	{
1304	if (BVERBOSE(V_REDEFINE))
1305	{
1306	Warn("redefining %s",IDID(old));
1307	}
1308	v->name=omStrDup(v->name);
1309	killhdl2(old,&(pack->idroot),currRing);
1310	}
1311	else
1312	{
1313	rv->CleanUp();
1314	return TRUE;
1315	}
1316	}
1317	//Print("iiExport: pack=%s\n",IDID(root));
1318	if(iiInternalExport(v, toLev, root))
1319	{
1320	rv->CleanUp();
1321	return TRUE;
1322	}
1323	}
1324	v=v->next;
1325	}
1326	rv->CleanUp();
1327	#ifndef NDEBUG
1328	checkall();
1329	#endif
1330	return nok;
1331	}
1332
1333	BOOLEAN iiCheckRing(int i)
1334	{
1335	if (currRingHdl==NULL)
1336	{
1337	#ifdef SIQ
1338	if (siq<=0)
1339	{
1340	#endif
1341	if (RingDependend(i))
1342	{
1343	WerrorS("no ring active");
1344	return TRUE;
1345	}
1346	#ifdef SIQ
1347	}
1348	#endif
1349	}
1350	return FALSE;
1351	}
1352
1353	poly iiHighCorner(ideal I, int ak)
1354	{
1355	int i;
1356	if(!idIsZeroDim(I)) return NULL; // not zero-dim.
1357	poly po=NULL;
1358	if (rHasLocalOrMixedOrdering_currRing())
1359	{
1360	scComputeHC(I,currQuotient,ak,po);
1361	if (po!=NULL)
1362	{
1363	pGetCoeff(po)=nInit(1);
1364	for (i=pVariables; i>0; i--)
1365	{
1366	if (pGetExp(po, i) > 0) pDecrExp(po,i);
1367	}
1368	pSetComp(po,ak);
1369	pSetm(po);
1370	}
1371	}
1372	else
1373	po=pOne();
1374	return po;
1375	}
1376
1377	void iiCheckPack(package &p)
1378	{
1379	if (p==basePack) return;
1380
1381	idhdl t=basePack->idroot;
1382
1383	while ((t!=NULL) && (IDTYP(t)!=PACKAGE_CMD) && (IDPACKAGE(t)!=p)) t=t->next;
1384
1385	if (t==NULL)
1386	{
1387	WarnS("package not found\n");
1388	p=basePack;
1389	}
1390	return;
1391	}
1392
1393	idhdl rDefault(const char *s)
1394	{
1395	idhdl tmp=NULL;
1396
1397	if (s!=NULL) tmp = enterid(s, myynest, RING_CMD, &IDROOT);
1398	if (tmp==NULL) return NULL;
1399
1400	if (ppNoether!=NULL) pDelete(&ppNoether);
1401	if (sLastPrinted.RingDependend())
1402	{
1403	sLastPrinted.CleanUp();
1404	memset(&sLastPrinted,0,sizeof(sleftv));
1405	}
1406
1407	ring r = IDRING(tmp);
1408
1409	r->ch = 32003;
1410	r->N = 3;
1411	/r->P = 0; Alloc0 in idhdl::set, ipid.cc/
1412	/names/
1413	r->names = (char *) omAlloc0(3 sizeof(char_ptr));
1414	r->names[0] = omStrDup("x");
1415	r->names[1] = omStrDup("y");
1416	r->names[2] = omStrDup("z");
1417	/weights: entries for 3 blocks: NULL/
1418	r->wvhdl = (int *)omAlloc0(3 sizeof(int_ptr));
1419	/order: dp,C,0/
1420	r->order = (int ) omAlloc(3 sizeof(int *));
1421	r->block0 = (int )omAlloc0(3 sizeof(int *));
1422	r->block1 = (int )omAlloc0(3 sizeof(int *));
1423	/* ringorder dp for the first block: var 1..3 */
1424	r->order[0] = ringorder_dp;
1425	r->block0[0] = 1;
1426	r->block1[0] = 3;
1427	/* ringorder C for the second block: no vars */
1428	r->order[1] = ringorder_C;
1429	/* the last block: everything is 0 */
1430	r->order[2] = 0;
1431	/polynomial ring/
1432	r->OrdSgn = 1;
1433
1434	/* complete ring intializations */
1435	rComplete(r);
1436	rSetHdl(tmp);
1437	return currRingHdl;
1438	}
1439
1440	idhdl rFindHdl(ring r, idhdl n, idhdl w)
1441	{
1442	idhdl h=rSimpleFindHdl(r,IDROOT,n);
1443	if (h!=NULL) return h;
1444	if (IDROOT!=basePack->idroot) h=rSimpleFindHdl(r,basePack->idroot,n);
1445	if (h!=NULL) return h;
1446	proclevel *p=procstack;
1447	while(p!=NULL)
1448	{
1449	if ((p->cPack!=basePack)
1450	&& (p->cPack!=currPack))
1451	h=rSimpleFindHdl(r,p->cPack->idroot,n);
1452	if (h!=NULL) return h;
1453	p=p->next;
1454	}
1455	idhdl tmp=basePack->idroot;
1456	while (tmp!=NULL)
1457	{
1458	if (IDTYP(tmp)==PACKAGE_CMD)
1459	h=rSimpleFindHdl(r,IDPACKAGE(tmp)->idroot,n);
1460	if (h!=NULL) return h;
1461	tmp=IDNEXT(tmp);
1462	}
1463	return NULL;
1464	}
1465
1466	void rDecomposeCF(leftv h,const ring r,const ring R)
1467	{
1468	lists L=(lists)omAlloc0Bin(slists_bin);
1469	L->Init(4);
1470	h->rtyp=LIST_CMD;
1471	h->data=(void *)L;
1472	// 0: char/ cf - ring
1473	// 1: list (var)
1474	// 2: list (ord)
1475	// 3: qideal
1476	// ----------------------------------------
1477	// 0: char/ cf - ring
1478	L->m[0].rtyp=INT_CMD;
1479	L->m[0].data=(void *)r->ch;
1480	// ----------------------------------------
1481	// 1: list (var)
1482	lists LL=(lists)omAlloc0Bin(slists_bin);
1483	LL->Init(r->N);
1484	int i;
1485	for(i=0; i<r->N; i++)
1486	{
1487	LL->m[i].rtyp=STRING_CMD;
1488	LL->m[i].data=(void *)omStrDup(r->names[i]);
1489	}
1490	L->m[1].rtyp=LIST_CMD;
1491	L->m[1].data=(void *)LL;
1492	// ----------------------------------------
1493	// 2: list (ord)
1494	LL=(lists)omAlloc0Bin(slists_bin);
1495	i=rBlocks(r)-1;
1496	LL->Init(i);
1497	i--;
1498	lists LLL;
1499	for(; i>=0; i--)
1500	{
1501	intvec *iv;
1502	int j;
1503	LL->m[i].rtyp=LIST_CMD;
1504	LLL=(lists)omAlloc0Bin(slists_bin);
1505	LLL->Init(2);
1506	LLL->m[0].rtyp=STRING_CMD;
1507	LLL->m[0].data=(void *)omStrDup(rSimpleOrdStr(r->order[i]));
1508	if (r->block1[i]-r->block0[i] >=0 )
1509	{
1510	j=r->block1[i]-r->block0[i];
1511	if(r->order[i]==ringorder_M) j=(j+1)*(j+1)-1;
1512	iv=new intvec(j+1);
1513	if ((r->wvhdl!=NULL) && (r->wvhdl[i]!=NULL))
1514	{
1515	for(;j>=0; j--) (*iv)[j]=r->wvhdl[i][j];
1516	}
1517	else switch (r->order[i])
1518	{
1519	case ringorder_dp:
1520	case ringorder_Dp:
1521	case ringorder_ds:
1522	case ringorder_Ds:
1523	case ringorder_lp:
1524	for(;j>=0; j--) (*iv)[j]=1;
1525	break;
1526	default: /* do nothing */;
1527	}
1528	}
1529	else
1530	{
1531	iv=new intvec(1);
1532	}
1533	LLL->m[1].rtyp=INTVEC_CMD;
1534	LLL->m[1].data=(void *)iv;
1535	LL->m[i].data=(void *)LLL;
1536	}
1537	L->m[2].rtyp=LIST_CMD;
1538	L->m[2].data=(void *)LL;
1539	// ----------------------------------------
1540	// 3: qideal
1541	L->m[3].rtyp=IDEAL_CMD;
1542	if (R->minpoly==NULL)
1543	L->m[3].data=(void *)idInit(1,1);
1544	else
1545	{
1546	ideal I=idInit(1,1);
1547	L->m[3].data=(void *)I;
1548	I->m[0]=pOne();
1549	pSetCoeff(I->m[0],R->minpoly);
1550	}
1551	// ----------------------------------------
1552	}
1553	void rDecomposeC(leftv h,const ring R)
1554	/* field is R or C */
1555	{
1556	lists L=(lists)omAlloc0Bin(slists_bin);
1557	if (rField_is_long_C(R)) L->Init(3);
1558	else L->Init(2);
1559	h->rtyp=LIST_CMD;
1560	h->data=(void *)L;
1561	// 0: char/ cf - ring
1562	// 1: list (var)
1563	// 2: list (ord)
1564	// ----------------------------------------
1565	// 0: char/ cf - ring
1566	L->m[0].rtyp=INT_CMD;
1567	L->m[0].data=(void *)0;
1568	// ----------------------------------------
1569	// 1:
1570	lists LL=(lists)omAlloc0Bin(slists_bin);
1571	LL->Init(2);
1572	LL->m[0].rtyp=INT_CMD;
1573	LL->m[0].data=(void *)si_max(R->float_len,SHORT_REAL_LENGTH/2);
1574	LL->m[1].rtyp=INT_CMD;
1575	LL->m[1].data=(void *)si_max(R->float_len2,SHORT_REAL_LENGTH);
1576	L->m[1].rtyp=LIST_CMD;
1577	L->m[1].data=(void *)LL;
1578	// ----------------------------------------
1579	// 2: list (par)
1580	if (rField_is_long_C(R))
1581	{
1582	L->m[2].rtyp=STRING_CMD;
1583	L->m[2].data=(void *)omStrDup(R->parameter[0]);
1584	}
1585	// ----------------------------------------
1586	}
1587
1588	#ifdef HAVE_RINGS
1589	void rDecomposeRing(leftv h,const ring R)
1590	/* field is R or C */
1591	{
1592	lists L=(lists)omAlloc0Bin(slists_bin);
1593	if (rField_is_Ring_Z(R)) L->Init(1);
1594	else L->Init(2);
1595	h->rtyp=LIST_CMD;
1596	h->data=(void *)L;
1597	// 0: char/ cf - ring
1598	// 1: list (module)
1599	// ----------------------------------------
1600	// 0: char/ cf - ring
1601	L->m[0].rtyp=STRING_CMD;
1602	L->m[0].data=(void *)omStrDup("integer");
1603	// ----------------------------------------
1604	// 1: module
1605	if (rField_is_Ring_Z(R)) return;
1606	lists LL=(lists)omAlloc0Bin(slists_bin);
1607	LL->Init(2);
1608	LL->m[0].rtyp=BIGINT_CMD;
1609	LL->m[0].data=nlMapGMP((number) R->ringflaga);
1610	LL->m[1].rtyp=INT_CMD;
1611	LL->m[1].data=(void *) R->ringflagb;
1612	L->m[1].rtyp=LIST_CMD;
1613	L->m[1].data=(void *)LL;
1614	}
1615	#endif
1616
1617
1618	lists rDecompose(const ring r)
1619	{
1620	// sanity check: require currRing==r for rings with polynomial data
1621	if ((r!=currRing)
1622	&& ((r->minpoly!=NULL) \|\| (r->qideal!=NULL) \|\| (r->minideal!=NULL)
1623	#ifdef HAVE_PLURAL
1624	\|\| (rIsPluralRing(r))
1625	#endif
1626	))
1627	{
1628	WerrorS("ring with polynomial data must be the base ring or compatible");
1629	return NULL;
1630	}
1631	// 0: char/ cf - ring
1632	// 1: list (var)
1633	// 2: list (ord)
1634	// 3: qideal
1635	// possibly:
1636	// 4: C
1637	// 5: D
1638	lists L=(lists)omAlloc0Bin(slists_bin);
1639	if (rIsPluralRing(r))
1640	L->Init(6);
1641	else
1642	L->Init(4);
1643	// ----------------------------------------
1644	// 0: char/ cf - ring
1645	#if 1 /* TODO */
1646	if (rField_is_numeric(r))
1647	{
1648	rDecomposeC(&(L->m[0]),r);
1649	}
1650	#ifdef HAVE_RINGS
1651	else if (rField_is_Ring(r))
1652	{
1653	rDecomposeRing(&(L->m[0]),r);
1654	}
1655	#endif
1656	else if (rIsExtension(r))
1657	{
1658	if (r->algring!=NULL)
1659	rDecomposeCF(&(L->m[0]),r->algring,r);
1660	else
1661	{
1662	lists Lc=(lists)omAlloc0Bin(slists_bin);
1663	Lc->Init(4);
1664	// char:
1665	Lc->m[0].rtyp=INT_CMD;
1666	Lc->m[0].data=(void*)r->ch;
1667	// var:
1668	lists Lv=(lists)omAlloc0Bin(slists_bin);
1669	Lv->Init(1);
1670	Lv->m[0].rtyp=STRING_CMD;
1671	Lv->m[0].data=(void *)omStrDup(r->parameter[0]);
1672	Lc->m[1].rtyp=LIST_CMD;
1673	Lc->m[1].data=(void*)Lv;
1674	// ord:
1675	lists Lo=(lists)omAlloc0Bin(slists_bin);
1676	Lo->Init(1);
1677	lists Loo=(lists)omAlloc0Bin(slists_bin);
1678	Loo->Init(2);
1679	Loo->m[0].rtyp=STRING_CMD;
1680	Loo->m[0].data=(void *)omStrDup(rSimpleOrdStr(ringorder_lp));
1681	intvec iv=new intvec(1); (iv)[0]=1;
1682	Loo->m[1].rtyp=INTVEC_CMD;
1683	Loo->m[1].data=(void *)iv;
1684	Lo->m[0].rtyp=LIST_CMD;
1685	Lo->m[0].data=(void*)Loo;
1686
1687	Lc->m[2].rtyp=LIST_CMD;
1688	Lc->m[2].data=(void*)Lo;
1689	// q-ideal:
1690	Lc->m[3].rtyp=IDEAL_CMD;
1691	Lc->m[3].data=(void *)idInit(1,1);
1692	// ----------------------
1693	L->m[0].rtyp=LIST_CMD;
1694	L->m[0].data=(void*)Lc;
1695	}
1696	if (L->m[0].rtyp==0)
1697	{
1698	//omFreeBin(slists_bin,(void *)L);
1699	return NULL;
1700	}
1701	}
1702	else
1703	#endif
1704	{
1705	L->m[0].rtyp=INT_CMD;
1706	L->m[0].data=(void *)r->ch;
1707	}
1708	// ----------------------------------------
1709	// 1: list (var)
1710	lists LL=(lists)omAlloc0Bin(slists_bin);
1711	LL->Init(r->N);
1712	int i;
1713	for(i=0; i<r->N; i++)
1714	{
1715	LL->m[i].rtyp=STRING_CMD;
1716	LL->m[i].data=(void *)omStrDup(r->names[i]);
1717	}
1718	L->m[1].rtyp=LIST_CMD;
1719	L->m[1].data=(void *)LL;
1720	// ----------------------------------------
1721	// 2: list (ord)
1722	LL=(lists)omAlloc0Bin(slists_bin);
1723	i=rBlocks(r)-1;
1724	LL->Init(i);
1725	i--;
1726	lists LLL;
1727	for(; i>=0; i--)
1728	{
1729	intvec *iv;
1730	int j;
1731	LL->m[i].rtyp=LIST_CMD;
1732	LLL=(lists)omAlloc0Bin(slists_bin);
1733	LLL->Init(2);
1734	LLL->m[0].rtyp=STRING_CMD;
1735	LLL->m[0].data=(void *)omStrDup(rSimpleOrdStr(r->order[i]));
1736	if (r->block1[i]-r->block0[i] >=0 )
1737	{
1738	j=r->block1[i]-r->block0[i];
1739	if (r->order[i]==ringorder_M) j=(j+1)*(j+1)-1;
1740	iv=new intvec(j+1);
1741	if ((r->wvhdl!=NULL) && (r->wvhdl[i]!=NULL))
1742	{
1743	for(;j>=0; j--) (*iv)[j]=r->wvhdl[i][j];
1744	}
1745	else switch (r->order[i])
1746	{
1747	case ringorder_dp:
1748	case ringorder_Dp:
1749	case ringorder_ds:
1750	case ringorder_Ds:
1751	case ringorder_lp:
1752	for(;j>=0; j--) (*iv)[j]=1;
1753	break;
1754	default: /* do nothing */;
1755	}
1756	}
1757	else
1758	{
1759	iv=new intvec(1);
1760	}
1761	LLL->m[1].rtyp=INTVEC_CMD;
1762	LLL->m[1].data=(void *)iv;
1763	LL->m[i].data=(void *)LLL;
1764	}
1765	L->m[2].rtyp=LIST_CMD;
1766	L->m[2].data=(void *)LL;
1767	// ----------------------------------------
1768	// 3: qideal
1769	L->m[3].rtyp=IDEAL_CMD;
1770	if (r->qideal==NULL)
1771	L->m[3].data=(void *)idInit(1,1);
1772	else
1773	L->m[3].data=(void *)idCopy(r->qideal);
1774	// ----------------------------------------
1775	#ifdef HAVE_PLURAL // NC! in rDecompose
1776	if (rIsPluralRing(r))
1777	{
1778	L->m[4].rtyp=MATRIX_CMD;
1779	L->m[4].data=(void *)mpCopy(r->GetNC()->C);
1780	L->m[5].rtyp=MATRIX_CMD;
1781	L->m[5].data=(void *)mpCopy(r->GetNC()->D);
1782	}
1783	#endif
1784	return L;
1785	}
1786
1787	void rComposeC(lists L, ring R)
1788	/* field is R or C */
1789	{
1790	// ----------------------------------------
1791	// 0: char/ cf - ring
1792	if ((L->m[0].rtyp!=INT_CMD) \|\| (L->m[0].data!=(char *)0))
1793	{
1794	Werror("invald coeff. field description, expecting 0");
1795	return;
1796	}
1797	R->ch=-1;
1798	// ----------------------------------------
1799	// 1:
1800	if (L->m[1].rtyp!=LIST_CMD)
1801	Werror("invald coeff. field description, expecting precision list");
1802	lists LL=(lists)L->m[1].data;
1803	int r1=(int)(long)LL->m[0].data;
1804	int r2=(int)(long)LL->m[1].data;
1805	if ((r1<=SHORT_REAL_LENGTH)
1806	&& (r2=SHORT_REAL_LENGTH))
1807	{
1808	R->float_len=SHORT_REAL_LENGTH/2;
1809	R->float_len2=SHORT_REAL_LENGTH;
1810	}
1811	else
1812	{
1813	R->float_len=si_min(r1,32767);
