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source: git/Singular/ipshell.cc @ c45b8f0

spielwiese

Last change on this file since c45b8f0 was c45b8f0, checked in by Frank Seelisch <seelisch@…>, 12 years ago
replaced two occ's of naSetChar by ntSetChar to fix assume viol's git-svn-id: file:///usr/local/Singular/svn/trunk@13964 2c84dea3-7e68-4137-9b89-c4e89433aadc
Property mode set to `100644`
File size: 128.5 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 <kernel/mod2.h>
16	#include <Singular/tok.h>
17	#include <kernel/options.h>
18	#include <Singular/ipid.h>
19	#include <kernel/intvec.h>
20	#include <omalloc/omalloc.h>
21	#include <kernel/febase.h>
22	#include <kernel/polys.h>
23	#include <kernel/prCopy.h>
24	#include <kernel/ideals.h>
25	#include <kernel/matpol.h>
26	#include <kernel/kstd1.h>
27	#include <kernel/ring.h>
28	#include <Singular/subexpr.h>
29	#include <kernel/maps.h>
30	#include <kernel/syz.h>
31	#include <kernel/numbers.h>
32	#include <kernel/modulop.h>
33	#include <kernel/longalg.h>
34	#include <Singular/lists.h>
35	#include <Singular/attrib.h>
36	#include <Singular/ipconv.h>
37	#include <Singular/silink.h>
38	#include <kernel/stairc.h>
39	#include <kernel/weight.h>
40	#include <kernel/semic.h>
41	#include <kernel/splist.h>
42	#include <kernel/spectrum.h>
43	#include <kernel/gnumpfl.h>
44	#include <kernel/mpr_base.h>
45	#include <kernel/ffields.h>
46	#include <kernel/clapsing.h>
47	#include <kernel/hutil.h>
48	#include <kernel/ring.h>
49	#include <Singular/ipshell.h>
50	#ifdef HAVE_FACTORY
51	#define SI_DONT_HAVE_GLOBAL_VARS
52	#include <factory/factory.h>
53	#endif
54
55	// define this if you want to use the fast_map routine for mapping ideals
56	#define FAST_MAP
57
58	#ifdef FAST_MAP
59	#include <kernel/fast_maps.h>
60	#endif
61
62	leftv iiCurrArgs=NULL;
63	idhdl iiCurrProc=NULL;
64	int traceit = 0;
65	const char *lastreserved=NULL;
66
67	int myynest = -1;
68
69	static BOOLEAN iiNoKeepRing=TRUE;
70
71	/0 implementation/
72
73	const char * iiTwoOps(int t)
74	{
75	if (t<127)
76	{
77	static char ch[2];
78	switch (t)
79	{
80	case '&':
81	return "and";
82	case '\|':
83	return "or";
84	default:
85	ch[0]=t;
86	ch[1]='\0';
87	return ch;
88	}
89	}
90	switch (t)
91	{
92	case COLONCOLON: return "::";
93	case DOTDOT: return "..";
94	//case PLUSEQUAL: return "+=";
95	//case MINUSEQUAL: return "-=";
96	case MINUSMINUS: return "--";
97	case PLUSPLUS: return "++";
98	case EQUAL_EQUAL: return "==";
99	case LE: return "<=";
100	case GE: return ">=";
101	case NOTEQUAL: return "<>";
102	default: return Tok2Cmdname(t);
103	}
104	}
105
106	static void list1(const char* s, idhdl h,BOOLEAN c, BOOLEAN fullname)
107	{
108	char buffer[22];
109	int l;
110	char buf2[128];
111
112	if(fullname) sprintf(buf2, "%s::%s", "", IDID(h));
113	else sprintf(buf2, "%s", IDID(h));
114
115	Print("%s%-20.20s [%d] ",s,buf2,IDLEV(h));
116	if (h == currRingHdl) PrintS("*");
117	PrintS(Tok2Cmdname((int)IDTYP(h)));
118
119	ipListFlag(h);
120	switch(IDTYP(h))
121	{
122	case INT_CMD: Print(" %d",IDINT(h)); break;
123	case INTVEC_CMD:Print(" (%d)",IDINTVEC(h)->length()); break;
124	case INTMAT_CMD:Print(" %d x %d",IDINTVEC(h)->rows(),IDINTVEC(h)->cols());
125	break;
126	case POLY_CMD:
127	case VECTOR_CMD:if (c)
128	{
129	PrintS(" ");wrp(IDPOLY(h));
130	if(IDPOLY(h) != NULL)
131	{
132	Print(", %d monomial(s)",pLength(IDPOLY(h)));
133	}
134	}
135	break;
136	case MODUL_CMD: Print(", rk %d", (int)(IDIDEAL(h)->rank));
137	case IDEAL_CMD: Print(", %u generator(s)",
138	IDELEMS(IDIDEAL(h))); break;
139	case MAP_CMD:
140	Print(" from %s",IDMAP(h)->preimage); break;
141	case MATRIX_CMD:Print(" %u x %u"
142	,MATROWS(IDMATRIX(h))
143	,MATCOLS(IDMATRIX(h))
144	);
145	break;
146	case PACKAGE_CMD:
147	PrintS(" (");
148	switch (IDPACKAGE(h)->language)
149	{
150	case LANG_SINGULAR: PrintS("S"); break;
151	case LANG_C: PrintS("C"); break;
152	case LANG_TOP: PrintS("T"); break;
153	case LANG_NONE: PrintS("N"); break;
154	default: PrintS("U");
155	}
156	if(IDPACKAGE(h)->libname!=NULL)
157	Print(",%s", IDPACKAGE(h)->libname);
158	PrintS(")");
159	break;
160	case PROC_CMD: if(strlen(IDPROC(h)->libname)>0)
161	Print(" from %s",IDPROC(h)->libname);
162	if(IDPROC(h)->is_static)
163	PrintS(" (static)");
164	break;
165	case STRING_CMD:
166	{
167	char *s;
168	l=strlen(IDSTRING(h));
169	memset(buffer,0,22);
170	strncpy(buffer,IDSTRING(h),si_min(l,20));
171	if ((s=strchr(buffer,'\n'))!=NULL)
172	{
173	*s='\0';
174	}
175	PrintS(" ");
176	PrintS(buffer);
177	if((s!=NULL) \|\|(l>20))
178	{
179	Print("..., %d char(s)",l);
180	}
181	break;
182	}
183	case LIST_CMD: Print(", size: %d",IDLIST(h)->nr+1);
184	break;
185	case QRING_CMD:
186	case RING_CMD:
187	if ((IDRING(h)==currRing) && (currRingHdl!=h))
188	PrintS("()"); / this is an alias to currRing */
189	#ifdef RDEBUG
190	if (traceit &TRACE_SHOW_RINGS)
191	Print(" <%lx>",(long)(IDRING(h)));
192	#endif
193	break;
194	/default: break;/
195	}
196	PrintLn();
197	}
198
199	void type_cmd(idhdl h)
200	{
201	BOOLEAN oldShortOut = FALSE;
202
203	if (currRing != NULL)
204	{
205	oldShortOut = currRing->ShortOut;
206	currRing->ShortOut = 1;
207	}
208	list1("// ",h,FALSE,FALSE);
209	if (IDTYP(h)!=INT_CMD)
210	{
211	sleftv expr;
212	memset(&expr,0,sizeof(expr));
213	expr.rtyp=IDHDL;
214	expr.name=IDID(h);
215	expr.data=(void *)h;
216	expr.Print();
217	}
218	if (currRing != NULL)
219	currRing->ShortOut = oldShortOut;
220	}
221
222	static void killlocals0(int v, idhdl * localhdl, const ring r)
223	{
224	idhdl h = *localhdl;
225	while (h!=NULL)
226	{
227	int vv;
228	//Print("consider %s, lev: %d:",IDID(h),IDLEV(h));
229	if ((vv=IDLEV(h))>0)
230	{
231	if (vv < v)
232	{
233	if (iiNoKeepRing)
234	{
235	//PrintS(" break\n");
236	return;
237	}
238	h = IDNEXT(h);
239	//PrintLn();
240	}
241	else //if (vv >= v)
242	{
243	idhdl nexth = IDNEXT(h);
244	killhdl2(h,localhdl,r);
245	h = nexth;
246	//PrintS("kill\n");
247	}
248	}
249	else
250	{
251	h = IDNEXT(h);
252	//PrintLn();
253	}
254	}
255	}
256	void killlocals_list(lists l,int v)
257	{
258	int i;
259	for(i=l->nr; i>=0; i--)
260	{
261	if (l->m[i].rtyp == LIST_CMD)
262	killlocals_list((lists)l->m[i].data,v);
263	else if ((l->m[i].rtyp == RING_CMD) \|\| (l->m[i].rtyp == QRING_CMD))
264	killlocals0(v,&(((ring)(l->m[i].data))->idroot),currRing);
265	}
266	}
267	void killlocals_rec(idhdl *root,int v, ring r)
268	{
269	idhdl h=*root;
270	while (h!=NULL)
271	{
272	if (IDLEV(h)>=v)
273	{
274	// Print("kill %s, lev %d for lev %d\n",IDID(h),IDLEV(h),v);
275	idhdl n=IDNEXT(h);
276	killhdl2(h,root,r);
277	h=n;
278	}
279	else if (IDTYP(h)==PACKAGE_CMD)
280	{
281	// Print("into pack %s, lev %d for lev %d\n",IDID(h),IDLEV(h),v);
282	if (IDPACKAGE(h)!=basePack)
283	killlocals_rec(&(IDRING(h)->idroot),v,r);
284	h=IDNEXT(h);
285	}
286	else if ((IDTYP(h)==RING_CMD)
287	\|\|(IDTYP(h)==QRING_CMD))
288	{
289	if ((IDRING(h)!=NULL) && (IDRING(h)->idroot!=NULL))
290	// we have to test IDRING(h)!=NULL: qring Q=groebner(...): killlocals
291	{
292	// Print("into ring %s, lev %d for lev %d\n",IDID(h),IDLEV(h),v);
293	killlocals_rec(&(IDRING(h)->idroot),v,IDRING(h));
294	}
295	h=IDNEXT(h);
296	}
297	else
298	{
299	// Print("skip %s lev %d for lev %d\n",IDID(h),IDLEV(h),v);
300	h=IDNEXT(h);
301	}
302	}
303	}
304	BOOLEAN killlocals_list(int v, lists L)
305	{
306	if (L==NULL) return FALSE;
307	BOOLEAN changed=FALSE;
308	int n=L->nr;
309	for(;n>=0;n--)
310	{
311	leftv h=&(L->m[n]);
312	void *d=h->data;
313	if (((h->rtyp==RING_CMD) \|\| (h->rtyp==QRING_CMD))
314	&& (((ring)d)->idroot!=NULL))
315	{
316	if (d!=currRing) {changed=TRUE;rChangeCurrRing((ring)d);}
317	killlocals0(v,&(((ring)h->data)->idroot),(ring)h->data);
318	}
319	else if (h->rtyp==LIST_CMD)
320	changed\|=killlocals_list(v,(lists)d);
321	}
322	return changed;
323	}
324	void killlocals(int v)
325	{
326	BOOLEAN changed=FALSE;
327	idhdl sh=currRingHdl;
328	ring cr=currRing;
329	if (sh!=NULL) changed=((IDLEV(sh)<v) \|\| (IDRING(sh)->ref>0));
330	//if (changed) Print("currRing=%s(%x), lev=%d,ref=%d\n",IDID(sh),IDRING(sh),IDLEV(sh),IDRING(sh)->ref);
331
332	killlocals_rec(&(basePack->idroot),v,currRing);
333
334	if (iiRETURNEXPR_len > myynest)
335	{
336	int t=iiRETURNEXPR[myynest].Typ();
337	if ((/iiRETURNEXPR[myynest].Typ()/ t==RING_CMD)
338	\|\| (/iiRETURNEXPR[myynest].Typ()/ t==QRING_CMD))
339	{
340	leftv h=&iiRETURNEXPR[myynest];
341	if (((ring)h->data)->idroot!=NULL)
342	killlocals0(v,&(((ring)h->data)->idroot),(ring)h->data);
343	}
344	else if (/iiRETURNEXPR[myynest].Typ()/ t==LIST_CMD)
345	{
346	leftv h=&iiRETURNEXPR[myynest];
347	changed \|=killlocals_list(v,(lists)h->data);
348	}
349	}
350	if (changed)
351	{
352	currRingHdl=rFindHdl(cr,NULL,NULL);
353	if (currRingHdl==NULL)
354	currRing=NULL;
355	else
356	rChangeCurrRing(cr);
357	}
358
359	if (myynest<=1) iiNoKeepRing=TRUE;
360	//Print("end killlocals >= %d\n",v);
361	//listall();
362	}
363
364	void list_cmd(int typ, const char* what, const char *prefix,BOOLEAN iterate, BOOLEAN fullname)
365	{
366	idhdl h,start;
367	BOOLEAN all = typ<0;
368	BOOLEAN really_all=FALSE;
369	BOOLEAN do_packages=FALSE;
370
371	if ( typ == -1 ) do_packages=TRUE;
372	if ( typ==0 )
373	{
374	if (strcmp(what,"all")==0)
375	{
376	really_all=TRUE;
377	h=basePack->idroot;
378	}
379	else
380	{
381	h = ggetid(what);
382	if (h!=NULL)
383	{
384	if (iterate) list1(prefix,h,TRUE,fullname);
385	if (IDTYP(h)==ALIAS_CMD) PrintS("A");
386	if ((IDTYP(h)==RING_CMD)
387	\|\| (IDTYP(h)==QRING_CMD)
388	//\|\| (IDTYP(h)==PACKE_CMD)
389	)
390	{
391	h=IDRING(h)->idroot;
392	}
393	else if((IDTYP(h)==PACKAGE_CMD) \|\| (IDTYP(h)==POINTER_CMD))
394	{
395	//Print("list_cmd:package or pointer\n");
396	all=TRUE;typ=PROC_CMD;fullname=TRUE;really_all=TRUE;
397	h=IDPACKAGE(h)->idroot;
398	}
399	else
400	return;
401	}
402	else
403	{
404	Werror("%s is undefined",what);
405	return;
406	}
407	}
408	all=TRUE;
409	}
410	else if (RingDependend(typ))
411	{
412	h = currRing->idroot;
413	}
414	else
415	h = IDROOT;
416	start=h;
417	while (h!=NULL)
418	{
419	if ((all && (IDTYP(h)!=PROC_CMD) &&(IDTYP(h)!=PACKAGE_CMD))
420	\|\| (typ == IDTYP(h))
421	\|\| ((IDTYP(h)==QRING_CMD) && (typ==RING_CMD)))
422	{
423	list1(prefix,h,start==currRingHdl, fullname);
424	if (((IDTYP(h)==RING_CMD)\|\|(IDTYP(h)==QRING_CMD))
425	&& (really_all \|\| (all && (h==currRingHdl)))
426	&& ((IDLEV(h)==0)\|\|(IDLEV(h)==myynest)))
427	{
428	list_cmd(0,IDID(h),"// ",FALSE);
429	}
430	if (IDTYP(h)==PACKAGE_CMD && really_all)
431	{
432	package save_p=currPack;
433	currPack=IDPACKAGE(h);
434	list_cmd(0,IDID(h),"// ",FALSE);
435	currPack=save_p;
436	}
437	}
438	h = IDNEXT(h);
439	}
440	}
441
442	void test_cmd(int i)
443	{
444	int ii;
445
446	if (i<0)
447	{
448	ii= -i;
449	if (ii < 32)
450	{
451	test &= ~Sy_bit(ii);
452	}
453	else if (ii < 64)
454	{
455	verbose &= ~Sy_bit(ii-32);
456	}
457	else
458	WerrorS("out of bounds\n");
459	}
460	else if (i<32)
461	{
462	ii=i;
463	if (Sy_bit(ii) & kOptions)
464	{
465	Warn("Gerhard, use the option command");
466	test \|= Sy_bit(ii);
467	}
468	else if (Sy_bit(ii) & validOpts)
469	test \|= Sy_bit(ii);
470	}
471	else if (i<64)
472	{
473	ii=i-32;
474	verbose \|= Sy_bit(ii);
475	}
476	else
477	WerrorS("out of bounds\n");
478	}
479
480	int exprlist_length(leftv v)
481	{
482	int rc = 0;
483	while (v!=NULL)
484	{
485	switch (v->Typ())
486	{
487	case INT_CMD:
488	case POLY_CMD:
489	case VECTOR_CMD:
490	case NUMBER_CMD:
491	rc++;
492	break;
493	case INTVEC_CMD:
494	case INTMAT_CMD:
495	rc += ((intvec *)(v->Data()))->length();
496	break;
497	case MATRIX_CMD:
498	case IDEAL_CMD:
499	case MODUL_CMD:
500	{
501	matrix mm = (matrix)(v->Data());
502	rc += mm->rows() * mm->cols();
503	}
504	break;
505	case LIST_CMD:
506	rc+=((lists)v->Data())->nr+1;
507	break;
508	default:
509	rc++;
510	}
511	v = v->next;
512	}
513	return rc;
514	}
515
516	int iiIsPrime0(unsigned p) /* brute force !!!! */
517	{
518	unsigned i,j=0 /only to avoid compiler warnings/;
519	#ifdef HAVE_FACTORY
520	if (p<=32749) // max. small prime in factory
521	{
522	int a=0;
523	int e=cf_getNumSmallPrimes()-1;
524	i=e/2;
525	do
526	{
527	j=cf_getSmallPrime(i);
528	if (p==j) return p;
529	if (p<j) e=i-1;
530	else a=i+1;
531	i=a+(e-a)/2;
532	} while ( a<= e);
533	if (p>j) return j;
534	else return cf_getSmallPrime(i-1);
535	}
536	#endif
537	#ifdef HAVE_FACTORY
538	unsigned end_i=cf_getNumSmallPrimes()-1;
539	#else
540	unsigned end_i=p/2;
541	#endif
542	unsigned end_p=(unsigned)sqrt((double)p);
543	restart:
544	for (i=0; i<end_i; i++)
545	{
546	#ifdef HAVE_FACTORY
547	j=cf_getSmallPrime(i);
548	#else
549	if (i==0) j=2;
550	else j=2*i-1;
551	#endif
552	if ((p%j) == 0)
553	{
554	#ifdef HAVE_FACTORY
555	if (p<=32751) return iiIsPrime0(p-2);
556	#endif
557	p-=2;
558	goto restart;
559	}
560	if (j > end_p) return p;
561	}
562	#ifdef HAVE_FACTORY
563	if (i>=end_i)
564	{
565	while(j<=end_p)
566	{
567	j+=2;
568	if ((p%j) == 0)
569	{
570	if (p<=32751) return iiIsPrime0(p-2);
571	p-=2;
572	goto restart;
573	}
574	}
575	}
576	#endif
577	return p;
578	}
579	int IsPrime(int p) /* brute force !!!! */
580	{
581	int i,j;
582	if (p == 0) return 0;
583	else if (p == 1) return 1/1/;
584	else if ((p == 2)\|\|(p==3)) return p;
585	else if (p < 0) return 2; //(iiIsPrime0((unsigned)(-p)));
586	else if ((p & 1)==0) return iiIsPrime0((unsigned)(p-1));
587	return iiIsPrime0((unsigned)(p));
588	}
589
590	BOOLEAN iiWRITE(leftv res,leftv v)
591	{
592	sleftv vf;
593	if (iiConvert(v->Typ(),LINK_CMD,iiTestConvert(v->Typ(),LINK_CMD),v,&vf))
594	{
595	WerrorS("link expected");
596	return TRUE;
597	}
598	si_link l=(si_link)vf.Data();
599	if (vf.next == NULL)
600	{
601	WerrorS("write: need at least two arguments");
602	return TRUE;
603	}
604
605	BOOLEAN b=slWrite(l,vf.next); /* iiConvert preserves next */
606	if (b)
607	{
608	const char *s;
609	if ((l!=NULL)&&(l->name!=NULL)) s=l->name;
610	else s=sNoName;
611	Werror("cannot write to %s",s);
612	}
613	vf.CleanUp();
614	return b;
615	}
616
617	leftv iiMap(map theMap, const char * what)
618	{
619	idhdl w,r;
620	leftv v;
621	int i;
622	nMapFunc nMap;
623
624	r=IDROOT->get(theMap->preimage,myynest);
625	if ((currPack!=basePack)
626	&&((r==NULL) \|\| ((r->typ != RING_CMD) && (r->typ != QRING_CMD))))
627	r=basePack->idroot->get(theMap->preimage,myynest);
628	if ((r==NULL) && (currRingHdl!=NULL)
629	&& (strcmp(theMap->preimage,IDID(currRingHdl))==0))
630	{
631	r=currRingHdl;
632	}
633	if ((r!=NULL) && ((r->typ == RING_CMD) \|\| (r->typ== QRING_CMD)))
634	{
635	//if ((nMap=nSetMap(rInternalChar(IDRING(r)),
636	// IDRING(r)->parameter,
637	// rPar(IDRING(r)),
638	// IDRING(r)->minpoly)))
639	if ((nMap=nSetMap(IDRING(r)))==NULL)
640	{
641	if (rEqual(IDRING(r),currRing))
642	{
643	nMap=nCopy;
644	}
645	else
646	{
647	Werror("can not map from ground field of %s to current ground field",
648	theMap->preimage);
649	return NULL;
650	}
651	}
652	if (IDELEMS(theMap)<IDRING(r)->N)
653	{
654	theMap->m=(polyset)omReallocSize((ADDRESS)theMap->m,
655	IDELEMS(theMap)*sizeof(poly),
656	(IDRING(r)->N)*sizeof(poly));
657	for(i=IDELEMS(theMap);i<IDRING(r)->N;i++)
658	theMap->m[i]=NULL;
659	IDELEMS(theMap)=IDRING(r)->N;
660	}
661	if (what==NULL)
662	{
663	WerrorS("argument of a map must have a name");
664	}
665	else if ((w=IDRING(r)->idroot->get(what,myynest))!=NULL)
666	{
667	char *save_r=NULL;
668	v=(leftv)omAlloc0Bin(sleftv_bin);
669	sleftv tmpW;
670	memset(&tmpW,0,sizeof(sleftv));
671	tmpW.rtyp=IDTYP(w);
672	if (tmpW.rtyp==MAP_CMD)
673	{
674	tmpW.rtyp=IDEAL_CMD;
675	save_r=IDMAP(w)->preimage;
676	IDMAP(w)->preimage=0;
677	}
678	tmpW.data=IDDATA(w);
679	#if 0
680	if (((tmpW.rtyp==IDEAL_CMD)\|\|(tmpW.rtyp==MODUL_CMD)) && idIs0(IDIDEAL(w)))
681	{
682	v->rtyp=tmpW.rtyp;
683	v->data=idInit(IDELEMS(IDIDEAL(w)),IDIDEAL(w)->rank);
684	}
685	else
686	#endif
687	{
688	#ifdef FAST_MAP
689	if ((tmpW.rtyp==IDEAL_CMD) && (nMap==nCopy)
690	#ifdef HAVE_PLURAL
691	&& (!rIsPluralRing(currRing))
692	#endif
693	)
694	{
695	v->rtyp=IDEAL_CMD;
696	v->data=fast_map(IDIDEAL(w), IDRING(r), (ideal)theMap, currRing);
697	}
698	else
699	#endif
700	if (maApplyFetch(MAP_CMD,theMap,v,&tmpW,IDRING(r),NULL,NULL,0,nMap))
701	{
702	Werror("cannot map %s(%d)",Tok2Cmdname(w->typ),w->typ);
703	omFreeBin((ADDRESS)v, sleftv_bin);
704	if (save_r!=NULL) IDMAP(w)->preimage=save_r;
705	return NULL;
706	}
707	}
708	if (save_r!=NULL)
709	{
710	IDMAP(w)->preimage=save_r;
711	IDMAP((idhdl)v)->preimage=omStrDup(save_r);
712	v->rtyp=MAP_CMD;
713	}
714	return v;
715	}
716	else
717	{
718	Werror("%s undefined in %s",what,theMap->preimage);
719	}
720	}
721	else
722	{
