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source: git/Singular/ipshell.cc @ 0c2f6d

spielwiese

Last change on this file since 0c2f6d was 0c2f6d, checked in by Frank Seelisch <seelisch@…>, 12 years ago
removed further assume violations git-svn-id: file:///usr/local/Singular/svn/trunk@13965 2c84dea3-7e68-4137-9b89-c4e89433aadc
Property mode set to `100644`
File size: 128.7 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	if ((orig_ring->minpoly != NULL) \|\| (orig_ring->minideal != NULL))
2342	naSetChar(rInternalChar(orig_ring),orig_ring);
2343	else ntSetChar(rInternalChar(orig_ring),orig_ring);
2344	nSetChar(currRing);
2345	test=save_test;
2346	}
2347	else
2348	{
2349	WerrorS("coefficient fields must be equal if q-ideal !=0");
2350	goto rCompose_err;
2351	}
2352	}
2353	perm=(int )omAlloc0((orig_ring->N+1)sizeof(int));
2354	if (par_perm_size!=0)
2355	par_perm=(int )omAlloc0(par_perm_sizesizeof(int));
2356	int i;
2357	#if 0
2358	// use imap:
2359	maFindPerm(orig_ring->names,orig_ring->N,orig_ring->parameter,orig_ring->P,
2360	currRing->names,currRing->N,currRing->parameter, currRing->P,
2361	perm,par_perm, currRing->ch);
2362	#else
2363	// use fetch
2364	if ((rPar(orig_ring)>0) && (rPar(currRing)==0))
2365	{
2366	for(i=si_min(rPar(orig_ring),rVar(currRing))-1;i>=0;i--) par_perm[i]=i+1;
2367	}
2368	else if (par_perm_size!=0)
2369	for(i=si_min(rPar(orig_ring),rPar(currRing))-1;i>=0;i--) par_perm[i]=-(i+1);
2370	for(i=si_min(orig_ring->N,pVariables);i>0;i--) perm[i]=i;
2371	#endif
2372	ideal dest_id=idInit(IDELEMS(q),1);
2373	for(i=IDELEMS(q)-1; i>=0; i--)
2374	{
2375	dest_id->m[i]=pPermPoly(q->m[i],perm,orig_ring,nMap,
2376	par_perm,par_perm_size);
2377	// PrintS("map:");pWrite(dest_id->m[i]);PrintLn();
2378	pTest(dest_id->m[i]);
2379	}
2380	R->qideal=dest_id;
2381	if (perm!=NULL)
2382	omFreeSize((ADDRESS)perm,(orig_ring->N+1)*sizeof(int));
2383	if (par_perm!=NULL)
2384	omFreeSize((ADDRESS)par_perm,par_perm_size*sizeof(int));
2385	rChangeCurrRing(orig_ring);
2386	#endif
2387	}
2388	else
2389	R->qideal=idrCopyR(q,currRing,R);
2390	}
2391	}
2392	else
2393	{
2394	WerrorS("q-ideal must be given as `ideal`");
2395	goto rCompose_err;
2396	}
2397
2398
2399	// ---------------------------------------------------------------
2400	#ifdef HAVE_PLURAL
2401	if (L->nr==5)
2402	{
2403	if (nc_CallPlural((matrix)L->m[4].Data(),(matrix)L->m[5].Data(),NULL,NULL,R, true)) goto rCompose_err;
2404	// takes care about non-comm. quotient! i.e. calls "nc_SetupQuotient" due to last true
2405	}
2406	#endif
2407	return R;
2408
2409	rCompose_err:
2410	if (R->N>0)
2411	{
2412	int i;
2413	if (R->names!=NULL)
2414	{
2415	i=R->N-1;
2416	while (i>=0) { if (R->names[i]!=NULL) omFree(R->names[i]); i--; }
2417	omFree(R->names);
2418	}
2419	}
2420	if (R->order!=NULL) omFree(R->order);
2421	if (R->block0!=NULL) omFree(R->block0);
2422	if (R->block1!=NULL) omFree(R->block1);
2423	if (R->wvhdl!=NULL) omFree(R->wvhdl);
2424	omFree(R);
2425	return NULL;
2426	}
2427
2428	// from matpol.cc
2429
2430	/*2
2431	* compute the jacobi matrix of an ideal
2432	*/
2433	BOOLEAN mpJacobi(leftv res,leftv a)
2434	{
2435	int i,j;
2436	matrix result;
2437	ideal id=(ideal)a->Data();
2438
2439	result =mpNew(IDELEMS(id),pVariables);
2440	for (i=1; i<=IDELEMS(id); i++)
2441	{
2442	for (j=1; j<=pVariables; j++)
2443	{
2444	MATELEM(result,i,j) = pDiff(id->m[i-1],j);
2445	}
2446	}
2447	res->data=(char *)result;
2448	return FALSE;
2449	}
2450
2451	/*2
2452	* returns the Koszul-matrix of degree d of a vectorspace with dimension n
2453	* uses the first n entrees of id, if id <> NULL
2454	*/
2455	BOOLEAN mpKoszul(leftv res,leftv c/ip/, leftv b/in/, leftv id)
2456	{
2457	int n=(int)(long)b->Data();
2458	int d=(int)(long)c->Data();
2459	int k,l,sign,row,col;
2460	matrix result;
2461	ideal temp;
2462	BOOLEAN bo;
2463	poly p;
2464
2465	if ((d>n) \|\| (d<1) \|\| (n<1))
2466	{
2467	res->data=(char *)mpNew(1,1);
2468	return FALSE;
2469	}
2470	int choise = (int)omAlloc(d*sizeof(int));
2471	if (id==NULL)
2472	temp=idMaxIdeal(1);
2473	else
2474	temp=(ideal)id->Data();
2475
2476	k = binom(n,d);
2477	l = k*d;
2478	l /= n-d+1;
2479	result =mpNew(l,k);
2480	col = 1;
2481	idInitChoise(d,1,n,&bo,choise);
2482	while (!bo)
2483	{
2484	sign = 1;
2485	for (l=1;l<=d;l++)
2486	{
2487	if (choise[l-1]<=IDELEMS(temp))
2488	{
2489	p = pCopy(temp->m[choise[l-1]-1]);
2490	if (sign == -1) p = pNeg(p);
2491	sign *= -1;
2492	row = idGetNumberOfChoise(l-1,d,1,n,choise);
2493	MATELEM(result,row,col) = p;
2494	}
2495	}
2496	col++;
2497	idGetNextChoise(d,n,&bo,choise);
2498	}
2499	if (id==NULL) idDelete(&temp);
2500
2501	res->data=(char *)result;
2502	return FALSE;
2503	}
2504
2505	// from syz1.cc
2506	/*2
2507	* read out the Betti numbers from resolution
2508	* (interpreter interface)
2509	*/
2510	BOOLEAN syBetti2(leftv res, leftv u, leftv w)
2511	{
2512	syStrategy syzstr=(syStrategy)u->Data();
2513	BOOLEAN minim=(int)(long)w->Data();
2514	int row_shift=0;
2515	int add_row_shift=0;
2516	intvec *weights=NULL;
2517	intvec ww=(intvec )atGet(u,"isHomog",INTVEC_CMD);
2518	if (ww!=NULL)
2519	{
2520	weights=ivCopy(ww);
2521	add_row_shift = ww->min_in();
2522	(*weights) -= add_row_shift;
2523	}
2524	res->data=(void *)syBettiOfComputation(syzstr,minim,&row_shift,weights);
2525	//row_shift += add_row_shift;
2526	//Print("row_shift=%d, add_row_shift=%d\n",row_shift,add_row_shift);
2527	atSet(res,omStrDup("rowShift"),(void*)add_row_shift,INT_CMD);
2528	return FALSE;
2529	}
2530	BOOLEAN syBetti1(leftv res, leftv u)
2531	{
2532	sleftv tmp;
2533	memset(&tmp,0,sizeof(tmp));
2534	tmp.rtyp=INT_CMD;
2535	tmp.data=(void *)1;
2536	return syBetti2(res,u,&tmp);
2537	}
2538
2539	/*3
2540	* converts a resolution into a list of modules
2541	*/
2542	lists syConvRes(syStrategy syzstr,BOOLEAN toDel,int add_row_shift)
2543	{
2544	if ((syzstr->fullres==NULL) && (syzstr->minres==NULL))
2545	{
2546	if (syzstr->hilb_coeffs==NULL)