1814	R->float_len2=si_min(r2,32767);
1815	}
1816	// ----------------------------------------
1817	// 2: list (par)
1818	if (L->nr==2)
1819	{
1820	R->P=1;
1821	if (L->m[2].rtyp!=STRING_CMD)
1822	{
1823	Werror("invald coeff. field description, expecting parameter name");
1824	return;
1825	}
1826	R->parameter=(char*)omAlloc0(R->Psizeof(char_ptr));
1827	R->parameter[0]=omStrDup((char *)L->m[2].data);
1828	}
1829	// ----------------------------------------
1830	}
1831
1832	#ifdef HAVE_RINGS
1833	void rComposeRing(lists L, ring R)
1834	/* field is R or C */
1835	{
1836	// ----------------------------------------
1837	// 0: string: integer
1838	// no further entries --> Z
1839	R->ringflaga = (int_number) omAlloc(sizeof(MP_INT));
1840	if (L->nr == 0)
1841	{
1842	mpz_init_set_ui(R->ringflaga,0);
1843	R->ringflagb = 1;
1844	}
1845	// ----------------------------------------
1846	// 1:
1847	else
1848	{
1849	if (L->m[1].rtyp!=LIST_CMD) Werror("invald data, expecting list of numbers");
1850	lists LL=(lists)L->m[1].data;
1851	mpz_init(R->ringflaga);
1852	if ((LL->nr >= 0) && LL->m[0].rtyp == BIGINT_CMD)
1853	{
1854	number ringflaga = (number) LL->m[0].data;
1855	nlGMP(ringflaga, (number) R->ringflaga);
1856	LL->m[0].data = (void *)ringflaga;
1857	}
1858	else if ((LL->nr >= 0) && LL->m[0].rtyp == INT_CMD)
1859	{
1860	mpz_set_ui(R->ringflaga,(unsigned long) LL->m[0].data);
1861	}
1862	else
1863	{
1864	mpz_set_ui(R->ringflaga,0);
1865	}
1866	if (LL->nr >= 1)
1867	{
1868	R->ringflagb = (unsigned long) LL->m[1].data;
1869	}
1870	else
1871	{
1872	R->ringflagb = 1;
1873	}
1874	}
1875	// ----------------------------------------
1876	if ((mpz_cmp_ui(R->ringflaga, 1) == 0) && (mpz_cmp_ui(R->ringflaga, 0) < 0))
1877	{
1878	Werror("Wrong ground ring specification (module is 1)");
1879	return;
1880	}
1881	if (R->ringflagb < 1)
1882	{
1883	Werror("Wrong ground ring specification (exponent smaller than 1");
1884	return;
1885	}
1886	// module is 0 ---> integers
1887	if (mpz_cmp_ui(R->ringflaga, 0) == 0)
1888	{
1889	R->ch = 0;
1890	R->ringtype = 4;
1891	}
1892	// we have an exponent
1893	else if (R->ringflagb > 1)
1894	{
1895	R->ch = R->ringflagb;
1896	if ((mpz_cmp_ui(R->ringflaga, 2) == 0) && (R->ringflagb + 2 <= 8*sizeof(NATNUMBER)))
1897	{
1898	R->ringtype = 1; // Use Z/2^ch
1899	}
1900	else
1901	{
1902	R->ringtype = 3;
1903	}
1904	}
1905	// just a module m > 1
1906	else
1907	{
1908	R->ringtype = 2;
1909	R->ch = mpz_get_ui(R->ringflaga);
1910	}
1911	}
1912	#endif
1913
1914	ring rCompose(const lists L)
1915	{
1916	if ((L->nr!=3)
1917	#ifdef HAVE_PLURAL
1918	&&(L->nr!=5)
1919	#endif
1920	)
1921	return NULL;
1922	int is_gf_char=0;
1923	// 0: char/ cf - ring
1924	// 1: list (var)
1925	// 2: list (ord)
1926	// 3: qideal
1927	// possibly:
1928	// 4: C
1929	// 5: D
1930	ring R=(ring) omAlloc0Bin(sip_sring_bin);
1931	// ------------------------- VARS ---------------------------
1932	if (L->m[1].Typ()==LIST_CMD)
1933	{
1934	lists v=(lists)L->m[1].Data();
1935	R->N = v->nr+1;
1936	R->names = (char *)omAlloc0(R->N sizeof(char_ptr));
1937	int i;
1938	for(i=0;i<R->N;i++)
1939	{
1940	if (v->m[i].Typ()==STRING_CMD)
1941	R->names[i]=omStrDup((char *)v->m[i].Data());
1942	else if (v->m[i].Typ()==POLY_CMD)
1943	{
1944	poly p=(poly)v->m[i].Data();
1945	int nr=pIsPurePower(p);
1946	if (nr>0)
1947	R->names[i]=omStrDup(currRing->names[nr-1]);
1948	else
1949	{
1950	Werror("var name %d must be a string or a ring variable",i+1);
1951	goto rCompose_err;
1952	}
1953	}
1954	else
1955	{
1956	Werror("var name %d must be `string`",i+1);
1957	goto rCompose_err;
1958	}
1959	}
1960	}
1961	else
1962	{
1963	WerrorS("variable must be given as `list`");
1964	goto rCompose_err;
1965	}
1966	// ------------------------ ORDER ------------------------------
1967	if (L->m[2].Typ()==LIST_CMD)
1968	{
1969	lists v=(lists)L->m[2].Data();
1970	int n= v->nr+2;
1971	int j;
1972	// initialize fields of R
1973	R->order=(int )omAlloc0(nsizeof(int));
1974	R->block0=(int )omAlloc0(nsizeof(int));
1975	R->block1=(int )omAlloc0(nsizeof(int));
1976	R->wvhdl=(int*)omAlloc0(nsizeof(int_ptr));
1977	// init order, so that rBlocks works correctly
1978	for (j=0; j < n-1; j++)
1979	R->order[j] = (int) ringorder_unspec;
1980	// orderings
1981	R->OrdSgn=1;
1982	for(j=0;j<n-1;j++)
1983	{
1984	// todo: a(..), M
1985	if (v->m[j].Typ()!=LIST_CMD)
1986	{
1987	WerrorS("ordering must be list of lists");
1988	goto rCompose_err;
1989	}
1990	lists vv=(lists)v->m[j].Data();
1991	if ((vv->nr!=1)
1992	\|\| (vv->m[0].Typ()!=STRING_CMD)
1993	\|\| ((vv->m[1].Typ()!=INTVEC_CMD) && (vv->m[1].Typ()!=INT_CMD)))
1994	{
1995	WerrorS("ordering name must be a (string,intvec)");
1996	goto rCompose_err;
1997	}
1998	R->order[j]=rOrderName(omStrDup((char*)vv->m[0].Data())); // assume STRING
1999	if (j==0) R->block0[0]=1;
2000	else
2001	{
2002	int jj=j-1;
2003	while((jj>=0)
2004	&& ((R->order[jj]== ringorder_a)
2005	\|\| (R->order[jj]== ringorder_aa)
2006	\|\| (R->order[jj]== ringorder_c)
2007	\|\| (R->order[jj]== ringorder_C)
2008	))
2009	{
2010	//Print("jj=%, skip %s\n",rSimpleOrdStr(R->order[jj]));
2011	jj--;
2012	}
2013	if (jj<0) R->block0[j]=1;
2014	else R->block0[j]=R->block1[jj]+1;
2015	}
2016	intvec *iv;
2017	if (vv->m[1].Typ()==INT_CMD)
2018	iv=new intvec((int)(long)vv->m[1].Data(),(int)(long)vv->m[1].Data());
2019	else
2020	iv=ivCopy((intvec*)vv->m[1].Data()); //assume INTVEC
2021	R->block1[j]=si_max(R->block0[j],R->block0[j]+iv->length()-1);
2022	//Print("block %d from %d to %d\n",j,R->block0[j], R->block1[j]);
2023	int i;
2024	switch (R->order[j])
2025	{
2026	case ringorder_ws:
2027	case ringorder_Ws:
2028	R->OrdSgn=-1;
2029	case ringorder_aa:
2030	case ringorder_a:
2031	case ringorder_wp:
2032	case ringorder_Wp:
2033	R->wvhdl[j] =( int )omAlloc((iv->length())sizeof(int));
2034	for (i=0; i<iv->length();i++)
2035	{
2036	R->wvhdl[j][i]=(*iv)[i];
2037	}
2038	break;
2039	case ringorder_M:
2040	R->wvhdl[j] =( int )omAlloc((iv->length())sizeof(int));
2041	for (i=0; i<iv->length();i++) R->wvhdl[j][i]=(*iv)[i];
2042	R->block1[j]=si_max(R->block0[j],R->block0[j]+(int)sqrt((double)(iv->length()-1)));
2043	break;
2044	case ringorder_ls:
2045	case ringorder_ds:
2046	case ringorder_Ds:
2047	case ringorder_rs:
2048	R->OrdSgn=-1;
2049	case ringorder_lp:
2050	case ringorder_dp:
2051	case ringorder_Dp:
2052	case ringorder_rp:
2053	break;
2054	case ringorder_S:
2055	break;
2056	case ringorder_c:
2057	case ringorder_C:
2058	R->block1[j]=R->block0[j]=0;
2059	break;
2060	case 0:
2061	case ringorder_unspec:
2062	break;
2063	}
2064	delete iv;
2065	}
2066	// sanity check
2067	j=n-2;
2068	if ((R->order[j]==ringorder_c)
2069	\|\| (R->order[j]==ringorder_C)
2070	\|\| (R->order[j]==ringorder_unspec)) j--;
2071	if (R->block1[j] != R->N)
2072	{
2073	if (((R->order[j]==ringorder_dp) \|\|
2074	(R->order[j]==ringorder_ds) \|\|
2075	(R->order[j]==ringorder_Dp) \|\|
2076	(R->order[j]==ringorder_Ds) \|\|
2077	(R->order[j]==ringorder_rp) \|\|
2078	(R->order[j]==ringorder_rs) \|\|
2079	(R->order[j]==ringorder_lp) \|\|
2080	(R->order[j]==ringorder_ls))
2081	&&
2082	R->block0[j] <= R->N)
2083	{
2084	R->block1[j] = R->N;
2085	}
2086	else
2087	{
2088	Werror("ordering incomplete: size (%d) should be %d",R->block1[j],R->N);
2089	goto rCompose_err;
2090	}
2091	}
2092	}
2093	else
2094	{
2095	WerrorS("ordering must be given as `list`");
2096	goto rCompose_err;
2097	}
2098	// ------------------------------------------------------------------
2099	// 0: char:
2100	if (L->m[0].Typ()==INT_CMD)
2101	{
2102	R->ch=(int)(long)L->m[0].Data();
2103	if (R->ch!=-1)
2104	{
2105	int l=0;
2106	if (((R->ch!=0) && (R->ch<2) && (is_gf_char=-1))
2107	#ifndef NV_OPS
2108	\|\| (R->ch > 32003)
2109	#endif
2110	\|\| ((l=IsPrime(R->ch))!=R->ch)
2111	)
2112	{
2113	Warn("%d is invalid characteristic of ground field. %d is used.", R->ch,l);
2114	R->ch=l;
2115	}
2116	}
2117	}
2118	else if (L->m[0].Typ()==LIST_CMD)
2119	{
2120	lists LL=(lists)L->m[0].Data();
2121	#ifdef HAVE_RINGS
2122	if (LL->m[0].Typ() == STRING_CMD)
2123	{
2124	rComposeRing(LL,R); /* Ring */
2125	}
2126	else
2127	#endif
2128	if (LL->nr<3)
2129	rComposeC(LL,R); /* R, long_R, long_C */
2130	else
2131	{
2132	if (LL->m[0].Typ()==INT_CMD)
2133	{
2134	int ch=(int)(long)LL->m[0].Data();
2135	while ((ch!=fftable[is_gf_char]) && (fftable[is_gf_char])) is_gf_char++;
2136	if (fftable[is_gf_char]==0) is_gf_char=-1;
2137	}
2138	if (is_gf_char==-1)
2139	{
2140	R->algring=rCompose((lists)L->m[0].Data());
2141	if (R->algring==NULL)
2142	{
2143	WerrorS("could not create rational function coefficient field");
2144	goto rCompose_err;
2145	}
2146	if (R->algring->ch>0)
2147	R->ch= -R->algring->ch;
2148	else
2149	R->ch=1;
2150	R->P=R->algring->N;
2151	R->parameter=(char*)omAlloc0(R->Psizeof(char_ptr));
2152	int i;
2153	for(i=R->P-1;i>=0;i--)
2154	R->parameter[i]=omStrDup(R->algring->names[i]);
2155	if (R->algring->qideal!=NULL)
2156	{
2157	if (IDELEMS(R->algring->qideal)==1)
2158	{
2159	R->minpoly=naInit(1,R);
2160	lnumber n=(lnumber)R->minpoly;
2161	n->z=R->algring->qideal->m[0];
2162	R->algring->qideal->m[0]=NULL;
2163	idDelete(&(R->algring->qideal));
2164	}
2165	else
2166	{
2167	WerrorS("not implemented yet.");
2168	}
2169	}
2170	}
2171	else
2172	{ // gf-char
2173	R->ch=fftable[is_gf_char];
2174	R->P=1;
2175	R->parameter=(char*)omAlloc0(1sizeof(char_ptr));
2176	R->parameter[0]=omStrDup((char*)((lists)(LL->m[1].Data()))->m[0].Data());
2177	}
2178	}
2179	}
2180	else
2181	{
2182	WerrorS("coefficient field must be described by `int` or `list`");
2183	goto rCompose_err;
2184	}
2185	rNameCheck(R);
2186	// ------------------------ Q-IDEAL ------------------------
2187	rComplete(R);
2188
2189	if (L->m[3].Typ()==IDEAL_CMD)
2190	{
2191	ideal q=(ideal)L->m[3].Data();
2192	if (q->m[0]!=NULL)
2193	{
2194	if (R->ch!=currRing->ch)
2195	{
2196	#if 0
2197	WerrorS("coefficient fields must be equal if q-ideal !=0");
2198	goto rCompose_err;
2199	#else
2200	ring orig_ring=currRing;
2201	rChangeCurrRing(R);
2202	int *perm=NULL;
2203	int *par_perm=NULL;
2204	int par_perm_size=0;
2205	nMapFunc nMap;
2206	BOOLEAN bo;
2207
2208	if ((nMap=nSetMap(orig_ring))==NULL)
2209	{
2210	if (rEqual(orig_ring,currRing))
2211	{
2212	nMap=nCopy;
2213	}
2214	else
2215	// Allow imap/fetch to be make an exception only for:
2216	if ( (rField_is_Q_a(orig_ring) && // Q(a..) -> Q(a..) \|\| Q \|\| Zp \|\| Zp(a)
2217	(rField_is_Q() \|\| rField_is_Q_a() \|\|
2218	(rField_is_Zp() \|\| rField_is_Zp_a())))
2219	\|\|
2220	(rField_is_Zp_a(orig_ring) && // Zp(a..) -> Zp(a..) \|\| Zp
2221	(rField_is_Zp(currRing, rInternalChar(orig_ring)) \|\|
2222	rField_is_Zp_a(currRing, rInternalChar(orig_ring)))) )
2223	{
2224	par_perm_size=rPar(orig_ring);
2225	BITSET save_test=test;
2226	naSetChar(rInternalChar(orig_ring),orig_ring);
2227	nSetChar(currRing);
2228	test=save_test;
2229	}
2230	else
2231	{
2232	WerrorS("coefficient fields must be equal if q-ideal !=0");
2233	goto rCompose_err;
2234	}
2235	}
2236	perm=(int )omAlloc0((orig_ring->N+1)sizeof(int));
2237	if (par_perm_size!=0)
2238	par_perm=(int )omAlloc0(par_perm_sizesizeof(int));
2239	int i;
2240	#if 0
2241	// use imap:
2242	maFindPerm(orig_ring->names,orig_ring->N,orig_ring->parameter,orig_ring->P,
2243	currRing->names,currRing->N,currRing->parameter, currRing->P,
2244	perm,par_perm, currRing->ch);
2245	#else
2246	// use fetch
2247	if ((rPar(orig_ring)>0) && (rPar(currRing)==0))
2248	{
2249	for(i=si_min(rPar(orig_ring),rVar(currRing))-1;i>=0;i--) par_perm[i]=i+1;
2250	}
2251	else if (par_perm_size!=0)
2252	for(i=si_min(rPar(orig_ring),rPar(currRing))-1;i>=0;i--) par_perm[i]=-(i+1);
2253	for(i=si_min(orig_ring->N,pVariables);i>0;i--) perm[i]=i;
2254	#endif
2255	ideal dest_id=idInit(IDELEMS(q),1);
2256	for(i=IDELEMS(q)-1; i>=0; i--)
2257	{
2258	dest_id->m[i]=pPermPoly(q->m[i],perm,orig_ring,nMap,
2259	par_perm,par_perm_size);
2260	// PrintS("map:");pWrite(dest_id->m[i]);PrintLn();
2261	pTest(dest_id->m[i]);
2262	}
2263	R->qideal=dest_id;
2264	if (perm!=NULL)
2265	omFreeSize((ADDRESS)perm,(orig_ring->N+1)*sizeof(int));
2266	if (par_perm!=NULL)
2267	omFreeSize((ADDRESS)par_perm,par_perm_size*sizeof(int));
2268	rChangeCurrRing(orig_ring);
2269	#endif
2270	}
2271	else
2272	R->qideal=idrCopyR(q,currRing,R);
2273	}
2274	}
2275	else
2276	{
2277	WerrorS("q-ideal must be given as `ideal`");
2278	goto rCompose_err;
2279	}
2280
2281
2282	// ---------------------------------------------------------------
2283	#ifdef HAVE_PLURAL
2284	if (L->nr==5)
2285	{
2286	if (nc_CallPlural((matrix)L->m[4].Data(),(matrix)L->m[5].Data(),NULL,NULL,R, true)) goto rCompose_err;
2287	// takes care about non-comm. quotient! i.e. calls "nc_SetupQuotient" due to last true
2288	}
2289	#endif
2290	return R;
2291
2292	rCompose_err:
2293	if (R->N>0)
2294	{
2295	int i;
2296	if (R->names!=NULL)
2297	{
2298	i=R->N-1;
2299	while (i>=0) { if (R->names[i]!=NULL) omFree(R->names[i]); i--; }
2300	omFree(R->names);
2301	}