723	Werror("cannot find preimage %s",theMap->preimage);
724	}
725	return NULL;
726	}
727
728	#ifdef OLD_RES
729	void iiMakeResolv(resolvente r, int length, int rlen, char * name, int typ0,
730	intvec ** weights)
731	{
732	lists L=liMakeResolv(r,length,rlen,typ0,weights);
733	int i=0;
734	idhdl h;
735	char * s=(char *)omAlloc(strlen(name)+5);
736
737	while (i<=L->nr)
738	{
739	sprintf(s,"%s(%d)",name,i+1);
740	if (i==0)
741	h=enterid(s,myynest,typ0,&(currRing->idroot), FALSE);
742	else
743	h=enterid(s,myynest,MODUL_CMD,&(currRing->idroot), FALSE);
744	if (h!=NULL)
745	{
746	h->data.uideal=(ideal)L->m[i].data;
747	h->attribute=L->m[i].attribute;
748	if (BVERBOSE(V_DEF_RES))
749	Print("//defining: %s as %d-th syzygy module\n",s,i+1);
750	}
751	else
752	{
753	idDelete((ideal *)&(L->m[i].data));
754	Warn("cannot define %s",s);
755	}
756	//L->m[i].data=NULL;
757	//L->m[i].rtyp=0;
758	//L->m[i].attribute=NULL;
759	i++;
760	}
761	omFreeSize((ADDRESS)L->m,(L->nr+1)*sizeof(sleftv));
762	omFreeBin((ADDRESS)L, slists_bin);
763	omFreeSize((ADDRESS)s,strlen(name)+5);
764	}
765	#endif
766
767	//resolvente iiFindRes(char * name, int * len, int *typ0)
768	//{
769	// char s=(char )omAlloc(strlen(name)+5);
770	// int i=-1;
771	// resolvente r;
772	// idhdl h;
773	//
774	// do
775	// {
776	// i++;
777	// sprintf(s,"%s(%d)",name,i+1);
778	// h=currRing->idroot->get(s,myynest);
779	// } while (h!=NULL);
780	// *len=i-1;
781	// if (*len<=0)
782	// {
783	// Werror("no objects %s(1),.. found",name);
784	// omFreeSize((ADDRESS)s,strlen(name)+5);
785	// return NULL;
786	// }
787	// r=(ideal )omAlloc(/(len+1)/ isizeof(ideal));
788	// memset(r,0,(len)sizeof(ideal));
789	// i=-1;
790	// *typ0=MODUL_CMD;
791	// while (i<(*len))
792	// {
793	// i++;
794	// sprintf(s,"%s(%d)",name,i+1);
795	// h=currRing->idroot->get(s,myynest);
796	// if (h->typ != MODUL_CMD)
797	// {
798	// if ((i!=0) \|\| (h->typ!=IDEAL_CMD))
799	// {
800	// Werror("%s is not of type module",s);
801	// omFreeSize((ADDRESS)r,(len)sizeof(ideal));
802	// omFreeSize((ADDRESS)s,strlen(name)+5);
803	// return NULL;
804	// }
805	// *typ0=IDEAL_CMD;
806	// }
807	// if ((i>0) && (idIs0(r[i-1])))
808	// {
809	// *len=i-1;
810	// break;
811	// }
812	// r[i]=IDIDEAL(h);
813	// }
814	// omFreeSize((ADDRESS)s,strlen(name)+5);
815	// return r;
816	//}
817
818	static resolvente iiCopyRes(resolvente r, int l)
819	{
820	int i;
821	resolvente res=(ideal )omAlloc0((l+1)sizeof(ideal));
822
823	for (i=0; i<l; i++)
824	res[i]=idCopy(r[i]);
825	return res;
826	}
827
828	BOOLEAN jjMINRES(leftv res, leftv v)
829	{
830	int len=0;
831	int typ0;
832	lists L=(lists)v->Data();
833	intvec weights=(intvec)atGet(v,"isHomog",INTVEC_CMD);
834	int add_row_shift = 0;
835	if (weights==NULL)
836	weights=(intvec*)atGet(&(L->m[0]),"isHomog",INTVEC_CMD);
837	if (weights!=NULL) add_row_shift=weights->min_in();
838	resolvente rr=liFindRes(L,&len,&typ0);
839	if (rr==NULL) return TRUE;
840	resolvente r=iiCopyRes(rr,len);
841
842	syMinimizeResolvente(r,len,0);
843	omFreeSize((ADDRESS)rr,len*sizeof(ideal));
844	len++;
845	res->data=(char *)liMakeResolv(r,len,-1,typ0,NULL,add_row_shift);
846	return FALSE;
847	}
848
849	BOOLEAN jjBETTI(leftv res, leftv u)
850	{
851	sleftv tmp;
852	memset(&tmp,0,sizeof(tmp));
853	tmp.rtyp=INT_CMD;
854	tmp.data=(void *)1;
855	if ((u->Typ()==IDEAL_CMD)
856	\|\| (u->Typ()==MODUL_CMD))
857	return jjBETTI2_ID(res,u,&tmp);
858	else
859	return jjBETTI2(res,u,&tmp);
860	}
861
862	BOOLEAN jjBETTI2_ID(leftv res, leftv u, leftv v)
863	{
864	lists l=(lists) omAllocBin(slists_bin);
865	l->Init(1);
866	l->m[0].rtyp=u->Typ();
867	l->m[0].data=u->Data();
868	l->m[0].attribute=u->attribute;
869	sleftv tmp2;
870	memset(&tmp2,0,sizeof(tmp2));
871	tmp2.rtyp=LIST_CMD;
872	tmp2.data=(void *)l;
873	BOOLEAN r=jjBETTI2(res,&tmp2,v);
874	l->m[0].data=NULL;
875	l->m[0].attribute=NULL;
876	l->m[0].rtyp=DEF_CMD;
877	l->Clean();
878	return r;
879	}
880
881	BOOLEAN jjBETTI2(leftv res, leftv u, leftv v)
882	{
883	resolvente r;
884	int len;
885	int reg,typ0;
886	lists l=(lists)u->Data();
887
888	intvec *weights=NULL;
889	int add_row_shift=0;
890	intvec ww=(intvec )atGet(&(l->m[0]),"isHomog",INTVEC_CMD);
891	if (ww!=NULL)
892	{
893	weights=ivCopy(ww);
894	add_row_shift = ww->min_in();
895	(*weights) -= add_row_shift;
896	}
897	//Print("attr:%x\n",weights);
898
899	r=liFindRes(l,&len,&typ0);
900	if (r==NULL) return TRUE;
901	res->data=(char *)syBetti(r,len,&reg,weights,(int)(long)v->Data());
902	omFreeSize((ADDRESS)r,(len)*sizeof(ideal));
903	atSet(res,omStrDup("rowShift"),(void*)add_row_shift,INT_CMD);
904	if (weights!=NULL) delete weights;
905	return FALSE;
906	}
907
908	int iiRegularity(lists L)
909	{
910	int len,reg,typ0;
911
912	resolvente r=liFindRes(L,&len,&typ0);
913
914	if (r==NULL)
915	return -2;
916	intvec *weights=NULL;
917	int add_row_shift=0;
918	intvec ww=(intvec )atGet(&(L->m[0]),"isHomog",INTVEC_CMD);
919	if (ww!=NULL)
920	{
921	weights=ivCopy(ww);
922	add_row_shift = ww->min_in();
923	(*weights) -= add_row_shift;
924	}
925	//Print("attr:%x\n",weights);
926
927	intvec *dummy=syBetti(r,len,&reg,weights);
928	if (weights!=NULL) delete weights;
929	delete dummy;
930	omFreeSize((ADDRESS)r,len*sizeof(ideal));
931	return reg+1+add_row_shift;
932	}
933
934	BOOLEAN iiDebugMarker=TRUE;
935	#define BREAK_LINE_LENGTH 80
936	void iiDebug()
937	{
938	Print("\n-- break point in %s --\n",VoiceName());
939	if (iiDebugMarker) VoiceBackTrack();
940	char * s;
941	iiDebugMarker=FALSE;
942	s = (char *)omAlloc(BREAK_LINE_LENGTH+4);
943	loop
944	{
945	memset(s,0,80);
946	fe_fgets_stdin("",s,BREAK_LINE_LENGTH);
947	if (s[BREAK_LINE_LENGTH-1]!='\0')
948	{
949	Print("line too long, max is %d chars\n",BREAK_LINE_LENGTH);
950	}
951	else
952	break;
953	}
954	if (*s=='\n')
955	{
956	iiDebugMarker=TRUE;
957	}
958	#if MDEBUG
959	else if(strncmp(s,"cont;",5)==0)
960	{
961	iiDebugMarker=TRUE;
962	}
963	#endif /* MDEBUG */
964	else
965	{
966	strcat( s, "\n;~\n");
967	newBuffer(s,BT_execute);
968	}
969	}
970
971	lists scIndIndset(ideal S, BOOLEAN all, ideal Q)
972	{
973	int i;
974	indset save;
975	lists res=(lists)omAlloc0Bin(slists_bin);
976
977	hexist = hInit(S, Q, &hNexist);
978	if (hNexist == 0)
979	{
980	intvec *iv=new intvec(pVariables);
981	for(i=0; i<pVariables; i++) (*iv)[i]=1;
982	res->Init(1);
983	res->m[0].rtyp=INTVEC_CMD;
984	res->m[0].data=(intvec*)iv;
985	return res;
986	}
987	else if (hisModule!=0)
988	{
989	res->Init(0);
990	return res;
991	}
992	save = ISet = (indset)omAlloc0Bin(indlist_bin);
993	hMu = 0;
994	hwork = (scfmon)omAlloc(hNexist * sizeof(scmon));
995	hvar = (varset)omAlloc((pVariables + 1) * sizeof(int));
996	hpure = (scmon)omAlloc((1 + (pVariables * pVariables)) * sizeof(long));
997	hrad = hexist;
998	hNrad = hNexist;
999	radmem = hCreate(pVariables - 1);
1000	hCo = pVariables + 1;
1001	hNvar = pVariables;
1002	hRadical(hrad, &hNrad, hNvar);
1003	hSupp(hrad, hNrad, hvar, &hNvar);
1004	if (hNvar)
1005	{
1006	hCo = hNvar;
1007	memset(hpure, 0, (pVariables + 1) * sizeof(long));
1008	hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure);
1009	hLexR(hrad, hNrad, hvar, hNvar);
1010	hDimSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar);
1011	}
1012	if (hCo && (hCo < pVariables))
1013	{
1014	hIndMult(hpure, hNpure, hrad, hNrad, hvar, hNvar);
1015	}
1016	if (hMu!=0)
1017	{
1018	ISet = save;
1019	hMu2 = 0;
1020	if (all && (hCo+1 < pVariables))
1021	{
1022	JSet = (indset)omAlloc0Bin(indlist_bin);
1023	hIndAllMult(hpure, hNpure, hrad, hNrad, hvar, hNvar);
1024	i=hMu+hMu2;
1025	res->Init(i);
1026	if (hMu2 == 0)
1027	{
1028	omFreeBin((ADDRESS)JSet, indlist_bin);
1029	}
1030	}
1031	else
1032	{
1033	res->Init(hMu);
1034	}
1035	for (i=0;i<hMu;i++)
1036	{
1037	res->m[i].data = (void *)save->set;
1038	res->m[i].rtyp = INTVEC_CMD;
1039	ISet = save;
1040	save = save->nx;
1041	omFreeBin((ADDRESS)ISet, indlist_bin);
1042	}
1043	omFreeBin((ADDRESS)save, indlist_bin);
1044	if (hMu2 != 0)
1045	{
1046	save = JSet;
1047	for (i=hMu;i<hMu+hMu2;i++)
1048	{
1049	res->m[i].data = (void *)save->set;
1050	res->m[i].rtyp = INTVEC_CMD;
1051	JSet = save;
1052	save = save->nx;
1053	omFreeBin((ADDRESS)JSet, indlist_bin);
1054	}
1055	omFreeBin((ADDRESS)save, indlist_bin);
1056	}
1057	}
1058	else
1059	{
1060	res->Init(0);
1061	omFreeBin((ADDRESS)ISet, indlist_bin);
1062	}
1063	hKill(radmem, pVariables - 1);
1064	omFreeSize((ADDRESS)hpure, (1 + (pVariables * pVariables)) * sizeof(long));
1065	omFreeSize((ADDRESS)hvar, (pVariables + 1) * sizeof(int));
1066	omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon));
1067	hDelete(hexist, hNexist);
1068	return res;
1069	}
1070
1071	int iiDeclCommand(leftv sy, leftv name, int lev,int t, idhdl* root,BOOLEAN isring, BOOLEAN init_b)
1072	{
1073	BOOLEAN res=FALSE;
1074	const char *id = name->name;
1075
1076	memset(sy,0,sizeof(sleftv));
1077	if ((name->name==NULL)\|\|(isdigit(name->name[0])))
1078	{
1079	WerrorS("object to declare is not a name");
1080	res=TRUE;
1081	}
1082	else
1083	{
1084	//if (name->rtyp!=0)
1085	//{
1086	// Warn("`%s` is already in use",name->name);
1087	//}
1088	{
1089	sy->data = (char *)enterid(id,lev,t,root,init_b);
1090	}
1091	if (sy->data!=NULL)
1092	{
1093	sy->rtyp=IDHDL;
1094	currid=sy->name=IDID((idhdl)sy->data);
1095	// name->name=NULL; /* used in enterid */
1096	//sy->e = NULL;
1097	if (name->next!=NULL)
1098	{
1099	sy->next=(leftv)omAllocBin(sleftv_bin);
1100	res=iiDeclCommand(sy->next,name->next,lev,t,root, isring);
1101	}
1102	}
1103	else res=TRUE;
1104	}
1105	name->CleanUp();
1106	return res;
1107	}
1108
1109	BOOLEAN iiDefaultParameter(leftv p)
1110	{
1111	attr at=NULL;
1112	if (iiCurrProc!=NULL)
1113	at=iiCurrProc->attribute->get("default_arg");
1114	if (at==NULL)
1115	return FALSE;
1116	sleftv tmp;
1117	memset(&tmp,0,sizeof(sleftv));
1118	tmp.rtyp=at->atyp;
1119	tmp.data=at->CopyA();
1120	return iiAssign(p,&tmp);
1121	}
1122	BOOLEAN iiParameter(leftv p)
1123	{
1124	if (iiCurrArgs==NULL)
1125	{
1126	if (strcmp(p->name,"#")==0)
1127	return iiDefaultParameter(p);
1128	Werror("not enough arguments for proc %s",VoiceName());
1129	p->CleanUp();
1130	return TRUE;
1131	}
1132	leftv h=iiCurrArgs;
1133	if (strcmp(p->name,"#")==0)
1134	{
1135	iiCurrArgs=NULL;
1136	}
1137	else
1138	{
1139	iiCurrArgs=h->next;
1140	h->next=NULL;
1141	}
1142	BOOLEAN res=iiAssign(p,h);
1143	h->CleanUp();
1144	omFreeBin((ADDRESS)h, sleftv_bin);
1145	return res;
1146	}
1147	BOOLEAN iiAlias(leftv p)
1148	{
1149	if (iiCurrArgs==NULL)
1150	{
1151	Werror("not enough arguments for proc %s",VoiceName());
1152	p->CleanUp();
1153	return TRUE;
1154	}
1155	leftv h=iiCurrArgs;
1156	iiCurrArgs=h->next;
1157	h->next=NULL;
1158	if (h->rtyp!=IDHDL)
1159	{
1160	WerrorS("identifier required");
1161	return TRUE;
1162	}
1163	if (h->Typ()!=p->Typ())
1164	{
1165	WerrorS("type mismatch");
1166	return TRUE;
1167	}
1168	idhdl pp=(idhdl)p->data;
1169	switch(pp->typ)
1170	{
1171	case INT_CMD:
1172	break;
1173	case INTVEC_CMD:
1174	case INTMAT_CMD:
1175	delete IDINTVEC(pp);
1176	break;
1177	case NUMBER_CMD:
1178	nDelete(&IDNUMBER(pp));
1179	break;
1180	case BIGINT_CMD:
1181	nlDelete(&IDNUMBER(pp),currRing);
1182	break;
1183	case MAP_CMD:
1184	{
1185	map im = IDMAP(pp);
1186	omFree((ADDRESS)im->preimage);
1187	}
1188	// continue as ideal:
1189	case IDEAL_CMD:
1190	case MODUL_CMD:
1191	case MATRIX_CMD:
1192	idDelete(&IDIDEAL(pp));
1193	break;
1194	case PROC_CMD:
1195	case RESOLUTION_CMD:
1196	case STRING_CMD:
1197	omFree((ADDRESS)IDSTRING(pp));
1198	break;
1199	case LIST_CMD:
1200	IDLIST(pp)->Clean();
1201	break;
1202	case LINK_CMD:
1203	omFreeBin(IDLINK(pp),sip_link_bin);
1204	break;
1205	// case ring: cannot happen
1206	default:
1207	Werror("unknown type %d",p->Typ());
1208	return TRUE;
1209	}
1210	pp->typ=ALIAS_CMD;
1211	IDDATA(pp)=(char*)h->data;
1212	h->CleanUp();
1213	omFreeBin((ADDRESS)h, sleftv_bin);
1214	return FALSE;
1215	}
1216
1217	static BOOLEAN iiInternalExport (leftv v, int toLev)
1218	{
1219	idhdl h=(idhdl)v->data;
1220	//Print("iiInternalExport('%s',%d)%s\n", v->name, toLev,"");
1221	if (IDLEV(h)==0) Warn("`%s` is already global",IDID(h));
1222	else
1223	{
1224	h=IDROOT->get(v->name,toLev);
1225	idhdl *root=&IDROOT;
1226	if ((h==NULL)&&(currRing!=NULL))
1227	{
1228	h=currRing->idroot->get(v->name,toLev);
1229	root=&currRing->idroot;
1230	}
1231	BOOLEAN keepring=FALSE;
1232	if ((h!=NULL)&&(IDLEV(h)==toLev))
1233	{
1234	if (IDTYP(h)==v->Typ())
1235	{
1236	if (((IDTYP(h)==RING_CMD)\|\|(IDTYP(h)==QRING_CMD))
1237	&& (v->Data()==IDDATA(h)))
1238	{
1239	IDRING(h)->ref++;
1240	keepring=TRUE;
1241	IDLEV(h)=toLev;
1242	//WarnS("keepring");
1243	return FALSE;
1244	}
1245	if (BVERBOSE(V_REDEFINE))
1246	{
1247	Warn("redefining %s",IDID(h));
1248	}
1249	#ifdef USE_IILOCALRING
1250	if (iiLocalRing[0]==IDRING(h) && (!keepring)) iiLocalRing[0]=NULL;
1251	#else
1252	proclevel *p=procstack;
1253	while (p->next!=NULL) p=p->next;
1254	if ((p->cRing==IDRING(h)) && (!keepring))
1255	{
1256	p->cRing=NULL;
1257	p->cRingHdl=NULL;
1258	}
1259	#endif
1260	killhdl2(h,root,currRing);
1261	}
1262	else
1263	{
1264	return TRUE;
1265	}
1266	}
1267	h=(idhdl)v->data;
1268	IDLEV(h)=toLev;
1269	if (keepring) IDRING(h)->ref--;
1270	iiNoKeepRing=FALSE;
1271	//Print("export %s\n",IDID(h));
1272	}
1273	return FALSE;
1274	}
1275
1276	BOOLEAN iiInternalExport (leftv v, int toLev, idhdl roothdl)
1277	{
1278	idhdl h=(idhdl)v->data;
1279	if(h==NULL)
1280	{
1281	Warn("'%s': no such identifier\n", v->name);
1282	return FALSE;
1283	}
1284	package frompack=v->req_packhdl;
1285	if (frompack==NULL) frompack=currPack;
1286	package rootpack = IDPACKAGE(roothdl);
1287	// Print("iiInternalExport('%s',%d,%s->%s) typ:%d\n", v->name, toLev, IDID(currPackHdl),IDID(roothdl),v->Typ());
1288	if ((RingDependend(IDTYP(h)))
1289	\|\| ((IDTYP(h)==LIST_CMD)
1290	&& (lRingDependend(IDLIST(h)))
1291	)
1292	)
1293	{
1294	//Print("// ==> Ringdependent set nesting to 0\n");
1295	return (iiInternalExport(v, toLev));
1296	}
1297	else
1298	{
1299	IDLEV(h)=toLev;
1300	v->req_packhdl=rootpack;
1301	if (h==frompack->idroot)
1302	{
1303	frompack->idroot=h->next;
1304	}
1305	else
1306	{
1307	idhdl hh=frompack->idroot;
1308	while ((hh!=NULL) && (hh->next!=h))
1309	hh=hh->next;
1310	if ((hh!=NULL) && (hh->next==h))
1311	hh->next=h->next;
1312	else
1313	{
1314	Werror("`%s` not found",v->Name());
1315	return TRUE;
1316	}
1317	}
1318	h->next=rootpack->idroot;
1319	rootpack->idroot=h;
1320	}
1321	return FALSE;
1322	}
1323
1324	BOOLEAN iiExport (leftv v, int toLev)
1325	{
1326	#ifndef NDEBUG
1327	checkall();
1328	#endif
1329	BOOLEAN nok=FALSE;
1330	leftv r=v;
1331	while (v!=NULL)
1332	{
1333	if ((v->name==NULL)\|\|(v->rtyp==0)\|\|(v->e!=NULL))
1334	{
1335	WerrorS("cannot export");
1336	nok=TRUE;
1337	}
1338	else
1339	{
1340	if(iiInternalExport(v, toLev))
1341	{
1342	r->CleanUp();
1343	return TRUE;
1344	}
1345	}
1346	v=v->next;
1347	}
1348	r->CleanUp();
1349	#ifndef NDEBUG
1350	checkall();
1351	#endif
1352	return nok;
1353	}
1354
1355	/assume root!=idroot/
1356	BOOLEAN iiExport (leftv v, int toLev, idhdl root)
1357	{
1358	#ifndef NDEBUG
1359	checkall();
1360	#endif
1361	// Print("iiExport1: pack=%s\n",IDID(root));
1362	package pack=IDPACKAGE(root);
1363	BOOLEAN nok=FALSE;
1364	leftv rv=v;
1365	while (v!=NULL)
1366	{
1367	if ((v->name==NULL)\|\|(v->rtyp==0)\|\|(v->e!=NULL)
1368	)
1369	{
1370	WerrorS("cannot export");
1371	nok=TRUE;
1372	}
1373	else
1374	{
1375	idhdl old=pack->idroot->get( v->name,toLev);
1376	if (old!=NULL)
1377	{
1378	if ((pack==currPack) && (old==(idhdl)v->data))
1379	{
1380	Warn("`%s` is already global",IDID(old));
1381	break;
1382	}
1383	else if (IDTYP(old)==v->Typ())
1384	{
1385	if (BVERBOSE(V_REDEFINE))
1386	{
1387	Warn("redefining %s",IDID(old));
1388	}
1389	v->name=omStrDup(v->name);
1390	killhdl2(old,&(pack->idroot),currRing);
1391	}
1392	else
1393	{
1394	rv->CleanUp();
1395	return TRUE;
1396	}
1397	}
1398	//Print("iiExport: pack=%s\n",IDID(root));
1399	if(iiInternalExport(v, toLev, root))
1400	{
1401	rv->CleanUp();
1402	return TRUE;
1403	}
1404	}
1405	v=v->next;
1406	}
1407	rv->CleanUp();
1408	#ifndef NDEBUG
1409	checkall();
1410	#endif
1411	return nok;
1412	}
1413
1414	BOOLEAN iiCheckRing(int i)
1415	{
1416	if (currRingHdl==NULL)
1417	{
1418	#ifdef SIQ
1419	if (siq<=0)
1420	{
1421	#endif
1422	if (RingDependend(i))
1423	{
1424	WerrorS("no ring active");
1425	return TRUE;
1426	}
1427	#ifdef SIQ
1428	}
1429	#endif
1430	}
1431	return FALSE;
1432	}
1433
1434	poly iiHighCorner(ideal I, int ak)
1435	{
1436	int i;
1437	if(!idIsZeroDim(I)) return NULL; // not zero-dim.