2547	{
2548	syzstr->fullres = syReorder(syzstr->res,syzstr->length,syzstr);
2549	}
2550	else
2551	{
2552	syzstr->minres = syReorder(syzstr->orderedRes,syzstr->length,syzstr);
2553	syKillEmptyEntres(syzstr->minres,syzstr->length);
2554	}
2555	}
2556	resolvente tr;
2557	int typ0=IDEAL_CMD;
2558	if (syzstr->minres!=NULL)
2559	tr = syzstr->minres;
2560	else
2561	tr = syzstr->fullres;
2562	resolvente trueres=NULL;
2563	intvec ** w=NULL;
2564	if (syzstr->length>0)
2565	{
2566	trueres=(resolvente)omAlloc0((syzstr->length)*sizeof(ideal));
2567	for (int i=(syzstr->length)-1;i>=0;i--)
2568	{
2569	if (tr[i]!=NULL)
2570	{
2571	trueres[i] = idCopy(tr[i]);
2572	}
2573	}
2574	if (idRankFreeModule(trueres[0]) > 0)
2575	typ0 = MODUL_CMD;
2576	if (syzstr->weights!=NULL)
2577	{
2578	w = (intvec*)omAlloc0((syzstr->length)sizeof(intvec*));
2579	for (int i=(syzstr->length)-1;i>=0;i--)
2580	{
2581	if (syzstr->weights[i]!=NULL) w[i] = ivCopy(syzstr->weights[i]);
2582	}
2583	}
2584	}
2585	lists li = liMakeResolv(trueres,syzstr->length,syzstr->list_length,typ0,
2586	w,add_row_shift);
2587	if (w != NULL) omFreeSize(w, (syzstr->length)sizeof(intvec));
2588	if (toDel) syKillComputation(syzstr);
2589	return li;
2590	}
2591
2592	/*3
2593	* converts a list of modules into a resolution
2594	*/
2595	syStrategy syConvList(lists li,BOOLEAN toDel)
2596	{
2597	int typ0;
2598	syStrategy result=(syStrategy)omAlloc0(sizeof(ssyStrategy));
2599
2600	resolvente fr = liFindRes(li,&(result->length),&typ0,&(result->weights));
2601	if (fr != NULL)
2602	{
2603
2604	result->fullres = (resolvente)omAlloc0((result->length+1)*sizeof(ideal));
2605	for (int i=result->length-1;i>=0;i--)
2606	{
2607	if (fr[i]!=NULL)
2608	result->fullres[i] = idCopy(fr[i]);
2609	}
2610	result->list_length=result->length;
2611	omFreeSize((ADDRESS)fr,(result->length)*sizeof(ideal));
2612	}
2613	else
2614	{
2615	omFreeSize(result, sizeof(ssyStrategy));
2616	result = NULL;
2617	}
2618	if (toDel) li->Clean();
2619	return result;
2620	}
2621
2622	/*3
2623	* converts a list of modules into a minimal resolution
2624	*/
2625	syStrategy syForceMin(lists li)
2626	{
2627	int typ0;
2628	syStrategy result=(syStrategy)omAlloc0(sizeof(ssyStrategy));
2629
2630	resolvente fr = liFindRes(li,&(result->length),&typ0);
2631	result->minres = (resolvente)omAlloc0((result->length+1)*sizeof(ideal));
2632	for (int i=result->length-1;i>=0;i--)
2633	{
2634	if (fr[i]!=NULL)
2635	result->minres[i] = idCopy(fr[i]);
2636	}
2637	omFreeSize((ADDRESS)fr,(result->length)*sizeof(ideal));
2638	return result;
2639	}
2640	// from weight.cc
2641	BOOLEAN kWeight(leftv res,leftv id)
2642	{
2643	ideal F=(ideal)id->Data();
2644	intvec * iv = new intvec(pVariables);
2645	polyset s;
2646	int sl, n, i;
2647	int *x;
2648
2649	res->data=(char *)iv;
2650	s = F->m;
2651	sl = IDELEMS(F) - 1;
2652	n = pVariables;
2653	double wNsqr = (double)2.0 / (double)n;
2654	wFunctional = wFunctionalBuch;
2655	x = (int * )omAlloc(2 * (n + 1) * sizeof(int));
2656	wCall(s, sl, x, wNsqr);
2657	for (i = n; i!=0; i--)
2658	(*iv)[i-1] = x[i + n + 1];
2659	omFreeSize((ADDRESS)x, 2 * (n + 1) * sizeof(int));
2660	return FALSE;
2661	}
2662
2663	BOOLEAN kQHWeight(leftv res,leftv v)
2664	{
2665	res->data=(char *)idQHomWeight((ideal)v->Data());
2666	if (res->data==NULL)
2667	res->data=(char *)new intvec(pVariables);
2668	return FALSE;
2669	}
2670	/==============================================================/
2671	// from clapsing.cc
2672	#if 0
2673	BOOLEAN jjIS_SQR_FREE(leftv res, leftv u)
2674	{
2675	BOOLEAN b=singclap_factorize((poly)(u->CopyD()), &v, 0);
2676	res->data=(void *)b;
2677	}
2678	#endif
2679
2680	#ifdef HAVE_FACTORY
2681	BOOLEAN jjRESULTANT(leftv res, leftv u, leftv v, leftv w)
2682	{
2683	res->data=singclap_resultant((poly)u->CopyD(),(poly)v->CopyD(), (poly)w->CopyD());
2684	return errorreported;
2685	}
2686	BOOLEAN jjCHARSERIES(leftv res, leftv u)
2687	{
2688	res->data=singclap_irrCharSeries((ideal)u->Data());
2689	return (res->data==NULL);
2690	}
2691	#endif
2692
2693	// from semic.cc
2694	#ifdef HAVE_SPECTRUM
2695
2696	// ----------------------------------------------------------------------------
2697	// Initialize a spectrum deep from another spectrum
2698	// ----------------------------------------------------------------------------
2699
2700	void spectrum::copy_deep( const spectrum &spec )
2701	{
2702	mu = spec.mu;
2703	pg = spec.pg;
2704	n = spec.n;
2705
2706	copy_new( n );
2707
2708	for( int i=0; i<n; i++ )
2709	{
2710	s[i] = spec.s[i];
2711	w[i] = spec.w[i];
2712	}
2713	}
2714
2715	// ----------------------------------------------------------------------------
2716	// Initialize a spectrum deep from a singular lists
2717	// ----------------------------------------------------------------------------
2718
2719	void spectrum::copy_deep( lists l )
2720	{
2721	mu = (int)(long)(l->m[0].Data( ));
2722	pg = (int)(long)(l->m[1].Data( ));
2723	n = (int)(long)(l->m[2].Data( ));
2724
2725	copy_new( n );
2726
2727	intvec num = (intvec)l->m[3].Data( );
2728	intvec den = (intvec)l->m[4].Data( );
2729	intvec mul = (intvec)l->m[5].Data( );
2730
2731	for( int i=0; i<n; i++ )
2732	{
2733	s[i] = (Rational)((num)[i])/(Rational)((den)[i]);
2734	w[i] = (*mul)[i];
2735	}
2736	}
2737
2738	// ----------------------------------------------------------------------------
2739	// singular lists constructor for spectrum
2740	// ----------------------------------------------------------------------------
2741
2742	spectrum::spectrum( lists l )
2743	{
2744	copy_deep( l );
2745	}
2746
2747	// ----------------------------------------------------------------------------
2748	// generate a Singular lists from a spectrum
2749	// ----------------------------------------------------------------------------
2750
2751	lists spectrum::thelist( void )
2752	{
2753	lists L = (lists)omAllocBin( slists_bin);
2754
2755	L->Init( 6 );
2756
2757	intvec *num = new intvec( n );