2302	}
2303	if (R->order!=NULL) omFree(R->order);
2304	if (R->block0!=NULL) omFree(R->block0);
2305	if (R->block1!=NULL) omFree(R->block1);
2306	if (R->wvhdl!=NULL) omFree(R->wvhdl);
2307	omFree(R);
2308	return NULL;
2309	}
2310
2311	// from matpol.cc
2312
2313	/*2
2314	* compute the jacobi matrix of an ideal
2315	*/
2316	BOOLEAN mpJacobi(leftv res,leftv a)
2317	{
2318	int i,j;
2319	matrix result;
2320	ideal id=(ideal)a->Data();
2321
2322	result =mpNew(IDELEMS(id),pVariables);
2323	for (i=1; i<=IDELEMS(id); i++)
2324	{
2325	for (j=1; j<=pVariables; j++)
2326	{
2327	MATELEM(result,i,j) = pDiff(id->m[i-1],j);
2328	}
2329	}
2330	res->data=(char *)result;
2331	return FALSE;
2332	}
2333
2334	/*2
2335	* returns the Koszul-matrix of degree d of a vectorspace with dimension n
2336	* uses the first n entrees of id, if id <> NULL
2337	*/
2338	BOOLEAN mpKoszul(leftv res,leftv c/ip/, leftv b/in/, leftv id)
2339	{
2340	int n=(int)(long)b->Data();
2341	int d=(int)(long)c->Data();
2342	int k,l,sign,row,col;
2343	matrix result;
2344	ideal temp;
2345	BOOLEAN bo;
2346	poly p;
2347
2348	if ((d>n) \|\| (d<1) \|\| (n<1))
2349	{
2350	res->data=(char *)mpNew(1,1);
2351	return FALSE;
2352	}
2353	int choise = (int)omAlloc(d*sizeof(int));
2354	if (id==NULL)
2355	temp=idMaxIdeal(1);
2356	else
2357	temp=(ideal)id->Data();
2358
2359	k = binom(n,d);
2360	l = k*d;
2361	l /= n-d+1;
2362	result =mpNew(l,k);
2363	col = 1;
2364	idInitChoise(d,1,n,&bo,choise);
2365	while (!bo)
2366	{
2367	sign = 1;
2368	for (l=1;l<=d;l++)
2369	{
2370	if (choise[l-1]<=IDELEMS(temp))
2371	{
2372	p = pCopy(temp->m[choise[l-1]-1]);
2373	if (sign == -1) p = pNeg(p);
2374	sign *= -1;
2375	row = idGetNumberOfChoise(l-1,d,1,n,choise);
2376	MATELEM(result,row,col) = p;
2377	}
2378	}
2379	col++;
2380	idGetNextChoise(d,n,&bo,choise);
2381	}
2382	if (id==NULL) idDelete(&temp);
2383
2384	res->data=(char *)result;
2385	return FALSE;
2386	}
2387
2388	// from syz1.cc
2389	/*2
2390	* read out the Betti numbers from resolution
2391	* (interpreter interface)
2392	*/
2393	BOOLEAN syBetti2(leftv res, leftv u, leftv w)
2394	{
2395	syStrategy syzstr=(syStrategy)u->Data();
2396	BOOLEAN minim=(int)(long)w->Data();
2397	int row_shift=0;
2398	int add_row_shift=0;
2399	intvec *weights=NULL;
2400	intvec ww=(intvec )atGet(u,"isHomog",INTVEC_CMD);
2401	if (ww!=NULL)
2402	{
2403	weights=ivCopy(ww);
2404	add_row_shift = ww->min_in();
2405	(*weights) -= add_row_shift;
2406	}
2407	res->data=(void *)syBettiOfComputation(syzstr,minim,&row_shift,weights);
2408	//row_shift += add_row_shift;
2409	//Print("row_shift=%d, add_row_shift=%d\n",row_shift,add_row_shift);
2410	atSet(res,omStrDup("rowShift"),(void*)add_row_shift,INT_CMD);
2411	return FALSE;
2412	}
2413	BOOLEAN syBetti1(leftv res, leftv u)
2414	{
2415	sleftv tmp;
2416	memset(&tmp,0,sizeof(tmp));
2417	tmp.rtyp=INT_CMD;
2418	tmp.data=(void *)1;
2419	return syBetti2(res,u,&tmp);
2420	}
2421
2422	/*3
2423	* converts a resolution into a list of modules
2424	*/
2425	lists syConvRes(syStrategy syzstr,BOOLEAN toDel,int add_row_shift)
2426	{
2427	if ((syzstr->fullres==NULL) && (syzstr->minres==NULL))
2428	{
2429	if (syzstr->hilb_coeffs==NULL)
2430	{
2431	syzstr->fullres = syReorder(syzstr->res,syzstr->length,syzstr);
2432	}
2433	else
2434	{
2435	syzstr->minres = syReorder(syzstr->orderedRes,syzstr->length,syzstr);
2436	syKillEmptyEntres(syzstr->minres,syzstr->length);
2437	}
2438	}
2439	resolvente tr;
2440	int typ0=IDEAL_CMD;
2441	if (syzstr->minres!=NULL)
2442	tr = syzstr->minres;
2443	else
2444	tr = syzstr->fullres;
2445	resolvente trueres=NULL;
2446	intvec ** w=NULL;
2447	if (syzstr->length>0)
2448	{
2449	trueres=(resolvente)omAlloc0((syzstr->length)*sizeof(ideal));
2450	for (int i=(syzstr->length)-1;i>=0;i--)
2451	{
2452	if (tr[i]!=NULL)
2453	{
2454	trueres[i] = idCopy(tr[i]);
2455	}
2456	}
2457	if (idRankFreeModule(trueres[0]) > 0)
2458	typ0 = MODUL_CMD;
2459	if (syzstr->weights!=NULL)
2460	{
2461	w = (intvec*)omAlloc0((syzstr->length)sizeof(intvec*));
2462	for (int i=(syzstr->length)-1;i>=0;i--)
2463	{
2464	if (syzstr->weights[i]!=NULL) w[i] = ivCopy(syzstr->weights[i]);
2465	}
2466	}
2467	}
2468	lists li = liMakeResolv(trueres,syzstr->length,syzstr->list_length,typ0,
2469	w,add_row_shift);
2470	if (w != NULL) omFreeSize(w, (syzstr->length)sizeof(intvec));
2471	if (toDel) syKillComputation(syzstr);
2472	return li;
2473	}
2474
2475	/*3
2476	* converts a list of modules into a resolution
2477	*/
2478	syStrategy syConvList(lists li,BOOLEAN toDel)
2479	{
2480	int typ0;
2481	syStrategy result=(syStrategy)omAlloc0(sizeof(ssyStrategy));
2482
2483	resolvente fr = liFindRes(li,&(result->length),&typ0,&(result->weights));
2484	if (fr != NULL)
2485	{
2486
2487	result->fullres = (resolvente)omAlloc0((result->length+1)*sizeof(ideal));
2488	for (int i=result->length-1;i>=0;i--)
2489	{
2490	if (fr[i]!=NULL)
2491	result->fullres[i] = idCopy(fr[i]);
2492	}
2493	result->list_length=result->length;
2494	omFreeSize((ADDRESS)fr,(result->length)*sizeof(ideal));
2495	}
2496	else
2497	{
2498	omFreeSize(result, sizeof(ssyStrategy));
2499	result = NULL;
2500	}
2501	if (toDel) li->Clean();
2502	return result;
2503	}
2504
2505	/*3
2506	* converts a list of modules into a minimal resolution
2507	*/
2508	syStrategy syForceMin(lists li)
2509	{
2510	int typ0;
2511	syStrategy result=(syStrategy)omAlloc0(sizeof(ssyStrategy));
2512
2513	resolvente fr = liFindRes(li,&(result->length),&typ0);
2514	result->minres = (resolvente)omAlloc0((result->length+1)*sizeof(ideal));
2515	for (int i=result->length-1;i>=0;i--)
2516	{
2517	if (fr[i]!=NULL)
2518	result->minres[i] = idCopy(fr[i]);
2519	}
2520	omFreeSize((ADDRESS)fr,(result->length)*sizeof(ideal));
2521	return result;
2522	}
2523	// from weight.cc
2524	BOOLEAN kWeight(leftv res,leftv id)
2525	{
2526	ideal F=(ideal)id->Data();
2527	intvec * iv = new intvec(pVariables);
2528	polyset s;
2529	int sl, n, i;
2530	int *x;
2531
2532	res->data=(char *)iv;
2533	s = F->m;
2534	sl = IDELEMS(F) - 1;
2535	n = pVariables;
2536	double wNsqr = (double)2.0 / (double)n;
2537	wFunctional = wFunctionalBuch;
2538	x = (int * )omAlloc(2 * (n + 1) * sizeof(int));
2539	wCall(s, sl, x, wNsqr);
2540	for (i = n; i!=0; i--)
2541	(*iv)[i-1] = x[i + n + 1];
2542	omFreeSize((ADDRESS)x, 2 * (n + 1) * sizeof(int));
2543	return FALSE;
2544	}
2545
2546	BOOLEAN kQHWeight(leftv res,leftv v)
2547	{
2548	res->data=(char *)idQHomWeight((ideal)v->Data());
2549	if (res->data==NULL)
2550	res->data=(char *)new intvec(pVariables);
2551	return FALSE;
2552	}
2553	/==============================================================/
2554	// from clapsing.cc
2555	#if 0
2556	BOOLEAN jjIS_SQR_FREE(leftv res, leftv u)
2557	{
2558	BOOLEAN b=singclap_factorize((poly)(u->CopyD()), &v, 0);
2559	res->data=(void *)b;
2560	}
2561	#endif
2562
2563	BOOLEAN jjRESULTANT(leftv res, leftv u, leftv v, leftv w)
2564	{
2565	res->data=singclap_resultant((poly)u->Data(),(poly)v->Data(), (poly)w->Data());
2566	return errorreported;
2567	}
2568	BOOLEAN jjCHARSERIES(leftv res, leftv u)
2569	{
2570	res->data=singclap_irrCharSeries((ideal)u->Data());
2571	return (res->data==NULL);
2572	}
2573
2574	// from semic.cc
2575	#ifdef HAVE_SPECTRUM
2576
2577	// ----------------------------------------------------------------------------
2578	// Initialize a spectrum deep from another spectrum
2579	// ----------------------------------------------------------------------------
2580
2581	void spectrum::copy_deep( const spectrum &spec )
2582	{
2583	mu = spec.mu;
2584	pg = spec.pg;
2585	n = spec.n;
2586
2587	copy_new( n );
2588
2589	for( int i=0; i<n; i++ )
2590	{
2591	s[i] = spec.s[i];
2592	w[i] = spec.w[i];
2593	}
2594	}
2595
2596	// ----------------------------------------------------------------------------
2597	// Initialize a spectrum deep from a singular lists
2598	// ----------------------------------------------------------------------------
2599
2600	void spectrum::copy_deep( lists l )
2601	{
2602	mu = (int)(long)(l->m[0].Data( ));
2603	pg = (int)(long)(l->m[1].Data( ));
2604	n = (int)(long)(l->m[2].Data( ));
2605
2606	copy_new( n );
2607
2608	intvec num = (intvec)l->m[3].Data( );
2609	intvec den = (intvec)l->m[4].Data( );
2610	intvec mul = (intvec)l->m[5].Data( );
2611
2612	for( int i=0; i<n; i++ )
2613	{
2614	s[i] = (Rational)((num)[i])/(Rational)((den)[i]);
2615	w[i] = (*mul)[i];
2616	}
2617	}
2618
2619	// ----------------------------------------------------------------------------
2620	// singular lists constructor for spectrum
2621	// ----------------------------------------------------------------------------
2622
2623	spectrum::spectrum( lists l )
2624	{
2625	copy_deep( l );
2626	}
2627
2628	// ----------------------------------------------------------------------------
2629	// generate a Singular lists from a spectrum
2630	// ----------------------------------------------------------------------------
2631
2632	lists spectrum::thelist( void )
2633	{
2634	lists L = (lists)omAllocBin( slists_bin);
2635
2636	L->Init( 6 );
2637
2638	intvec *num = new intvec( n );
2639	intvec *den = new intvec( n );
2640	intvec *mult = new intvec( n );
2641
2642	for( int i=0; i<n; i++ )
2643	{
2644	(*num) [i] = s[i].get_num_si( );
2645	(*den) [i] = s[i].get_den_si( );
2646	(*mult)[i] = w[i];
2647	}
2648
2649	L->m[0].rtyp = INT_CMD; // milnor number
2650	L->m[1].rtyp = INT_CMD; // geometrical genus
2651	L->m[2].rtyp = INT_CMD; // # of spectrum numbers
2652	L->m[3].rtyp = INTVEC_CMD; // numerators
2653	L->m[4].rtyp = INTVEC_CMD; // denomiantors
2654	L->m[5].rtyp = INTVEC_CMD; // multiplicities
2655
2656	L->m[0].data = (void*)mu;
2657	L->m[1].data = (void*)pg;
2658	L->m[2].data = (void*)n;
2659	L->m[3].data = (void*)num;
2660	L->m[4].data = (void*)den;
2661	L->m[5].data = (void*)mult;
2662
2663	return L;
2664	}
2665	// from spectrum.cc
2666	// ----------------------------------------------------------------------------
2667	// print out an error message for a spectrum list
2668	// ----------------------------------------------------------------------------
2669
2670	void list_error( semicState state )
2671	{
2672	switch( state )
2673	{
2674	case semicListTooShort:
2675	WerrorS( "the list is too short" );
2676	break;
2677	case semicListTooLong:
2678	WerrorS( "the list is too long" );
2679	break;
2680
2681	case semicListFirstElementWrongType:
2682	WerrorS( "first element of the list should be int" );
2683	break;
2684	case semicListSecondElementWrongType:
2685	WerrorS( "second element of the list should be int" );
2686	break;
2687	case semicListThirdElementWrongType:
2688	WerrorS( "third element of the list should be int" );
2689	break;
2690	case semicListFourthElementWrongType:
2691	WerrorS( "fourth element of the list should be intvec" );
2692	break;
2693	case semicListFifthElementWrongType:
2694	WerrorS( "fifth element of the list should be intvec" );
2695	break;
2696	case semicListSixthElementWrongType:
2697	WerrorS( "sixth element of the list should be intvec" );
2698	break;
2699
2700	case semicListNNegative:
2701	WerrorS( "first element of the list should be positive" );
2702	break;
2703	case semicListWrongNumberOfNumerators:
2704	WerrorS( "wrong number of numerators" );
2705	break;
2706	case semicListWrongNumberOfDenominators:
2707	WerrorS( "wrong number of denominators" );
2708	break;
2709	case semicListWrongNumberOfMultiplicities:
2710	WerrorS( "wrong number of multiplicities" );
2711	break;
2712
2713	case semicListMuNegative:
2714	WerrorS( "the Milnor number should be positive" );
2715	break;
2716	case semicListPgNegative:
2717	WerrorS( "the geometrical genus should be nonnegative" );
2718	break;
2719	case semicListNumNegative:
2720	WerrorS( "all numerators should be positive" );
2721	break;
2722	case semicListDenNegative:
2723	WerrorS( "all denominators should be positive" );
2724	break;
2725	case semicListMulNegative:
2726	WerrorS( "all multiplicities should be positive" );
2727	break;
2728
2729	case semicListNotSymmetric:
2730	WerrorS( "it is not symmetric" );
2731	break;
2732	case semicListNotMonotonous:
2733	WerrorS( "it is not monotonous" );
2734	break;
2735
2736	case semicListMilnorWrong:
2737	WerrorS( "the Milnor number is wrong" );
2738	break;
2739	case semicListPGWrong:
2740	WerrorS( "the geometrical genus is wrong" );
2741	break;
2742
2743	default:
2744	WerrorS( "unspecific error" );
2745	break;
2746	}
2747	}
2748	// ----------------------------------------------------------------------------
2749	// this is the main spectrum computation function
2750	// ----------------------------------------------------------------------------
2751
2752	spectrumState spectrumCompute( poly h,lists *L,int fast )
2753	{
2754	int i,j;
2755
2756	#ifdef SPECTRUM_DEBUG
2757	#ifdef SPECTRUM_PRINT
2758	#ifdef SPECTRUM_IOSTREAM
2759	cout << "spectrumCompute\n";
2760	if( fast==0 ) cout << " no optimization" << endl;
2761	if( fast==1 ) cout << " weight optimization" << endl;