1438	poly po=NULL;
1439	if (rHasLocalOrMixedOrdering_currRing())
1440	{
1441	scComputeHC(I,currQuotient,ak,po);
1442	if (po!=NULL)
1443	{
1444	pGetCoeff(po)=nInit(1);
1445	for (i=pVariables; i>0; i--)
1446	{
1447	if (pGetExp(po, i) > 0) pDecrExp(po,i);
1448	}
1449	pSetComp(po,ak);
1450	pSetm(po);
1451	}
1452	}
1453	else
1454	po=pOne();
1455	return po;
1456	}
1457
1458	void iiCheckPack(package &p)
1459	{
1460	if (p==basePack) return;
1461
1462	idhdl t=basePack->idroot;
1463
1464	while ((t!=NULL) && (IDTYP(t)!=PACKAGE_CMD) && (IDPACKAGE(t)!=p)) t=t->next;
1465
1466	if (t==NULL)
1467	{
1468	WarnS("package not found\n");
1469	p=basePack;
1470	}
1471	return;
1472	}
1473
1474	idhdl rDefault(const char *s)
1475	{
1476	idhdl tmp=NULL;
1477
1478	if (s!=NULL) tmp = enterid(s, myynest, RING_CMD, &IDROOT);
1479	if (tmp==NULL) return NULL;
1480
1481	if (ppNoether!=NULL) pDelete(&ppNoether);
1482	if (sLastPrinted.RingDependend())
1483	{
1484	sLastPrinted.CleanUp();
1485	memset(&sLastPrinted,0,sizeof(sleftv));
1486	}
1487
1488	ring r = IDRING(tmp);
1489
1490	r->ch = 32003;
1491	r->N = 3;
1492	/r->P = 0; Alloc0 in idhdl::set, ipid.cc/
1493	/names/
1494	r->names = (char *) omAlloc0(3 sizeof(char_ptr));
1495	r->names[0] = omStrDup("x");
1496	r->names[1] = omStrDup("y");
1497	r->names[2] = omStrDup("z");
1498	/weights: entries for 3 blocks: NULL/
1499	r->wvhdl = (int *)omAlloc0(3 sizeof(int_ptr));
1500	/order: dp,C,0/
1501	r->order = (int ) omAlloc(3 sizeof(int *));
1502	r->block0 = (int )omAlloc0(3 sizeof(int *));
1503	r->block1 = (int )omAlloc0(3 sizeof(int *));
1504	/* ringorder dp for the first block: var 1..3 */
1505	r->order[0] = ringorder_dp;
1506	r->block0[0] = 1;
1507	r->block1[0] = 3;
1508	/* ringorder C for the second block: no vars */
1509	r->order[1] = ringorder_C;
1510	/* the last block: everything is 0 */
1511	r->order[2] = 0;
1512	/polynomial ring/
1513	r->OrdSgn = 1;
1514
1515	/* complete ring intializations */
1516	rComplete(r);
1517	rSetHdl(tmp);
1518	return currRingHdl;
1519	}
1520
1521	idhdl rFindHdl(ring r, idhdl n, idhdl w)
1522	{
1523	idhdl h=rSimpleFindHdl(r,IDROOT,n);
1524	if (h!=NULL) return h;
1525	if (IDROOT!=basePack->idroot) h=rSimpleFindHdl(r,basePack->idroot,n);
1526	if (h!=NULL) return h;
1527	proclevel *p=procstack;
1528	while(p!=NULL)
1529	{
1530	if ((p->cPack!=basePack)
1531	&& (p->cPack!=currPack))
1532	h=rSimpleFindHdl(r,p->cPack->idroot,n);
1533	if (h!=NULL) return h;
1534	p=p->next;
1535	}
1536	idhdl tmp=basePack->idroot;
1537	while (tmp!=NULL)
1538	{
1539	if (IDTYP(tmp)==PACKAGE_CMD)
1540	h=rSimpleFindHdl(r,IDPACKAGE(tmp)->idroot,n);
1541	if (h!=NULL) return h;
1542	tmp=IDNEXT(tmp);
1543	}
1544	return NULL;
1545	}
1546
1547	void rDecomposeCF(leftv h,const ring r,const ring R)
1548	{
1549	lists L=(lists)omAlloc0Bin(slists_bin);
1550	L->Init(4);
1551	h->rtyp=LIST_CMD;
1552	h->data=(void *)L;
1553	// 0: char/ cf - ring
1554	// 1: list (var)
1555	// 2: list (ord)
1556	// 3: qideal
1557	// ----------------------------------------
1558	// 0: char/ cf - ring
1559	L->m[0].rtyp=INT_CMD;
1560	L->m[0].data=(void *)r->ch;
1561	// ----------------------------------------
1562	// 1: list (var)
1563	lists LL=(lists)omAlloc0Bin(slists_bin);
1564	LL->Init(r->N);
1565	int i;
1566	for(i=0; i<r->N; i++)
1567	{
1568	LL->m[i].rtyp=STRING_CMD;
1569	LL->m[i].data=(void *)omStrDup(r->names[i]);
1570	}
1571	L->m[1].rtyp=LIST_CMD;
1572	L->m[1].data=(void *)LL;
1573	// ----------------------------------------
1574	// 2: list (ord)
1575	LL=(lists)omAlloc0Bin(slists_bin);
1576	i=rBlocks(r)-1;
1577	LL->Init(i);
1578	i--;
1579	lists LLL;
1580	for(; i>=0; i--)
1581	{
1582	intvec *iv;
1583	int j;
1584	LL->m[i].rtyp=LIST_CMD;
1585	LLL=(lists)omAlloc0Bin(slists_bin);
1586	LLL->Init(2);
1587	LLL->m[0].rtyp=STRING_CMD;
1588	LLL->m[0].data=(void *)omStrDup(rSimpleOrdStr(r->order[i]));
1589	if (r->block1[i]-r->block0[i] >=0 )
1590	{
1591	j=r->block1[i]-r->block0[i];
1592	if(r->order[i]==ringorder_M) j=(j+1)*(j+1)-1;
1593	iv=new intvec(j+1);
1594	if ((r->wvhdl!=NULL) && (r->wvhdl[i]!=NULL))
1595	{
1596	for(;j>=0; j--) (*iv)[j]=r->wvhdl[i][j];
1597	}
1598	else switch (r->order[i])
1599	{
1600	case ringorder_dp:
1601	case ringorder_Dp:
1602	case ringorder_ds:
1603	case ringorder_Ds:
1604	case ringorder_lp:
1605	for(;j>=0; j--) (*iv)[j]=1;
1606	break;
1607	default: /* do nothing */;
1608	}
1609	}
1610	else
1611	{
1612	iv=new intvec(1);
1613	}
1614	LLL->m[1].rtyp=INTVEC_CMD;
1615	LLL->m[1].data=(void *)iv;
1616	LL->m[i].data=(void *)LLL;
1617	}
1618	L->m[2].rtyp=LIST_CMD;
1619	L->m[2].data=(void *)LL;
1620	// ----------------------------------------
1621	// 3: qideal
1622	L->m[3].rtyp=IDEAL_CMD;
1623	if (R->minpoly==NULL)
1624	L->m[3].data=(void *)idInit(1,1);
1625	else
1626	{
1627	ideal I=idInit(1,1);
1628	L->m[3].data=(void *)I;
1629	I->m[0]=pNSet(R->minpoly);
1630	}
1631	// ----------------------------------------
1632	}
1633	void rDecomposeC(leftv h,const ring R)
1634	/* field is R or C */
1635	{
1636	lists L=(lists)omAlloc0Bin(slists_bin);
1637	if (rField_is_long_C(R)) L->Init(3);
1638	else L->Init(2);
1639	h->rtyp=LIST_CMD;
1640	h->data=(void *)L;
1641	// 0: char/ cf - ring
1642	// 1: list (var)
1643	// 2: list (ord)
1644	// ----------------------------------------
1645	// 0: char/ cf - ring
1646	L->m[0].rtyp=INT_CMD;
1647	L->m[0].data=(void *)0;
1648	// ----------------------------------------
1649	// 1:
1650	lists LL=(lists)omAlloc0Bin(slists_bin);
1651	LL->Init(2);
1652	LL->m[0].rtyp=INT_CMD;
1653	LL->m[0].data=(void *)si_max(R->float_len,SHORT_REAL_LENGTH/2);
1654	LL->m[1].rtyp=INT_CMD;
1655	LL->m[1].data=(void *)si_max(R->float_len2,SHORT_REAL_LENGTH);
1656	L->m[1].rtyp=LIST_CMD;
1657	L->m[1].data=(void *)LL;
1658	// ----------------------------------------
1659	// 2: list (par)
1660	if (rField_is_long_C(R))
1661	{
1662	L->m[2].rtyp=STRING_CMD;
1663	L->m[2].data=(void *)omStrDup(R->parameter[0]);
1664	}
1665	// ----------------------------------------
1666	}
1667
1668	#ifdef HAVE_RINGS
1669	void rDecomposeRing(leftv h,const ring R)
1670	/* field is R or C */
1671	{
1672	lists L=(lists)omAlloc0Bin(slists_bin);
1673	if (rField_is_Ring_Z(R)) L->Init(1);
1674	else L->Init(2);
1675	h->rtyp=LIST_CMD;
1676	h->data=(void *)L;
1677	// 0: char/ cf - ring
1678	// 1: list (module)
1679	// ----------------------------------------
1680	// 0: char/ cf - ring
1681	L->m[0].rtyp=STRING_CMD;
1682	L->m[0].data=(void *)omStrDup("integer");
1683	// ----------------------------------------
1684	// 1: module
1685	if (rField_is_Ring_Z(R)) return;
1686	lists LL=(lists)omAlloc0Bin(slists_bin);
1687	LL->Init(2);
1688	LL->m[0].rtyp=BIGINT_CMD;
1689	LL->m[0].data=nlMapGMP((number) R->ringflaga);
1690	LL->m[1].rtyp=INT_CMD;
1691	LL->m[1].data=(void *) R->ringflagb;
1692	L->m[1].rtyp=LIST_CMD;
1693	L->m[1].data=(void *)LL;
1694	}
1695	#endif
1696
1697
1698	lists rDecompose(const ring r)
1699	{
1700	// sanity check: require currRing==r for rings with polynomial data
1701	if ((r!=currRing)
1702	&& ((r->minpoly!=NULL) \|\| (r->qideal!=NULL) \|\| (r->minideal!=NULL)
1703	#ifdef HAVE_PLURAL
1704	\|\| (rIsPluralRing(r))
1705	#endif
1706	))
1707	{
1708	WerrorS("ring with polynomial data must be the base ring or compatible");
1709	return NULL;
1710	}
1711	// 0: char/ cf - ring
1712	// 1: list (var)
1713	// 2: list (ord)
1714	// 3: qideal
1715	// possibly:
1716	// 4: C
1717	// 5: D
1718	lists L=(lists)omAlloc0Bin(slists_bin);
1719	if (rIsPluralRing(r))
1720	L->Init(6);
1721	else
1722	L->Init(4);
1723	// ----------------------------------------
1724	// 0: char/ cf - ring
1725	#if 1 /* TODO */
1726	if (rField_is_numeric(r))
1727	{
1728	rDecomposeC(&(L->m[0]),r);
1729	}
1730	#ifdef HAVE_RINGS
1731	else if (rField_is_Ring(r))
1732	{
1733	rDecomposeRing(&(L->m[0]),r);
1734	}
1735	#endif
1736	else if (rIsExtension(r))
1737	{
1738	if (r->algring!=NULL)
1739	rDecomposeCF(&(L->m[0]),r->algring,r);
1740	else
1741	{
1742	lists Lc=(lists)omAlloc0Bin(slists_bin);
1743	Lc->Init(4);
1744	// char:
1745	Lc->m[0].rtyp=INT_CMD;
1746	Lc->m[0].data=(void*)r->ch;
1747	// var:
1748	lists Lv=(lists)omAlloc0Bin(slists_bin);
1749	Lv->Init(1);
1750	Lv->m[0].rtyp=STRING_CMD;
1751	Lv->m[0].data=(void *)omStrDup(r->parameter[0]);
1752	Lc->m[1].rtyp=LIST_CMD;
1753	Lc->m[1].data=(void*)Lv;
1754	// ord:
1755	lists Lo=(lists)omAlloc0Bin(slists_bin);
1756	Lo->Init(1);
1757	lists Loo=(lists)omAlloc0Bin(slists_bin);
1758	Loo->Init(2);
1759	Loo->m[0].rtyp=STRING_CMD;
1760	Loo->m[0].data=(void *)omStrDup(rSimpleOrdStr(ringorder_lp));
1761	intvec iv=new intvec(1); (iv)[0]=1;
1762	Loo->m[1].rtyp=INTVEC_CMD;
1763	Loo->m[1].data=(void *)iv;
1764	Lo->m[0].rtyp=LIST_CMD;
1765	Lo->m[0].data=(void*)Loo;
1766
1767	Lc->m[2].rtyp=LIST_CMD;
1768	Lc->m[2].data=(void*)Lo;
1769	// q-ideal:
1770	Lc->m[3].rtyp=IDEAL_CMD;
1771	Lc->m[3].data=(void *)idInit(1,1);
1772	// ----------------------
1773	L->m[0].rtyp=LIST_CMD;
1774	L->m[0].data=(void*)Lc;
1775	}
1776	if (L->m[0].rtyp==0)
1777	{
1778	//omFreeBin(slists_bin,(void *)L);
1779	return NULL;
1780	}
1781	}
1782	else
1783	#endif
1784	{
1785	L->m[0].rtyp=INT_CMD;
1786	L->m[0].data=(void *)r->ch;
1787	}
1788	// ----------------------------------------
1789	// 1: list (var)
1790	lists LL=(lists)omAlloc0Bin(slists_bin);
1791	LL->Init(r->N);
1792	int i;
1793	for(i=0; i<r->N; i++)
1794	{
1795	LL->m[i].rtyp=STRING_CMD;
1796	LL->m[i].data=(void *)omStrDup(r->names[i]);
1797	}
1798	L->m[1].rtyp=LIST_CMD;
1799	L->m[1].data=(void *)LL;
1800	// ----------------------------------------
1801	// 2: list (ord)
1802	LL=(lists)omAlloc0Bin(slists_bin);
1803	i=rBlocks(r)-1;
1804	LL->Init(i);
1805	i--;
1806	lists LLL;
1807	for(; i>=0; i--)
1808	{
1809	intvec *iv;
1810	int j;
1811	LL->m[i].rtyp=LIST_CMD;
1812	LLL=(lists)omAlloc0Bin(slists_bin);
1813	LLL->Init(2);
1814	LLL->m[0].rtyp=STRING_CMD;
1815	LLL->m[0].data=(void *)omStrDup(rSimpleOrdStr(r->order[i]));
1816	if (r->block1[i]-r->block0[i] >=0 )
1817	{
1818	j=r->block1[i]-r->block0[i];
1819	if (r->order[i]==ringorder_M) j=(j+1)*(j+1)-1;
1820	iv=new intvec(j+1);
1821	if ((r->wvhdl!=NULL) && (r->wvhdl[i]!=NULL))
1822	{
1823	for(;j>=0; j--) (*iv)[j]=r->wvhdl[i][j];
1824	}
1825	else switch (r->order[i])
1826	{
1827	case ringorder_dp:
1828	case ringorder_Dp:
1829	case ringorder_ds:
1830	case ringorder_Ds:
1831	case ringorder_lp:
1832	for(;j>=0; j--) (*iv)[j]=1;
1833	break;
1834	default: /* do nothing */;
1835	}
1836	}
1837	else
1838	{
1839	iv=new intvec(1);
1840	}
1841	LLL->m[1].rtyp=INTVEC_CMD;
1842	LLL->m[1].data=(void *)iv;
1843	LL->m[i].data=(void *)LLL;
1844	}
1845	L->m[2].rtyp=LIST_CMD;
1846	L->m[2].data=(void *)LL;
1847	// ----------------------------------------
1848	// 3: qideal
1849	L->m[3].rtyp=IDEAL_CMD;
1850	if (r->qideal==NULL)
1851	L->m[3].data=(void *)idInit(1,1);
1852	else
1853	L->m[3].data=(void *)idCopy(r->qideal);
1854	// ----------------------------------------
1855	#ifdef HAVE_PLURAL // NC! in rDecompose
1856	if (rIsPluralRing(r))
1857	{
1858	L->m[4].rtyp=MATRIX_CMD;
1859	L->m[4].data=(void *)mpCopy(r->GetNC()->C);
1860	L->m[5].rtyp=MATRIX_CMD;
1861	L->m[5].data=(void *)mpCopy(r->GetNC()->D);
1862	}
1863	#endif
1864	return L;
1865	}
1866
1867	void rComposeC(lists L, ring R)
1868	/* field is R or C */
1869	{
1870	// ----------------------------------------
1871	// 0: char/ cf - ring
1872	if ((L->m[0].rtyp!=INT_CMD) \|\| (L->m[0].data!=(char *)0))
1873	{
1874	Werror("invald coeff. field description, expecting 0");
1875	return;
1876	}
1877	R->ch=-1;
1878	// ----------------------------------------
1879	// 1:
1880	if (L->m[1].rtyp!=LIST_CMD)
1881	Werror("invald coeff. field description, expecting precision list");
1882	lists LL=(lists)L->m[1].data;
1883	int r1=(int)(long)LL->m[0].data;
1884	int r2=(int)(long)LL->m[1].data;
1885	if ((r1<=SHORT_REAL_LENGTH)
1886	&& (r2=SHORT_REAL_LENGTH))
1887	{
1888	R->float_len=SHORT_REAL_LENGTH/2;
1889	R->float_len2=SHORT_REAL_LENGTH;
1890	}
1891	else
1892	{
1893	R->float_len=si_min(r1,32767);
1894	R->float_len2=si_min(r2,32767);
1895	}
1896	// ----------------------------------------
1897	// 2: list (par)
1898	if (L->nr==2)
1899	{
1900	R->P=1;
1901	if (L->m[2].rtyp!=STRING_CMD)
1902	{
1903	Werror("invald coeff. field description, expecting parameter name");
1904	return;
1905	}
1906	R->parameter=(char*)omAlloc0(R->Psizeof(char_ptr));
1907	R->parameter[0]=omStrDup((char *)L->m[2].data);
1908	}
1909	// ----------------------------------------
1910	}
1911
1912	#ifdef HAVE_RINGS
1913	void rComposeRing(lists L, ring R)
1914	/* field is R or C */
1915	{
1916	// ----------------------------------------
1917	// 0: string: integer
1918	// no further entries --> Z
1919	R->ringflaga = (int_number) omAlloc(sizeof(mpz_t));
1920	if (L->nr == 0)
1921	{
1922	mpz_init_set_ui(R->ringflaga,0);
1923	R->ringflagb = 1;
1924	}
1925	// ----------------------------------------
1926	// 1:
1927	else
1928	{
1929	if (L->m[1].rtyp!=LIST_CMD) Werror("invald data, expecting list of numbers");
1930	lists LL=(lists)L->m[1].data;
1931	mpz_init(R->ringflaga);
1932	if ((LL->nr >= 0) && LL->m[0].rtyp == BIGINT_CMD)
1933	{
1934	number ringflaga = (number) LL->m[0].data;
1935	nlGMP(ringflaga, (number) R->ringflaga);
1936	LL->m[0].data = (void *)ringflaga;
1937	}
1938	else if ((LL->nr >= 0) && LL->m[0].rtyp == INT_CMD)
1939	{
1940	mpz_set_ui(R->ringflaga,(unsigned long) LL->m[0].data);
1941	}
1942	else
1943	{
1944	mpz_set_ui(R->ringflaga,0);
1945	}
1946	if (LL->nr >= 1)
1947	{
1948	R->ringflagb = (unsigned long) LL->m[1].data;
1949	}
1950	else
1951	{
1952	R->ringflagb = 1;
1953	}
1954	}
1955	// ----------------------------------------
1956	if ((mpz_cmp_ui(R->ringflaga, 1) == 0) && (mpz_cmp_ui(R->ringflaga, 0) < 0))
1957	{
1958	Werror("Wrong ground ring specification (module is 1)");
1959	return;
1960	}
1961	if (R->ringflagb < 1)
1962	{
1963	Werror("Wrong ground ring specification (exponent smaller than 1");
1964	return;
1965	}
1966	// module is 0 ---> integers
1967	if (mpz_cmp_ui(R->ringflaga, 0) == 0)
1968	{
1969	R->ch = 0;
1970	R->ringtype = 4;
1971	}
1972	// we have an exponent
1973	else if (R->ringflagb > 1)
1974	{
1975	R->ch = R->ringflagb;
1976	if ((mpz_cmp_ui(R->ringflaga, 2) == 0) && (R->ringflagb <= 8*sizeof(NATNUMBER)))
1977	{
1978	/* this branch should be active for ringflagb = 2..32 resp. 2..64,
1979	depending on the size of a long on the respective platform */
1980	R->ringtype = 1; // Use Z/2^ch
1981	}
1982	else
1983	{
1984	R->ringtype = 3;
1985	}
1986	}
1987	// just a module m > 1
1988	else
1989	{
1990	R->ringtype = 2;
1991	R->ch = mpz_get_ui(R->ringflaga);
1992	}
1993	}
1994	#endif
1995
1996	static void rRenameVars(ring R)
1997	{
1998	int i,j;
1999	for(i=0;i<R->N-1;i++)
2000	{
2001	for(j=i+1;j<R->N;j++)
2002	{
2003	if (strcmp(R->names[i],R->names[j])==0)
2004	{
2005	Warn("name conflict var(%d) and var(%d): `%s`, rename to `@(%d)`",i+1,j+1,R->names[i],j+1);
2006	omFree(R->names[j]);
2007	R->names[j]=(char *)omAlloc(10);
2008	sprintf(R->names[j],"@(%d)",j+1);
2009	}
2010	}
2011	}
2012	for(i=0;i<R->P; i++)
2013	{
2014	for(j=0;j<R->N;j++)
2015	{
2016	if (strcmp(R->parameter[i],R->names[j])==0)
2017	{
2018	Warn("name conflict par(%d) and var(%d): `%s`, rename to `@@(%d)`",i+1,j+1,R->names[j],i+1);
2019	omFree(R->parameter[i]);
2020	R->parameter[i]=(char *)omAlloc(10);
2021	sprintf(R->parameter[i],"@@(%d)",i+1);
2022	}
2023	}
2024	}
2025	}
2026
2027	ring rCompose(const lists L)
2028	{
2029	if ((L->nr!=3)
2030	#ifdef HAVE_PLURAL
2031	&&(L->nr!=5)
2032	#endif
2033	)
2034	return NULL;
2035	int is_gf_char=0;
2036	// 0: char/ cf - ring
2037	// 1: list (var)
2038	// 2: list (ord)
2039	// 3: qideal
2040	// possibly:
2041	// 4: C
2042	// 5: D
2043	ring R=(ring) omAlloc0Bin(sip_sring_bin);
2044	// ------------------------- VARS ---------------------------
2045	if (L->m[1].Typ()==LIST_CMD)
2046	{
2047	lists v=(lists)L->m[1].Data();
2048	R->N = v->nr+1;
2049	R->names = (char *)omAlloc0(R->N sizeof(char_ptr));
2050	int i;
2051	for(i=0;i<R->N;i++)
2052	{
2053	if (v->m[i].Typ()==STRING_CMD)
2054	R->names[i]=omStrDup((char *)v->m[i].Data());
2055	else if (v->m[i].Typ()==POLY_CMD)
2056	{
2057	poly p=(poly)v->m[i].Data();
2058	int nr=pIsPurePower(p);
2059	if (nr>0)
2060	R->names[i]=omStrDup(currRing->names[nr-1]);
2061	else
2062	{
2063	Werror("var name %d must be a string or a ring variable",i+1);
2064	goto rCompose_err;
2065	}
2066	}
2067	else
2068	{
2069	Werror("var name %d must be `string`",i+1);
2070	goto rCompose_err;
2071	}
2072	}
2073	}
2074	else
2075	{
2076	WerrorS("variable must be given as `list`");
2077	goto rCompose_err;
2078	}
2079	// ------------------------ ORDER ------------------------------
2080	if (L->m[2].Typ()==LIST_CMD)
2081	{
2082	lists v=(lists)L->m[2].Data();
2083	int n= v->nr+2;
2084	int j;
2085	// initialize fields of R
2086	R->order=(int )omAlloc0(nsizeof(int));
2087	R->block0=(int )omAlloc0(nsizeof(int));
2088	R->block1=(int )omAlloc0(nsizeof(int));
2089	R->wvhdl=(int*)omAlloc0(nsizeof(int_ptr));
2090	// init order, so that rBlocks works correctly
2091	for (j=0; j < n-1; j++)
2092	R->order[j] = (int) ringorder_unspec;
2093	// orderings
2094	R->OrdSgn=1;
2095	for(j=0;j<n-1;j++)
2096	{
2097	// todo: a(..), M
2098	if (v->m[j].Typ()!=LIST_CMD)
2099	{
2100	WerrorS("ordering must be list of lists");