2758	intvec *den = new intvec( n );
2759	intvec *mult = new intvec( n );
2760
2761	for( int i=0; i<n; i++ )
2762	{
2763	(*num) [i] = s[i].get_num_si( );
2764	(*den) [i] = s[i].get_den_si( );
2765	(*mult)[i] = w[i];
2766	}
2767
2768	L->m[0].rtyp = INT_CMD; // milnor number
2769	L->m[1].rtyp = INT_CMD; // geometrical genus
2770	L->m[2].rtyp = INT_CMD; // # of spectrum numbers
2771	L->m[3].rtyp = INTVEC_CMD; // numerators
2772	L->m[4].rtyp = INTVEC_CMD; // denomiantors
2773	L->m[5].rtyp = INTVEC_CMD; // multiplicities
2774
2775	L->m[0].data = (void*)mu;
2776	L->m[1].data = (void*)pg;
2777	L->m[2].data = (void*)n;
2778	L->m[3].data = (void*)num;
2779	L->m[4].data = (void*)den;
2780	L->m[5].data = (void*)mult;
2781
2782	return L;
2783	}
2784	// from spectrum.cc
2785	// ----------------------------------------------------------------------------
2786	// print out an error message for a spectrum list
2787	// ----------------------------------------------------------------------------
2788
2789	void list_error( semicState state )
2790	{
2791	switch( state )
2792	{
2793	case semicListTooShort:
2794	WerrorS( "the list is too short" );
2795	break;
2796	case semicListTooLong:
2797	WerrorS( "the list is too long" );
2798	break;
2799
2800	case semicListFirstElementWrongType:
2801	WerrorS( "first element of the list should be int" );
2802	break;
2803	case semicListSecondElementWrongType:
2804	WerrorS( "second element of the list should be int" );
2805	break;
2806	case semicListThirdElementWrongType:
2807	WerrorS( "third element of the list should be int" );
2808	break;
2809	case semicListFourthElementWrongType:
2810	WerrorS( "fourth element of the list should be intvec" );
2811	break;
2812	case semicListFifthElementWrongType:
2813	WerrorS( "fifth element of the list should be intvec" );
2814	break;
2815	case semicListSixthElementWrongType:
2816	WerrorS( "sixth element of the list should be intvec" );
2817	break;
2818
2819	case semicListNNegative:
2820	WerrorS( "first element of the list should be positive" );
2821	break;
2822	case semicListWrongNumberOfNumerators:
2823	WerrorS( "wrong number of numerators" );
2824	break;
2825	case semicListWrongNumberOfDenominators:
2826	WerrorS( "wrong number of denominators" );
2827	break;
2828	case semicListWrongNumberOfMultiplicities:
2829	WerrorS( "wrong number of multiplicities" );
2830	break;
2831
2832	case semicListMuNegative:
2833	WerrorS( "the Milnor number should be positive" );
2834	break;
2835	case semicListPgNegative:
2836	WerrorS( "the geometrical genus should be nonnegative" );
2837	break;
2838	case semicListNumNegative:
2839	WerrorS( "all numerators should be positive" );
2840	break;
2841	case semicListDenNegative:
2842	WerrorS( "all denominators should be positive" );
2843	break;
2844	case semicListMulNegative:
2845	WerrorS( "all multiplicities should be positive" );
2846	break;
2847
2848	case semicListNotSymmetric:
2849	WerrorS( "it is not symmetric" );
2850	break;
2851	case semicListNotMonotonous:
2852	WerrorS( "it is not monotonous" );
2853	break;
2854
2855	case semicListMilnorWrong:
2856	WerrorS( "the Milnor number is wrong" );
2857	break;
2858	case semicListPGWrong:
2859	WerrorS( "the geometrical genus is wrong" );
2860	break;
2861
2862	default:
2863	WerrorS( "unspecific error" );
2864	break;
2865	}
2866	}
2867	// ----------------------------------------------------------------------------
2868	// this is the main spectrum computation function
2869	// ----------------------------------------------------------------------------
2870
2871	spectrumState spectrumCompute( poly h,lists *L,int fast )
2872	{
2873	int i,j;
2874
2875	#ifdef SPECTRUM_DEBUG
2876	#ifdef SPECTRUM_PRINT
2877	#ifdef SPECTRUM_IOSTREAM
2878	cout << "spectrumCompute\n";
2879	if( fast==0 ) cout << " no optimization" << endl;
2880	if( fast==1 ) cout << " weight optimization" << endl;
2881	if( fast==2 ) cout << " symmetry optimization" << endl;
2882	#else
2883	fprintf( stdout,"spectrumCompute\n" );
2884	if( fast==0 ) fprintf( stdout," no optimization\n" );
2885	if( fast==1 ) fprintf( stdout," weight optimization\n" );
2886	if( fast==2 ) fprintf( stdout," symmetry optimization\n" );
2887	#endif
2888	#endif
2889	#endif
2890
2891	// ----------------------
2892	// check if h is zero
2893	// ----------------------
2894
2895	if( h==(poly)NULL )
2896	{
2897	return spectrumZero;
2898	}
2899
2900	// ----------------------------------
2901	// check if h has a constant term
2902	// ----------------------------------
2903
2904	if( hasConstTerm( h ) )
2905	{
2906	return spectrumBadPoly;
2907	}
2908
2909	// --------------------------------
2910	// check if h has a linear term
2911	// --------------------------------
2912
2913	if( hasLinearTerm( h ) )
2914	{
2915	*L = (lists)omAllocBin( slists_bin);
2916	(*L)->Init( 1 );
2917	(*L)->m[0].rtyp = INT_CMD; // milnor number
2918	/* (L)->m[0].data = (void)0;a -- done by Init */
2919
2920	return spectrumNoSingularity;
2921	}
2922
2923	// ----------------------------------
2924	// compute the jacobi ideal of (h)
2925	// ----------------------------------
2926
2927	ideal J = NULL;
2928	J = idInit( pVariables,1 );
2929
2930	#ifdef SPECTRUM_DEBUG
2931	#ifdef SPECTRUM_PRINT
2932	#ifdef SPECTRUM_IOSTREAM
2933	cout << "\n computing the Jacobi ideal...\n";
2934	#else
2935	fprintf( stdout,"\n computing the Jacobi ideal...\n" );
2936	#endif
2937	#endif
2938	#endif
2939
2940	for( i=0; i<pVariables; i++ )
2941	{
2942	J->m[i] = pDiff( h,i+1); //j );
2943
2944	#ifdef SPECTRUM_DEBUG
2945	#ifdef SPECTRUM_PRINT
2946	#ifdef SPECTRUM_IOSTREAM
2947	cout << " ";
2948	#else
2949	fprintf( stdout," " );
2950	#endif
2951	pWrite( J->m[i] );
2952	#endif
2953	#endif
2954	}
2955
2956	// --------------------------------------------
2957	// compute a standard basis stdJ of jac(h)
2958	// --------------------------------------------
2959
2960	#ifdef SPECTRUM_DEBUG
2961	#ifdef SPECTRUM_PRINT
2962	#ifdef SPECTRUM_IOSTREAM