2762	if( fast==2 ) cout << " symmetry optimization" << endl;
2763	#else
2764	fprintf( stdout,"spectrumCompute\n" );
2765	if( fast==0 ) fprintf( stdout," no optimization\n" );
2766	if( fast==1 ) fprintf( stdout," weight optimization\n" );
2767	if( fast==2 ) fprintf( stdout," symmetry optimization\n" );
2768	#endif
2769	#endif
2770	#endif
2771
2772	// ----------------------
2773	// check if h is zero
2774	// ----------------------
2775
2776	if( h==(poly)NULL )
2777	{
2778	return spectrumZero;
2779	}
2780
2781	// ----------------------------------
2782	// check if h has a constant term
2783	// ----------------------------------
2784
2785	if( hasConstTerm( h ) )
2786	{
2787	return spectrumBadPoly;
2788	}
2789
2790	// --------------------------------
2791	// check if h has a linear term
2792	// --------------------------------
2793
2794	if( hasLinearTerm( h ) )
2795	{
2796	*L = (lists)omAllocBin( slists_bin);
2797	(*L)->Init( 1 );
2798	(*L)->m[0].rtyp = INT_CMD; // milnor number
2799	/* (L)->m[0].data = (void)0;a -- done by Init */
2800
2801	return spectrumNoSingularity;
2802	}
2803
2804	// ----------------------------------
2805	// compute the jacobi ideal of (h)
2806	// ----------------------------------
2807
2808	ideal J = NULL;
2809	J = idInit( pVariables,1 );
2810
2811	#ifdef SPECTRUM_DEBUG
2812	#ifdef SPECTRUM_PRINT
2813	#ifdef SPECTRUM_IOSTREAM
2814	cout << "\n computing the Jacobi ideal...\n";
2815	#else
2816	fprintf( stdout,"\n computing the Jacobi ideal...\n" );
2817	#endif
2818	#endif
2819	#endif
2820
2821	for( i=0; i<pVariables; i++ )
2822	{
2823	J->m[i] = pDiff( h,i+1); //j );
2824
2825	#ifdef SPECTRUM_DEBUG
2826	#ifdef SPECTRUM_PRINT
2827	#ifdef SPECTRUM_IOSTREAM
2828	cout << " ";
2829	#else
2830	fprintf( stdout," " );
2831	#endif
2832	pWrite( J->m[i] );
2833	#endif
2834	#endif
2835	}
2836
2837	// --------------------------------------------
2838	// compute a standard basis stdJ of jac(h)
2839	// --------------------------------------------
2840
2841	#ifdef SPECTRUM_DEBUG
2842	#ifdef SPECTRUM_PRINT
2843	#ifdef SPECTRUM_IOSTREAM
2844	cout << endl;
2845	cout << " computing a standard basis..." << endl;
2846	#else
2847	fprintf( stdout,"\n" );
2848	fprintf( stdout," computing a standard basis...\n" );
2849	#endif
2850	#endif
2851	#endif
2852
2853	ideal stdJ = kStd(J,currQuotient,isNotHomog,NULL);
2854	idSkipZeroes( stdJ );
2855
2856	#ifdef SPECTRUM_DEBUG
2857	#ifdef SPECTRUM_PRINT
2858	for( i=0; i<IDELEMS(stdJ); i++ )
2859	{
2860	#ifdef SPECTRUM_IOSTREAM
2861	cout << " ";
2862	#else
2863	fprintf( stdout," " );
2864	#endif
2865
2866	pWrite( stdJ->m[i] );
2867	}
2868	#endif
2869	#endif
2870
2871	idDelete( &J );
2872
2873	// ------------------------------------------
2874	// check if the h has a singularity
2875	// ------------------------------------------
2876
2877	if( hasOne( stdJ ) )
2878	{
2879	// -------------------------------
2880	// h is smooth in the origin
2881	// return only the Milnor number
2882	// -------------------------------
2883
2884	*L = (lists)omAllocBin( slists_bin);
2885	(*L)->Init( 1 );
2886	(*L)->m[0].rtyp = INT_CMD; // milnor number
2887	/* (L)->m[0].data = (void)0;a -- done by Init */
2888
2889	return spectrumNoSingularity;
2890	}
2891
2892	// ------------------------------------------
2893	// check if the singularity h is isolated
2894	// ------------------------------------------
2895
2896	for( i=pVariables; i>0; i-- )
2897	{
2898	if( hasAxis( stdJ,i )==FALSE )
2899	{
2900	return spectrumNotIsolated;
2901	}
2902	}
2903
2904	// ------------------------------------------
2905	// compute the highest corner hc of stdJ
2906	// ------------------------------------------
2907
2908	#ifdef SPECTRUM_DEBUG
2909	#ifdef SPECTRUM_PRINT
2910	#ifdef SPECTRUM_IOSTREAM
2911	cout << "\n computing the highest corner...\n";
2912	#else
2913	fprintf( stdout,"\n computing the highest corner...\n" );
2914	#endif
2915	#endif
2916	#endif
2917
2918	poly hc = (poly)NULL;
2919
2920	scComputeHC( stdJ,currQuotient, 0,hc );
2921
2922	if( hc!=(poly)NULL )
2923	{
2924	pGetCoeff(hc) = nInit(1);
2925
2926	for( i=pVariables; i>0; i-- )
2927	{
2928	if( pGetExp( hc,i )>0 ) pDecrExp( hc,i );
2929	}
2930	pSetm( hc );
2931	}
2932	else
2933	{
2934	return spectrumNoHC;
2935	}
2936
2937	#ifdef SPECTRUM_DEBUG
2938	#ifdef SPECTRUM_PRINT
2939	#ifdef SPECTRUM_IOSTREAM
2940	cout << " ";
2941	#else
2942	fprintf( stdout," " );
2943	#endif
2944	pWrite( hc );
2945	#endif
2946	#endif
2947
2948	// ----------------------------------------
2949	// compute the Newton polygon nph of h
2950	// ----------------------------------------
2951
2952	#ifdef SPECTRUM_DEBUG
2953	#ifdef SPECTRUM_PRINT
2954	#ifdef SPECTRUM_IOSTREAM
2955	cout << "\n computing the newton polygon...\n";
2956	#else
2957	fprintf( stdout,"\n computing the newton polygon...\n" );
2958	#endif
2959	#endif
2960	#endif
2961
2962	newtonPolygon nph( h );
2963
2964	#ifdef SPECTRUM_DEBUG
2965	#ifdef SPECTRUM_PRINT
2966	cout << nph;
2967	#endif
2968	#endif
2969
2970	// -----------------------------------------------
2971	// compute the weight corner wc of (stdj,nph)
2972	// -----------------------------------------------
2973
2974	#ifdef SPECTRUM_DEBUG
2975	#ifdef SPECTRUM_PRINT
2976	#ifdef SPECTRUM_IOSTREAM
2977	cout << "\n computing the weight corner...\n";
2978	#else
2979	fprintf( stdout,"\n computing the weight corner...\n" );
2980	#endif
2981	#endif
2982	#endif
2983
2984	poly wc = ( fast==0 ? pCopy( hc ) :
2985	( fast==1 ? computeWC( nph,(Rational)pVariables ) :
2986	/* fast==2 */computeWC( nph,((Rational)pVariables)/(Rational)2 ) ) );
2987
2988	#ifdef SPECTRUM_DEBUG
2989	#ifdef SPECTRUM_PRINT
2990	#ifdef SPECTRUM_IOSTREAM
2991	cout << " ";
2992	#else
2993	fprintf( stdout," " );
2994	#endif
2995	pWrite( wc );
2996	#endif
2997	#endif
2998
2999	// -------------
3000	// compute NF
3001	// -------------
3002
3003	#ifdef SPECTRUM_DEBUG
3004	#ifdef SPECTRUM_PRINT
3005	#ifdef SPECTRUM_IOSTREAM
3006	cout << "\n computing NF...\n" << endl;
3007	#else
3008	fprintf( stdout,"\n computing NF...\n" );
3009	#endif
3010	#endif
3011	#endif
3012
3013	spectrumPolyList NF( &nph );
3014
3015	computeNF( stdJ,hc,wc,&NF );
3016
3017	#ifdef SPECTRUM_DEBUG
3018	#ifdef SPECTRUM_PRINT
3019	cout << NF;
3020	#ifdef SPECTRUM_IOSTREAM
3021	cout << endl;
3022	#else
3023	fprintf( stdout,"\n" );
3024	#endif
3025	#endif
3026	#endif
3027
3028	// ----------------------------
3029	// compute the spectrum of h
3030	// ----------------------------
3031
3032	return NF.spectrum( L,fast );
3033	}
3034
3035	// ----------------------------------------------------------------------------
3036	// this procedure is called from the interpreter
3037	// ----------------------------------------------------------------------------
3038	// first = polynomial
3039	// result = list of spectrum numbers
3040	// ----------------------------------------------------------------------------
3041
3042	BOOLEAN spectrumProc( leftv result,leftv first )
3043	{
3044	spectrumState state = spectrumOK;
3045
3046	// -------------------
3047	// check consistency
3048	// -------------------
3049
3050	// check for a local ring
3051
3052	if( !ringIsLocal( ) )
3053	{
3054	WerrorS( "only works for local orderings" );
3055	state = spectrumWrongRing;
3056	}
3057
3058	// no quotient rings are allowed
3059
3060	else if( currRing->qideal != NULL )
3061	{
3062	WerrorS( "does not work in quotient rings" );
3063	state = spectrumWrongRing;
3064	}
3065	else
3066	{
3067	lists L = (lists)NULL;
3068	int flag = 1; // weight corner optimization is safe
3069
3070	state = spectrumCompute( (poly)first->Data( ),&L,flag );
3071
3072	if( state==spectrumOK )
3073	{
3074	result->rtyp = LIST_CMD;
3075	result->data = (char*)L;
3076	}
3077	else
3078	{
3079	spectrumPrintError(state);
3080	}
3081	}
3082
3083	return (state!=spectrumOK);
3084	}
3085
3086	// ----------------------------------------------------------------------------
3087	// this procedure is called from the interpreter
3088	// ----------------------------------------------------------------------------
3089	// first = polynomial
3090	// result = list of spectrum numbers
3091	// ----------------------------------------------------------------------------
3092
3093	BOOLEAN spectrumfProc( leftv result,leftv first )
3094	{
3095	spectrumState state = spectrumOK;
3096
3097	// -------------------
3098	// check consistency
3099	// -------------------
3100
3101	// check for a local polynomial ring
3102
3103	if( currRing->OrdSgn != -1 )
3104	// ?? HS: the test above is also true for k[x][[y]], k[[x]][y]
3105	// or should we use:
3106	//if( !ringIsLocal( ) )
3107	{
3108	WerrorS( "only works for local orderings" );
3109	state = spectrumWrongRing;
3110	}
3111	else if( currRing->qideal != NULL )
3112	{
3113	WerrorS( "does not work in quotient rings" );
3114	state = spectrumWrongRing;
3115	}
3116	else
3117	{
3118	lists L = (lists)NULL;
3119	int flag = 2; // symmetric optimization
3120
3121	state = spectrumCompute( (poly)first->Data( ),&L,flag );
3122
3123	if( state==spectrumOK )
3124	{
3125	result->rtyp = LIST_CMD;
3126	result->data = (char*)L;
3127	}
3128	else
3129	{
3130	spectrumPrintError(state);
3131	}
3132	}
3133
3134	return (state!=spectrumOK);
3135	}
3136
3137	// ----------------------------------------------------------------------------
3138	// check if a list is a spectrum
3139	// check for:
3140	// list has 6 elements
3141	// 1st element is int (mu=Milnor number)
3142	// 2nd element is int (pg=geometrical genus)
3143	// 3rd element is int (n =number of different spectrum numbers)
3144	// 4th element is intvec (num=numerators)
3145	// 5th element is intvec (den=denomiantors)
3146	// 6th element is intvec (mul=multiplicities)
3147	// exactly n numerators
3148	// exactly n denominators
3149	// exactly n multiplicities
3150	// mu>0
3151	// pg>=0
3152	// n>0
3153	// num>0
3154	// den>0
3155	// mul>0
3156	// symmetriy with respect to numberofvariables/2
3157	// monotony
3158	// mu = sum of all multiplicities
3159	// pg = sum of all multiplicities where num/den<=1
3160	// ----------------------------------------------------------------------------
3161
3162	semicState list_is_spectrum( lists l )
3163	{
3164	// -------------------
3165	// check list length
3166	// -------------------
3167
3168	if( l->nr < 5 )
3169	{
3170	return semicListTooShort;
3171	}
3172	else if( l->nr > 5 )
3173	{
3174	return semicListTooLong;
3175	}
3176
3177	// -------------
3178	// check types
3179	// -------------
3180
3181	if( l->m[0].rtyp != INT_CMD )
3182	{
3183	return semicListFirstElementWrongType;
3184	}
3185	else if( l->m[1].rtyp != INT_CMD )
3186	{
3187	return semicListSecondElementWrongType;
3188	}
3189	else if( l->m[2].rtyp != INT_CMD )
3190	{
3191	return semicListThirdElementWrongType;
3192	}
3193	else if( l->m[3].rtyp != INTVEC_CMD )
3194	{
3195	return semicListFourthElementWrongType;
3196	}
3197	else if( l->m[4].rtyp != INTVEC_CMD )
3198	{
3199	return semicListFifthElementWrongType;
3200	}
3201	else if( l->m[5].rtyp != INTVEC_CMD )
3202	{
3203	return semicListSixthElementWrongType;
3204	}
3205
3206	// -------------------------
3207	// check number of entries
3208	// -------------------------
3209
3210	int mu = (int)(long)(l->m[0].Data( ));
3211	int pg = (int)(long)(l->m[1].Data( ));
3212	int n = (int)(long)(l->m[2].Data( ));
3213
3214	if( n <= 0 )
3215	{
3216	return semicListNNegative;
3217	}
3218
3219	intvec num = (intvec)l->m[3].Data( );
3220	intvec den = (intvec)l->m[4].Data( );
3221	intvec mul = (intvec)l->m[5].Data( );
3222
3223	if( n != num->length( ) )
3224	{
3225	return semicListWrongNumberOfNumerators;
3226	}
3227	else if( n != den->length( ) )
3228	{
3229	return semicListWrongNumberOfDenominators;
3230	}
3231	else if( n != mul->length( ) )
3232	{
3233	return semicListWrongNumberOfMultiplicities;
3234	}
3235
3236	// --------
3237	// values
3238	// --------
3239
3240	if( mu <= 0 )
3241	{
3242	return semicListMuNegative;
3243	}
3244	if( pg < 0 )
3245	{
3246	return semicListPgNegative;
3247	}
3248
3249	int i;
3250
3251	for( i=0; i<n; i++ )
3252	{
3253	if( (*num)[i] <= 0 )
3254	{
3255	return semicListNumNegative;
3256	}
3257	if( (*den)[i] <= 0 )
3258	{
3259	return semicListDenNegative;
3260	}
3261	if( (*mul)[i] <= 0 )
3262	{
3263	return semicListMulNegative;
3264	}
3265	}
3266
3267	// ----------------
3268	// check symmetry
3269	// ----------------
3270
3271	int j;
3272
3273	for( i=0, j=n-1; i<=j; i++,j-- )
3274	{
3275	if( (num)[i] != pVariables((den)[i]) - (num)[j] \|\|
3276	(den)[i] != (den)[j] \|\|
3277	(mul)[i] != (mul)[j] )
3278	{
3279	return semicListNotSymmetric;
3280	}
3281	}
3282
3283	// ----------------
3284	// check monotony
3285	// ----------------
3286
3287	for( i=0, j=1; i<n/2; i++,j++ )
3288	{
3289	if( (num)[i](den)[j] >= (num)[j](den)[i] )
3290	{
3291	return semicListNotMonotonous;
3292	}
3293	}
3294
3295	// ---------------------