2101	goto rCompose_err;
2102	}
2103	lists vv=(lists)v->m[j].Data();
2104	if ((vv->nr!=1)
2105	\|\| (vv->m[0].Typ()!=STRING_CMD)
2106	\|\| ((vv->m[1].Typ()!=INTVEC_CMD) && (vv->m[1].Typ()!=INT_CMD)))
2107	{
2108	WerrorS("ordering name must be a (string,intvec)");
2109	goto rCompose_err;
2110	}
2111	R->order[j]=rOrderName(omStrDup((char*)vv->m[0].Data())); // assume STRING
2112	if (j==0) R->block0[0]=1;
2113	else
2114	{
2115	int jj=j-1;
2116	while((jj>=0)
2117	&& ((R->order[jj]== ringorder_a)
2118	\|\| (R->order[jj]== ringorder_aa)
2119	\|\| (R->order[jj]== ringorder_c)
2120	\|\| (R->order[jj]== ringorder_C)
2121	))
2122	{
2123	//Print("jj=%, skip %s\n",rSimpleOrdStr(R->order[jj]));
2124	jj--;
2125	}
2126	if (jj<0) R->block0[j]=1;
2127	else R->block0[j]=R->block1[jj]+1;
2128	}
2129	intvec *iv;
2130	if (vv->m[1].Typ()==INT_CMD)
2131	iv=new intvec((int)(long)vv->m[1].Data(),(int)(long)vv->m[1].Data());
2132	else
2133	iv=ivCopy((intvec*)vv->m[1].Data()); //assume INTVEC
2134	R->block1[j]=si_max(R->block0[j],R->block0[j]+iv->length()-1);
2135	//Print("block %d from %d to %d\n",j,R->block0[j], R->block1[j]);
2136	int i;
2137	switch (R->order[j])
2138	{
2139	case ringorder_ws:
2140	case ringorder_Ws:
2141	R->OrdSgn=-1;
2142	case ringorder_aa:
2143	case ringorder_a:
2144	case ringorder_wp:
2145	case ringorder_Wp:
2146	R->wvhdl[j] =( int )omAlloc((iv->length())sizeof(int));
2147	for (i=0; i<iv->length();i++)
2148	{
2149	R->wvhdl[j][i]=(*iv)[i];
2150	}
2151	break;
2152	case ringorder_M:
2153	R->wvhdl[j] =( int )omAlloc((iv->length())sizeof(int));
2154	for (i=0; i<iv->length();i++) R->wvhdl[j][i]=(*iv)[i];
2155	R->block1[j]=si_max(R->block0[j],R->block0[j]+(int)sqrt((double)(iv->length()-1)));
2156	break;
2157	case ringorder_ls:
2158	case ringorder_ds:
2159	case ringorder_Ds:
2160	case ringorder_rs:
2161	R->OrdSgn=-1;
2162	case ringorder_lp:
2163	case ringorder_dp:
2164	case ringorder_Dp:
2165	case ringorder_rp:
2166	break;
2167	case ringorder_S:
2168	break;
2169	case ringorder_c:
2170	case ringorder_C:
2171	R->block1[j]=R->block0[j]=0;
2172	break;
2173	case 0:
2174	case ringorder_unspec:
2175	break;
2176	}
2177	delete iv;
2178	}
2179	// sanity check
2180	j=n-2;
2181	if ((R->order[j]==ringorder_c)
2182	\|\| (R->order[j]==ringorder_C)
2183	\|\| (R->order[j]==ringorder_unspec)) j--;
2184	if (R->block1[j] != R->N)
2185	{
2186	if (((R->order[j]==ringorder_dp) \|\|
2187	(R->order[j]==ringorder_ds) \|\|
2188	(R->order[j]==ringorder_Dp) \|\|
2189	(R->order[j]==ringorder_Ds) \|\|
2190	(R->order[j]==ringorder_rp) \|\|
2191	(R->order[j]==ringorder_rs) \|\|
2192	(R->order[j]==ringorder_lp) \|\|
2193	(R->order[j]==ringorder_ls))
2194	&&
2195	R->block0[j] <= R->N)
2196	{
2197	R->block1[j] = R->N;
2198	}
2199	else
2200	{
2201	Werror("ordering incomplete: size (%d) should be %d",R->block1[j],R->N);
2202	goto rCompose_err;
2203	}
2204	}
2205	}
2206	else
2207	{
2208	WerrorS("ordering must be given as `list`");
2209	goto rCompose_err;
2210	}
2211	// ------------------------------------------------------------------
2212	// 0: char:
2213	if (L->m[0].Typ()==INT_CMD)
2214	{
2215	R->ch=(int)(long)L->m[0].Data();
2216	if (R->ch!=-1)
2217	{
2218	int l=0;
2219	if (((R->ch!=0) && (R->ch<2) && (is_gf_char=-1))
2220	#ifndef NV_OPS
2221	\|\| (R->ch > 32003)
2222	#endif
2223	\|\| ((l=IsPrime(R->ch))!=R->ch)
2224	)
2225	{
2226	Warn("%d is invalid characteristic of ground field. %d is used.", R->ch,l);
2227	R->ch=l;
2228	}
2229	}
2230	}
2231	else if (L->m[0].Typ()==LIST_CMD)
2232	{
2233	lists LL=(lists)L->m[0].Data();
2234	#ifdef HAVE_RINGS
2235	if (LL->m[0].Typ() == STRING_CMD)
2236	{
2237	rComposeRing(LL,R); /* Ring */
2238	}
2239	else
2240	#endif
2241	if (LL->nr<3)
2242	rComposeC(LL,R); /* R, long_R, long_C */
2243	else
2244	{
2245	if (LL->m[0].Typ()==INT_CMD)
2246	{
2247	int ch=(int)(long)LL->m[0].Data();
2248	while ((ch!=fftable[is_gf_char]) && (fftable[is_gf_char])) is_gf_char++;
2249	if (fftable[is_gf_char]==0) is_gf_char=-1;
2250	}
2251	if (is_gf_char==-1)
2252	{
2253	R->algring=rCompose((lists)L->m[0].Data());
2254	if (R->algring==NULL)
2255	{
2256	WerrorS("could not create rational function coefficient field");
2257	goto rCompose_err;
2258	}
2259	if (R->algring->ch>0)
2260	R->ch= -R->algring->ch;
2261	else
2262	R->ch=1;
2263	R->P=R->algring->N;
2264	R->parameter=(char*)omAlloc0(R->Psizeof(char_ptr));
2265	int i;
2266	for(i=R->P-1;i>=0;i--)
2267	R->parameter[i]=omStrDup(R->algring->names[i]);
2268	if (R->algring->qideal!=NULL)
2269	{
2270	if (IDELEMS(R->algring->qideal)==1)
2271	{
2272	R->minpoly=naInit(1,R);
2273	lnumber n=(lnumber)R->minpoly;
2274	n->z=R->algring->qideal->m[0];
2275	naMinimalPoly=n->z;
2276	R->algring->qideal->m[0]=NULL;
2277	idDelete(&(R->algring->qideal));
2278	redefineFunctionPointers();
2279	}
2280	else
2281	{
2282	WerrorS("not implemented yet.");
2283	}
2284	}
2285	}
2286	else
2287	{ // gf-char
2288	R->ch=fftable[is_gf_char];
2289	R->P=1;
2290	R->parameter=(char*)omAlloc0(1sizeof(char_ptr));
2291	R->parameter[0]=omStrDup((char*)((lists)(LL->m[1].Data()))->m[0].Data());
2292	}
2293	}
2294	}
2295	else
2296	{
2297	WerrorS("coefficient field must be described by `int` or `list`");
2298	goto rCompose_err;
2299	}
2300	rRenameVars(R);
2301	// ------------------------ Q-IDEAL ------------------------
2302	rComplete(R);
2303
2304	if (L->m[3].Typ()==IDEAL_CMD)
2305	{
2306	ideal q=(ideal)L->m[3].Data();
2307	if (q->m[0]!=NULL)
2308	{
2309	if (R->ch!=currRing->ch)
2310	{
2311	#if 0
2312	WerrorS("coefficient fields must be equal if q-ideal !=0");
2313	goto rCompose_err;
2314	#else
2315	ring orig_ring=currRing;
2316	rChangeCurrRing(R);
2317	int *perm=NULL;
2318	int *par_perm=NULL;
2319	int par_perm_size=0;
2320	nMapFunc nMap;
2321	BOOLEAN bo;
2322
2323	if ((nMap=nSetMap(orig_ring))==NULL)
2324	{
2325	if (rEqual(orig_ring,currRing))
2326	{
2327	nMap=nCopy;
2328	}
2329	else
2330	// Allow imap/fetch to be make an exception only for:
2331	if ( (rField_is_Q_a(orig_ring) && // Q(a..) -> Q(a..) \|\| Q \|\| Zp \|\| Zp(a)
2332	(rField_is_Q() \|\| rField_is_Q_a() \|\|
2333	(rField_is_Zp() \|\| rField_is_Zp_a())))
2334	\|\|
2335	(rField_is_Zp_a(orig_ring) && // Zp(a..) -> Zp(a..) \|\| Zp
2336	(rField_is_Zp(currRing, rInternalChar(orig_ring)) \|\|
2337	rField_is_Zp_a(currRing, rInternalChar(orig_ring)))) )
2338	{
2339	par_perm_size=rPar(orig_ring);
2340	BITSET save_test=test;
2341	ntSetChar(rInternalChar(orig_ring),orig_ring);
2342	nSetChar(currRing);
2343	test=save_test;
2344	}
2345	else
2346	{
2347	WerrorS("coefficient fields must be equal if q-ideal !=0");
2348	goto rCompose_err;
2349	}
2350	}
2351	perm=(int )omAlloc0((orig_ring->N+1)sizeof(int));
2352	if (par_perm_size!=0)
2353	par_perm=(int )omAlloc0(par_perm_sizesizeof(int));
2354	int i;
2355	#if 0
2356	// use imap:
2357	maFindPerm(orig_ring->names,orig_ring->N,orig_ring->parameter,orig_ring->P,
2358	currRing->names,currRing->N,currRing->parameter, currRing->P,
2359	perm,par_perm, currRing->ch);
2360	#else
2361	// use fetch
2362	if ((rPar(orig_ring)>0) && (rPar(currRing)==0))
2363	{
2364	for(i=si_min(rPar(orig_ring),rVar(currRing))-1;i>=0;i--) par_perm[i]=i+1;
2365	}
2366	else if (par_perm_size!=0)
2367	for(i=si_min(rPar(orig_ring),rPar(currRing))-1;i>=0;i--) par_perm[i]=-(i+1);
2368	for(i=si_min(orig_ring->N,pVariables);i>0;i--) perm[i]=i;
2369	#endif
2370	ideal dest_id=idInit(IDELEMS(q),1);
2371	for(i=IDELEMS(q)-1; i>=0; i--)
2372	{
2373	dest_id->m[i]=pPermPoly(q->m[i],perm,orig_ring,nMap,
2374	par_perm,par_perm_size);
2375	// PrintS("map:");pWrite(dest_id->m[i]);PrintLn();
2376	pTest(dest_id->m[i]);
2377	}
2378	R->qideal=dest_id;
2379	if (perm!=NULL)
2380	omFreeSize((ADDRESS)perm,(orig_ring->N+1)*sizeof(int));
2381	if (par_perm!=NULL)
2382	omFreeSize((ADDRESS)par_perm,par_perm_size*sizeof(int));
2383	rChangeCurrRing(orig_ring);
2384	#endif
2385	}
2386	else
2387	R->qideal=idrCopyR(q,currRing,R);
2388	}
2389	}
2390	else
2391	{
2392	WerrorS("q-ideal must be given as `ideal`");
2393	goto rCompose_err;
2394	}
2395
2396
2397	// ---------------------------------------------------------------
2398	#ifdef HAVE_PLURAL
2399	if (L->nr==5)
2400	{
2401	if (nc_CallPlural((matrix)L->m[4].Data(),(matrix)L->m[5].Data(),NULL,NULL,R, true)) goto rCompose_err;
2402	// takes care about non-comm. quotient! i.e. calls "nc_SetupQuotient" due to last true
2403	}
2404	#endif
2405	return R;
2406
2407	rCompose_err:
2408	if (R->N>0)
2409	{
2410	int i;
2411	if (R->names!=NULL)
2412	{
2413	i=R->N-1;
2414	while (i>=0) { if (R->names[i]!=NULL) omFree(R->names[i]); i--; }
2415	omFree(R->names);
2416	}
2417	}
2418	if (R->order!=NULL) omFree(R->order);
2419	if (R->block0!=NULL) omFree(R->block0);
2420	if (R->block1!=NULL) omFree(R->block1);
2421	if (R->wvhdl!=NULL) omFree(R->wvhdl);
2422	omFree(R);
2423	return NULL;
2424	}
2425
2426	// from matpol.cc
2427
2428	/*2
2429	* compute the jacobi matrix of an ideal
2430	*/
2431	BOOLEAN mpJacobi(leftv res,leftv a)
2432	{
2433	int i,j;
2434	matrix result;
2435	ideal id=(ideal)a->Data();
2436
2437	result =mpNew(IDELEMS(id),pVariables);
2438	for (i=1; i<=IDELEMS(id); i++)
2439	{
2440	for (j=1; j<=pVariables; j++)
2441	{
2442	MATELEM(result,i,j) = pDiff(id->m[i-1],j);
2443	}
2444	}
2445	res->data=(char *)result;
2446	return FALSE;
2447	}
2448
2449	/*2
2450	* returns the Koszul-matrix of degree d of a vectorspace with dimension n
2451	* uses the first n entrees of id, if id <> NULL
2452	*/
2453	BOOLEAN mpKoszul(leftv res,leftv c/ip/, leftv b/in/, leftv id)
2454	{
2455	int n=(int)(long)b->Data();
2456	int d=(int)(long)c->Data();
2457	int k,l,sign,row,col;
2458	matrix result;
2459	ideal temp;
2460	BOOLEAN bo;
2461	poly p;
2462
2463	if ((d>n) \|\| (d<1) \|\| (n<1))
2464	{
2465	res->data=(char *)mpNew(1,1);
2466	return FALSE;
2467	}
2468	int choise = (int)omAlloc(d*sizeof(int));
2469	if (id==NULL)
2470	temp=idMaxIdeal(1);
2471	else
2472	temp=(ideal)id->Data();
2473
2474	k = binom(n,d);
2475	l = k*d;
2476	l /= n-d+1;
2477	result =mpNew(l,k);
2478	col = 1;
2479	idInitChoise(d,1,n,&bo,choise);
2480	while (!bo)
2481	{
2482	sign = 1;
2483	for (l=1;l<=d;l++)
2484	{
2485	if (choise[l-1]<=IDELEMS(temp))
2486	{
2487	p = pCopy(temp->m[choise[l-1]-1]);
2488	if (sign == -1) p = pNeg(p);
2489	sign *= -1;
2490	row = idGetNumberOfChoise(l-1,d,1,n,choise);
2491	MATELEM(result,row,col) = p;
2492	}
2493	}
2494	col++;
2495	idGetNextChoise(d,n,&bo,choise);
2496	}
2497	if (id==NULL) idDelete(&temp);
2498
2499	res->data=(char *)result;
2500	return FALSE;
2501	}
2502
2503	// from syz1.cc
2504	/*2
2505	* read out the Betti numbers from resolution
2506	* (interpreter interface)
2507	*/
2508	BOOLEAN syBetti2(leftv res, leftv u, leftv w)
2509	{
2510	syStrategy syzstr=(syStrategy)u->Data();
2511	BOOLEAN minim=(int)(long)w->Data();
2512	int row_shift=0;
2513	int add_row_shift=0;
2514	intvec *weights=NULL;
2515	intvec ww=(intvec )atGet(u,"isHomog",INTVEC_CMD);
2516	if (ww!=NULL)
2517	{
2518	weights=ivCopy(ww);
2519	add_row_shift = ww->min_in();
2520	(*weights) -= add_row_shift;
2521	}
2522	res->data=(void *)syBettiOfComputation(syzstr,minim,&row_shift,weights);
2523	//row_shift += add_row_shift;
2524	//Print("row_shift=%d, add_row_shift=%d\n",row_shift,add_row_shift);
2525	atSet(res,omStrDup("rowShift"),(void*)add_row_shift,INT_CMD);
2526	return FALSE;
2527	}
2528	BOOLEAN syBetti1(leftv res, leftv u)
2529	{
2530	sleftv tmp;
2531	memset(&tmp,0,sizeof(tmp));
2532	tmp.rtyp=INT_CMD;
2533	tmp.data=(void *)1;
2534	return syBetti2(res,u,&tmp);
2535	}
2536
2537	/*3
2538	* converts a resolution into a list of modules
2539	*/
2540	lists syConvRes(syStrategy syzstr,BOOLEAN toDel,int add_row_shift)
2541	{
2542	if ((syzstr->fullres==NULL) && (syzstr->minres==NULL))
2543	{
2544	if (syzstr->hilb_coeffs==NULL)
2545	{
2546	syzstr->fullres = syReorder(syzstr->res,syzstr->length,syzstr);
2547	}
2548	else
2549	{
2550	syzstr->minres = syReorder(syzstr->orderedRes,syzstr->length,syzstr);
2551	syKillEmptyEntres(syzstr->minres,syzstr->length);
2552	}
2553	}
2554	resolvente tr;
2555	int typ0=IDEAL_CMD;
2556	if (syzstr->minres!=NULL)
2557	tr = syzstr->minres;
2558	else
2559	tr = syzstr->fullres;
2560	resolvente trueres=NULL;
2561	intvec ** w=NULL;
2562	if (syzstr->length>0)
2563	{
2564	trueres=(resolvente)omAlloc0((syzstr->length)*sizeof(ideal));
2565	for (int i=(syzstr->length)-1;i>=0;i--)
2566	{
2567	if (tr[i]!=NULL)
2568	{
2569	trueres[i] = idCopy(tr[i]);
2570	}
2571	}
2572	if (idRankFreeModule(trueres[0]) > 0)
2573	typ0 = MODUL_CMD;
2574	if (syzstr->weights!=NULL)
2575	{
2576	w = (intvec*)omAlloc0((syzstr->length)sizeof(intvec*));
2577	for (int i=(syzstr->length)-1;i>=0;i--)
2578	{
2579	if (syzstr->weights[i]!=NULL) w[i] = ivCopy(syzstr->weights[i]);
2580	}
2581	}
2582	}
2583	lists li = liMakeResolv(trueres,syzstr->length,syzstr->list_length,typ0,
2584	w,add_row_shift);
2585	if (w != NULL) omFreeSize(w, (syzstr->length)sizeof(intvec));
2586	if (toDel) syKillComputation(syzstr);
2587	return li;
2588	}
2589
2590	/*3
2591	* converts a list of modules into a resolution
2592	*/
2593	syStrategy syConvList(lists li,BOOLEAN toDel)
2594	{
2595	int typ0;
2596	syStrategy result=(syStrategy)omAlloc0(sizeof(ssyStrategy));
2597
2598	resolvente fr = liFindRes(li,&(result->length),&typ0,&(result->weights));
2599	if (fr != NULL)
2600	{
2601
2602	result->fullres = (resolvente)omAlloc0((result->length+1)*sizeof(ideal));
2603	for (int i=result->length-1;i>=0;i--)
2604	{
2605	if (fr[i]!=NULL)
2606	result->fullres[i] = idCopy(fr[i]);
2607	}
2608	result->list_length=result->length;
2609	omFreeSize((ADDRESS)fr,(result->length)*sizeof(ideal));
2610	}
2611	else
2612	{
2613	omFreeSize(result, sizeof(ssyStrategy));
2614	result = NULL;
2615	}
2616	if (toDel) li->Clean();
2617	return result;
2618	}
2619
2620	/*3
2621	* converts a list of modules into a minimal resolution
2622	*/
2623	syStrategy syForceMin(lists li)
2624	{
2625	int typ0;
2626	syStrategy result=(syStrategy)omAlloc0(sizeof(ssyStrategy));
2627
2628	resolvente fr = liFindRes(li,&(result->length),&typ0);
2629	result->minres = (resolvente)omAlloc0((result->length+1)*sizeof(ideal));
2630	for (int i=result->length-1;i>=0;i--)
2631	{
2632	if (fr[i]!=NULL)
2633	result->minres[i] = idCopy(fr[i]);
2634	}
2635	omFreeSize((ADDRESS)fr,(result->length)*sizeof(ideal));
2636	return result;
2637	}
2638	// from weight.cc
2639	BOOLEAN kWeight(leftv res,leftv id)
2640	{
2641	ideal F=(ideal)id->Data();
2642	intvec * iv = new intvec(pVariables);
2643	polyset s;
2644	int sl, n, i;
2645	int *x;
2646
2647	res->data=(char *)iv;
2648	s = F->m;
2649	sl = IDELEMS(F) - 1;
2650	n = pVariables;
2651	double wNsqr = (double)2.0 / (double)n;
2652	wFunctional = wFunctionalBuch;
2653	x = (int * )omAlloc(2 * (n + 1) * sizeof(int));
2654	wCall(s, sl, x, wNsqr);
2655	for (i = n; i!=0; i--)
2656	(*iv)[i-1] = x[i + n + 1];
2657	omFreeSize((ADDRESS)x, 2 * (n + 1) * sizeof(int));
2658	return FALSE;
2659	}
2660
2661	BOOLEAN kQHWeight(leftv res,leftv v)
2662	{
2663	res->data=(char *)idQHomWeight((ideal)v->Data());
2664	if (res->data==NULL)
2665	res->data=(char *)new intvec(pVariables);
2666	return FALSE;
2667	}
2668	/==============================================================/
2669	// from clapsing.cc
2670	#if 0
2671	BOOLEAN jjIS_SQR_FREE(leftv res, leftv u)
2672	{
2673	BOOLEAN b=singclap_factorize((poly)(u->CopyD()), &v, 0);
2674	res->data=(void *)b;
2675	}
2676	#endif
2677
2678	#ifdef HAVE_FACTORY
2679	BOOLEAN jjRESULTANT(leftv res, leftv u, leftv v, leftv w)
2680	{
2681	res->data=singclap_resultant((poly)u->CopyD(),(poly)v->CopyD(), (poly)w->CopyD());
2682	return errorreported;
2683	}
2684	BOOLEAN jjCHARSERIES(leftv res, leftv u)
2685	{
2686	res->data=singclap_irrCharSeries((ideal)u->Data());
2687	return (res->data==NULL);
2688	}
2689	#endif
2690
2691	// from semic.cc
2692	#ifdef HAVE_SPECTRUM
2693
2694	// ----------------------------------------------------------------------------
2695	// Initialize a spectrum deep from another spectrum
2696	// ----------------------------------------------------------------------------
2697
2698	void spectrum::copy_deep( const spectrum &spec )
2699	{
2700	mu = spec.mu;
2701	pg = spec.pg;
2702	n = spec.n;
2703
2704	copy_new( n );
2705
2706	for( int i=0; i<n; i++ )
2707	{
2708	s[i] = spec.s[i];
2709	w[i] = spec.w[i];
2710	}
2711	}
2712
2713	// ----------------------------------------------------------------------------
2714	// Initialize a spectrum deep from a singular lists
2715	// ----------------------------------------------------------------------------
2716
2717	void spectrum::copy_deep( lists l )
2718	{
2719	mu = (int)(long)(l->m[0].Data( ));
2720	pg = (int)(long)(l->m[1].Data( ));
2721	n = (int)(long)(l->m[2].Data( ));
2722
2723	copy_new( n );
2724
2725	intvec num = (intvec)l->m[3].Data( );
2726	intvec den = (intvec)l->m[4].Data( );
2727	intvec mul = (intvec)l->m[5].Data( );
2728
2729	for( int i=0; i<n; i++ )
2730	{
2731	s[i] = (Rational)((num)[i])/(Rational)((den)[i]);
2732	w[i] = (*mul)[i];
2733	}
2734	}
2735
2736	// ----------------------------------------------------------------------------
2737	// singular lists constructor for spectrum
2738	// ----------------------------------------------------------------------------
2739
2740	spectrum::spectrum( lists l )
2741	{