2963	cout << endl;
2964	cout << " computing a standard basis..." << endl;
2965	#else
2966	fprintf( stdout,"\n" );
2967	fprintf( stdout," computing a standard basis...\n" );
2968	#endif
2969	#endif
2970	#endif
2971
2972	ideal stdJ = kStd(J,currQuotient,isNotHomog,NULL);
2973	idSkipZeroes( stdJ );
2974
2975	#ifdef SPECTRUM_DEBUG
2976	#ifdef SPECTRUM_PRINT
2977	for( i=0; i<IDELEMS(stdJ); i++ )
2978	{
2979	#ifdef SPECTRUM_IOSTREAM
2980	cout << " ";
2981	#else
2982	fprintf( stdout," " );
2983	#endif
2984
2985	pWrite( stdJ->m[i] );
2986	}
2987	#endif
2988	#endif
2989
2990	idDelete( &J );
2991
2992	// ------------------------------------------
2993	// check if the h has a singularity
2994	// ------------------------------------------
2995
2996	if( hasOne( stdJ ) )
2997	{
2998	// -------------------------------
2999	// h is smooth in the origin
3000	// return only the Milnor number
3001	// -------------------------------
3002
3003	*L = (lists)omAllocBin( slists_bin);
3004	(*L)->Init( 1 );
3005	(*L)->m[0].rtyp = INT_CMD; // milnor number
3006	/* (L)->m[0].data = (void)0;a -- done by Init */
3007
3008	return spectrumNoSingularity;
3009	}
3010
3011	// ------------------------------------------
3012	// check if the singularity h is isolated
3013	// ------------------------------------------
3014
3015	for( i=pVariables; i>0; i-- )
3016	{
3017	if( hasAxis( stdJ,i )==FALSE )
3018	{
3019	return spectrumNotIsolated;
3020	}
3021	}
3022
3023	// ------------------------------------------
3024	// compute the highest corner hc of stdJ
3025	// ------------------------------------------
3026
3027	#ifdef SPECTRUM_DEBUG
3028	#ifdef SPECTRUM_PRINT
3029	#ifdef SPECTRUM_IOSTREAM
3030	cout << "\n computing the highest corner...\n";
3031	#else
3032	fprintf( stdout,"\n computing the highest corner...\n" );
3033	#endif
3034	#endif
3035	#endif
3036
3037	poly hc = (poly)NULL;
3038
3039	scComputeHC( stdJ,currQuotient, 0,hc );
3040
3041	if( hc!=(poly)NULL )
3042	{
3043	pGetCoeff(hc) = nInit(1);
3044
3045	for( i=pVariables; i>0; i-- )
3046	{
3047	if( pGetExp( hc,i )>0 ) pDecrExp( hc,i );
3048	}
3049	pSetm( hc );
3050	}
3051	else
3052	{
3053	return spectrumNoHC;
3054	}
3055
3056	#ifdef SPECTRUM_DEBUG
3057	#ifdef SPECTRUM_PRINT
3058	#ifdef SPECTRUM_IOSTREAM
3059	cout << " ";
3060	#else
3061	fprintf( stdout," " );
3062	#endif
3063	pWrite( hc );
3064	#endif
3065	#endif
3066
3067	// ----------------------------------------
3068	// compute the Newton polygon nph of h
3069	// ----------------------------------------
3070
3071	#ifdef SPECTRUM_DEBUG
3072	#ifdef SPECTRUM_PRINT
3073	#ifdef SPECTRUM_IOSTREAM
3074	cout << "\n computing the newton polygon...\n";
3075	#else
3076	fprintf( stdout,"\n computing the newton polygon...\n" );
3077	#endif
3078	#endif
3079	#endif
3080
3081	newtonPolygon nph( h );
3082
3083	#ifdef SPECTRUM_DEBUG
3084	#ifdef SPECTRUM_PRINT
3085	cout << nph;
3086	#endif
3087	#endif
3088
3089	// -----------------------------------------------
3090	// compute the weight corner wc of (stdj,nph)
3091	// -----------------------------------------------
3092
3093	#ifdef SPECTRUM_DEBUG
3094	#ifdef SPECTRUM_PRINT
3095	#ifdef SPECTRUM_IOSTREAM
3096	cout << "\n computing the weight corner...\n";
3097	#else
3098	fprintf( stdout,"\n computing the weight corner...\n" );
3099	#endif
3100	#endif
3101	#endif
3102
3103	poly wc = ( fast==0 ? pCopy( hc ) :
3104	( fast==1 ? computeWC( nph,(Rational)pVariables ) :
3105	/* fast==2 */computeWC( nph,((Rational)pVariables)/(Rational)2 ) ) );
3106
3107	#ifdef SPECTRUM_DEBUG
3108	#ifdef SPECTRUM_PRINT
3109	#ifdef SPECTRUM_IOSTREAM
3110	cout << " ";
3111	#else
3112	fprintf( stdout," " );
3113	#endif
3114	pWrite( wc );
3115	#endif
3116	#endif
3117
3118	// -------------
3119	// compute NF
3120	// -------------
3121
3122	#ifdef SPECTRUM_DEBUG
3123	#ifdef SPECTRUM_PRINT
3124	#ifdef SPECTRUM_IOSTREAM
3125	cout << "\n computing NF...\n" << endl;
3126	#else
3127	fprintf( stdout,"\n computing NF...\n" );
3128	#endif
3129	#endif
3130	#endif
3131
3132	spectrumPolyList NF( &nph );
3133
3134	computeNF( stdJ,hc,wc,&NF );
3135
3136	#ifdef SPECTRUM_DEBUG
3137	#ifdef SPECTRUM_PRINT
3138	cout << NF;
3139	#ifdef SPECTRUM_IOSTREAM
3140	cout << endl;
3141	#else
3142	fprintf( stdout,"\n" );
3143	#endif
3144	#endif
3145	#endif
3146
3147	// ----------------------------
3148	// compute the spectrum of h
3149	// ----------------------------
3150
3151	return NF.spectrum( L,fast );
3152	}
3153
3154	// ----------------------------------------------------------------------------
3155	// this procedure is called from the interpreter
3156	// ----------------------------------------------------------------------------
3157	// first = polynomial
3158	// result = list of spectrum numbers
3159	// ----------------------------------------------------------------------------
3160
3161	BOOLEAN spectrumProc( leftv result,leftv first )
3162	{
3163	spectrumState state = spectrumOK;
3164
3165	// -------------------
3166	// check consistency
3167	// -------------------
3168
3169	// check for a local ring
3170
3171	if( !ringIsLocal( ) )
3172	{
3173	WerrorS( "only works for local orderings" );
3174	state = spectrumWrongRing;
3175	}
3176
3177	// no quotient rings are allowed
3178
3179	else if( currRing->qideal != NULL )
3180	{
3181	WerrorS( "does not work in quotient rings" );
3182	state = spectrumWrongRing;
3183	}
3184	else
3185	{
3186	lists L = (lists)NULL;
3187	int flag = 1; // weight corner optimization is safe
3188
3189	state = spectrumCompute( (poly)first->Data( ),&L,flag );
3190
3191	if( state==spectrumOK )
3192	{
3193	result->rtyp = LIST_CMD;
3194	result->data = (char*)L;
3195	}
3196	else
3197	{
3198	spectrumPrintError(state);
3199	}
3200	}
3201
3202	return (state!=spectrumOK);
3203	}
3204
3205	// ----------------------------------------------------------------------------
3206	// this procedure is called from the interpreter