3296	// check Milnor number
3297	// ---------------------
3298
3299	for( mu=0, i=0; i<n; i++ )
3300	{
3301	mu += (*mul)[i];
3302	}
3303
3304	if( mu != (int)(long)(l->m[0].Data( )) )
3305	{
3306	return semicListMilnorWrong;
3307	}
3308
3309	// -------------------------
3310	// check geometrical genus
3311	// -------------------------
3312
3313	for( pg=0, i=0; i<n; i++ )
3314	{
3315	if( (num)[i]<=(den)[i] )
3316	{
3317	pg += (*mul)[i];
3318	}
3319	}
3320
3321	if( pg != (int)(long)(l->m[1].Data( )) )
3322	{
3323	return semicListPGWrong;
3324	}
3325
3326	return semicOK;
3327	}
3328
3329	// ----------------------------------------------------------------------------
3330	// this procedure is called from the interpreter
3331	// ----------------------------------------------------------------------------
3332	// first = list of spectrum numbers
3333	// second = list of spectrum numbers
3334	// result = sum of the two lists
3335	// ----------------------------------------------------------------------------
3336
3337	BOOLEAN spaddProc( leftv result,leftv first,leftv second )
3338	{
3339	semicState state;
3340
3341	// -----------------
3342	// check arguments
3343	// -----------------
3344
3345	lists l1 = (lists)first->Data( );
3346	lists l2 = (lists)second->Data( );
3347
3348	if( (state=list_is_spectrum( l1 )) != semicOK )
3349	{
3350	WerrorS( "first argument is not a spectrum:" );
3351	list_error( state );
3352	}
3353	else if( (state=list_is_spectrum( l2 )) != semicOK )
3354	{
3355	WerrorS( "second argument is not a spectrum:" );
3356	list_error( state );
3357	}
3358	else
3359	{
3360	spectrum s1( l1 );
3361	spectrum s2( l2 );
3362	spectrum sum( s1+s2 );
3363
3364	result->rtyp = LIST_CMD;
3365	result->data = (char*)(sum.thelist( ));
3366	}
3367
3368	return (state!=semicOK);
3369	}
3370
3371	// ----------------------------------------------------------------------------
3372	// this procedure is called from the interpreter
3373	// ----------------------------------------------------------------------------
3374	// first = list of spectrum numbers
3375	// second = integer
3376	// result = the multiple of the first list by the second factor
3377	// ----------------------------------------------------------------------------
3378
3379	BOOLEAN spmulProc( leftv result,leftv first,leftv second )
3380	{
3381	semicState state;
3382
3383	// -----------------
3384	// check arguments
3385	// -----------------
3386
3387	lists l = (lists)first->Data( );
3388	int k = (int)(long)second->Data( );
3389
3390	if( (state=list_is_spectrum( l ))!=semicOK )
3391	{
3392	WerrorS( "first argument is not a spectrum" );
3393	list_error( state );
3394	}
3395	else if( k < 0 )
3396	{
3397	WerrorS( "second argument should be positive" );
3398	state = semicMulNegative;
3399	}
3400	else
3401	{
3402	spectrum s( l );
3403	spectrum product( k*s );
3404
3405	result->rtyp = LIST_CMD;
3406	result->data = (char*)product.thelist( );
3407	}
3408
3409	return (state!=semicOK);
3410	}
3411
3412	// ----------------------------------------------------------------------------
3413	// this procedure is called from the interpreter
3414	// ----------------------------------------------------------------------------
3415	// first = list of spectrum numbers
3416	// second = list of spectrum numbers
3417	// result = semicontinuity index
3418	// ----------------------------------------------------------------------------
3419
3420	BOOLEAN semicProc3 ( leftv res,leftv u,leftv v,leftv w )
3421	{
3422	semicState state;
3423	BOOLEAN qh=(((int)(long)w->Data())==1);
3424
3425	// -----------------
3426	// check arguments
3427	// -----------------
3428
3429	lists l1 = (lists)u->Data( );
3430	lists l2 = (lists)v->Data( );
3431
3432	if( (state=list_is_spectrum( l1 ))!=semicOK )
3433	{
3434	WerrorS( "first argument is not a spectrum" );
3435	list_error( state );
3436	}
3437	else if( (state=list_is_spectrum( l2 ))!=semicOK )
3438	{
3439	WerrorS( "second argument is not a spectrum" );
3440	list_error( state );
3441	}
3442	else
3443	{
3444	spectrum s1( l1 );
3445	spectrum s2( l2 );
3446
3447	res->rtyp = INT_CMD;
3448	if (qh)
3449	res->data = (void*)(s1.mult_spectrumh( s2 ));
3450	else
3451	res->data = (void*)(s1.mult_spectrum( s2 ));
3452	}
3453
3454	// -----------------
3455	// check status
3456	// -----------------
3457
3458	return (state!=semicOK);
3459	}
3460	BOOLEAN semicProc ( leftv res,leftv u,leftv v )
3461	{
3462	sleftv tmp;
3463	memset(&tmp,0,sizeof(tmp));
3464	tmp.rtyp=INT_CMD;
3465	/* tmp.data = (void )0; -- done by memset /
3466
3467	return semicProc3(res,u,v,&tmp);
3468	}
3469	// from splist.cc
3470	// ----------------------------------------------------------------------------
3471	// Compute the spectrum of a spectrumPolyList
3472	// ----------------------------------------------------------------------------
3473
3474	spectrumState spectrumPolyList::spectrum( lists *L,int fast )
3475	{
3476	spectrumPolyNode **node = &root;
3477	spectrumPolyNode *search;
3478
3479	poly f,tmp;
3480	int found,cmp;
3481
3482	Rational smax( ( fast==0 ? 0 : pVariables ),
3483	( fast==2 ? 2 : 1 ) );
3484
3485	Rational weight_prev( 0,1 );
3486
3487	int mu = 0; // the milnor number
3488	int pg = 0; // the geometrical genus
3489	int n = 0; // number of different spectral numbers
3490	int z = 0; // number of spectral number equal to smax
3491
3492	int k = 0;
3493
3494	while( (node)!=(spectrumPolyNode)NULL &&
3495	( fast==0 \|\| (*node)->weight<=smax ) )
3496	{
3497	// ---------------------------------------
3498	// determine the first normal form which
3499	// contains the monomial node->mon
3500	// ---------------------------------------
3501
3502	found = FALSE;
3503	search = *node;
3504
3505	while( search!=(spectrumPolyNode*)NULL && found==FALSE )
3506	{
3507	if( search->nf!=(poly)NULL )
3508	{
3509	f = search->nf;
3510
3511	do
3512	{
3513	// --------------------------------
3514	// look for (*node)->mon in f
3515	// --------------------------------
3516
3517	cmp = pCmp( (*node)->mon,f );
3518
3519	if( cmp<0 )
3520	{
3521	f = pNext( f );
3522	}
3523	else if( cmp==0 )
3524	{
3525	// -----------------------------
3526	// we have found a normal form
3527	// -----------------------------
3528
3529	found = TRUE;
3530
3531	// normalize coefficient
3532
3533	number inv = nInvers( pGetCoeff( f ) );
3534	pMult_nn( search->nf,inv );
3535	nDelete( &inv );
3536
3537	// exchange normal forms
3538
3539	tmp = (*node)->nf;
3540	(*node)->nf = search->nf;
3541	search->nf = tmp;
3542	}
3543	}
3544	while( cmp<0 && f!=(poly)NULL );
3545	}
3546	search = search->next;
3547	}
3548
3549	if( found==FALSE )
3550	{
3551	// ------------------------------------------------
3552	// the weight of node->mon is a spectrum number
3553	// ------------------------------------------------
3554
3555	mu++;
3556
3557	if( (*node)->weight<=(Rational)1 ) pg++;
3558	if( (*node)->weight==smax ) z++;
3559	if( (*node)->weight>weight_prev ) n++;
3560
3561	weight_prev = (*node)->weight;
3562	node = &((*node)->next);
3563	}
3564	else
3565	{
3566	// -----------------------------------------------
3567	// determine all other normal form which contain
3568	// the monomial node->mon
3569	// replace for node->mon its normal form
3570	// -----------------------------------------------
3571
3572	while( search!=(spectrumPolyNode*)NULL )
3573	{
3574	if( search->nf!=(poly)NULL )
3575	{
3576	f = search->nf;
3577
3578	do
3579	{
3580	// --------------------------------
3581	// look for (*node)->mon in f
3582	// --------------------------------
3583
3584	cmp = pCmp( (*node)->mon,f );
3585
3586	if( cmp<0 )
3587	{
3588	f = pNext( f );
3589	}
3590	else if( cmp==0 )
3591	{
3592	search->nf = pSub( search->nf,
3593	ppMult_nn( (*node)->nf,pGetCoeff( f ) ) );
3594	pNorm( search->nf );
3595	}
3596	}
3597	while( cmp<0 && f!=(poly)NULL );
3598	}
3599	search = search->next;
3600	}
3601	delete_node( node );
3602	}
3603
3604	}
3605
3606	// --------------------------------------------------------
3607	// fast computation exploits the symmetry of the spectrum
3608	// --------------------------------------------------------
3609
3610	if( fast==2 )
3611	{
3612	mu = 2*mu - z;
3613	n = ( z > 0 ? 2n - 1 : 2n );
3614	}
3615
3616	// --------------------------------------------------------
3617	// compute the spectrum numbers with their multiplicities
3618	// --------------------------------------------------------
3619
3620	intvec *nom = new intvec( n );
3621	intvec *den = new intvec( n );
3622	intvec *mult = new intvec( n );
3623
3624	int count = 0;
3625	int multiplicity = 1;
3626
3627	for( search=root; search!=(spectrumPolyNode*)NULL &&
3628	( fast==0 \|\| search->weight<=smax );
3629	search=search->next )
3630	{
3631	if( search->next==(spectrumPolyNode*)NULL \|\|
3632	search->weight<search->next->weight )
3633	{
3634	(*nom) [count] = search->weight.get_num_si( );
3635	(*den) [count] = search->weight.get_den_si( );
3636	(*mult)[count] = multiplicity;
3637
3638	multiplicity=1;
3639	count++;
3640	}
3641	else
3642	{
3643	multiplicity++;
3644	}
3645	}
3646
3647	// --------------------------------------------------------
3648	// fast computation exploits the symmetry of the spectrum
3649	// --------------------------------------------------------
3650
3651	if( fast==2 )
3652	{
3653	int n1,n2;
3654	for( n1=0, n2=n-1; n1<n2; n1++, n2-- )
3655	{
3656	(nom) [n2] = pVariables(den)[n1]-(nom)[n1];
3657	(den) [n2] = (den)[n1];
3658	(mult)[n2] = (mult)[n1];
3659	}
3660	}
3661
3662	// -----------------------------------
3663	// test if the spectrum is symmetric
3664	// -----------------------------------
3665
3666	if( fast==0 \|\| fast==1 )
3667	{
3668	int symmetric=TRUE;
3669
3670	for( int n1=0, n2=n-1 ; n1<n2 && symmetric==TRUE; n1++, n2-- )
3671	{
3672	if( (mult)[n1]!=(mult)[n2] \|\|
3673	(den) [n1]!= (den)[n2] \|\|
3674	(nom)[n1]+(nom)[n2]!=pVariables(den) [n1] )
3675	{
3676	symmetric = FALSE;
3677	}
3678	}
3679
3680	if( symmetric==FALSE )
3681	{
3682	// ---------------------------------------------
3683	// the spectrum is not symmetric => degenerate
3684	// principal part
3685	// ---------------------------------------------
3686
3687	*L = (lists)omAllocBin( slists_bin);
3688	(*L)->Init( 1 );
3689	(*L)->m[0].rtyp = INT_CMD; // milnor number
3690	(L)->m[0].data = (void)mu;
3691
3692	return spectrumDegenerate;
3693	}
3694	}
3695
3696	*L = (lists)omAllocBin( slists_bin);
3697
3698	(*L)->Init( 6 );
3699
3700	(*L)->m[0].rtyp = INT_CMD; // milnor number
3701	(*L)->m[1].rtyp = INT_CMD; // geometrical genus
3702	(*L)->m[2].rtyp = INT_CMD; // number of spectrum values
3703	(*L)->m[3].rtyp = INTVEC_CMD; // nominators
3704	(*L)->m[4].rtyp = INTVEC_CMD; // denomiantors
3705	(*L)->m[5].rtyp = INTVEC_CMD; // multiplicities
3706
3707	(L)->m[0].data = (void)mu;
3708	(L)->m[1].data = (void)pg;
3709	(L)->m[2].data = (void)n;
3710	(L)->m[3].data = (void)nom;
3711	(L)->m[4].data = (void)den;
3712	(L)->m[5].data = (void)mult;
3713
3714	return spectrumOK;
3715	}
3716
3717	#endif
3718
3719	//from mpr_inout.cc
3720	extern void nPrint(number n);
3721
3722	BOOLEAN loNewtonP( leftv res, leftv arg1 )
3723	{
3724	res->data= (void*)loNewtonPolytope( (ideal)arg1->Data() );
3725	return FALSE;
3726	}
3727
3728	BOOLEAN loSimplex( leftv res, leftv args )
3729	{
3730	if ( !(rField_is_long_R()) )
3731	{
3732	WerrorS("Ground field not implemented!");
3733	return TRUE;
3734	}
3735
3736	simplex * LP;
3737	matrix m;
3738
3739	leftv v= args;
3740	if ( v->Typ() != MATRIX_CMD ) // 1: matrix
3741	return TRUE;
3742	else
3743	m= (matrix)(v->CopyD());
3744
3745	LP = new simplex(MATROWS(m),MATCOLS(m));
3746	LP->mapFromMatrix(m);
3747
3748	v= v->next;
3749	if ( v->Typ() != INT_CMD ) // 2: m = number of constraints
3750	return TRUE;
3751	else
3752	LP->m= (int)(long)(v->Data());
3753
3754	v= v->next;
3755	if ( v->Typ() != INT_CMD ) // 3: n = number of variables
3756	return TRUE;
3757	else
3758	LP->n= (int)(long)(v->Data());
3759
3760	v= v->next;
3761	if ( v->Typ() != INT_CMD ) // 4: m1 = number of <= constraints
3762	return TRUE;
3763	else
3764	LP->m1= (int)(long)(v->Data());
3765
3766	v= v->next;
3767	if ( v->Typ() != INT_CMD ) // 5: m2 = number of >= constraints
3768	return TRUE;
3769	else
3770	LP->m2= (int)(long)(v->Data());
3771
3772	v= v->next;
3773	if ( v->Typ() != INT_CMD ) // 6: m3 = number of == constraints
3774	return TRUE;
3775	else
3776	LP->m3= (int)(long)(v->Data());
3777
3778	#ifdef mprDEBUG_PROT
3779	Print("m (constraints) %d\n",LP->m);
3780	Print("n (columns) %d\n",LP->n);
3781	Print("m1 (<=) %d\n",LP->m1);
3782	Print("m2 (>=) %d\n",LP->m2);
3783	Print("m3 (==) %d\n",LP->m3);
3784	#endif
3785
3786	LP->compute();
3787
3788	lists lres= (lists)omAlloc( sizeof(slists) );
3789	lres->Init( 6 );
3790
3791	lres->m[0].rtyp= MATRIX_CMD; // output matrix
3792	lres->m[0].data=(void*)LP->mapToMatrix(m);
3793
3794	lres->m[1].rtyp= INT_CMD; // found a solution?