2742	copy_deep( l );
2743	}
2744
2745	// ----------------------------------------------------------------------------
2746	// generate a Singular lists from a spectrum
2747	// ----------------------------------------------------------------------------
2748
2749	lists spectrum::thelist( void )
2750	{
2751	lists L = (lists)omAllocBin( slists_bin);
2752
2753	L->Init( 6 );
2754
2755	intvec *num = new intvec( n );
2756	intvec *den = new intvec( n );
2757	intvec *mult = new intvec( n );
2758
2759	for( int i=0; i<n; i++ )
2760	{
2761	(*num) [i] = s[i].get_num_si( );
2762	(*den) [i] = s[i].get_den_si( );
2763	(*mult)[i] = w[i];
2764	}
2765
2766	L->m[0].rtyp = INT_CMD; // milnor number
2767	L->m[1].rtyp = INT_CMD; // geometrical genus
2768	L->m[2].rtyp = INT_CMD; // # of spectrum numbers
2769	L->m[3].rtyp = INTVEC_CMD; // numerators
2770	L->m[4].rtyp = INTVEC_CMD; // denomiantors
2771	L->m[5].rtyp = INTVEC_CMD; // multiplicities
2772
2773	L->m[0].data = (void*)mu;
2774	L->m[1].data = (void*)pg;
2775	L->m[2].data = (void*)n;
2776	L->m[3].data = (void*)num;
2777	L->m[4].data = (void*)den;
2778	L->m[5].data = (void*)mult;
2779
2780	return L;
2781	}
2782	// from spectrum.cc
2783	// ----------------------------------------------------------------------------
2784	// print out an error message for a spectrum list
2785	// ----------------------------------------------------------------------------
2786
2787	void list_error( semicState state )
2788	{
2789	switch( state )
2790	{
2791	case semicListTooShort:
2792	WerrorS( "the list is too short" );
2793	break;
2794	case semicListTooLong:
2795	WerrorS( "the list is too long" );
2796	break;
2797
2798	case semicListFirstElementWrongType:
2799	WerrorS( "first element of the list should be int" );
2800	break;
2801	case semicListSecondElementWrongType:
2802	WerrorS( "second element of the list should be int" );
2803	break;
2804	case semicListThirdElementWrongType:
2805	WerrorS( "third element of the list should be int" );
2806	break;
2807	case semicListFourthElementWrongType:
2808	WerrorS( "fourth element of the list should be intvec" );
2809	break;
2810	case semicListFifthElementWrongType:
2811	WerrorS( "fifth element of the list should be intvec" );
2812	break;
2813	case semicListSixthElementWrongType:
2814	WerrorS( "sixth element of the list should be intvec" );
2815	break;
2816
2817	case semicListNNegative:
2818	WerrorS( "first element of the list should be positive" );
2819	break;
2820	case semicListWrongNumberOfNumerators:
2821	WerrorS( "wrong number of numerators" );
2822	break;
2823	case semicListWrongNumberOfDenominators:
2824	WerrorS( "wrong number of denominators" );
2825	break;
2826	case semicListWrongNumberOfMultiplicities:
2827	WerrorS( "wrong number of multiplicities" );
2828	break;
2829
2830	case semicListMuNegative:
2831	WerrorS( "the Milnor number should be positive" );
2832	break;
2833	case semicListPgNegative:
2834	WerrorS( "the geometrical genus should be nonnegative" );
2835	break;
2836	case semicListNumNegative:
2837	WerrorS( "all numerators should be positive" );
2838	break;
2839	case semicListDenNegative:
2840	WerrorS( "all denominators should be positive" );
2841	break;
2842	case semicListMulNegative:
2843	WerrorS( "all multiplicities should be positive" );
2844	break;
2845
2846	case semicListNotSymmetric:
2847	WerrorS( "it is not symmetric" );
2848	break;
2849	case semicListNotMonotonous:
2850	WerrorS( "it is not monotonous" );
2851	break;
2852
2853	case semicListMilnorWrong:
2854	WerrorS( "the Milnor number is wrong" );
2855	break;
2856	case semicListPGWrong:
2857	WerrorS( "the geometrical genus is wrong" );
2858	break;
2859
2860	default:
2861	WerrorS( "unspecific error" );
2862	break;
2863	}
2864	}
2865	// ----------------------------------------------------------------------------
2866	// this is the main spectrum computation function
2867	// ----------------------------------------------------------------------------
2868
2869	spectrumState spectrumCompute( poly h,lists *L,int fast )
2870	{
2871	int i,j;
2872
2873	#ifdef SPECTRUM_DEBUG
2874	#ifdef SPECTRUM_PRINT
2875	#ifdef SPECTRUM_IOSTREAM
2876	cout << "spectrumCompute\n";
2877	if( fast==0 ) cout << " no optimization" << endl;
2878	if( fast==1 ) cout << " weight optimization" << endl;
2879	if( fast==2 ) cout << " symmetry optimization" << endl;
2880	#else
2881	fprintf( stdout,"spectrumCompute\n" );
2882	if( fast==0 ) fprintf( stdout," no optimization\n" );
2883	if( fast==1 ) fprintf( stdout," weight optimization\n" );
2884	if( fast==2 ) fprintf( stdout," symmetry optimization\n" );
2885	#endif
2886	#endif
2887	#endif
2888
2889	// ----------------------
2890	// check if h is zero
2891	// ----------------------
2892
2893	if( h==(poly)NULL )
2894	{
2895	return spectrumZero;
2896	}
2897
2898	// ----------------------------------
2899	// check if h has a constant term
2900	// ----------------------------------
2901
2902	if( hasConstTerm( h ) )
2903	{
2904	return spectrumBadPoly;
2905	}
2906
2907	// --------------------------------
2908	// check if h has a linear term
2909	// --------------------------------
2910
2911	if( hasLinearTerm( h ) )
2912	{
2913	*L = (lists)omAllocBin( slists_bin);
2914	(*L)->Init( 1 );
2915	(*L)->m[0].rtyp = INT_CMD; // milnor number
2916	/* (L)->m[0].data = (void)0;a -- done by Init */
2917
2918	return spectrumNoSingularity;
2919	}
2920
2921	// ----------------------------------
2922	// compute the jacobi ideal of (h)
2923	// ----------------------------------
2924
2925	ideal J = NULL;
2926	J = idInit( pVariables,1 );
2927
2928	#ifdef SPECTRUM_DEBUG
2929	#ifdef SPECTRUM_PRINT
2930	#ifdef SPECTRUM_IOSTREAM
2931	cout << "\n computing the Jacobi ideal...\n";
2932	#else
2933	fprintf( stdout,"\n computing the Jacobi ideal...\n" );
2934	#endif
2935	#endif
2936	#endif
2937
2938	for( i=0; i<pVariables; i++ )
2939	{
2940	J->m[i] = pDiff( h,i+1); //j );
2941
2942	#ifdef SPECTRUM_DEBUG
2943	#ifdef SPECTRUM_PRINT
2944	#ifdef SPECTRUM_IOSTREAM
2945	cout << " ";
2946	#else
2947	fprintf( stdout," " );
2948	#endif
2949	pWrite( J->m[i] );
2950	#endif
2951	#endif
2952	}
2953
2954	// --------------------------------------------
2955	// compute a standard basis stdJ of jac(h)
2956	// --------------------------------------------
2957
2958	#ifdef SPECTRUM_DEBUG
2959	#ifdef SPECTRUM_PRINT
2960	#ifdef SPECTRUM_IOSTREAM
2961	cout << endl;
2962	cout << " computing a standard basis..." << endl;
2963	#else
2964	fprintf( stdout,"\n" );
2965	fprintf( stdout," computing a standard basis...\n" );
2966	#endif
2967	#endif
2968	#endif
2969
2970	ideal stdJ = kStd(J,currQuotient,isNotHomog,NULL);
2971	idSkipZeroes( stdJ );
2972
2973	#ifdef SPECTRUM_DEBUG
2974	#ifdef SPECTRUM_PRINT
2975	for( i=0; i<IDELEMS(stdJ); i++ )
2976	{
2977	#ifdef SPECTRUM_IOSTREAM
2978	cout << " ";
2979	#else
2980	fprintf( stdout," " );
2981	#endif
2982
2983	pWrite( stdJ->m[i] );
2984	}
2985	#endif
2986	#endif
2987
2988	idDelete( &J );
2989
2990	// ------------------------------------------
2991	// check if the h has a singularity
2992	// ------------------------------------------
2993
2994	if( hasOne( stdJ ) )
2995	{
2996	// -------------------------------
2997	// h is smooth in the origin
2998	// return only the Milnor number
2999	// -------------------------------
3000
3001	*L = (lists)omAllocBin( slists_bin);
3002	(*L)->Init( 1 );
3003	(*L)->m[0].rtyp = INT_CMD; // milnor number
3004	/* (L)->m[0].data = (void)0;a -- done by Init */
3005
3006	return spectrumNoSingularity;
3007	}
3008
3009	// ------------------------------------------
3010	// check if the singularity h is isolated
3011	// ------------------------------------------
3012
3013	for( i=pVariables; i>0; i-- )
3014	{
3015	if( hasAxis( stdJ,i )==FALSE )
3016	{
3017	return spectrumNotIsolated;
3018	}
3019	}
3020
3021	// ------------------------------------------
3022	// compute the highest corner hc of stdJ
3023	// ------------------------------------------
3024
3025	#ifdef SPECTRUM_DEBUG
3026	#ifdef SPECTRUM_PRINT
3027	#ifdef SPECTRUM_IOSTREAM
3028	cout << "\n computing the highest corner...\n";
3029	#else
3030	fprintf( stdout,"\n computing the highest corner...\n" );
3031	#endif
3032	#endif
3033	#endif
3034
3035	poly hc = (poly)NULL;
3036
3037	scComputeHC( stdJ,currQuotient, 0,hc );
3038
3039	if( hc!=(poly)NULL )
3040	{
3041	pGetCoeff(hc) = nInit(1);
3042
3043	for( i=pVariables; i>0; i-- )
3044	{
3045	if( pGetExp( hc,i )>0 ) pDecrExp( hc,i );
3046	}
3047	pSetm( hc );
3048	}
3049	else
3050	{
3051	return spectrumNoHC;
3052	}
3053
3054	#ifdef SPECTRUM_DEBUG
3055	#ifdef SPECTRUM_PRINT
3056	#ifdef SPECTRUM_IOSTREAM
3057	cout << " ";
3058	#else
3059	fprintf( stdout," " );
3060	#endif
3061	pWrite( hc );
3062	#endif
3063	#endif
3064
3065	// ----------------------------------------
3066	// compute the Newton polygon nph of h
3067	// ----------------------------------------
3068
3069	#ifdef SPECTRUM_DEBUG
3070	#ifdef SPECTRUM_PRINT
3071	#ifdef SPECTRUM_IOSTREAM
3072	cout << "\n computing the newton polygon...\n";
3073	#else
3074	fprintf( stdout,"\n computing the newton polygon...\n" );
3075	#endif
3076	#endif
3077	#endif
3078
3079	newtonPolygon nph( h );
3080
3081	#ifdef SPECTRUM_DEBUG
3082	#ifdef SPECTRUM_PRINT
3083	cout << nph;
3084	#endif
3085	#endif
3086
3087	// -----------------------------------------------
3088	// compute the weight corner wc of (stdj,nph)
3089	// -----------------------------------------------
3090
3091	#ifdef SPECTRUM_DEBUG
3092	#ifdef SPECTRUM_PRINT
3093	#ifdef SPECTRUM_IOSTREAM
3094	cout << "\n computing the weight corner...\n";
3095	#else
3096	fprintf( stdout,"\n computing the weight corner...\n" );
3097	#endif
3098	#endif
3099	#endif
3100
3101	poly wc = ( fast==0 ? pCopy( hc ) :
3102	( fast==1 ? computeWC( nph,(Rational)pVariables ) :
3103	/* fast==2 */computeWC( nph,((Rational)pVariables)/(Rational)2 ) ) );
3104
3105	#ifdef SPECTRUM_DEBUG
3106	#ifdef SPECTRUM_PRINT
3107	#ifdef SPECTRUM_IOSTREAM
3108	cout << " ";
3109	#else
3110	fprintf( stdout," " );
3111	#endif
3112	pWrite( wc );
3113	#endif
3114	#endif
3115
3116	// -------------
3117	// compute NF
3118	// -------------
3119
3120	#ifdef SPECTRUM_DEBUG
3121	#ifdef SPECTRUM_PRINT
3122	#ifdef SPECTRUM_IOSTREAM
3123	cout << "\n computing NF...\n" << endl;
3124	#else
3125	fprintf( stdout,"\n computing NF...\n" );
3126	#endif
3127	#endif
3128	#endif
3129
3130	spectrumPolyList NF( &nph );
3131
3132	computeNF( stdJ,hc,wc,&NF );
3133
3134	#ifdef SPECTRUM_DEBUG
3135	#ifdef SPECTRUM_PRINT
3136	cout << NF;
3137	#ifdef SPECTRUM_IOSTREAM
3138	cout << endl;
3139	#else
3140	fprintf( stdout,"\n" );
3141	#endif
3142	#endif
3143	#endif
3144
3145	// ----------------------------
3146	// compute the spectrum of h
3147	// ----------------------------
3148
3149	return NF.spectrum( L,fast );
3150	}
3151
3152	// ----------------------------------------------------------------------------
3153	// this procedure is called from the interpreter
3154	// ----------------------------------------------------------------------------
3155	// first = polynomial
3156	// result = list of spectrum numbers
3157	// ----------------------------------------------------------------------------
3158
3159	BOOLEAN spectrumProc( leftv result,leftv first )
3160	{
3161	spectrumState state = spectrumOK;
3162
3163	// -------------------
3164	// check consistency
3165	// -------------------
3166
3167	// check for a local ring
3168
3169	if( !ringIsLocal( ) )
3170	{
3171	WerrorS( "only works for local orderings" );
3172	state = spectrumWrongRing;
3173	}
3174
3175	// no quotient rings are allowed
3176
3177	else if( currRing->qideal != NULL )
3178	{
3179	WerrorS( "does not work in quotient rings" );
3180	state = spectrumWrongRing;
3181	}
3182	else
3183	{
3184	lists L = (lists)NULL;
3185	int flag = 1; // weight corner optimization is safe
3186
3187	state = spectrumCompute( (poly)first->Data( ),&L,flag );
3188
3189	if( state==spectrumOK )
3190	{
3191	result->rtyp = LIST_CMD;
3192	result->data = (char*)L;
3193	}
3194	else
3195	{
3196	spectrumPrintError(state);
3197	}
3198	}
3199
3200	return (state!=spectrumOK);
3201	}
3202
3203	// ----------------------------------------------------------------------------
3204	// this procedure is called from the interpreter
3205	// ----------------------------------------------------------------------------
3206	// first = polynomial
3207	// result = list of spectrum numbers
3208	// ----------------------------------------------------------------------------
3209
3210	BOOLEAN spectrumfProc( leftv result,leftv first )
3211	{
3212	spectrumState state = spectrumOK;
3213
3214	// -------------------
3215	// check consistency
3216	// -------------------
3217
3218	// check for a local polynomial ring
3219
3220	if( currRing->OrdSgn != -1 )
3221	// ?? HS: the test above is also true for k[x][[y]], k[[x]][y]
3222	// or should we use:
3223	//if( !ringIsLocal( ) )
3224	{
3225	WerrorS( "only works for local orderings" );
3226	state = spectrumWrongRing;
3227	}
3228	else if( currRing->qideal != NULL )
3229	{
3230	WerrorS( "does not work in quotient rings" );
3231	state = spectrumWrongRing;
3232	}
3233	else
3234	{
3235	lists L = (lists)NULL;
3236	int flag = 2; // symmetric optimization
3237
3238	state = spectrumCompute( (poly)first->Data( ),&L,flag );
3239
3240	if( state==spectrumOK )
3241	{
3242	result->rtyp = LIST_CMD;
3243	result->data = (char*)L;
3244	}
3245	else
3246	{
3247	spectrumPrintError(state);
3248	}
3249	}
3250
3251	return (state!=spectrumOK);
3252	}
3253
3254	// ----------------------------------------------------------------------------
3255	// check if a list is a spectrum
3256	// check for:
3257	// list has 6 elements
3258	// 1st element is int (mu=Milnor number)
3259	// 2nd element is int (pg=geometrical genus)
3260	// 3rd element is int (n =number of different spectrum numbers)
3261	// 4th element is intvec (num=numerators)
3262	// 5th element is intvec (den=denomiantors)
3263	// 6th element is intvec (mul=multiplicities)
3264	// exactly n numerators
3265	// exactly n denominators
3266	// exactly n multiplicities
3267	// mu>0
3268	// pg>=0
3269	// n>0
3270	// num>0
3271	// den>0
3272	// mul>0
3273	// symmetriy with respect to numberofvariables/2
3274	// monotony
3275	// mu = sum of all multiplicities
3276	// pg = sum of all multiplicities where num/den<=1
3277	// ----------------------------------------------------------------------------
3278
3279	semicState list_is_spectrum( lists l )
3280	{
3281	// -------------------
3282	// check list length
3283	// -------------------
3284
3285	if( l->nr < 5 )
3286	{
3287	return semicListTooShort;
3288	}
3289	else if( l->nr > 5 )
3290	{
3291	return semicListTooLong;
3292	}
3293
3294	// -------------
3295	// check types
3296	// -------------
3297
3298	if( l->m[0].rtyp != INT_CMD )
3299	{
3300	return semicListFirstElementWrongType;
3301	}
3302	else if( l->m[1].rtyp != INT_CMD )
3303	{
3304	return semicListSecondElementWrongType;
3305	}
3306	else if( l->m[2].rtyp != INT_CMD )
3307	{
3308	return semicListThirdElementWrongType;
3309	}
3310	else if( l->m[3].rtyp != INTVEC_CMD )
3311	{
3312	return semicListFourthElementWrongType;
3313	}
3314	else if( l->m[4].rtyp != INTVEC_CMD )
3315	{
3316	return semicListFifthElementWrongType;
3317	}
3318	else if( l->m[5].rtyp != INTVEC_CMD )
3319	{
3320	return semicListSixthElementWrongType;
3321	}
3322
3323	// -------------------------
3324	// check number of entries
3325	// -------------------------
3326
3327	int mu = (int)(long)(l->m[0].Data( ));
3328	int pg = (int)(long)(l->m[1].Data( ));
3329	int n = (int)(long)(l->m[2].Data( ));
3330
3331	if( n <= 0 )
3332	{
3333	return semicListNNegative;
3334	}
3335
3336	intvec num = (intvec)l->m[3].Data( );
3337	intvec den = (intvec)l->m[4].Data( );
3338	intvec mul = (intvec)l->m[5].Data( );
3339
3340	if( n != num->length( ) )
3341	{
3342	return semicListWrongNumberOfNumerators;
3343	}
3344	else if( n != den->length( ) )
3345	{
3346	return semicListWrongNumberOfDenominators;
3347	}
3348	else if( n != mul->length( ) )
3349	{
3350	return semicListWrongNumberOfMultiplicities;
3351	}
3352
3353	// --------
3354	// values
3355	// --------
3356
3357	if( mu <= 0 )
3358	{
3359	return semicListMuNegative;
3360	}
3361	if( pg < 0 )
3362	{
3363	return semicListPgNegative;
3364	}
3365
3366	int i;
3367
3368	for( i=0; i<n; i++ )
3369	{
3370	if( (*num)[i] <= 0 )
3371	{
3372	return semicListNumNegative;
3373	}
3374	if( (*den)[i] <= 0 )
3375	{
3376	return semicListDenNegative;
3377	}
3378	if( (*mul)[i] <= 0 )
3379	{
3380	return semicListMulNegative;
3381	}
3382	}
3383
3384	// ----------------
3385	// check symmetry
3386	// ----------------
3387
3388	int j;
3389
3390	for( i=0, j=n-1; i<=j; i++,j-- )
3391	{
3392	if( (num)[i] != pVariables((den)[i]) - (num)[j] \|\|
3393	(den)[i] != (den)[j] \|\|
3394	(mul)[i] != (mul)[j] )
3395	{
3396	return semicListNotSymmetric;
3397	}
3398	}
3399
3400	// ----------------
3401	// check monotony
3402	// ----------------
3403
3404	for( i=0, j=1; i<n/2; i++,j++ )
3405	{
3406	if( (num)[i](den)[j] >= (num)[j](den)[i] )
3407	{
3408	return semicListNotMonotonous;
3409	}
3410	}
3411
3412	// ---------------------
3413	// check Milnor number
3414	// ---------------------
3415
3416	for( mu=0, i=0; i<n; i++ )