3207	// ----------------------------------------------------------------------------
3208	// first = polynomial
3209	// result = list of spectrum numbers
3210	// ----------------------------------------------------------------------------
3211
3212	BOOLEAN spectrumfProc( leftv result,leftv first )
3213	{
3214	spectrumState state = spectrumOK;
3215
3216	// -------------------
3217	// check consistency
3218	// -------------------
3219
3220	// check for a local polynomial ring
3221
3222	if( currRing->OrdSgn != -1 )
3223	// ?? HS: the test above is also true for k[x][[y]], k[[x]][y]
3224	// or should we use:
3225	//if( !ringIsLocal( ) )
3226	{
3227	WerrorS( "only works for local orderings" );
3228	state = spectrumWrongRing;
3229	}
3230	else if( currRing->qideal != NULL )
3231	{
3232	WerrorS( "does not work in quotient rings" );
3233	state = spectrumWrongRing;
3234	}
3235	else
3236	{
3237	lists L = (lists)NULL;
3238	int flag = 2; // symmetric optimization
3239
3240	state = spectrumCompute( (poly)first->Data( ),&L,flag );
3241
3242	if( state==spectrumOK )
3243	{
3244	result->rtyp = LIST_CMD;
3245	result->data = (char*)L;
3246	}
3247	else
3248	{
3249	spectrumPrintError(state);
3250	}
3251	}
3252
3253	return (state!=spectrumOK);
3254	}
3255
3256	// ----------------------------------------------------------------------------
3257	// check if a list is a spectrum
3258	// check for:
3259	// list has 6 elements
3260	// 1st element is int (mu=Milnor number)
3261	// 2nd element is int (pg=geometrical genus)
3262	// 3rd element is int (n =number of different spectrum numbers)
3263	// 4th element is intvec (num=numerators)
3264	// 5th element is intvec (den=denomiantors)
3265	// 6th element is intvec (mul=multiplicities)
3266	// exactly n numerators
3267	// exactly n denominators
3268	// exactly n multiplicities
3269	// mu>0
3270	// pg>=0
3271	// n>0
3272	// num>0
3273	// den>0
3274	// mul>0
3275	// symmetriy with respect to numberofvariables/2
3276	// monotony
3277	// mu = sum of all multiplicities
3278	// pg = sum of all multiplicities where num/den<=1
3279	// ----------------------------------------------------------------------------
3280
3281	semicState list_is_spectrum( lists l )
3282	{
3283	// -------------------
3284	// check list length
3285	// -------------------
3286
3287	if( l->nr < 5 )
3288	{
3289	return semicListTooShort;
3290	}
3291	else if( l->nr > 5 )
3292	{
3293	return semicListTooLong;
3294	}
3295
3296	// -------------
3297	// check types
3298	// -------------
3299
3300	if( l->m[0].rtyp != INT_CMD )
3301	{
3302	return semicListFirstElementWrongType;
3303	}
3304	else if( l->m[1].rtyp != INT_CMD )
3305	{
3306	return semicListSecondElementWrongType;
3307	}
3308	else if( l->m[2].rtyp != INT_CMD )
3309	{
3310	return semicListThirdElementWrongType;
3311	}
3312	else if( l->m[3].rtyp != INTVEC_CMD )
3313	{
3314	return semicListFourthElementWrongType;
3315	}
3316	else if( l->m[4].rtyp != INTVEC_CMD )
3317	{
3318	return semicListFifthElementWrongType;
3319	}
3320	else if( l->m[5].rtyp != INTVEC_CMD )
3321	{
3322	return semicListSixthElementWrongType;
3323	}
3324
3325	// -------------------------
3326	// check number of entries
3327	// -------------------------
3328
3329	int mu = (int)(long)(l->m[0].Data( ));
3330	int pg = (int)(long)(l->m[1].Data( ));
3331	int n = (int)(long)(l->m[2].Data( ));
3332
3333	if( n <= 0 )
3334	{
3335	return semicListNNegative;
3336	}
3337
3338	intvec num = (intvec)l->m[3].Data( );
3339	intvec den = (intvec)l->m[4].Data( );
3340	intvec mul = (intvec)l->m[5].Data( );
3341
3342	if( n != num->length( ) )
3343	{
3344	return semicListWrongNumberOfNumerators;
3345	}
3346	else if( n != den->length( ) )
3347	{
3348	return semicListWrongNumberOfDenominators;
3349	}
3350	else if( n != mul->length( ) )
3351	{
3352	return semicListWrongNumberOfMultiplicities;
3353	}
3354
3355	// --------
3356	// values
3357	// --------
3358
3359	if( mu <= 0 )
3360	{
3361	return semicListMuNegative;
3362	}
3363	if( pg < 0 )
3364	{
3365	return semicListPgNegative;
3366	}
3367
3368	int i;
3369
3370	for( i=0; i<n; i++ )
3371	{
3372	if( (*num)[i] <= 0 )
3373	{
3374	return semicListNumNegative;
3375	}
3376	if( (*den)[i] <= 0 )
3377	{
3378	return semicListDenNegative;
3379	}
3380	if( (*mul)[i] <= 0 )
3381	{
3382	return semicListMulNegative;
3383	}
3384	}
3385
3386	// ----------------
3387	// check symmetry
3388	// ----------------
3389
3390	int j;
3391
3392	for( i=0, j=n-1; i<=j; i++,j-- )
3393	{
3394	if( (num)[i] != pVariables((den)[i]) - (num)[j] \|\|
3395	(den)[i] != (den)[j] \|\|
3396	(mul)[i] != (mul)[j] )
3397	{
3398	return semicListNotSymmetric;
3399	}
3400	}
3401
3402	// ----------------
3403	// check monotony
3404	// ----------------
3405
3406	for( i=0, j=1; i<n/2; i++,j++ )
3407	{
3408	if( (num)[i](den)[j] >= (num)[j](den)[i] )
3409	{
3410	return semicListNotMonotonous;
3411	}
3412	}
3413
3414	// ---------------------
3415	// check Milnor number
3416	// ---------------------
3417
3418	for( mu=0, i=0; i<n; i++ )
3419	{
3420	mu += (*mul)[i];
3421	}
3422
3423	if( mu != (int)(long)(l->m[0].Data( )) )
3424	{
3425	return semicListMilnorWrong;
3426	}
3427
3428	// -------------------------
3429	// check geometrical genus
3430	// -------------------------
3431
3432	for( pg=0, i=0; i<n; i++ )
3433	{
3434	if( (num)[i]<=(den)[i] )
3435	{
3436	pg += (*mul)[i];
3437	}
3438	}
3439
3440	if( pg != (int)(long)(l->m[1].Data( )) )
3441	{
3442	return semicListPGWrong;
3443	}
3444
3445	return semicOK;
3446	}
3447
3448	// ----------------------------------------------------------------------------
3449	// this procedure is called from the interpreter
3450	// ----------------------------------------------------------------------------
3451	// first = list of spectrum numbers
3452	// second = list of spectrum numbers
3453	// result = sum of the two lists
3454	// ----------------------------------------------------------------------------
3455