3795	lres->m[1].data=(void*)LP->icase;
3796
3797	lres->m[2].rtyp= INTVEC_CMD;
3798	lres->m[2].data=(void*)LP->posvToIV();
3799
3800	lres->m[3].rtyp= INTVEC_CMD;
3801	lres->m[3].data=(void*)LP->zrovToIV();
3802
3803	lres->m[4].rtyp= INT_CMD;
3804	lres->m[4].data=(void*)LP->m;
3805
3806	lres->m[5].rtyp= INT_CMD;
3807	lres->m[5].data=(void*)LP->n;
3808
3809	res->data= (void*)lres;
3810
3811	return FALSE;
3812	}
3813
3814	BOOLEAN nuMPResMat( leftv res, leftv arg1, leftv arg2 )
3815	{
3816	ideal gls = (ideal)(arg1->Data());
3817	int imtype= (int)(long)arg2->Data();
3818
3819	uResultant::resMatType mtype= determineMType( imtype );
3820
3821	// check input ideal ( = polynomial system )
3822	if ( mprIdealCheck( gls, arg1->Name(), mtype, true ) != mprOk )
3823	{
3824	return TRUE;
3825	}
3826
3827	uResultant *resMat= new uResultant( gls, mtype, false );
3828	if (resMat!=NULL)
3829	{
3830	res->rtyp = MODUL_CMD;
3831	res->data= (void*)resMat->accessResMat()->getMatrix();
3832	if (!errorreported) delete resMat;
3833	}
3834	return errorreported;
3835	}
3836
3837	BOOLEAN nuLagSolve( leftv res, leftv arg1, leftv arg2, leftv arg3 )
3838	{
3839
3840	poly gls;
3841	gls= (poly)(arg1->Data());
3842	int howclean= (int)(long)arg3->Data();
3843
3844	if ( !(rField_is_R() \|\|
3845	rField_is_Q() \|\|
3846	rField_is_long_R() \|\|
3847	rField_is_long_C()) )
3848	{
3849	WerrorS("Ground field not implemented!");
3850	return TRUE;
3851	}
3852
3853	if ( !(rField_is_R()\|\|rField_is_long_R()\|\|rField_is_long_C()) )
3854	{
3855	unsigned long int ii = (unsigned long int)arg2->Data();
3856	setGMPFloatDigits( ii, ii );
3857	}
3858
3859	if ( gls == NULL \|\| pIsConstant( gls ) )
3860	{
3861	WerrorS("Input polynomial is constant!");
3862	return TRUE;
3863	}
3864
3865	int ldummy;
3866	int deg= pLDeg( gls, &ldummy, currRing );
3867	// int deg= pDeg( gls );
3868	int len= pLength( gls );
3869	int i,vpos=0;
3870	poly piter;
3871	lists elist;
3872	lists rlist;
3873
3874	elist= (lists)omAlloc( sizeof(slists) );
3875	elist->Init( 0 );
3876
3877	if ( pVariables > 1 )
3878	{
3879	piter= gls;
3880	for ( i= 1; i <= pVariables; i++ )
3881	if ( pGetExp( piter, i ) )
3882	{
3883	vpos= i;
3884	break;
3885	}
3886	while ( piter )
3887	{
3888	for ( i= 1; i <= pVariables; i++ )
3889	if ( (vpos != i) && (pGetExp( piter, i ) != 0) )
3890	{
3891	WerrorS("The input polynomial must be univariate!");
3892	return TRUE;
3893	}
3894	pIter( piter );
3895	}
3896	}
3897
3898	rootContainer * roots= new rootContainer();
3899	number * pcoeffs= (number )omAlloc( (deg+1) sizeof( number ) );
3900	piter= gls;
3901	for ( i= deg; i >= 0; i-- )
3902	{
3903	//if ( piter ) Print("deg %d, pDeg(piter) %d\n",i,pTotaldegree(piter));
3904	if ( piter && pTotaldegree(piter) == i )
3905	{
3906	pcoeffs[i]= nCopy( pGetCoeff( piter ) );
3907	//nPrint( pcoeffs[i] );PrintS(" ");
3908	pIter( piter );
3909	}
3910	else
3911	{
3912	pcoeffs[i]= nInit(0);
3913	}
3914	}
3915
3916	#ifdef mprDEBUG_PROT
3917	for (i=deg; i >= 0; i--)
3918	{
3919	nPrint( pcoeffs[i] );PrintS(" ");
3920	}
3921	PrintLn();
3922	#endif
3923
3924	roots->fillContainer( pcoeffs, NULL, 1, deg, rootContainer::onepoly, 1 );
3925	roots->solver( howclean );
3926
3927	int elem= roots->getAnzRoots();
3928	char *out;
3929	char *dummy;
3930	int j;
3931
3932	rlist= (lists)omAlloc( sizeof(slists) );
3933	rlist->Init( elem );
3934
3935	if (rField_is_long_C())
3936	{
3937	for ( j= 0; j < elem; j++ )
3938	{
3939	rlist->m[j].rtyp=NUMBER_CMD;
3940	rlist->m[j].data=(void *)nCopy((number)(roots->getRoot(j)));
3941	//rlist->m[j].data=(void *)(number)(roots->getRoot(j));
3942	}
3943	}
3944	else
3945	{
3946	for ( j= 0; j < elem; j++ )
3947	{
3948	dummy = complexToStr( (*roots)[j], gmp_output_digits );
3949	rlist->m[j].rtyp=STRING_CMD;
3950	rlist->m[j].data=(void *)dummy;
3951	}
3952	}
3953
3954	elist->Clean();
3955	//omFreeSize( (ADDRESS) elist, sizeof(slists) );
3956
3957	// this is (via fillContainer) the same data as in root
3958	//for ( i= deg; i >= 0; i-- ) nDelete( &pcoeffs[i] );
3959	//omFreeSize( (ADDRESS) pcoeffs, (deg+1) * sizeof( number ) );
3960
3961	delete roots;
3962
3963	res->rtyp= LIST_CMD;
3964	res->data= (void*)rlist;
3965
3966	return FALSE;
3967	}
3968
3969	BOOLEAN nuVanderSys( leftv res, leftv arg1, leftv arg2, leftv arg3)
3970	{
3971	int i;
3972	ideal p,w;
3973	p= (ideal)arg1->Data();
3974	w= (ideal)arg2->Data();
3975
3976	// w[0] = f(p^0)
3977	// w[1] = f(p^1)
3978	// ...
3979	// p can be a vector of numbers (multivariate polynom)
3980	// or one number (univariate polynom)
3981	// tdg = deg(f)
3982
3983	int n= IDELEMS( p );
3984	int m= IDELEMS( w );
3985	int tdg= (int)(long)arg3->Data();
3986
3987	res->data= (void*)NULL;
3988
3989	// check the input
3990	if ( tdg < 1 )
3991	{
3992	WerrorS("Last input parameter must be > 0!");
3993	return TRUE;
3994	}
3995	if ( n != pVariables )
3996	{
3997	Werror("Size of first input ideal must be equal to %d!",pVariables);
3998	return TRUE;
3999	}
4000	if ( m != (int)pow((double)tdg+1,(double)n) )
4001	{
4002	Werror("Size of second input ideal must be equal to %d!",
4003	(int)pow((double)tdg+1,(double)n));
4004	return TRUE;
4005	}
4006	if ( !(rField_is_Q() /* \|\|
4007	rField_is_R() \|\| rField_is_long_R() \|\|
4008	rField_is_long_C()*/ ) )
4009	{
4010	WerrorS("Ground field not implemented!");
4011	return TRUE;
4012	}
4013
4014	number tmp;
4015	number pevpoint= (number )omAlloc( n * sizeof( number ) );
4016	for ( i= 0; i < n; i++ )
4017	{
4018	pevpoint[i]=nInit(0);
4019	if ( (p->m)[i] )
4020	{
4021	tmp = pGetCoeff( (p->m)[i] );
4022	if ( nIsZero(tmp) \|\| nIsOne(tmp) \|\| nIsMOne(tmp) )
4023	{
4024	omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
4025	WerrorS("Elements of first input ideal must not be equal to -1, 0, 1!");
4026	return TRUE;
4027	}
4028	} else tmp= NULL;
4029	if ( !nIsZero(tmp) )
4030	{
4031	if ( !pIsConstant((p->m)[i]))
4032	{
4033	omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
4034	WerrorS("Elements of first input ideal must be numbers!");
4035	return TRUE;
4036	}
4037	pevpoint[i]= nCopy( tmp );
4038	}
4039	}
4040
4041	number wresults= (number )omAlloc( m * sizeof( number ) );
4042	for ( i= 0; i < m; i++ )
4043	{
4044	wresults[i]= nInit(0);
4045	if ( (w->m)[i] && !nIsZero(pGetCoeff((w->m)[i])) )
4046	{
4047	if ( !pIsConstant((w->m)[i]))
4048	{
4049	omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
4050	omFreeSize( (ADDRESS)wresults, m * sizeof( number ) );
4051	WerrorS("Elements of second input ideal must be numbers!");
4052	return TRUE;
4053	}
4054	wresults[i]= nCopy(pGetCoeff((w->m)[i]));
4055	}
4056	}
4057
4058	vandermonde vm( m, n, tdg, pevpoint, FALSE );
4059	number *ncpoly= vm.interpolateDense( wresults );
4060	// do not free ncpoly[]!!
4061	poly rpoly= vm.numvec2poly( ncpoly );
4062
4063	omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
4064	omFreeSize( (ADDRESS)wresults, m * sizeof( number ) );
4065
4066	res->data= (void*)rpoly;
4067	return FALSE;
4068	}
4069
4070	BOOLEAN nuUResSolve( leftv res, leftv args )
4071	{
4072	leftv v= args;
4073
4074	ideal gls;
4075	int imtype;
4076	int howclean;
4077
4078	// get ideal
4079	if ( v->Typ() != IDEAL_CMD )
4080	return TRUE;
4081	else gls= (ideal)(v->Data());
4082	v= v->next;
4083
4084	// get resultant matrix type to use (0,1)
4085	if ( v->Typ() != INT_CMD )
4086	return TRUE;
4087	else imtype= (int)(long)v->Data();
4088	v= v->next;
4089
4090	if (imtype==0)
4091	{
4092	ideal test_id=idInit(1,1);
4093	int j;
4094	for(j=IDELEMS(gls)-1;j>=0;j--)
4095	{
4096	if (gls->m[j]!=NULL)
4097	{
4098	test_id->m[0]=gls->m[j];
4099	intvec *dummy_w=idQHomWeight(test_id);
4100	if (dummy_w!=NULL)
4101	{
4102	WerrorS("Newton polytope not of expected dimension");
4103	delete dummy_w;
4104	return TRUE;
4105	}
4106	}
4107	}
4108	}
4109
4110	// get and set precision in digits ( > 0 )
4111	if ( v->Typ() != INT_CMD )
4112	return TRUE;
4113	else if ( !(rField_is_R()\|\|rField_is_long_R()\|\|rField_is_long_C()) )
4114	{
4115	unsigned long int ii=(unsigned long int)v->Data();
4116	setGMPFloatDigits( ii, ii );
4117	}
4118	v= v->next;
4119
4120	// get interpolation steps (0,1,2)
4121	if ( v->Typ() != INT_CMD )
4122	return TRUE;
4123	else howclean= (int)(long)v->Data();
4124
4125	uResultant::resMatType mtype= determineMType( imtype );
4126	int i,c,count;
4127	lists listofroots= NULL;
4128	lists emptylist;
4129	number smv= NULL;
4130	BOOLEAN interpolate_det= (mtype==uResultant::denseResMat)?TRUE:FALSE;
4131
4132	//emptylist= (lists)omAlloc( sizeof(slists) );
4133	//emptylist->Init( 0 );
4134
4135	//res->rtyp = LIST_CMD;
4136	//res->data= (void *)emptylist;
4137
4138	// check input ideal ( = polynomial system )
4139	if ( mprIdealCheck( gls, args->Name(), mtype ) != mprOk )
4140	{
4141	return TRUE;
4142	}
4143
4144	uResultant * ures;
4145	rootContainer ** iproots;
4146	rootContainer ** muiproots;
4147	rootArranger * arranger;
4148
4149	// main task 1: setup of resultant matrix
4150	ures= new uResultant( gls, mtype );
4151	if ( ures->accessResMat()->initState() != resMatrixBase::ready )
4152	{
4153	WerrorS("Error occurred during matrix setup!");
4154	return TRUE;
4155	}
4156
4157	// if dense resultant, check if minor nonsingular
4158	if ( mtype == uResultant::denseResMat )
4159	{
4160	smv= ures->accessResMat()->getSubDet();
4161	#ifdef mprDEBUG_PROT
4162	PrintS("// Determinant of submatrix: ");nPrint(smv);PrintLn();
4163	#endif
4164	if ( nIsZero(smv) )
4165	{
4166	WerrorS("Unsuitable input ideal: Minor of resultant matrix is singular!");
4167	return TRUE;
4168	}
4169	}
4170
4171	// main task 2: Interpolate specialized resultant polynomials
4172	if ( interpolate_det )
4173	iproots= ures->interpolateDenseSP( false, smv );
4174	else
4175	iproots= ures->specializeInU( false, smv );
4176
4177	// main task 3: Interpolate specialized resultant polynomials
4178	if ( interpolate_det )
4179	muiproots= ures->interpolateDenseSP( true, smv );
4180	else
4181	muiproots= ures->specializeInU( true, smv );
4182
4183	#ifdef mprDEBUG_PROT
4184	c= iproots[0]->getAnzElems();
4185	for (i=0; i < c; i++) pWrite(iproots[i]->getPoly());
4186	c= muiproots[0]->getAnzElems();
4187	for (i=0; i < c; i++) pWrite(muiproots[i]->getPoly());
4188	#endif
4189
4190	// main task 4: Compute roots of specialized polys and match them up
4191	arranger= new rootArranger( iproots, muiproots, howclean );
4192	arranger->solve_all();
4193
4194	// get list of roots
4195	if ( arranger->success() )
4196	{
4197	arranger->arrange();
4198	listofroots= arranger->listOfRoots( gmp_output_digits );
4199	}
4200	else
4201	{
4202	WerrorS("Solver was unable to find any roots!");
4203	return TRUE;
4204	}
4205
4206	// free everything
4207	count= iproots[0]->getAnzElems();
4208	for (i=0; i < count; i++) delete iproots[i];
4209	omFreeSize( (ADDRESS) iproots, count * sizeof(rootContainer*) );
4210	count= muiproots[0]->getAnzElems();
4211	for (i=0; i < count; i++) delete muiproots[i];
4212	omFreeSize( (ADDRESS) muiproots, count * sizeof(rootContainer*) );
4213
4214	delete ures;
4215	delete arranger;
4216	nDelete( &smv );
4217
4218	res->data= (void *)listofroots;
4219
4220	//emptylist->Clean();
4221	// omFreeSize( (ADDRESS) emptylist, sizeof(slists) );
4222
4223	return FALSE;
4224	}
4225
4226	// from mpr_numeric.cc
4227	lists rootArranger::listOfRoots( const unsigned int oprec )
4228	{
4229	int i,j,tr;
4230	int count= roots[0]->getAnzRoots(); // number of roots
4231	int elem= roots[0]->getAnzElems(); // number of koordinates per root
4232
4233	lists listofroots= (lists)omAlloc( sizeof(slists) ); // must be done this way!
4234
4235	if ( found_roots )
4236	{
4237	listofroots->Init( count );
4238
4239	for (i=0; i < count; i++)
4240	{
4241	lists onepoint= (lists)omAlloc(sizeof(slists)); // must be done this way!