3417	{
3418	mu += (*mul)[i];
3419	}
3420
3421	if( mu != (int)(long)(l->m[0].Data( )) )
3422	{
3423	return semicListMilnorWrong;
3424	}
3425
3426	// -------------------------
3427	// check geometrical genus
3428	// -------------------------
3429
3430	for( pg=0, i=0; i<n; i++ )
3431	{
3432	if( (num)[i]<=(den)[i] )
3433	{
3434	pg += (*mul)[i];
3435	}
3436	}
3437
3438	if( pg != (int)(long)(l->m[1].Data( )) )
3439	{
3440	return semicListPGWrong;
3441	}
3442
3443	return semicOK;
3444	}
3445
3446	// ----------------------------------------------------------------------------
3447	// this procedure is called from the interpreter
3448	// ----------------------------------------------------------------------------
3449	// first = list of spectrum numbers
3450	// second = list of spectrum numbers
3451	// result = sum of the two lists
3452	// ----------------------------------------------------------------------------
3453
3454	BOOLEAN spaddProc( leftv result,leftv first,leftv second )
3455	{
3456	semicState state;
3457
3458	// -----------------
3459	// check arguments
3460	// -----------------
3461
3462	lists l1 = (lists)first->Data( );
3463	lists l2 = (lists)second->Data( );
3464
3465	if( (state=list_is_spectrum( l1 )) != semicOK )
3466	{
3467	WerrorS( "first argument is not a spectrum:" );
3468	list_error( state );
3469	}
3470	else if( (state=list_is_spectrum( l2 )) != semicOK )
3471	{
3472	WerrorS( "second argument is not a spectrum:" );
3473	list_error( state );
3474	}
3475	else
3476	{
3477	spectrum s1( l1 );
3478	spectrum s2( l2 );
3479	spectrum sum( s1+s2 );
3480
3481	result->rtyp = LIST_CMD;
3482	result->data = (char*)(sum.thelist( ));
3483	}
3484
3485	return (state!=semicOK);
3486	}
3487
3488	// ----------------------------------------------------------------------------
3489	// this procedure is called from the interpreter
3490	// ----------------------------------------------------------------------------
3491	// first = list of spectrum numbers
3492	// second = integer
3493	// result = the multiple of the first list by the second factor
3494	// ----------------------------------------------------------------------------
3495
3496	BOOLEAN spmulProc( leftv result,leftv first,leftv second )
3497	{
3498	semicState state;
3499
3500	// -----------------
3501	// check arguments
3502	// -----------------
3503
3504	lists l = (lists)first->Data( );
3505	int k = (int)(long)second->Data( );
3506
3507	if( (state=list_is_spectrum( l ))!=semicOK )
3508	{
3509	WerrorS( "first argument is not a spectrum" );
3510	list_error( state );
3511	}
3512	else if( k < 0 )
3513	{
3514	WerrorS( "second argument should be positive" );
3515	state = semicMulNegative;
3516	}
3517	else
3518	{
3519	spectrum s( l );
3520	spectrum product( k*s );
3521
3522	result->rtyp = LIST_CMD;
3523	result->data = (char*)product.thelist( );
3524	}
3525
3526	return (state!=semicOK);
3527	}
3528
3529	// ----------------------------------------------------------------------------
3530	// this procedure is called from the interpreter
3531	// ----------------------------------------------------------------------------
3532	// first = list of spectrum numbers
3533	// second = list of spectrum numbers
3534	// result = semicontinuity index
3535	// ----------------------------------------------------------------------------
3536
3537	BOOLEAN semicProc3 ( leftv res,leftv u,leftv v,leftv w )
3538	{
3539	semicState state;
3540	BOOLEAN qh=(((int)(long)w->Data())==1);
3541
3542	// -----------------
3543	// check arguments
3544	// -----------------
3545
3546	lists l1 = (lists)u->Data( );
3547	lists l2 = (lists)v->Data( );
3548
3549	if( (state=list_is_spectrum( l1 ))!=semicOK )
3550	{
3551	WerrorS( "first argument is not a spectrum" );
3552	list_error( state );
3553	}
3554	else if( (state=list_is_spectrum( l2 ))!=semicOK )
3555	{
3556	WerrorS( "second argument is not a spectrum" );
3557	list_error( state );
3558	}
3559	else
3560	{
3561	spectrum s1( l1 );
3562	spectrum s2( l2 );
3563
3564	res->rtyp = INT_CMD;
3565	if (qh)
3566	res->data = (void*)(s1.mult_spectrumh( s2 ));
3567	else
3568	res->data = (void*)(s1.mult_spectrum( s2 ));
3569	}
3570
3571	// -----------------
3572	// check status
3573	// -----------------
3574
3575	return (state!=semicOK);
3576	}
3577	BOOLEAN semicProc ( leftv res,leftv u,leftv v )
3578	{
3579	sleftv tmp;
3580	memset(&tmp,0,sizeof(tmp));
3581	tmp.rtyp=INT_CMD;
3582	/* tmp.data = (void )0; -- done by memset /
3583
3584	return semicProc3(res,u,v,&tmp);
3585	}
3586	// from splist.cc
3587	// ----------------------------------------------------------------------------
3588	// Compute the spectrum of a spectrumPolyList
3589	// ----------------------------------------------------------------------------
3590
3591	spectrumState spectrumPolyList::spectrum( lists *L,int fast )
3592	{
3593	spectrumPolyNode **node = &root;
3594	spectrumPolyNode *search;
3595
3596	poly f,tmp;
3597	int found,cmp;
3598
3599	Rational smax( ( fast==0 ? 0 : pVariables ),
3600	( fast==2 ? 2 : 1 ) );
3601
3602	Rational weight_prev( 0,1 );
3603
3604	int mu = 0; // the milnor number
3605	int pg = 0; // the geometrical genus
3606	int n = 0; // number of different spectral numbers
3607	int z = 0; // number of spectral number equal to smax
3608
3609	int k = 0;
3610
3611	while( (node)!=(spectrumPolyNode)NULL &&
3612	( fast==0 \|\| (*node)->weight<=smax ) )
3613	{
3614	// ---------------------------------------
3615	// determine the first normal form which
3616	// contains the monomial node->mon
3617	// ---------------------------------------
3618
3619	found = FALSE;
3620	search = *node;
3621
3622	while( search!=(spectrumPolyNode*)NULL && found==FALSE )
3623	{
3624	if( search->nf!=(poly)NULL )
3625	{
3626	f = search->nf;
3627
3628	do
3629	{
3630	// --------------------------------
3631	// look for (*node)->mon in f
3632	// --------------------------------
3633
3634	cmp = pCmp( (*node)->mon,f );
3635
3636	if( cmp<0 )
3637	{
3638	f = pNext( f );
3639	}
3640	else if( cmp==0 )
3641	{
3642	// -----------------------------
3643	// we have found a normal form
3644	// -----------------------------
3645
3646	found = TRUE;
3647
3648	// normalize coefficient
3649
3650	number inv = nInvers( pGetCoeff( f ) );
3651	pMult_nn( search->nf,inv );
3652	nDelete( &inv );
3653
3654	// exchange normal forms
3655
3656	tmp = (*node)->nf;
3657	(*node)->nf = search->nf;
3658	search->nf = tmp;
3659	}
3660	}
3661	while( cmp<0 && f!=(poly)NULL );
3662	}
3663	search = search->next;
3664	}
3665
3666	if( found==FALSE )
3667	{
3668	// ------------------------------------------------
3669	// the weight of node->mon is a spectrum number
3670	// ------------------------------------------------
3671
3672	mu++;
3673
3674	if( (*node)->weight<=(Rational)1 ) pg++;
3675	if( (*node)->weight==smax ) z++;
3676	if( (*node)->weight>weight_prev ) n++;
3677
3678	weight_prev = (*node)->weight;
3679	node = &((*node)->next);
3680	}
3681	else
3682	{
3683	// -----------------------------------------------
3684	// determine all other normal form which contain
3685	// the monomial node->mon
3686	// replace for node->mon its normal form
3687	// -----------------------------------------------
3688
3689	while( search!=(spectrumPolyNode*)NULL )
3690	{
3691	if( search->nf!=(poly)NULL )
3692	{
3693	f = search->nf;
3694
3695	do
3696	{
3697	// --------------------------------
3698	// look for (*node)->mon in f
3699	// --------------------------------
3700
3701	cmp = pCmp( (*node)->mon,f );
3702
3703	if( cmp<0 )
3704	{
3705	f = pNext( f );
3706	}
3707	else if( cmp==0 )
3708	{
3709	search->nf = pSub( search->nf,
3710	ppMult_nn( (*node)->nf,pGetCoeff( f ) ) );
3711	pNorm( search->nf );
3712	}
3713	}
3714	while( cmp<0 && f!=(poly)NULL );
3715	}
3716	search = search->next;
3717	}
3718	delete_node( node );
3719	}
3720
3721	}
3722
3723	// --------------------------------------------------------
3724	// fast computation exploits the symmetry of the spectrum
3725	// --------------------------------------------------------
3726
3727	if( fast==2 )
3728	{
3729	mu = 2*mu - z;
3730	n = ( z > 0 ? 2n - 1 : 2n );
3731	}
3732
3733	// --------------------------------------------------------
3734	// compute the spectrum numbers with their multiplicities
3735	// --------------------------------------------------------
3736
3737	intvec *nom = new intvec( n );
3738	intvec *den = new intvec( n );
3739	intvec *mult = new intvec( n );
3740
3741	int count = 0;
3742	int multiplicity = 1;
3743
3744	for( search=root; search!=(spectrumPolyNode*)NULL &&
3745	( fast==0 \|\| search->weight<=smax );
3746	search=search->next )
3747	{
3748	if( search->next==(spectrumPolyNode*)NULL \|\|
3749	search->weight<search->next->weight )
3750	{
3751	(*nom) [count] = search->weight.get_num_si( );
3752	(*den) [count] = search->weight.get_den_si( );
3753	(*mult)[count] = multiplicity;
3754
3755	multiplicity=1;
3756	count++;
3757	}
3758	else
3759	{
3760	multiplicity++;
3761	}
3762	}
3763
3764	// --------------------------------------------------------
3765	// fast computation exploits the symmetry of the spectrum
3766	// --------------------------------------------------------
3767
3768	if( fast==2 )
3769	{
3770	int n1,n2;
3771	for( n1=0, n2=n-1; n1<n2; n1++, n2-- )
3772	{
3773	(nom) [n2] = pVariables(den)[n1]-(nom)[n1];
3774	(den) [n2] = (den)[n1];
3775	(mult)[n2] = (mult)[n1];
3776	}
3777	}
3778
3779	// -----------------------------------
3780	// test if the spectrum is symmetric
3781	// -----------------------------------
3782
3783	if( fast==0 \|\| fast==1 )
3784	{
3785	int symmetric=TRUE;
3786
3787	for( int n1=0, n2=n-1 ; n1<n2 && symmetric==TRUE; n1++, n2-- )
3788	{
3789	if( (mult)[n1]!=(mult)[n2] \|\|
3790	(den) [n1]!= (den)[n2] \|\|
3791	(nom)[n1]+(nom)[n2]!=pVariables(den) [n1] )
3792	{
3793	symmetric = FALSE;
3794	}
3795	}
3796
3797	if( symmetric==FALSE )
3798	{
3799	// ---------------------------------------------
3800	// the spectrum is not symmetric => degenerate
3801	// principal part
3802	// ---------------------------------------------
3803
3804	*L = (lists)omAllocBin( slists_bin);
3805	(*L)->Init( 1 );
3806	(*L)->m[0].rtyp = INT_CMD; // milnor number
3807	(L)->m[0].data = (void)mu;
3808
3809	return spectrumDegenerate;
3810	}
3811	}
3812
3813	*L = (lists)omAllocBin( slists_bin);
3814
3815	(*L)->Init( 6 );
3816
3817	(*L)->m[0].rtyp = INT_CMD; // milnor number
3818	(*L)->m[1].rtyp = INT_CMD; // geometrical genus
3819	(*L)->m[2].rtyp = INT_CMD; // number of spectrum values
3820	(*L)->m[3].rtyp = INTVEC_CMD; // nominators
3821	(*L)->m[4].rtyp = INTVEC_CMD; // denomiantors
3822	(*L)->m[5].rtyp = INTVEC_CMD; // multiplicities
3823
3824	(L)->m[0].data = (void)mu;
3825	(L)->m[1].data = (void)pg;
3826	(L)->m[2].data = (void)n;
3827	(L)->m[3].data = (void)nom;
3828	(L)->m[4].data = (void)den;
3829	(L)->m[5].data = (void)mult;
3830
3831	return spectrumOK;
3832	}
3833
3834	#endif
3835
3836	//from mpr_inout.cc
3837	extern void nPrint(number n);
3838
3839	BOOLEAN loNewtonP( leftv res, leftv arg1 )
3840	{
3841	res->data= (void*)loNewtonPolytope( (ideal)arg1->Data() );
3842	return FALSE;
3843	}
3844
3845	BOOLEAN loSimplex( leftv res, leftv args )
3846	{
3847	if ( !(rField_is_long_R()) )
3848	{
3849	WerrorS("Ground field not implemented!");
3850	return TRUE;
3851	}
3852
3853	simplex * LP;
3854	matrix m;
3855
3856	leftv v= args;
3857	if ( v->Typ() != MATRIX_CMD ) // 1: matrix
3858	return TRUE;
3859	else
3860	m= (matrix)(v->CopyD());
3861
3862	LP = new simplex(MATROWS(m),MATCOLS(m));
3863	LP->mapFromMatrix(m);
3864
3865	v= v->next;
3866	if ( v->Typ() != INT_CMD ) // 2: m = number of constraints
3867	return TRUE;
3868	else
3869	LP->m= (int)(long)(v->Data());
3870
3871	v= v->next;
3872	if ( v->Typ() != INT_CMD ) // 3: n = number of variables
3873	return TRUE;
3874	else
3875	LP->n= (int)(long)(v->Data());
3876
3877	v= v->next;
3878	if ( v->Typ() != INT_CMD ) // 4: m1 = number of <= constraints
3879	return TRUE;
3880	else
3881	LP->m1= (int)(long)(v->Data());
3882
3883	v= v->next;
3884	if ( v->Typ() != INT_CMD ) // 5: m2 = number of >= constraints
3885	return TRUE;
3886	else
3887	LP->m2= (int)(long)(v->Data());
3888
3889	v= v->next;
3890	if ( v->Typ() != INT_CMD ) // 6: m3 = number of == constraints
3891	return TRUE;
3892	else
3893	LP->m3= (int)(long)(v->Data());
3894
3895	#ifdef mprDEBUG_PROT
3896	Print("m (constraints) %d\n",LP->m);
3897	Print("n (columns) %d\n",LP->n);
3898	Print("m1 (<=) %d\n",LP->m1);
3899	Print("m2 (>=) %d\n",LP->m2);
3900	Print("m3 (==) %d\n",LP->m3);
3901	#endif
3902
3903	LP->compute();
3904
3905	lists lres= (lists)omAlloc( sizeof(slists) );
3906	lres->Init( 6 );
3907
3908	lres->m[0].rtyp= MATRIX_CMD; // output matrix
3909	lres->m[0].data=(void*)LP->mapToMatrix(m);
3910
3911	lres->m[1].rtyp= INT_CMD; // found a solution?
3912	lres->m[1].data=(void*)LP->icase;
3913
3914	lres->m[2].rtyp= INTVEC_CMD;
3915	lres->m[2].data=(void*)LP->posvToIV();
3916
3917	lres->m[3].rtyp= INTVEC_CMD;
3918	lres->m[3].data=(void*)LP->zrovToIV();
3919
3920	lres->m[4].rtyp= INT_CMD;
3921	lres->m[4].data=(void*)LP->m;
3922
3923	lres->m[5].rtyp= INT_CMD;
3924	lres->m[5].data=(void*)LP->n;
3925
3926	res->data= (void*)lres;
3927
3928	return FALSE;
3929	}
3930
3931	BOOLEAN nuMPResMat( leftv res, leftv arg1, leftv arg2 )
3932	{
3933	ideal gls = (ideal)(arg1->Data());
3934	int imtype= (int)(long)arg2->Data();
3935
3936	uResultant::resMatType mtype= determineMType( imtype );
3937
3938	// check input ideal ( = polynomial system )
3939	if ( mprIdealCheck( gls, arg1->Name(), mtype, true ) != mprOk )
3940	{
3941	return TRUE;
3942	}
3943
3944	uResultant *resMat= new uResultant( gls, mtype, false );
3945	if (resMat!=NULL)
3946	{
3947	res->rtyp = MODUL_CMD;
3948	res->data= (void*)resMat->accessResMat()->getMatrix();
3949	if (!errorreported) delete resMat;
3950	}
3951	return errorreported;
3952	}
3953
3954	BOOLEAN nuLagSolve( leftv res, leftv arg1, leftv arg2, leftv arg3 )
3955	{
3956
3957	poly gls;
3958	gls= (poly)(arg1->Data());
3959	int howclean= (int)(long)arg3->Data();
3960
3961	if ( !(rField_is_R() \|\|
3962	rField_is_Q() \|\|
3963	rField_is_long_R() \|\|
3964	rField_is_long_C()) )
3965	{
3966	WerrorS("Ground field not implemented!");
3967	return TRUE;
3968	}
3969
3970	if ( !(rField_is_R()\|\|rField_is_long_R()\|\|rField_is_long_C()) )
3971	{
3972	unsigned long int ii = (unsigned long int)arg2->Data();
3973	setGMPFloatDigits( ii, ii );
3974	}
3975
3976	if ( gls == NULL \|\| pIsConstant( gls ) )
3977	{
3978	WerrorS("Input polynomial is constant!");
3979	return TRUE;
3980	}
3981
3982	int ldummy;
3983	int deg= pLDeg( gls, &ldummy, currRing );
3984	// int deg= pDeg( gls );
3985	int len= pLength( gls );
3986	int i,vpos=0;
3987	poly piter;
3988	lists elist;
3989	lists rlist;
3990
3991	elist= (lists)omAlloc( sizeof(slists) );
3992	elist->Init( 0 );
3993
3994	if ( pVariables > 1 )
3995	{
3996	piter= gls;
3997	for ( i= 1; i <= pVariables; i++ )
3998	if ( pGetExp( piter, i ) )
3999	{
4000	vpos= i;
4001	break;
4002	}
4003	while ( piter )
4004	{
4005	for ( i= 1; i <= pVariables; i++ )
4006	if ( (vpos != i) && (pGetExp( piter, i ) != 0) )
4007	{
4008	WerrorS("The input polynomial must be univariate!");
4009	return TRUE;
4010	}
4011	pIter( piter );
4012	}
4013	}
4014
4015	rootContainer * roots= new rootContainer();
4016	number * pcoeffs= (number )omAlloc( (deg+1) sizeof( number ) );
4017	piter= gls;
4018	for ( i= deg; i >= 0; i-- )
4019	{
4020	//if ( piter ) Print("deg %d, pDeg(piter) %d\n",i,pTotaldegree(piter));
4021	if ( piter && pTotaldegree(piter) == i )
4022	{
4023	pcoeffs[i]= nCopy( pGetCoeff( piter ) );
4024	//nPrint( pcoeffs[i] );PrintS(" ");
4025	pIter( piter );
4026	}
4027	else
4028	{
4029	pcoeffs[i]= nInit(0);
4030	}
4031	}
4032
4033	#ifdef mprDEBUG_PROT
4034	for (i=deg; i >= 0; i--)
4035	{
4036	nPrint( pcoeffs[i] );PrintS(" ");
4037	}
4038	PrintLn();
4039	#endif
4040
4041	roots->fillContainer( pcoeffs, NULL, 1, deg, rootContainer::onepoly, 1 );
4042	roots->solver( howclean );
4043
4044	int elem= roots->getAnzRoots();
4045	char *out;
4046	char *dummy;
4047	int j;
4048
4049	rlist= (lists)omAlloc( sizeof(slists) );
4050	rlist->Init( elem );
4051
4052	if (rField_is_long_C())
4053	{
4054	for ( j= 0; j < elem; j++ )
4055	{
4056	rlist->m[j].rtyp=NUMBER_CMD;
4057	rlist->m[j].data=(void *)nCopy((number)(roots->getRoot(j)));
4058	//rlist->m[j].data=(void *)(number)(roots->getRoot(j));
4059	}
4060	}
4061	else
4062	{
4063	for ( j= 0; j < elem; j++ )
4064	{
4065	dummy = complexToStr( (*roots)[j], gmp_output_digits );
4066	rlist->m[j].rtyp=STRING_CMD;
4067	rlist->m[j].data=(void *)dummy;
4068	}
4069	}
4070
4071	elist->Clean();
4072	//omFreeSize( (ADDRESS) elist, sizeof(slists) );
4073
4074	// this is (via fillContainer) the same data as in root
4075	//for ( i= deg; i >= 0; i-- ) nDelete( &pcoeffs[i] );
4076	//omFreeSize( (ADDRESS) pcoeffs, (deg+1) * sizeof( number ) );
4077
4078	delete roots;
4079
4080	res->rtyp= LIST_CMD;
4081	res->data= (void*)rlist;
4082
4083	return FALSE;
4084	}
4085
4086	BOOLEAN nuVanderSys( leftv res, leftv arg1, leftv arg2, leftv arg3)
4087	{
4088	int i;
4089	ideal p,w;
4090	p= (ideal)arg1->Data();
4091	w= (ideal)arg2->Data();
4092
4093	// w[0] = f(p^0)
4094	// w[1] = f(p^1)
4095	// ...