3456	BOOLEAN spaddProc( leftv result,leftv first,leftv second )
3457	{
3458	semicState state;
3459
3460	// -----------------
3461	// check arguments
3462	// -----------------
3463
3464	lists l1 = (lists)first->Data( );
3465	lists l2 = (lists)second->Data( );
3466
3467	if( (state=list_is_spectrum( l1 )) != semicOK )
3468	{
3469	WerrorS( "first argument is not a spectrum:" );
3470	list_error( state );
3471	}
3472	else if( (state=list_is_spectrum( l2 )) != semicOK )
3473	{
3474	WerrorS( "second argument is not a spectrum:" );
3475	list_error( state );
3476	}
3477	else
3478	{
3479	spectrum s1( l1 );
3480	spectrum s2( l2 );
3481	spectrum sum( s1+s2 );
3482
3483	result->rtyp = LIST_CMD;
3484	result->data = (char*)(sum.thelist( ));
3485	}
3486
3487	return (state!=semicOK);
3488	}
3489
3490	// ----------------------------------------------------------------------------
3491	// this procedure is called from the interpreter
3492	// ----------------------------------------------------------------------------
3493	// first = list of spectrum numbers
3494	// second = integer
3495	// result = the multiple of the first list by the second factor
3496	// ----------------------------------------------------------------------------
3497
3498	BOOLEAN spmulProc( leftv result,leftv first,leftv second )
3499	{
3500	semicState state;
3501
3502	// -----------------
3503	// check arguments
3504	// -----------------
3505
3506	lists l = (lists)first->Data( );
3507	int k = (int)(long)second->Data( );
3508
3509	if( (state=list_is_spectrum( l ))!=semicOK )
3510	{
3511	WerrorS( "first argument is not a spectrum" );
3512	list_error( state );
3513	}
3514	else if( k < 0 )
3515	{
3516	WerrorS( "second argument should be positive" );
3517	state = semicMulNegative;
3518	}
3519	else
3520	{
3521	spectrum s( l );
3522	spectrum product( k*s );
3523
3524	result->rtyp = LIST_CMD;
3525	result->data = (char*)product.thelist( );
3526	}
3527
3528	return (state!=semicOK);
3529	}
3530
3531	// ----------------------------------------------------------------------------
3532	// this procedure is called from the interpreter
3533	// ----------------------------------------------------------------------------
3534	// first = list of spectrum numbers
3535	// second = list of spectrum numbers
3536	// result = semicontinuity index
3537	// ----------------------------------------------------------------------------
3538
3539	BOOLEAN semicProc3 ( leftv res,leftv u,leftv v,leftv w )
3540	{
3541	semicState state;
3542	BOOLEAN qh=(((int)(long)w->Data())==1);
3543
3544	// -----------------
3545	// check arguments
3546	// -----------------
3547
3548	lists l1 = (lists)u->Data( );
3549	lists l2 = (lists)v->Data( );
3550
3551	if( (state=list_is_spectrum( l1 ))!=semicOK )
3552	{
3553	WerrorS( "first argument is not a spectrum" );
3554	list_error( state );
3555	}
3556	else if( (state=list_is_spectrum( l2 ))!=semicOK )
3557	{
3558	WerrorS( "second argument is not a spectrum" );
3559	list_error( state );
3560	}
3561	else
3562	{
3563	spectrum s1( l1 );
3564	spectrum s2( l2 );
3565
3566	res->rtyp = INT_CMD;
3567	if (qh)
3568	res->data = (void*)(s1.mult_spectrumh( s2 ));
3569	else
3570	res->data = (void*)(s1.mult_spectrum( s2 ));
3571	}
3572
3573	// -----------------
3574	// check status
3575	// -----------------
3576
3577	return (state!=semicOK);
3578	}
3579	BOOLEAN semicProc ( leftv res,leftv u,leftv v )
3580	{
3581	sleftv tmp;
3582	memset(&tmp,0,sizeof(tmp));
3583	tmp.rtyp=INT_CMD;
3584	/* tmp.data = (void )0; -- done by memset /
3585
3586	return semicProc3(res,u,v,&tmp);
3587	}
3588	// from splist.cc
3589	// ----------------------------------------------------------------------------
3590	// Compute the spectrum of a spectrumPolyList
3591	// ----------------------------------------------------------------------------
3592
3593	spectrumState spectrumPolyList::spectrum( lists *L,int fast )
3594	{
3595	spectrumPolyNode **node = &root;
3596	spectrumPolyNode *search;
3597
3598	poly f,tmp;
3599	int found,cmp;
3600
3601	Rational smax( ( fast==0 ? 0 : pVariables ),
3602	( fast==2 ? 2 : 1 ) );
3603
3604	Rational weight_prev( 0,1 );
3605
3606	int mu = 0; // the milnor number
3607	int pg = 0; // the geometrical genus
3608	int n = 0; // number of different spectral numbers
3609	int z = 0; // number of spectral number equal to smax
3610
3611	int k = 0;
3612
3613	while( (node)!=(spectrumPolyNode)NULL &&
3614	( fast==0 \|\| (*node)->weight<=smax ) )
3615	{
3616	// ---------------------------------------
3617	// determine the first normal form which
3618	// contains the monomial node->mon
3619	// ---------------------------------------
3620
3621	found = FALSE;
3622	search = *node;
3623
3624	while( search!=(spectrumPolyNode*)NULL && found==FALSE )
3625	{
3626	if( search->nf!=(poly)NULL )
3627	{
3628	f = search->nf;
3629
3630	do
3631	{
3632	// --------------------------------
3633	// look for (*node)->mon in f
3634	// --------------------------------
3635
3636	cmp = pCmp( (*node)->mon,f );
3637
3638	if( cmp<0 )
3639	{
3640	f = pNext( f );
3641	}
3642	else if( cmp==0 )
3643	{
3644	// -----------------------------
3645	// we have found a normal form
3646	// -----------------------------
3647
3648	found = TRUE;
3649
3650	// normalize coefficient
3651
3652	number inv = nInvers( pGetCoeff( f ) );
3653	pMult_nn( search->nf,inv );
3654	nDelete( &inv );
3655
3656	// exchange normal forms
3657
3658	tmp = (*node)->nf;
3659	(*node)->nf = search->nf;
3660	search->nf = tmp;
3661	}
3662	}
3663	while( cmp<0 && f!=(poly)NULL );
3664	}
3665	search = search->next;
3666	}
3667
3668	if( found==FALSE )
3669	{
3670	// ------------------------------------------------
3671	// the weight of node->mon is a spectrum number
3672	// ------------------------------------------------
3673
3674	mu++;
3675
3676	if( (*node)->weight<=(Rational)1 ) pg++;
3677	if( (*node)->weight==smax ) z++;
3678	if( (*node)->weight>weight_prev ) n++;
3679