4242	onepoint->Init(elem);
4243	for ( j= 0; j < elem; j++ )
4244	{
4245	if ( !rField_is_long_C() )
4246	{
4247	onepoint->m[j].rtyp=STRING_CMD;
4248	onepoint->m[j].data=(void )complexToStr((roots[j])[i],oprec);
4249	}
4250	else
4251	{
4252	onepoint->m[j].rtyp=NUMBER_CMD;
4253	onepoint->m[j].data=(void *)nCopy((number)(roots[j]->getRoot(i)));
4254	}
4255	onepoint->m[j].next= NULL;
4256	onepoint->m[j].name= NULL;
4257	}
4258	listofroots->m[i].rtyp=LIST_CMD;
4259	listofroots->m[i].data=(void *)onepoint;
4260	listofroots->m[j].next= NULL;
4261	listofroots->m[j].name= NULL;
4262	}
4263
4264	}
4265	else
4266	{
4267	listofroots->Init( 0 );
4268	}
4269
4270	return listofroots;
4271	}
4272
4273	// from ring.cc
4274	void rSetHdl(idhdl h)
4275	{
4276	int i;
4277	ring rg = NULL;
4278	if (h!=NULL)
4279	{
4280	// Print(" new ring:%s (l:%d)\n",IDID(h),IDLEV(h));
4281	rg = IDRING(h);
4282	if (rg==NULL) return; //id <>NULL, ring==NULL
4283	omCheckAddrSize((ADDRESS)h,sizeof(idrec));
4284	if (IDID(h)) // OB: ????
4285	omCheckAddr((ADDRESS)IDID(h));
4286	rTest(rg);
4287	}
4288
4289	// clean up history
4290	if (sLastPrinted.RingDependend())
4291	{
4292	sLastPrinted.CleanUp();
4293	memset(&sLastPrinted,0,sizeof(sleftv));
4294	}
4295
4296	// test for valid "currRing":
4297	if ((rg!=NULL) && (rg->idroot==NULL))
4298	{
4299	ring old=rg;
4300	rg=rAssure_HasComp(rg);
4301	if (old!=rg)
4302	{
4303	rKill(old);
4304	IDRING(h)=rg;
4305	}
4306	}
4307	/------------ change the global ring -----------------------/
4308	rChangeCurrRing(rg);
4309	currRingHdl = h;
4310	}
4311
4312	BOOLEAN rSleftvOrdering2Ordering(sleftv *ord, ring R)
4313	{
4314	int last = 0, o=0, n = 1, i=0, typ = 1, j;
4315	sleftv *sl = ord;
4316
4317	// determine nBlocks
4318	while (sl!=NULL)
4319	{
4320	intvec iv = (intvec )(sl->data);
4321	if (((iv)[1]==ringorder_c)\|\|((iv)[1]==ringorder_C))
4322	i++;
4323	else if ((*iv)[1]==ringorder_L)
4324	{
4325	R->bitmask=(*iv)[2];
4326	n--;
4327	}
4328	else if (((*iv)[1]!=ringorder_a)
4329	&& ((*iv)[1]!=ringorder_a64))
4330	o++;
4331	n++;
4332	sl=sl->next;
4333	}
4334	// check whether at least one real ordering
4335	if (o==0)
4336	{
4337	WerrorS("invalid combination of orderings");
4338	return TRUE;
4339	}
4340	// if no c/C ordering is given, increment n
4341	if (i==0) n++;
4342	else if (i != 1)
4343	{
4344	// throw error if more than one is given
4345	WerrorS("more than one ordering c/C specified");
4346	return TRUE;
4347	}
4348
4349	// initialize fields of R
4350	R->order=(int )omAlloc0(nsizeof(int));
4351	R->block0=(int )omAlloc0(nsizeof(int));
4352	R->block1=(int )omAlloc0(nsizeof(int));
4353	R->wvhdl=(int*)omAlloc0(nsizeof(int_ptr));
4354
4355	int weights=(int)omAlloc0((R->N+1)*sizeof(int));
4356
4357	// init order, so that rBlocks works correctly
4358	for (j=0; j < n-1; j++)
4359	R->order[j] = (int) ringorder_unspec;
4360	// set last _C order, if no c/C order was given
4361	if (i == 0) R->order[n-2] = ringorder_C;
4362
4363	/* init orders */
4364	sl=ord;
4365	n=-1;
4366	while (sl!=NULL)
4367	{
4368	intvec *iv;
4369	iv = (intvec *)(sl->data);
4370	if ((*iv)[1]!=ringorder_L)
4371	{
4372	n++;
4373
4374	/* the format of an ordering:
4375	* iv[0]: factor
4376	* iv[1]: ordering
4377	* iv[2..end]: weights
4378	*/
4379	R->order[n] = (*iv)[1];
4380	typ=1;
4381	switch ((*iv)[1])
4382	{
4383	case ringorder_ws:
4384	case ringorder_Ws:
4385	typ=-1;
4386	case ringorder_wp:
4387	case ringorder_Wp:
4388	R->wvhdl[n]=(int)omAlloc((iv->length()-1)sizeof(int));
4389	R->block0[n] = last+1;
4390	for (i=2; i<iv->length(); i++)
4391	{
4392	R->wvhdl[n][i-2] = (*iv)[i];
4393	last++;
4394	if (weights[last]==0) weights[last]=(iv)[i]typ;
4395	}
4396	R->block1[n] = last;
4397	break;
4398	case ringorder_ls:
4399	case ringorder_ds:
4400	case ringorder_Ds:
4401	case ringorder_rs:
4402	typ=-1;
4403	case ringorder_lp:
4404	case ringorder_dp:
4405	case ringorder_Dp:
4406	case ringorder_rp:
4407	R->block0[n] = last+1;
4408	if (iv->length() == 3) last+=(*iv)[2];
4409	else last += (*iv)[0];
4410	R->block1[n] = last;
4411	if (R->block0[n]>R->block1[n]) return TRUE;
4412	if (rCheckIV(iv)) return TRUE;
4413	for(i=R->block0[n];i<=R->block1[n];i++)
4414	{
4415	if (weights[i]==0) weights[i]=typ;
4416	}
4417	break;
4418	case ringorder_S:
4419	case ringorder_c:
4420	case ringorder_C:
4421	if (rCheckIV(iv)) return TRUE;
4422	break;
4423	case ringorder_aa:
4424	case ringorder_a:
4425	R->block0[n] = last+1;
4426	R->block1[n] = si_min(last+iv->length()-2 , R->N);
4427	R->wvhdl[n] = (int)omAlloc((iv->length()-1)sizeof(int));
4428	for (i=2; i<iv->length(); i++)
4429	{
4430	R->wvhdl[n][i-2]=(*iv)[i];
4431	last++;
4432	if (weights[last]==0) weights[last]=(iv)[i]typ;
4433	}
4434	last=R->block0[n]-1;
4435	break;
4436	case ringorder_a64:
4437	{
4438	R->block0[n] = last+1;
4439	R->block1[n] = si_min(last+iv->length()-2 , R->N);
4440	R->wvhdl[n] = (int)omAlloc((iv->length()-1)sizeof(int64));
4441	int64 w=(int64 )R->wvhdl[n];
4442	for (i=2; i<iv->length(); i++)
4443	{
4444	w[i-2]=(*iv)[i];
4445	last++;
4446	if (weights[last]==0) weights[last]=(iv)[i]typ;
4447	}
4448	last=R->block0[n]-1;
4449	break;
4450	}
4451	case ringorder_M:
4452	{
4453	int Mtyp=rTypeOfMatrixOrder(iv);
4454	if (Mtyp==0) return TRUE;
4455	if (Mtyp==-1) typ = -1;
4456
4457	R->wvhdl[n] =( int )omAlloc((iv->length()-1)sizeof(int));
4458	for (i=2; i<iv->length();i++)
4459	R->wvhdl[n][i-2]=(*iv)[i];
4460
4461	R->block0[n] = last+1;
4462	last += (int)sqrt((double)(iv->length()-2));
4463	R->block1[n] = last;
4464	for(i=R->block0[n];i<=R->block1[n];i++)
4465	{
4466	if (weights[i]==0) weights[i]=typ;
4467	}
4468	break;
4469	}
4470
4471	case ringorder_no:
4472	R->order[n] = ringorder_unspec;
4473	return TRUE;
4474
4475	default:
4476	Werror("Internal Error: Unknown ordering %d", (*iv)[1]);
4477	R->order[n] = ringorder_unspec;
4478	return TRUE;
4479	}
4480	}
4481	sl=sl->next;
4482	}
4483
4484	// check for complete coverage
4485	if ((R->order[n]==ringorder_c) \|\| (R->order[n]==ringorder_C)) n--;
4486	if (R->block1[n] != R->N)
4487	{
4488	if (((R->order[n]==ringorder_dp) \|\|
4489	(R->order[n]==ringorder_ds) \|\|
4490	(R->order[n]==ringorder_Dp) \|\|
4491	(R->order[n]==ringorder_Ds) \|\|
4492	(R->order[n]==ringorder_rp) \|\|
4493	(R->order[n]==ringorder_rs) \|\|
4494	(R->order[n]==ringorder_lp) \|\|
4495	(R->order[n]==ringorder_ls))
4496	&&
4497	R->block0[n] <= R->N)
4498	{
4499	R->block1[n] = R->N;
4500	}
4501	else
4502	{
4503	Werror("mismatch of number of vars (%d) and ordering (%d vars)",
4504	R->N,R->block1[n]);
4505	return TRUE;
4506	}
4507	}
4508	// find OrdSgn:
4509	R->OrdSgn = 1;
4510	for(i=1;i<=R->N;i++)
4511	{ if (weights[i]<0) { R->OrdSgn=-1;break; }}
4512	omFree(weights);
4513	return FALSE;
4514	}
4515
4516	BOOLEAN rSleftvList2StringArray(sleftv* sl, char** p)
4517	{
4518
4519	while(sl!=NULL)
4520	{
4521	if (sl->Name() == sNoName)
4522	{
4523	if (sl->Typ()==POLY_CMD)
4524	{
4525	sleftv s_sl;
4526	iiConvert(POLY_CMD,ANY_TYPE,-1,sl,&s_sl);
4527	if (s_sl.Name() != sNoName)
4528	*p = omStrDup(s_sl.Name());
4529	else
4530	*p = NULL;
4531	sl->next = s_sl.next;
4532	s_sl.next = NULL;
4533	s_sl.CleanUp();
4534	if (*p == NULL) return TRUE;
4535	}
4536	else
4537	return TRUE;
4538	}
4539	else
4540	*p = omStrDup(sl->Name());
4541	p++;
4542	sl=sl->next;
4543	}
4544	return FALSE;
4545	}
4546
4547	////////////////////
4548	//
4549	// rInit itself:
4550	//
4551	// INPUT: s: name, pn: ch & parameter (names), rv: variable (names)
4552	// ord: ordering
4553	// RETURN: currRingHdl on success
4554	// NULL on error
4555	// NOTE: * makes new ring to current ring, on success
4556	// * considers input sleftv's as read-only
4557	//idhdl rInit(char s, sleftv pn, sleftv* rv, sleftv* ord)
4558	ring rInit(sleftv* pn, sleftv* rv, sleftv* ord)
4559	{
4560	int ch;
4561	#ifdef HAVE_RINGS
4562	unsigned int ringtype = 0;
4563	int_number ringflaga = NULL;
4564	unsigned int ringflagb = 1;
4565	#endif
4566	int float_len=0;
4567	int float_len2=0;
4568	ring R = NULL;
4569	idhdl tmp = NULL;
4570	BOOLEAN ffChar=FALSE;
4571	int typ = 1;
4572
4573	/* ch -------------------------------------------------------*/
4574	// get ch of ground field
4575	int numberOfAllocatedBlocks;
4576
4577	if (pn->Typ()==INT_CMD)
4578	{
4579	ch=(int)(long)pn->Data();
4580	}
4581	else if ((pn->name != NULL)
4582	&& ((strcmp(pn->name,"real")==0) \|\| (strcmp(pn->name,"complex")==0)))
4583	{
4584	BOOLEAN complex_flag=(strcmp(pn->name,"complex")==0);
4585	ch=-1;
4586	if ((pn->next!=NULL) && (pn->next->Typ()==INT_CMD))
4587	{
4588	float_len=(int)(long)pn->next->Data();
4589	float_len2=float_len;
4590	pn=pn->next;
4591	if ((pn->next!=NULL) && (pn->next->Typ()==INT_CMD))
4592	{
4593	float_len2=(int)(long)pn->next->Data();
4594	pn=pn->next;
4595	}
4596	}
4597	if ((pn->next==NULL) && complex_flag)
4598	{
4599	pn->next=(leftv)omAlloc0Bin(sleftv_bin);
4600	pn->next->name=omStrDup("i");
4601	}
4602	}
4603	#ifdef HAVE_RINGS
4604	else if ((pn->name != NULL) && (strcmp(pn->name, "integer") == 0))
4605	{
4606	ringflaga = (int_number) omAlloc(sizeof(MP_INT));
4607	mpz_init_set_si(ringflaga, 0);
4608	if ((pn->next!=NULL) && (pn->next->Typ()==INT_CMD))
4609	{
4610	mpz_set_ui(ringflaga, (int)(long) pn->next->Data());
4611	pn=pn->next;
4612	if ((pn->next!=NULL) && (pn->next->Typ()==INT_CMD))
4613	{
4614	ringflagb = (long) pn->next->Data();
4615	pn=pn->next;
4616	}
4617	while ((pn->next!=NULL) && (pn->next->Typ()==INT_CMD))
4618	{
4619	mpz_mul_ui(ringflaga, ringflaga, (int)(long) pn->next->Data());
4620	pn=pn->next;
4621	}
4622	}
4623	if ((mpz_cmp_ui(ringflaga, 1) == 0) && (mpz_cmp_ui(ringflaga, 0) < 0))
4624	{
4625	Werror("Wrong ground ring specification (module is 1)");
4626	goto rInitError;
4627	}
4628	if (ringflagb < 1)
4629	{
4630	Werror("Wrong ground ring specification (exponent smaller than 1");
4631	goto rInitError;
4632	}
4633	// module is 0 ---> integers
4634	if (mpz_cmp_ui(ringflaga, 0) == 0)
4635	{
4636	ch = 0;
4637	ringtype = 4;
4638	}
4639	// we have an exponent
4640	else if (ringflagb > 1)
4641	{
4642	ch = ringflagb;
4643	if ((mpz_cmp_ui(ringflaga, 2) == 0) && (ringflagb + 2 <= 8*sizeof(NATNUMBER)))
4644	{
4645	ringtype = 1; // Use Z/2^ch
4646	}
4647	else
4648	{
4649	ringtype = 3;
4650	}
4651	}
4652	// just a module m > 1
4653	else
4654	{
4655	ringtype = 2;
4656	ch = mpz_get_ui(ringflaga);
4657	}
4658	}
4659	#endif
4660	else
4661	{
4662	Werror("Wrong ground field specification");
4663	goto rInitError;
4664	}
4665	pn=pn->next;
4666
4667	#ifdef HAVE_RINGS
4668	if (ringtype > 0)
4669	{
4670	WarnS("You are using coefficient rings which are not fields.");
4671	WarnS("Please note that only limited functionality is available");
4672	WarnS("for these coefficients.");
4673	WarnS("");
4674	WarnS("The following commands are meant to work:");
4675	WarnS("- basic polynomial arithmetic");
4676	WarnS("- std");
4677	WarnS("- syz");
4678	WarnS("- lift");
4679	WarnS("- reduce");
4680	}
4681	#endif
4682
4683	int l, last;
4684	sleftv * sl;
4685	/every entry in the new ring is initialized to 0/
4686
4687	/* characteristic -----------------------------------------------*/
4688	/* input: 0 ch=0 : Q parameter=NULL ffChar=FALSE float_len
4689	* 0 1 : Q(a,...) *names FALSE
4690	* 0 -1 : R NULL FALSE 0
4691	* 0 -1 : R NULL FALSE prec. >6
4692	* 0 -1 : C *names FALSE prec. 0..?