4096	// p can be a vector of numbers (multivariate polynom)
4097	// or one number (univariate polynom)
4098	// tdg = deg(f)
4099
4100	int n= IDELEMS( p );
4101	int m= IDELEMS( w );
4102	int tdg= (int)(long)arg3->Data();
4103
4104	res->data= (void*)NULL;
4105
4106	// check the input
4107	if ( tdg < 1 )
4108	{
4109	WerrorS("Last input parameter must be > 0!");
4110	return TRUE;
4111	}
4112	if ( n != pVariables )
4113	{
4114	Werror("Size of first input ideal must be equal to %d!",pVariables);
4115	return TRUE;
4116	}
4117	if ( m != (int)pow((double)tdg+1,(double)n) )
4118	{
4119	Werror("Size of second input ideal must be equal to %d!",
4120	(int)pow((double)tdg+1,(double)n));
4121	return TRUE;
4122	}
4123	if ( !(rField_is_Q() /* \|\|
4124	rField_is_R() \|\| rField_is_long_R() \|\|
4125	rField_is_long_C()*/ ) )
4126	{
4127	WerrorS("Ground field not implemented!");
4128	return TRUE;
4129	}
4130
4131	number tmp;
4132	number pevpoint= (number )omAlloc( n * sizeof( number ) );
4133	for ( i= 0; i < n; i++ )
4134	{
4135	pevpoint[i]=nInit(0);
4136	if ( (p->m)[i] )
4137	{
4138	tmp = pGetCoeff( (p->m)[i] );
4139	if ( nIsZero(tmp) \|\| nIsOne(tmp) \|\| nIsMOne(tmp) )
4140	{
4141	omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
4142	WerrorS("Elements of first input ideal must not be equal to -1, 0, 1!");
4143	return TRUE;
4144	}
4145	} else tmp= NULL;
4146	if ( !nIsZero(tmp) )
4147	{
4148	if ( !pIsConstant((p->m)[i]))
4149	{
4150	omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
4151	WerrorS("Elements of first input ideal must be numbers!");
4152	return TRUE;
4153	}
4154	pevpoint[i]= nCopy( tmp );
4155	}
4156	}
4157
4158	number wresults= (number )omAlloc( m * sizeof( number ) );
4159	for ( i= 0; i < m; i++ )
4160	{
4161	wresults[i]= nInit(0);
4162	if ( (w->m)[i] && !nIsZero(pGetCoeff((w->m)[i])) )
4163	{
4164	if ( !pIsConstant((w->m)[i]))
4165	{
4166	omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
4167	omFreeSize( (ADDRESS)wresults, m * sizeof( number ) );
4168	WerrorS("Elements of second input ideal must be numbers!");
4169	return TRUE;
4170	}
4171	wresults[i]= nCopy(pGetCoeff((w->m)[i]));
4172	}
4173	}
4174
4175	vandermonde vm( m, n, tdg, pevpoint, FALSE );
4176	number *ncpoly= vm.interpolateDense( wresults );
4177	// do not free ncpoly[]!!
4178	poly rpoly= vm.numvec2poly( ncpoly );
4179
4180	omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
4181	omFreeSize( (ADDRESS)wresults, m * sizeof( number ) );
4182
4183	res->data= (void*)rpoly;
4184	return FALSE;
4185	}
4186
4187	BOOLEAN nuUResSolve( leftv res, leftv args )
4188	{
4189	leftv v= args;
4190
4191	ideal gls;
4192	int imtype;
4193	int howclean;
4194
4195	// get ideal
4196	if ( v->Typ() != IDEAL_CMD )
4197	return TRUE;
4198	else gls= (ideal)(v->Data());
4199	v= v->next;
4200
4201	// get resultant matrix type to use (0,1)
4202	if ( v->Typ() != INT_CMD )
4203	return TRUE;
4204	else imtype= (int)(long)v->Data();
4205	v= v->next;
4206
4207	if (imtype==0)
4208	{
4209	ideal test_id=idInit(1,1);
4210	int j;
4211	for(j=IDELEMS(gls)-1;j>=0;j--)
4212	{
4213	if (gls->m[j]!=NULL)
4214	{
4215	test_id->m[0]=gls->m[j];
4216	intvec *dummy_w=idQHomWeight(test_id);
4217	if (dummy_w!=NULL)
4218	{
4219	WerrorS("Newton polytope not of expected dimension");
4220	delete dummy_w;
4221	return TRUE;
4222	}
4223	}
4224	}
4225	}
4226
4227	// get and set precision in digits ( > 0 )
4228	if ( v->Typ() != INT_CMD )
4229	return TRUE;
4230	else if ( !(rField_is_R()\|\|rField_is_long_R()\|\|rField_is_long_C()) )
4231	{
4232	unsigned long int ii=(unsigned long int)v->Data();
4233	setGMPFloatDigits( ii, ii );
4234	}
4235	v= v->next;
4236
4237	// get interpolation steps (0,1,2)
4238	if ( v->Typ() != INT_CMD )
4239	return TRUE;
4240	else howclean= (int)(long)v->Data();
4241
4242	uResultant::resMatType mtype= determineMType( imtype );
4243	int i,c,count;
4244	lists listofroots= NULL;
4245	lists emptylist;
4246	number smv= NULL;
4247	BOOLEAN interpolate_det= (mtype==uResultant::denseResMat)?TRUE:FALSE;
4248
4249	//emptylist= (lists)omAlloc( sizeof(slists) );
4250	//emptylist->Init( 0 );
4251
4252	//res->rtyp = LIST_CMD;
4253	//res->data= (void *)emptylist;
4254
4255	// check input ideal ( = polynomial system )
4256	if ( mprIdealCheck( gls, args->Name(), mtype ) != mprOk )
4257	{
4258	return TRUE;
4259	}
4260
4261	uResultant * ures;
4262	rootContainer ** iproots;
4263	rootContainer ** muiproots;
4264	rootArranger * arranger;
4265
4266	// main task 1: setup of resultant matrix
4267	ures= new uResultant( gls, mtype );
4268	if ( ures->accessResMat()->initState() != resMatrixBase::ready )
4269	{
4270	WerrorS("Error occurred during matrix setup!");
4271	return TRUE;
4272	}
4273
4274	// if dense resultant, check if minor nonsingular
4275	if ( mtype == uResultant::denseResMat )
4276	{
4277	smv= ures->accessResMat()->getSubDet();
4278	#ifdef mprDEBUG_PROT
4279	PrintS("// Determinant of submatrix: ");nPrint(smv);PrintLn();
4280	#endif
4281	if ( nIsZero(smv) )
4282	{
4283	WerrorS("Unsuitable input ideal: Minor of resultant matrix is singular!");
4284	return TRUE;
4285	}
4286	}
4287
4288	// main task 2: Interpolate specialized resultant polynomials
4289	if ( interpolate_det )
4290	iproots= ures->interpolateDenseSP( false, smv );
4291	else
4292	iproots= ures->specializeInU( false, smv );
4293
4294	// main task 3: Interpolate specialized resultant polynomials
4295	if ( interpolate_det )
4296	muiproots= ures->interpolateDenseSP( true, smv );
4297	else
4298	muiproots= ures->specializeInU( true, smv );
4299
4300	#ifdef mprDEBUG_PROT
4301	c= iproots[0]->getAnzElems();
4302	for (i=0; i < c; i++) pWrite(iproots[i]->getPoly());
4303	c= muiproots[0]->getAnzElems();
4304	for (i=0; i < c; i++) pWrite(muiproots[i]->getPoly());
4305	#endif
4306
4307	// main task 4: Compute roots of specialized polys and match them up
4308	arranger= new rootArranger( iproots, muiproots, howclean );
4309	arranger->solve_all();
4310
4311	// get list of roots
4312	if ( arranger->success() )
4313	{
4314	arranger->arrange();
4315	listofroots= arranger->listOfRoots( gmp_output_digits );
4316	}
4317	else
4318	{
4319	WerrorS("Solver was unable to find any roots!");
4320	return TRUE;
4321	}
4322
4323	// free everything
4324	count= iproots[0]->getAnzElems();
4325	for (i=0; i < count; i++) delete iproots[i];
4326	omFreeSize( (ADDRESS) iproots, count * sizeof(rootContainer*) );
4327	count= muiproots[0]->getAnzElems();
4328	for (i=0; i < count; i++) delete muiproots[i];
4329	omFreeSize( (ADDRESS) muiproots, count * sizeof(rootContainer*) );
4330
4331	delete ures;
4332	delete arranger;
4333	nDelete( &smv );
4334
4335	res->data= (void *)listofroots;
4336
4337	//emptylist->Clean();
4338	// omFreeSize( (ADDRESS) emptylist, sizeof(slists) );
4339
4340	return FALSE;
4341	}
4342
4343	// from mpr_numeric.cc
4344	lists rootArranger::listOfRoots( const unsigned int oprec )
4345	{
4346	int i,j,tr;
4347	int count= roots[0]->getAnzRoots(); // number of roots
4348	int elem= roots[0]->getAnzElems(); // number of koordinates per root
4349
4350	lists listofroots= (lists)omAlloc( sizeof(slists) ); // must be done this way!
4351
4352	if ( found_roots )
4353	{
4354	listofroots->Init( count );
4355
4356	for (i=0; i < count; i++)
4357	{
4358	lists onepoint= (lists)omAlloc(sizeof(slists)); // must be done this way!
4359	onepoint->Init(elem);
4360	for ( j= 0; j < elem; j++ )
4361	{
4362	if ( !rField_is_long_C() )
4363	{
4364	onepoint->m[j].rtyp=STRING_CMD;
4365	onepoint->m[j].data=(void )complexToStr((roots[j])[i],oprec);
4366	}
4367	else
4368	{
4369	onepoint->m[j].rtyp=NUMBER_CMD;
4370	onepoint->m[j].data=(void *)nCopy((number)(roots[j]->getRoot(i)));
4371	}
4372	onepoint->m[j].next= NULL;
4373	onepoint->m[j].name= NULL;
4374	}
4375	listofroots->m[i].rtyp=LIST_CMD;
4376	listofroots->m[i].data=(void *)onepoint;
4377	listofroots->m[j].next= NULL;
4378	listofroots->m[j].name= NULL;
4379	}
4380
4381	}
4382	else
4383	{
4384	listofroots->Init( 0 );
4385	}
4386
4387	return listofroots;
4388	}
4389
4390	// from ring.cc
4391	void rSetHdl(idhdl h)
4392	{
4393	int i;
4394	ring rg = NULL;
4395	if (h!=NULL)
4396	{
4397	// Print(" new ring:%s (l:%d)\n",IDID(h),IDLEV(h));
4398	rg = IDRING(h);
4399	if (rg==NULL) return; //id <>NULL, ring==NULL
4400	omCheckAddrSize((ADDRESS)h,sizeof(idrec));
4401	if (IDID(h)) // OB: ????
4402	omCheckAddr((ADDRESS)IDID(h));
4403	rTest(rg);
4404	}
4405
4406	// clean up history
4407	if (sLastPrinted.RingDependend())
4408	{
4409	sLastPrinted.CleanUp();
4410	memset(&sLastPrinted,0,sizeof(sleftv));
4411	}
4412
4413	// test for valid "currRing":
4414	if ((rg!=NULL) && (rg->idroot==NULL))
4415	{
4416	ring old=rg;
4417	rg=rAssure_HasComp(rg);
4418	if (old!=rg)
4419	{
4420	rKill(old);
4421	IDRING(h)=rg;
4422	}
4423	}
4424	/------------ change the global ring -----------------------/
4425	rChangeCurrRing(rg);
4426	currRingHdl = h;
4427	}
4428
4429	BOOLEAN rSleftvOrdering2Ordering(sleftv *ord, ring R)
4430	{
4431	int last = 0, o=0, n = 1, i=0, typ = 1, j;
4432	sleftv *sl = ord;
4433
4434	// determine nBlocks
4435	while (sl!=NULL)
4436	{
4437	intvec iv = (intvec )(sl->data);
4438	if (((iv)[1]==ringorder_c)\|\|((iv)[1]==ringorder_C))
4439	i++;
4440	else if ((*iv)[1]==ringorder_L)
4441	{
4442	R->bitmask=(*iv)[2];
4443	n--;
4444	}
4445	else if (((*iv)[1]!=ringorder_a)
4446	&& ((*iv)[1]!=ringorder_a64))
4447	o++;
4448	n++;
4449	sl=sl->next;
4450	}
4451	// check whether at least one real ordering
4452	if (o==0)
4453	{
4454	WerrorS("invalid combination of orderings");
4455	return TRUE;
4456	}
4457	// if no c/C ordering is given, increment n
4458	if (i==0) n++;
4459	else if (i != 1)
4460	{
4461	// throw error if more than one is given
4462	WerrorS("more than one ordering c/C specified");
4463	return TRUE;
4464	}
4465
4466	// initialize fields of R
4467	R->order=(int )omAlloc0(nsizeof(int));
4468	R->block0=(int )omAlloc0(nsizeof(int));
4469	R->block1=(int )omAlloc0(nsizeof(int));
4470	R->wvhdl=(int*)omAlloc0(nsizeof(int_ptr));
4471
4472	int weights=(int)omAlloc0((R->N+1)*sizeof(int));
4473
4474	// init order, so that rBlocks works correctly
4475	for (j=0; j < n-1; j++)
4476	R->order[j] = (int) ringorder_unspec;
4477	// set last _C order, if no c/C order was given
4478	if (i == 0) R->order[n-2] = ringorder_C;
4479
4480	/* init orders */
4481	sl=ord;
4482	n=-1;
4483	while (sl!=NULL)
4484	{
4485	intvec *iv;
4486	iv = (intvec *)(sl->data);
4487	if ((*iv)[1]!=ringorder_L)
4488	{
4489	n++;
4490
4491	/* the format of an ordering:
4492	* iv[0]: factor
4493	* iv[1]: ordering
4494	* iv[2..end]: weights
4495	*/
4496	R->order[n] = (*iv)[1];
4497	typ=1;
4498	switch ((*iv)[1])
4499	{
4500	case ringorder_ws:
4501	case ringorder_Ws:
4502	typ=-1;
4503	case ringorder_wp:
4504	case ringorder_Wp:
4505	R->wvhdl[n]=(int)omAlloc((iv->length()-1)sizeof(int));
4506	R->block0[n] = last+1;
4507	for (i=2; i<iv->length(); i++)
4508	{
4509	R->wvhdl[n][i-2] = (*iv)[i];
4510	last++;
4511	if (weights[last]==0) weights[last]=(iv)[i]typ;
4512	}
4513	R->block1[n] = last;
4514	break;
4515	case ringorder_ls:
4516	case ringorder_ds:
4517	case ringorder_Ds:
4518	case ringorder_rs:
4519	typ=-1;
4520	case ringorder_lp:
4521	case ringorder_dp:
4522	case ringorder_Dp:
4523	case ringorder_rp:
4524	R->block0[n] = last+1;
4525	if (iv->length() == 3) last+=(*iv)[2];
4526	else last += (*iv)[0];
4527	R->block1[n] = last;
4528	//if ((R->block0[n]>R->block1[n])
4529	//\|\| (R->block1[n]>rVar(R)))
4530	//{
4531	// R->block1[n]=rVar(R);
4532	// //WerrorS("ordering larger than number of variables");
4533	// break;
4534	//}
4535	if (rCheckIV(iv)) return TRUE;
4536	for(i=si_min(rVar(R),R->block1[n]);i>=R->block0[n];i--)
4537	{
4538	if (weights[i]==0) weights[i]=typ;
4539	}
4540	break;
4541	case ringorder_S:
4542	case ringorder_c:
4543	case ringorder_C:
4544	if (rCheckIV(iv)) return TRUE;
4545	break;
4546	case ringorder_aa:
4547	case ringorder_a:
4548	R->block0[n] = last+1;
4549	R->block1[n] = si_min(last+iv->length()-2 , rVar(R));
4550	R->wvhdl[n] = (int)omAlloc((iv->length()-1)sizeof(int));
4551	for (i=2; i<iv->length(); i++)
4552	{
4553	R->wvhdl[n][i-2]=(*iv)[i];
4554	last++;
4555	if (weights[last]==0) weights[last]=(iv)[i]typ;
4556	}
4557	last=R->block0[n]-1;
4558	break;
4559	case ringorder_a64:
4560	{
4561	R->block0[n] = last+1;
4562	R->block1[n] = si_min(last+iv->length()-2 , rVar(R));
4563	R->wvhdl[n] = (int)omAlloc((iv->length()-1)sizeof(int64));
4564	int64 w=(int64 )R->wvhdl[n];
4565	for (i=2; i<iv->length(); i++)
4566	{
4567	w[i-2]=(*iv)[i];
4568	last++;
4569	if (weights[last]==0) weights[last]=(iv)[i]typ;
4570	}
4571	last=R->block0[n]-1;
4572	break;
4573	}
4574	case ringorder_M:
4575	{
4576	int Mtyp=rTypeOfMatrixOrder(iv);
4577	if (Mtyp==0) return TRUE;
4578	if (Mtyp==-1) typ = -1;
4579
4580	R->wvhdl[n] =( int )omAlloc((iv->length()-1)sizeof(int));
4581	for (i=2; i<iv->length();i++)
4582	R->wvhdl[n][i-2]=(*iv)[i];
4583
4584	R->block0[n] = last+1;
4585	last += (int)sqrt((double)(iv->length()-2));
4586	R->block1[n] = last;
4587	for(i=si_min(rVar(R),R->block1[n]);i>=R->block0[n];i--)
4588	{
4589	if (weights[i]==0) weights[i]=typ;
4590	}
4591	break;
4592	}
4593
4594	case ringorder_no:
4595	R->order[n] = ringorder_unspec;
4596	return TRUE;
4597
4598	default:
4599	Werror("Internal Error: Unknown ordering %d", (*iv)[1]);
4600	R->order[n] = ringorder_unspec;
4601	return TRUE;
4602	}
4603	}
4604	sl=sl->next;
4605	}
4606
4607	// check for complete coverage
4608	if ((R->order[n]==ringorder_c) \|\| (R->order[n]==ringorder_C)) n--;
4609	if (R->block1[n] != R->N)
4610	{
4611	if (((R->order[n]==ringorder_dp) \|\|
4612	(R->order[n]==ringorder_ds) \|\|
4613	(R->order[n]==ringorder_Dp) \|\|
4614	(R->order[n]==ringorder_Ds) \|\|
4615	(R->order[n]==ringorder_rp) \|\|
4616	(R->order[n]==ringorder_rs) \|\|
4617	(R->order[n]==ringorder_lp) \|\|
4618	(R->order[n]==ringorder_ls))
4619	&&
4620	R->block0[n] <= R->N)
4621	{
4622	R->block1[n] = R->N;
4623	}
4624	else
4625	{
4626	Werror("mismatch of number of vars (%d) and ordering (%d vars)",
4627	R->N,R->block1[n]);
4628	return TRUE;
4629	}
4630	}
4631	// find OrdSgn:
4632	R->OrdSgn = 1;
4633	for(i=1;i<=R->N;i++)
4634	{ if (weights[i]<0) { R->OrdSgn=-1;break; }}
4635	omFree(weights);
4636	return FALSE;
4637	}
4638
4639	BOOLEAN rSleftvList2StringArray(sleftv* sl, char** p)
4640	{
4641
4642	while(sl!=NULL)
4643	{
4644	if (sl->Name() == sNoName)
4645	{
4646	if (sl->Typ()==POLY_CMD)
4647	{
4648	sleftv s_sl;
4649	iiConvert(POLY_CMD,ANY_TYPE,-1,sl,&s_sl);
4650	if (s_sl.Name() != sNoName)
4651	*p = omStrDup(s_sl.Name());
4652	else
4653	*p = NULL;
4654	sl->next = s_sl.next;
4655	s_sl.next = NULL;
4656	s_sl.CleanUp();
4657	if (*p == NULL) return TRUE;
4658	}
4659	else
4660	return TRUE;
4661	}
4662	else
4663	*p = omStrDup(sl->Name());
4664	p++;
4665	sl=sl->next;
4666	}
4667	return FALSE;
4668	}
4669
4670	#ifdef HAVE_RINGS
4671	char ring_warn_done=0;
4672	#endif
4673
4674	////////////////////
4675	//
4676	// rInit itself:
4677	//
4678	// INPUT: s: name, pn: ch & parameter (names), rv: variable (names)
4679	// ord: ordering
4680	// RETURN: currRingHdl on success
4681	// NULL on error
4682	// NOTE: * makes new ring to current ring, on success
4683	// * considers input sleftv's as read-only
4684	//idhdl rInit(char s, sleftv pn, sleftv* rv, sleftv* ord)
4685	ring rInit(sleftv* pn, sleftv* rv, sleftv* ord)
4686	{
4687	int ch;
4688	#ifdef HAVE_RINGS
4689	unsigned int ringtype = 0;
4690	int_number ringflaga = NULL;
4691	unsigned int ringflagb = 1;
4692	#endif
4693	int float_len=0;
4694	int float_len2=0;
4695	ring R = NULL;
4696	idhdl tmp = NULL;
4697	BOOLEAN ffChar=FALSE;
4698	int typ = 1;
4699
4700	/* ch -------------------------------------------------------*/
4701	// get ch of ground field
4702	int numberOfAllocatedBlocks;
4703
4704	if (pn->Typ()==INT_CMD)
4705	{
4706	ch=(int)(long)pn->Data();
4707	}
4708	else if ((pn->name != NULL)
4709	&& ((strcmp(pn->name,"real")==0) \|\| (strcmp(pn->name,"complex")==0)))
4710	{
4711	BOOLEAN complex_flag=(strcmp(pn->name,"complex")==0);
4712	ch=-1;
4713	if ((pn->next!=NULL) && (pn->next->Typ()==INT_CMD))
4714	{
4715	float_len=(int)(long)pn->next->Data();
4716	float_len2=float_len;
4717	pn=pn->next;
4718	if ((pn->next!=NULL) && (pn->next->Typ()==INT_CMD))
4719	{
4720	float_len2=(int)(long)pn->next->Data();
4721	pn=pn->next;
4722	}
4723	}
4724	if ((pn->next==NULL) && complex_flag)
4725	{
4726	pn->next=(leftv)omAlloc0Bin(sleftv_bin);
4727	pn->next->name=omStrDup("i");
4728	}
4729	}
4730	#ifdef HAVE_RINGS
4731	else if ((pn->name != NULL) && (strcmp(pn->name, "integer") == 0))
4732	{
4733	ringflaga = (int_number) omAlloc(sizeof(mpz_t));
4734	mpz_init_set_si(ringflaga, 0);
4735	if ((pn->next!=NULL) && (pn->next->Typ()==INT_CMD))
4736	{
4737	mpz_set_ui(ringflaga, (int)(long) pn->next->Data());
4738	pn=pn->next;
4739	if ((pn->next!=NULL) && (pn->next->Typ()==INT_CMD))
4740	{
4741	ringflagb = (long) pn->next->Data();
4742	pn=pn->next;
4743	}
4744	while ((pn->next!=NULL) && (pn->next->Typ()==INT_CMD))
4745	{
4746	mpz_mul_ui(ringflaga, ringflaga, (int)(long) pn->next->Data());
4747	pn=pn->next;
4748	}
4749	}
4750	if ((mpz_cmp_ui(ringflaga, 1) == 0) && (mpz_cmp_ui(ringflaga, 0) < 0))
4751	{
4752	Werror("Wrong ground ring specification (module is 1)");
4753	goto rInitError;
4754	}
4755	if (ringflagb < 1)
4756	{
4757	Werror("Wrong ground ring specification (exponent smaller than 1");
4758	goto rInitError;
4759	}
4760	// module is 0 ---> integers
4761	if (mpz_cmp_ui(ringflaga, 0) == 0)
4762	{
4763	ch = 0;
4764	ringtype = 4;
4765	}
4766	// we have an exponent
4767	else if (ringflagb > 1)
4768	{
4769	ch = ringflagb;
4770	if ((mpz_cmp_ui(ringflaga, 2) == 0) && (ringflagb <= 8*sizeof(NATNUMBER)))
4771	{
4772	/* this branch should be active for ringflagb = 2..32 resp. 2..64,
4773	depending on the size of a long on the respective platform */
4774	ringtype = 1; // Use Z/2^ch
4775	}
4776	else
4777	{
4778	ringtype = 3;
4779	}
4780	}
4781	// just a module m > 1
4782	else
4783	{
4784	ringtype = 2;
4785	ch = mpz_get_ui(ringflaga);
4786	}
4787	}
4788	#endif
4789	else
4790	{
4791	Werror("Wrong ground field specification");
4792	goto rInitError;
4793	}
4794	pn=pn->next;
4795
4796	#ifdef HAVE_RINGS
4797	if ((ringtype > 0)&&(ring_warn_done==0))
4798	{
4799	WarnS("You are using coefficient rings which are not fields.");
4800	WarnS("Please note that only limited functionality is available");
4801	WarnS("for these coefficients.");
4802	WarnS("");
4803	WarnS("The following commands are meant to work:");
4804	WarnS("- basic polynomial arithmetic");
4805	WarnS("- std");
4806	WarnS("- syz");
4807	WarnS("- lift");
4808	WarnS("- reduce");
4809	ring_warn_done=1;
4810	}
4811	#endif
4812
4813	int l, last;
4814	sleftv * sl;
4815	/every entry in the new ring is initialized to 0/
4816
4817	/* characteristic -----------------------------------------------*/
4818	/* input: 0 ch=0 : Q parameter=NULL ffChar=FALSE float_len
4819	* 0 1 : Q(a,...) *names FALSE
4820	* 0 -1 : R NULL FALSE 0
4821	* 0 -1 : R NULL FALSE prec. >6
4822	* 0 -1 : C *names FALSE prec. 0..?