3680	weight_prev = (*node)->weight;
3681	node = &((*node)->next);
3682	}
3683	else
3684	{
3685	// -----------------------------------------------
3686	// determine all other normal form which contain
3687	// the monomial node->mon
3688	// replace for node->mon its normal form
3689	// -----------------------------------------------
3690
3691	while( search!=(spectrumPolyNode*)NULL )
3692	{
3693	if( search->nf!=(poly)NULL )
3694	{
3695	f = search->nf;
3696
3697	do
3698	{
3699	// --------------------------------
3700	// look for (*node)->mon in f
3701	// --------------------------------
3702
3703	cmp = pCmp( (*node)->mon,f );
3704
3705	if( cmp<0 )
3706	{
3707	f = pNext( f );
3708	}
3709	else if( cmp==0 )
3710	{
3711	search->nf = pSub( search->nf,
3712	ppMult_nn( (*node)->nf,pGetCoeff( f ) ) );
3713	pNorm( search->nf );
3714	}
3715	}
3716	while( cmp<0 && f!=(poly)NULL );
3717	}
3718	search = search->next;
3719	}
3720	delete_node( node );
3721	}
3722
3723	}
3724
3725	// --------------------------------------------------------
3726	// fast computation exploits the symmetry of the spectrum
3727	// --------------------------------------------------------
3728
3729	if( fast==2 )
3730	{
3731	mu = 2*mu - z;
3732	n = ( z > 0 ? 2n - 1 : 2n );
3733	}
3734
3735	// --------------------------------------------------------
3736	// compute the spectrum numbers with their multiplicities
3737	// --------------------------------------------------------
3738
3739	intvec *nom = new intvec( n );
3740	intvec *den = new intvec( n );
3741	intvec *mult = new intvec( n );
3742
3743	int count = 0;
3744	int multiplicity = 1;
3745
3746	for( search=root; search!=(spectrumPolyNode*)NULL &&
3747	( fast==0 \|\| search->weight<=smax );
3748	search=search->next )
3749	{
3750	if( search->next==(spectrumPolyNode*)NULL \|\|
3751	search->weight<search->next->weight )
3752	{
3753	(*nom) [count] = search->weight.get_num_si( );
3754	(*den) [count] = search->weight.get_den_si( );
3755	(*mult)[count] = multiplicity;
3756
3757	multiplicity=1;
3758	count++;
3759	}
3760	else
3761	{
3762	multiplicity++;
3763	}
3764	}
3765
3766	// --------------------------------------------------------
3767	// fast computation exploits the symmetry of the spectrum
3768	// --------------------------------------------------------
3769
3770	if( fast==2 )
3771	{
3772	int n1,n2;
3773	for( n1=0, n2=n-1; n1<n2; n1++, n2-- )
3774	{
3775	(nom) [n2] = pVariables(den)[n1]-(nom)[n1];
3776	(den) [n2] = (den)[n1];
3777	(mult)[n2] = (mult)[n1];
3778	}
3779	}
3780
3781	// -----------------------------------
3782	// test if the spectrum is symmetric
3783	// -----------------------------------
3784
3785	if( fast==0 \|\| fast==1 )
3786	{
3787	int symmetric=TRUE;
3788
3789	for( int n1=0, n2=n-1 ; n1<n2 && symmetric==TRUE; n1++, n2-- )
3790	{
3791	if( (mult)[n1]!=(mult)[n2] \|\|
3792	(den) [n1]!= (den)[n2] \|\|
3793	(nom)[n1]+(nom)[n2]!=pVariables(den) [n1] )
3794	{
3795	symmetric = FALSE;
3796	}
3797	}
3798
3799	if( symmetric==FALSE )
3800	{
3801	// ---------------------------------------------
3802	// the spectrum is not symmetric => degenerate
3803	// principal part
3804	// ---------------------------------------------
3805
3806	*L = (lists)omAllocBin( slists_bin);
3807	(*L)->Init( 1 );
3808	(*L)->m[0].rtyp = INT_CMD; // milnor number
3809	(L)->m[0].data = (void)mu;
3810
3811	return spectrumDegenerate;
3812	}
3813	}
3814
3815	*L = (lists)omAllocBin( slists_bin);
3816
3817	(*L)->Init( 6 );
3818
3819	(*L)->m[0].rtyp = INT_CMD; // milnor number
3820	(*L)->m[1].rtyp = INT_CMD; // geometrical genus
3821	(*L)->m[2].rtyp = INT_CMD; // number of spectrum values
3822	(*L)->m[3].rtyp = INTVEC_CMD; // nominators
3823	(*L)->m[4].rtyp = INTVEC_CMD; // denomiantors
3824	(*L)->m[5].rtyp = INTVEC_CMD; // multiplicities
3825
3826	(L)->m[0].data = (void)mu;
3827	(L)->m[1].data = (void)pg;
3828	(L)->m[2].data = (void)n;
3829	(L)->m[3].data = (void)nom;
3830	(L)->m[4].data = (void)den;
3831	(L)->m[5].data = (void)mult;
3832
3833	return spectrumOK;
3834	}
3835
3836	#endif
3837
3838	//from mpr_inout.cc
3839	extern void nPrint(number n);
3840
3841	BOOLEAN loNewtonP( leftv res, leftv arg1 )
3842	{
3843	res->data= (void*)loNewtonPolytope( (ideal)arg1->Data() );
3844	return FALSE;
3845	}
3846
3847	BOOLEAN loSimplex( leftv res, leftv args )
3848	{
3849	if ( !(rField_is_long_R()) )
3850	{
3851	WerrorS("Ground field not implemented!");
3852	return TRUE;
3853	}
3854
3855	simplex * LP;
3856	matrix m;
3857
3858	leftv v= args;
3859	if ( v->Typ() != MATRIX_CMD ) // 1: matrix
3860	return TRUE;
3861	else
3862	m= (matrix)(v->CopyD());
3863
3864	LP = new simplex(MATROWS(m),MATCOLS(m));
3865	LP->mapFromMatrix(m);
3866
3867	v= v->next;
3868	if ( v->Typ() != INT_CMD ) // 2: m = number of constraints
3869	return TRUE;
3870	else
3871	LP->m= (int)(long)(v->Data());
3872
3873	v= v->next;
3874	if ( v->Typ() != INT_CMD ) // 3: n = number of variables
3875	return TRUE;
3876	else
3877	LP->n= (int)(long)(v->Data());
3878
3879	v= v->next;
3880	if ( v->Typ() != INT_CMD ) // 4: m1 = number of <= constraints
3881	return TRUE;
3882	else
3883	LP->m1= (int)(long)(v->Data());
3884
3885	v= v->next;
3886	if ( v->Typ() != INT_CMD ) // 5: m2 = number of >= constraints
3887	return TRUE;
3888	else
3889	LP->m2= (int)(long)(v->Data());
3890
3891	v= v->next;
3892	if ( v->Typ() != INT_CMD ) // 6: m3 = number of == constraints
3893	return TRUE;
3894	else
3895	LP->m3= (int)(long)(v->Data());
3896
3897	#ifdef mprDEBUG_PROT
3898	Print("m (constraints) %d\n",LP->m);
3899	Print("n (columns) %d\n",LP->n);
3900	Print("m1 (<=) %d\n",LP->m1);
3901	Print("m2 (>=) %d\n",LP->m2);
3902	Print("m3 (==) %d\n",LP->m3);
3903	#endif
3904
3905	LP->compute();
3906
3907	lists lres= (lists)omAlloc( sizeof(slists) );
3908	lres->Init( 6 );
3909
3910	lres->m[0].rtyp= MATRIX_CMD; // output matrix
3911	lres->m[0].data=(void*)LP->mapToMatrix(m);
3912
3913	lres->m[1].rtyp= INT_CMD; // found a solution?