4693	* p p : Fp NULL FALSE
4694	* p -p : Fp(a) *names FALSE
4695	* q q : GF(q=p^n) *names TRUE
4696	*/
4697	if ((ch!=-1)
4698	#ifdef HAVE_RINGS
4699	&& (ringtype == 0)
4700	#endif
4701	)
4702	{
4703	int l = 0;
4704
4705	if (((ch!=0) && (ch<2))
4706	#ifndef NV_OPS
4707	\|\| (ch > 32003)
4708	#endif
4709	)
4710	{
4711	Warn("%d is invalid characteristic of ground field. 32003 is used.", ch);
4712	ch=32003;
4713	}
4714	// load fftable, if necessary
4715	if (pn!=NULL)
4716	{
4717	while ((ch!=fftable[l]) && (fftable[l])) l++;
4718	if (fftable[l]==0) ch = IsPrime(ch);
4719	else
4720	{
4721	char m[1]={(char )sNoName};
4722	nfSetChar(ch,m);
4723	if (errorreported) goto rInitError;
4724	else ffChar=TRUE;
4725	}
4726	}
4727	else
4728	{
4729	ch = IsPrime(ch);
4730	}
4731	}
4732	// allocated ring and set ch
4733	R = (ring) omAlloc0Bin(sip_sring_bin);
4734	R->ch = ch;
4735	#ifdef HAVE_RINGS
4736	R->ringtype = ringtype;
4737	R->ringflaga = ringflaga;
4738	R->ringflagb = ringflagb;
4739	#endif
4740	if (ch == -1)
4741	{
4742	R->float_len= si_min(float_len,32767);
4743	R->float_len2= si_min(float_len2,32767);
4744	}
4745
4746	/* parameter -------------------------------------------------------*/
4747	if (pn!=NULL)
4748	{
4749	R->P=pn->listLength();
4750	//if ((ffChar\|\| (ch == 1)) && (R->P > 1))
4751	if ((R->P > 1) && (ffChar \|\| (ch == -1)))
4752	{
4753	WerrorS("too many parameters");
4754	goto rInitError;
4755	}
4756	R->parameter=(char*)omAlloc0(R->Psizeof(char_ptr));
4757	if (rSleftvList2StringArray(pn, R->parameter))
4758	{
4759	WerrorS("parameter expected");
4760	goto rInitError;
4761	}
4762	if (ch>1 && !ffChar) R->ch=-ch;
4763	else if (ch==0) R->ch=1;
4764	}
4765	else if (ffChar)
4766	{
4767	WerrorS("need one parameter");
4768	goto rInitError;
4769	}
4770	/* post-processing of field description */
4771	// we have short reals, but no short complex
4772	if ((R->ch == - 1)
4773	&& (R->parameter !=NULL)
4774	&& (R->float_len < SHORT_REAL_LENGTH))
4775	{
4776	R->float_len = SHORT_REAL_LENGTH;
4777	R->float_len2 = SHORT_REAL_LENGTH;
4778	}
4779
4780	/* names and number of variables-------------------------------------*/
4781	{
4782	int l=rv->listLength();
4783	#if SIZEOF_SHORT == 2
4784	#define MAX_SHORT 0x7fff
4785	#endif
4786	if (l>MAX_SHORT)
4787	{
4788	Werror("too many ring variables(%d), max is %d",l,MAX_SHORT);
4789	goto rInitError;
4790	}
4791	R->N = l; /rv->listLength();/
4792	}
4793	R->names = (char *)omAlloc0(R->N sizeof(char_ptr));
4794	if (rSleftvList2StringArray(rv, R->names))
4795	{
4796	WerrorS("name of ring variable expected");
4797	goto rInitError;
4798	}
4799
4800	/* check names and parameters for conflicts ------------------------- */
4801	rNameCheck(R); // conflicting variables will be renamed
4802	/* ordering -------------------------------------------------------------*/
4803	if (rSleftvOrdering2Ordering(ord, R))
4804	goto rInitError;
4805
4806	// Complete the initialization
4807	if (rComplete(R,1))
4808	goto rInitError;
4809
4810	rTest(R);
4811
4812	// try to enter the ring into the name list
4813	// need to clean up sleftv here, before this ring can be set to
4814	// new currRing or currRing can be killed beacuse new ring has
4815	// same name
4816	if (pn != NULL) pn->CleanUp();
4817	if (rv != NULL) rv->CleanUp();
4818	if (ord != NULL) ord->CleanUp();
4819	//if ((tmp = enterid(s, myynest, RING_CMD, &IDROOT))==NULL)
4820	// goto rInitError;
4821
4822	//memcpy(IDRING(tmp),R,sizeof(*R));
4823	// set current ring
4824	//omFreeBin(R, ip_sring_bin);
4825	//return tmp;
4826	return R;
4827
4828	// error case:
4829	rInitError:
4830	if (R != NULL) rDelete(R);
4831	if (pn != NULL) pn->CleanUp();
4832	if (rv != NULL) rv->CleanUp();
4833	if (ord != NULL) ord->CleanUp();
4834	return NULL;
4835	}
4836
4837	ring rSubring(ring org_ring, sleftv* rv)
4838	{
4839	ring R = rCopy0(org_ring);
4840	int perm=(int )omAlloc0((org_ring->N+1)*sizeof(int));
4841	int last = 0, o=0, n = rBlocks(org_ring), i=0, typ = 1, j;
4842
4843	/* names and number of variables-------------------------------------*/
4844	{
4845	int l=rv->listLength();
4846	if (l>MAX_SHORT)
4847	{
4848	Werror("too many ring variables(%d), max is %d",l,MAX_SHORT);
4849	goto rInitError;
4850	}
4851	R->N = l; /rv->listLength();/
4852	}
4853	omFree(R->names);
4854	R->names = (char *)omAlloc0(R->N sizeof(char_ptr));
4855	if (rSleftvList2StringArray(rv, R->names))
4856	{
4857	WerrorS("name of ring variable expected");
4858	goto rInitError;
4859	}
4860
4861	/* check names for subring in org_ring ------------------------- */
4862	{
4863	i=0;
4864
4865	for(j=0;j<R->N;j++)
4866	{
4867	for(;i<org_ring->N;i++)
4868	{
4869	if (strcmp(org_ring->names[i],R->names[j])==0)
4870	{
4871	perm[i+1]=j+1;
4872	break;
4873	}
4874	}
4875	if (i>org_ring->N)
4876	{
4877	Werror("variable %d (%s) not in basering",j+1,R->names[j]);
4878	break;
4879	}
4880	}
4881	}
4882	//Print("perm=");
4883	//for(i=1;i<org_ring->N;i++) Print("v%d -> v%d\n",i,perm[i]);
4884	/* ordering -------------------------------------------------------------*/
4885
4886	for(i=0;i<n;i++)
4887	{
4888	int min_var=-1;
4889	int max_var=-1;
4890	for(j=R->block0[i];j<=R->block1[i];j++)
4891	{
4892	if (perm[j]>0)
4893	{
4894	if (min_var==-1) min_var=perm[j];
4895	max_var=perm[j];
4896	}
4897	}
4898	if (min_var!=-1)
4899	{
4900	//Print("block %d: old %d..%d, now:%d..%d\n",
4901	// i,R->block0[i],R->block1[i],min_var,max_var);
4902	R->block0[i]=min_var;
4903	R->block1[i]=max_var;
4904	if (R->wvhdl[i]!=NULL)
4905	{
4906	omFree(R->wvhdl[i]);
4907	R->wvhdl[i]=(int)omAlloc0((max_var-min_var+1)sizeof(int));
4908	for(j=org_ring->block0[i];j<=org_ring->block1[i];j++)
4909	{
4910	if (perm[j]>0)
4911	{
4912	R->wvhdl[i][perm[j]-R->block0[i]]=
4913	org_ring->wvhdl[i][j-org_ring->block0[i]];
4914	//Print("w%d=%d (orig_w%d)\n",perm[j],R->wvhdl[i][perm[j]-R->block0[i]],j);
4915	}
4916	}
4917	}
4918	}
4919	else
4920	{
4921	if(R->block0[i]>0)
4922	{
4923	//Print("skip block %d\n",i);
4924	R->order[i]=ringorder_unspec;
4925	if (R->wvhdl[i] !=NULL) omFree(R->wvhdl[i]);
4926	R->wvhdl[i]=NULL;
4927	}
4928	//else Print("keep block %d\n",i);
4929	}
4930	}
4931	i=n-1;
4932	while(i>0)
4933	{
4934	// removed unneded blocks
4935	if(R->order[i-1]==ringorder_unspec)
4936	{
4937	for(j=i;j<=n;j++)
4938	{
4939	R->order[j-1]=R->order[j];
4940	R->block0[j-1]=R->block0[j];
4941	R->block1[j-1]=R->block1[j];
4942	if (R->wvhdl[j-1] !=NULL) omFree(R->wvhdl[j-1]);
4943	R->wvhdl[j-1]=R->wvhdl[j];
4944	}
4945	R->order[n]=ringorder_unspec;
4946	n--;
4947	}
4948	i--;
4949	}
4950	n=rBlocks(org_ring)-1;
4951	while (R->order[n]==0) n--;
4952	while (R->order[n]==ringorder_unspec) n--;
4953	if ((R->order[n]==ringorder_c) \|\| (R->order[n]==ringorder_C)) n--;
4954	if (R->block1[n] != R->N)
4955	{
4956	if (((R->order[n]==ringorder_dp) \|\|
4957	(R->order[n]==ringorder_ds) \|\|
4958	(R->order[n]==ringorder_Dp) \|\|
4959	(R->order[n]==ringorder_Ds) \|\|
4960	(R->order[n]==ringorder_rp) \|\|
4961	(R->order[n]==ringorder_rs) \|\|
4962	(R->order[n]==ringorder_lp) \|\|
4963	(R->order[n]==ringorder_ls))
4964	&&
4965	R->block0[n] <= R->N)
4966	{
4967	R->block1[n] = R->N;
4968	}
4969	else
4970	{
4971	Werror("mismatch of number of vars (%d) and ordering (%d vars) in block %d",
4972	R->N,R->block1[n],n);
4973	return NULL;
4974	}
4975	}
4976	omFree(perm);
4977	// find OrdSgn:
4978	R->OrdSgn = org_ring->OrdSgn; // IMPROVE!
4979	//for(i=1;i<=R->N;i++)
4980	//{ if (weights[i]<0) { R->OrdSgn=-1;break; }}
4981	//omFree(weights);
4982	// Complete the initialization
4983	if (rComplete(R,1))
4984	goto rInitError;
4985
4986	rTest(R);
4987
4988	if (rv != NULL) rv->CleanUp();
4989
4990	return R;
4991
4992	// error case:
4993	rInitError:
4994	if (R != NULL) rDelete(R);
4995	if (rv != NULL) rv->CleanUp();
4996	return NULL;
4997	}
4998
4999	void rKill(ring r)
5000	{
5001	if ((r->ref<=0)&&(r->order!=NULL))
5002	{
5003	#ifdef RDEBUG
5004	if (traceit &TRACE_SHOW_RINGS) Print("kill ring %lx\n",(long)r);
5005	#endif
5006	if (r->qideal!=NULL)
5007	{
5008	id_Delete(&r->qideal, r);
5009	r->qideal = NULL;
5010	}
5011	int i=1;
5012	int j;
5013	int *pi=r->order;
5014	#ifdef USE_IILOCALRING
5015	for (j=0;j<iiRETURNEXPR_len;j++)
5016	{
5017	if (iiLocalRing[j]==r)
5018	{
5019	if (j<myynest) Warn("killing the basering for level %d",j);
5020	iiLocalRing[j]=NULL;
5021	}
5022	}
5023	#else /* USE_IILOCALRING */
5024	//#endif /* USE_IILOCALRING */
5025	{
5026	proclevel * nshdl = procstack;
5027	int lev=myynest-1;
5028
5029	for(; nshdl != NULL; nshdl = nshdl->next)
5030	{
5031	if (nshdl->cRing==r)
5032	{
5033	Warn("killing the basering for level %d",lev);
5034	nshdl->cRing=NULL;
5035	nshdl->cRingHdl=NULL;
5036	}
5037	}
5038	}
5039	#endif /* USE_IILOCALRING */
5040	// any variables depending on r ?
5041	while (r->idroot!=NULL)
5042	{
5043	killhdl2(r->idroot,&(r->idroot),r);
5044	}
5045	if (r==currRing)
5046	{
5047	// all dependend stuff is done, clean global vars:
5048	if (r->qideal!=NULL)
5049	{
5050	currQuotient=NULL;
5051	}
5052	if (ppNoether!=NULL) pDelete(&ppNoether);
5053	if (sLastPrinted.RingDependend())
5054	{
5055	sLastPrinted.CleanUp();
5056	}
5057	if ((myynest>0) && (iiRETURNEXPR[myynest].RingDependend()))
5058	{
5059	WerrorS("return value depends on local ring variable (export missing ?)");
5060	iiRETURNEXPR[myynest].CleanUp();
5061	}
5062	currRing=NULL;
5063	currRingHdl=NULL;
5064	}
5065
5066	/* nKillChar(r); will be called from inside of rDelete */
5067	rDelete(r);
5068	return;
5069	}
5070	r->ref--;
5071	}
5072
5073	void rKill(idhdl h)
5074	{
5075	ring r = IDRING(h);
5076	int ref=0;
5077	if (r!=NULL)
5078	{
5079	ref=r->ref;
5080	rKill(r);
5081	}
5082	if (h==currRingHdl)
5083	{
5084	if (ref<=0) { currRing=NULL; currRingHdl=NULL;}
5085	else
5086	{
5087	currRingHdl=rFindHdl(r,currRingHdl,NULL);
5088	}
5089	}
5090	}
5091
5092	idhdl rSimpleFindHdl(ring r, idhdl root, idhdl n=NULL)
5093	{
5094	//idhdl next_best=NULL;
5095	idhdl h=root;
5096	while (h!=NULL)
5097	{
5098	if (((IDTYP(h)==RING_CMD)\|\|(IDTYP(h)==QRING_CMD))
5099	&& (h!=n)
5100	&& (IDRING(h)==r)
5101	)
5102	{
5103	// if (IDLEV(h)==myynest)
5104	// return h;
5105	// if ((IDLEV(h)==0) \|\| (next_best==NULL))
5106	// next_best=h;
5107	// else if (IDLEV(next_best)<IDLEV(h))
5108	// next_best=h;
5109	return h;
5110	}
5111	h=IDNEXT(h);
5112	}
5113	//return next_best;
5114	return NULL;
5115	}
5116
5117	extern BOOLEAN jjPROC(leftv res, leftv u, leftv v);
5118	ideal kGroebner(ideal F, ideal Q)
5119	{
5120	//test\|=Sy_bit(OPT_PROT);
5121	idhdl save_ringhdl=currRingHdl;
5122	ideal resid;
5123	idhdl new_ring=NULL;
5124	if ((currRingHdl==NULL) \|\| (IDRING(currRingHdl)!=currRing))
5125	{
5126	currRingHdl=enterid(omStrDup(" GROEBNERring"),0,RING_CMD,&IDROOT,FALSE);
5127	new_ring=currRingHdl;
5128	IDRING(currRingHdl)=currRing;
5129	}
5130	sleftv v; memset(&v,0,sizeof(v)); v.rtyp=IDEAL_CMD; v.data=(char *) F;
5131	idhdl h=ggetid("groebner",FALSE);
5132	sleftv u; memset(&u,0,sizeof(u)); u.rtyp=IDHDL; u.data=(char *) h;
5133	u.name=IDID(h);
5134
5135	sleftv res; memset(&res,0,sizeof(res));
5136	if(jjPROC(&res,&u,&v))
5137	{
5138	resid=kStd(F,Q,testHomog,NULL);
5139	}
5140	else
5141	{
5142	//printf("typ:%d\n",res.rtyp);
5143	resid=(ideal)(res.data);
5144	}
5145	// cleanup GROEBNERring, save_ringhdl, u,v,(res )
5146	if (new_ring!=NULL)
5147	{
5148	idhdl h=IDROOT;
5149	if (h==new_ring) IDROOT=h->next;
5150	else
5151	{
5152	while ((h!=NULL) &&(h->next!=new_ring)) h=h->next;
5153	if (h!=NULL) h->next=h->next->next;
5154	}
5155	if (h!=NULL) omFreeSize(h,sizeof(*h));
5156	}
5157	currRingHdl=save_ringhdl;
5158	u.CleanUp();
5159	v.CleanUp();
5160	return resid;
5161	}
5162
5163	void jjINT_S_TO_ID(int n,int *e, leftv res)
5164	{
5165	if (n==0) n=1;
5166	ideal l=idInit(n,1);
5167	int i;
5168	poly p;
5169	for(i=pVariables;i>0;i--)
5170	{
5171	if (e[i]>0)
5172	{
5173	n--;
5174	p=pOne();
5175	pSetExp(p,i,1);
5176	pSetm(p);
5177	l->m[n]=p;
5178	if (n==0) break;
5179	}
5180	}
5181	res->data=(char*)l;
5182	omFreeSize((ADDRESS)e,(pVariables+1)*sizeof(int));
5183	}
5184	BOOLEAN jjVARIABLES_P(leftv res, leftv u)
5185	{
5186	int e=(int )omAlloc0((pVariables+1)*sizeof(int));
5187	int n=pGetVariables((poly)u->Data(),e);
5188	jjINT_S_TO_ID(n,e,res);
5189	return FALSE;
5190	}
5191
5192	BOOLEAN jjVARIABLES_ID(leftv res, leftv u)
5193	{
5194	int e=(int )omAlloc0((pVariables+1)*sizeof(int));
5195	ideal I=(ideal)u->Data();
5196	int i;
5197	int n=0;
5198	for(i=I->nrows*I->ncols-1;i>=0;i--)
5199	{
5200	n=pGetVariables(I->m[i],e);
5201	}
5202	jjINT_S_TO_ID(n,e,res);
5203	return FALSE;
5204	}

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