4823	* p p : Fp NULL FALSE
4824	* p -p : Fp(a) *names FALSE
4825	* q q : GF(q=p^n) *names TRUE
4826	*/
4827	if ((ch!=-1)
4828	#ifdef HAVE_RINGS
4829	&& (ringtype == 0)
4830	#endif
4831	)
4832	{
4833	int l = 0;
4834
4835	if (((ch!=0) && (ch<2))
4836	#ifndef NV_OPS
4837	\|\| (ch > 32003)
4838	#endif
4839	)
4840	{
4841	Warn("%d is invalid characteristic of ground field. 32003 is used.", ch);
4842	ch=32003;
4843	}
4844	// load fftable, if necessary
4845	if (pn!=NULL)
4846	{
4847	while ((ch!=fftable[l]) && (fftable[l])) l++;
4848	if (fftable[l]==0) ch = IsPrime(ch);
4849	else
4850	{
4851	char m[1]={(char )sNoName};
4852	nfSetChar(ch,m);
4853	if (errorreported) goto rInitError;
4854	else ffChar=TRUE;
4855	}
4856	}
4857	else
4858	{
4859	ch = IsPrime(ch);
4860	}
4861	}
4862	// allocated ring and set ch
4863	R = (ring) omAlloc0Bin(sip_sring_bin);
4864	R->ch = ch;
4865	#ifdef HAVE_RINGS
4866	R->ringtype = ringtype;
4867	R->ringflaga = ringflaga;
4868	R->ringflagb = ringflagb;
4869	#endif
4870	if (ch == -1)
4871	{
4872	R->float_len= si_min(float_len,32767);
4873	R->float_len2= si_min(float_len2,32767);
4874	}
4875
4876	/* parameter -------------------------------------------------------*/
4877	if (pn!=NULL)
4878	{
4879	R->P=pn->listLength();
4880	//if ((ffChar\|\| (ch == 1)) && (R->P > 1))
4881	if ((R->P > 1) && (ffChar \|\| (ch == -1)))
4882	{
4883	WerrorS("too many parameters");
4884	goto rInitError;
4885	}
4886	R->parameter=(char*)omAlloc0(R->Psizeof(char_ptr));
4887	if (rSleftvList2StringArray(pn, R->parameter))
4888	{
4889	WerrorS("parameter expected");
4890	goto rInitError;
4891	}
4892	if (ch>1 && !ffChar) R->ch=-ch;
4893	else if (ch==0) R->ch=1;
4894	}
4895	else if (ffChar)
4896	{
4897	WerrorS("need one parameter");
4898	goto rInitError;
4899	}
4900	/* post-processing of field description */
4901	// we have short reals, but no short complex
4902	if ((R->ch == - 1)
4903	&& (R->parameter !=NULL)
4904	&& (R->float_len < SHORT_REAL_LENGTH))
4905	{
4906	R->float_len = SHORT_REAL_LENGTH;
4907	R->float_len2 = SHORT_REAL_LENGTH;
4908	}
4909
4910	/* names and number of variables-------------------------------------*/
4911	{
4912	int l=rv->listLength();
4913	#if SIZEOF_SHORT == 2
4914	#define MAX_SHORT 0x7fff
4915	#endif
4916	if (l>MAX_SHORT)
4917	{
4918	Werror("too many ring variables(%d), max is %d",l,MAX_SHORT);
4919	goto rInitError;
4920	}
4921	R->N = l; /rv->listLength();/
4922	}
4923	R->names = (char *)omAlloc0(R->N sizeof(char_ptr));
4924	if (rSleftvList2StringArray(rv, R->names))
4925	{
4926	WerrorS("name of ring variable expected");
4927	goto rInitError;
4928	}
4929
4930	/* check names and parameters for conflicts ------------------------- */
4931	rRenameVars(R); // conflicting variables will be renamed
4932	/* ordering -------------------------------------------------------------*/
4933	if (rSleftvOrdering2Ordering(ord, R))
4934	goto rInitError;
4935
4936	// Complete the initialization
4937	if (rComplete(R,1))
4938	goto rInitError;
4939
4940	rTest(R);
4941
4942	// try to enter the ring into the name list
4943	// need to clean up sleftv here, before this ring can be set to
4944	// new currRing or currRing can be killed beacuse new ring has
4945	// same name
4946	if (pn != NULL) pn->CleanUp();
4947	if (rv != NULL) rv->CleanUp();
4948	if (ord != NULL) ord->CleanUp();
4949	//if ((tmp = enterid(s, myynest, RING_CMD, &IDROOT))==NULL)
4950	// goto rInitError;
4951
4952	//memcpy(IDRING(tmp),R,sizeof(*R));
4953	// set current ring
4954	//omFreeBin(R, ip_sring_bin);
4955	//return tmp;
4956	return R;
4957
4958	// error case:
4959	rInitError:
4960	if (R != NULL) rDelete(R);
4961	if (pn != NULL) pn->CleanUp();
4962	if (rv != NULL) rv->CleanUp();
4963	if (ord != NULL) ord->CleanUp();
4964	return NULL;
4965	}
4966
4967	ring rSubring(ring org_ring, sleftv* rv)
4968	{
4969	ring R = rCopy0(org_ring);
4970	int perm=(int )omAlloc0((org_ring->N+1)*sizeof(int));
4971	int last = 0, o=0, n = rBlocks(org_ring), i=0, typ = 1, j;
4972
4973	/* names and number of variables-------------------------------------*/
4974	{
4975	int l=rv->listLength();
4976	if (l>MAX_SHORT)
4977	{
4978	Werror("too many ring variables(%d), max is %d",l,MAX_SHORT);
4979	goto rInitError;
4980	}
4981	R->N = l; /rv->listLength();/
4982	}
4983	omFree(R->names);
4984	R->names = (char *)omAlloc0(R->N sizeof(char_ptr));
4985	if (rSleftvList2StringArray(rv, R->names))
4986	{
4987	WerrorS("name of ring variable expected");
4988	goto rInitError;
4989	}
4990
4991	/* check names for subring in org_ring ------------------------- */
4992	{
4993	i=0;
4994
4995	for(j=0;j<R->N;j++)
4996	{
4997	for(;i<org_ring->N;i++)
4998	{
4999	if (strcmp(org_ring->names[i],R->names[j])==0)
5000	{
5001	perm[i+1]=j+1;
5002	break;
5003	}
5004	}
5005	if (i>org_ring->N)
5006	{
5007	Werror("variable %d (%s) not in basering",j+1,R->names[j]);
5008	break;
5009	}
5010	}
5011	}
5012	//Print("perm=");
5013	//for(i=1;i<org_ring->N;i++) Print("v%d -> v%d\n",i,perm[i]);
5014	/* ordering -------------------------------------------------------------*/
5015
5016	for(i=0;i<n;i++)
5017	{
5018	int min_var=-1;
5019	int max_var=-1;
5020	for(j=R->block0[i];j<=R->block1[i];j++)
5021	{
5022	if (perm[j]>0)
5023	{
5024	if (min_var==-1) min_var=perm[j];
5025	max_var=perm[j];
5026	}
5027	}
5028	if (min_var!=-1)
5029	{
5030	//Print("block %d: old %d..%d, now:%d..%d\n",
5031	// i,R->block0[i],R->block1[i],min_var,max_var);
5032	R->block0[i]=min_var;
5033	R->block1[i]=max_var;
5034	if (R->wvhdl[i]!=NULL)
5035	{
5036	omFree(R->wvhdl[i]);
5037	R->wvhdl[i]=(int)omAlloc0((max_var-min_var+1)sizeof(int));
5038	for(j=org_ring->block0[i];j<=org_ring->block1[i];j++)
5039	{
5040	if (perm[j]>0)
5041	{
5042	R->wvhdl[i][perm[j]-R->block0[i]]=
5043	org_ring->wvhdl[i][j-org_ring->block0[i]];
5044	//Print("w%d=%d (orig_w%d)\n",perm[j],R->wvhdl[i][perm[j]-R->block0[i]],j);
5045	}
5046	}
5047	}
5048	}
5049	else
5050	{
5051	if(R->block0[i]>0)
5052	{
5053	//Print("skip block %d\n",i);
5054	R->order[i]=ringorder_unspec;
5055	if (R->wvhdl[i] !=NULL) omFree(R->wvhdl[i]);
5056	R->wvhdl[i]=NULL;
5057	}
5058	//else Print("keep block %d\n",i);
5059	}
5060	}
5061	i=n-1;
5062	while(i>0)
5063	{
5064	// removed unneded blocks
5065	if(R->order[i-1]==ringorder_unspec)
5066	{
5067	for(j=i;j<=n;j++)
5068	{
5069	R->order[j-1]=R->order[j];
5070	R->block0[j-1]=R->block0[j];
5071	R->block1[j-1]=R->block1[j];
5072	if (R->wvhdl[j-1] !=NULL) omFree(R->wvhdl[j-1]);
5073	R->wvhdl[j-1]=R->wvhdl[j];
5074	}
5075	R->order[n]=ringorder_unspec;
5076	n--;
5077	}
5078	i--;
5079	}
5080	n=rBlocks(org_ring)-1;
5081	while (R->order[n]==0) n--;
5082	while (R->order[n]==ringorder_unspec) n--;
5083	if ((R->order[n]==ringorder_c) \|\| (R->order[n]==ringorder_C)) n--;
5084	if (R->block1[n] != R->N)
5085	{
5086	if (((R->order[n]==ringorder_dp) \|\|
5087	(R->order[n]==ringorder_ds) \|\|
5088	(R->order[n]==ringorder_Dp) \|\|
5089	(R->order[n]==ringorder_Ds) \|\|
5090	(R->order[n]==ringorder_rp) \|\|
5091	(R->order[n]==ringorder_rs) \|\|
5092	(R->order[n]==ringorder_lp) \|\|
5093	(R->order[n]==ringorder_ls))
5094	&&
5095	R->block0[n] <= R->N)
5096	{
5097	R->block1[n] = R->N;
5098	}
5099	else
5100	{
5101	Werror("mismatch of number of vars (%d) and ordering (%d vars) in block %d",
5102	R->N,R->block1[n],n);
5103	return NULL;
5104	}
5105	}
5106	omFree(perm);
5107	// find OrdSgn:
5108	R->OrdSgn = org_ring->OrdSgn; // IMPROVE!
5109	//for(i=1;i<=R->N;i++)
5110	//{ if (weights[i]<0) { R->OrdSgn=-1;break; }}
5111	//omFree(weights);
5112	// Complete the initialization
5113	if (rComplete(R,1))
5114	goto rInitError;
5115
5116	rTest(R);
5117
5118	if (rv != NULL) rv->CleanUp();
5119
5120	return R;
5121
5122	// error case:
5123	rInitError:
5124	if (R != NULL) rDelete(R);
5125	if (rv != NULL) rv->CleanUp();
5126	return NULL;
5127	}
5128
5129	void rKill(ring r)
5130	{
5131	if ((r->ref<=0)&&(r->order!=NULL))
5132	{
5133	#ifdef RDEBUG
5134	if (traceit &TRACE_SHOW_RINGS) Print("kill ring %lx\n",(long)r);
5135	#endif
5136	if (r->qideal!=NULL)
5137	{
5138	id_Delete(&r->qideal, r);
5139	r->qideal = NULL;
5140	}
5141	int i=1;
5142	int j;
5143	int *pi=r->order;
5144	#ifdef USE_IILOCALRING
5145	for (j=0;j<iiRETURNEXPR_len;j++)
5146	{
5147	if (iiLocalRing[j]==r)
5148	{
5149	if (j<myynest) Warn("killing the basering for level %d",j);
5150	iiLocalRing[j]=NULL;
5151	}
5152	}
5153	#else /* USE_IILOCALRING */
5154	//#endif /* USE_IILOCALRING */
5155	{
5156	proclevel * nshdl = procstack;
5157	int lev=myynest-1;
5158
5159	for(; nshdl != NULL; nshdl = nshdl->next)
5160	{
5161	if (nshdl->cRing==r)
5162	{
5163	Warn("killing the basering for level %d",lev);
5164	nshdl->cRing=NULL;
5165	nshdl->cRingHdl=NULL;
5166	}
5167	}
5168	}
5169	#endif /* USE_IILOCALRING */
5170	// any variables depending on r ?
5171	while (r->idroot!=NULL)
5172	{
5173	killhdl2(r->idroot,&(r->idroot),r);
5174	}
5175	if (r==currRing)
5176	{
5177	// all dependend stuff is done, clean global vars:
5178	if (r->qideal!=NULL)
5179	{
5180	currQuotient=NULL;
5181	}
5182	if (ppNoether!=NULL) pDelete(&ppNoether);
5183	if (sLastPrinted.RingDependend())
5184	{
5185	sLastPrinted.CleanUp();
5186	}
5187	if ((myynest>0) && (iiRETURNEXPR[myynest].RingDependend()))
5188	{
5189	WerrorS("return value depends on local ring variable (export missing ?)");
5190	iiRETURNEXPR[myynest].CleanUp();
5191	}
5192	currRing=NULL;
5193	currRingHdl=NULL;
5194	}
5195
5196	/* nKillChar(r); will be called from inside of rDelete */
5197	rDelete(r);
5198	return;
5199	}
5200	r->ref--;
5201	}
5202
5203	void rKill(idhdl h)
5204	{
5205	ring r = IDRING(h);
5206	int ref=0;
5207	if (r!=NULL)
5208	{
5209	ref=r->ref;
5210	rKill(r);
5211	}
5212	if (h==currRingHdl)
5213	{
5214	if (ref<=0) { currRing=NULL; currRingHdl=NULL;}
5215	else
5216	{
5217	currRingHdl=rFindHdl(r,currRingHdl,NULL);
5218	}
5219	}
5220	}
5221
5222	idhdl rSimpleFindHdl(ring r, idhdl root, idhdl n=NULL)
5223	{
5224	//idhdl next_best=NULL;
5225	idhdl h=root;
5226	while (h!=NULL)
5227	{
5228	if (((IDTYP(h)==RING_CMD)\|\|(IDTYP(h)==QRING_CMD))
5229	&& (h!=n)
5230	&& (IDRING(h)==r)
5231	)
5232	{
5233	// if (IDLEV(h)==myynest)
5234	// return h;
5235	// if ((IDLEV(h)==0) \|\| (next_best==NULL))
5236	// next_best=h;
5237	// else if (IDLEV(next_best)<IDLEV(h))
5238	// next_best=h;
5239	return h;
5240	}
5241	h=IDNEXT(h);
5242	}
5243	//return next_best;
5244	return NULL;
5245	}
5246
5247	extern BOOLEAN jjPROC(leftv res, leftv u, leftv v);
5248	ideal kGroebner(ideal F, ideal Q)
5249	{
5250	//test\|=Sy_bit(OPT_PROT);
5251	idhdl save_ringhdl=currRingHdl;
5252	ideal resid;
5253	idhdl new_ring=NULL;
5254	if ((currRingHdl==NULL) \|\| (IDRING(currRingHdl)!=currRing))
5255	{
5256	currRingHdl=enterid(omStrDup(" GROEBNERring"),0,RING_CMD,&IDROOT,FALSE);
5257	new_ring=currRingHdl;
5258	IDRING(currRingHdl)=currRing;
5259	}
5260	sleftv v; memset(&v,0,sizeof(v)); v.rtyp=IDEAL_CMD; v.data=(char *) F;
5261	idhdl h=ggetid("groebner");
5262	sleftv u; memset(&u,0,sizeof(u)); u.rtyp=IDHDL; u.data=(char *) h;
5263	u.name=IDID(h);
5264
5265	sleftv res; memset(&res,0,sizeof(res));
5266	if(jjPROC(&res,&u,&v))
5267	{
5268	resid=kStd(F,Q,testHomog,NULL);
5269	}
5270	else
5271	{
5272	//printf("typ:%d\n",res.rtyp);
5273	resid=(ideal)(res.data);
5274	}
5275	// cleanup GROEBNERring, save_ringhdl, u,v,(res )
5276	if (new_ring!=NULL)
5277	{
5278	idhdl h=IDROOT;
5279	if (h==new_ring) IDROOT=h->next;
5280	else
5281	{
5282	while ((h!=NULL) &&(h->next!=new_ring)) h=h->next;
5283	if (h!=NULL) h->next=h->next->next;
5284	}
5285	if (h!=NULL) omFreeSize(h,sizeof(*h));
5286	}
5287	currRingHdl=save_ringhdl;
5288	u.CleanUp();
5289	v.CleanUp();
5290	return resid;
5291	}
5292
5293	void jjINT_S_TO_ID(int n,int *e, leftv res)
5294	{
5295	if (n==0) n=1;
5296	ideal l=idInit(n,1);
5297	int i;
5298	poly p;
5299	for(i=pVariables;i>0;i--)
5300	{
5301	if (e[i]>0)
5302	{
5303	n--;
5304	p=pOne();
5305	pSetExp(p,i,1);
5306	pSetm(p);
5307	l->m[n]=p;
5308	if (n==0) break;
5309	}
5310	}
5311	res->data=(char*)l;
5312	omFreeSize((ADDRESS)e,(pVariables+1)*sizeof(int));
5313	}
5314	BOOLEAN jjVARIABLES_P(leftv res, leftv u)
5315	{
5316	int e=(int )omAlloc0((pVariables+1)*sizeof(int));
5317	int n=pGetVariables((poly)u->Data(),e);
5318	jjINT_S_TO_ID(n,e,res);
5319	return FALSE;
5320	}
5321
5322	BOOLEAN jjVARIABLES_ID(leftv res, leftv u)
5323	{
5324	int e=(int )omAlloc0((pVariables+1)*sizeof(int));
5325	ideal I=(ideal)u->Data();
5326	int i;
5327	int n=0;
5328	for(i=I->nrows*I->ncols-1;i>=0;i--)
5329	{
5330	n=pGetVariables(I->m[i],e);
5331	}
5332	jjINT_S_TO_ID(n,e,res);
5333	return FALSE;
5334	}

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