3914	lres->m[1].data=(void*)LP->icase;
3915
3916	lres->m[2].rtyp= INTVEC_CMD;
3917	lres->m[2].data=(void*)LP->posvToIV();
3918
3919	lres->m[3].rtyp= INTVEC_CMD;
3920	lres->m[3].data=(void*)LP->zrovToIV();
3921
3922	lres->m[4].rtyp= INT_CMD;
3923	lres->m[4].data=(void*)LP->m;
3924
3925	lres->m[5].rtyp= INT_CMD;
3926	lres->m[5].data=(void*)LP->n;
3927
3928	res->data= (void*)lres;
3929
3930	return FALSE;
3931	}
3932
3933	BOOLEAN nuMPResMat( leftv res, leftv arg1, leftv arg2 )
3934	{
3935	ideal gls = (ideal)(arg1->Data());
3936	int imtype= (int)(long)arg2->Data();
3937
3938	uResultant::resMatType mtype= determineMType( imtype );
3939
3940	// check input ideal ( = polynomial system )
3941	if ( mprIdealCheck( gls, arg1->Name(), mtype, true ) != mprOk )
3942	{
3943	return TRUE;
3944	}
3945
3946	uResultant *resMat= new uResultant( gls, mtype, false );
3947	if (resMat!=NULL)
3948	{
3949	res->rtyp = MODUL_CMD;
3950	res->data= (void*)resMat->accessResMat()->getMatrix();
3951	if (!errorreported) delete resMat;
3952	}
3953	return errorreported;
3954	}
3955
3956	BOOLEAN nuLagSolve( leftv res, leftv arg1, leftv arg2, leftv arg3 )
3957	{
3958
3959	poly gls;
3960	gls= (poly)(arg1->Data());
3961	int howclean= (int)(long)arg3->Data();
3962
3963	if ( !(rField_is_R() \|\|
3964	rField_is_Q() \|\|
3965	rField_is_long_R() \|\|
3966	rField_is_long_C()) )
3967	{
3968	WerrorS("Ground field not implemented!");
3969	return TRUE;
3970	}
3971
3972	if ( !(rField_is_R()\|\|rField_is_long_R()\|\|rField_is_long_C()) )
3973	{
3974	unsigned long int ii = (unsigned long int)arg2->Data();
3975	setGMPFloatDigits( ii, ii );
3976	}
3977
3978	if ( gls == NULL \|\| pIsConstant( gls ) )
3979	{
3980	WerrorS("Input polynomial is constant!");
3981	return TRUE;
3982	}
3983
3984	int ldummy;
3985	int deg= pLDeg( gls, &ldummy, currRing );
3986	// int deg= pDeg( gls );
3987	int len= pLength( gls );
3988	int i,vpos=0;
3989	poly piter;
3990	lists elist;
3991	lists rlist;
3992
3993	elist= (lists)omAlloc( sizeof(slists) );
3994	elist->Init( 0 );
3995
3996	if ( pVariables > 1 )
3997	{
3998	piter= gls;
3999	for ( i= 1; i <= pVariables; i++ )
4000	if ( pGetExp( piter, i ) )
4001	{
4002	vpos= i;
4003	break;
4004	}
4005	while ( piter )
4006	{
4007	for ( i= 1; i <= pVariables; i++ )
4008	if ( (vpos != i) && (pGetExp( piter, i ) != 0) )
4009	{
4010	WerrorS("The input polynomial must be univariate!");
4011	return TRUE;
4012	}
4013	pIter( piter );
4014	}
4015	}
4016
4017	rootContainer * roots= new rootContainer();
4018	number * pcoeffs= (number )omAlloc( (deg+1) sizeof( number ) );
4019	piter= gls;
4020	for ( i= deg; i >= 0; i-- )
4021	{
4022	//if ( piter ) Print("deg %d, pDeg(piter) %d\n",i,pTotaldegree(piter));
4023	if ( piter && pTotaldegree(piter) == i )
4024	{
4025	pcoeffs[i]= nCopy( pGetCoeff( piter ) );
4026	//nPrint( pcoeffs[i] );PrintS(" ");
4027	pIter( piter );
4028	}
4029	else
4030	{
4031	pcoeffs[i]= nInit(0);
4032	}
4033	}
4034
4035	#ifdef mprDEBUG_PROT
4036	for (i=deg; i >= 0; i--)
4037	{
4038	nPrint( pcoeffs[i] );PrintS(" ");
4039	}
4040	PrintLn();
4041	#endif
4042
4043	roots->fillContainer( pcoeffs, NULL, 1, deg, rootContainer::onepoly, 1 );
4044	roots->solver( howclean );
4045
4046	int elem= roots->getAnzRoots();
4047	char *out;
4048	char *dummy;
4049	int j;
4050
4051	rlist= (lists)omAlloc( sizeof(slists) );
4052	rlist->Init( elem );
4053
4054	if (rField_is_long_C())
4055	{
4056	for ( j= 0; j < elem; j++ )
4057	{
4058	rlist->m[j].rtyp=NUMBER_CMD;
4059	rlist->m[j].data=(void *)nCopy((number)(roots->getRoot(j)));
4060	//rlist->m[j].data=(void *)(number)(roots->getRoot(j));
4061	}
4062	}
4063	else
4064	{
4065	for ( j= 0; j < elem; j++ )
4066	{
4067	dummy = complexToStr( (*roots)[j], gmp_output_digits );
4068	rlist->m[j].rtyp=STRING_CMD;
4069	rlist->m[j].data=(void *)dummy;
4070	}
4071	}
4072
4073	elist->Clean();
4074	//omFreeSize( (ADDRESS) elist, sizeof(slists) );
4075
4076	// this is (via fillContainer) the same data as in root
4077	//for ( i= deg; i >= 0; i-- ) nDelete( &pcoeffs[i] );
4078	//omFreeSize( (ADDRESS) pcoeffs, (deg+1) * sizeof( number ) );
4079
4080	delete roots;
4081
4082	res->rtyp= LIST_CMD;
4083	res->data= (void*)rlist;
4084
4085	return FALSE;
4086	}
4087
4088	BOOLEAN nuVanderSys( leftv res, leftv arg1, leftv arg2, leftv arg3)
4089	{
4090	int i;
4091	ideal p,w;
4092	p= (ideal)arg1->Data();
4093	w= (ideal)arg2->Data();
4094
4095	// w[0] = f(p^0)
4096	// w[1] = f(p^1)
4097	// ...
4098	// p can be a vector of numbers (multivariate polynom)
4099	// or one number (univariate polynom)
4100	// tdg = deg(f)
4101
4102	int n= IDELEMS( p );
4103	int m= IDELEMS( w );
4104	int tdg= (int)(long)arg3->Data();
4105
4106	res->data= (void*)NULL;
4107
4108	// check the input
4109	if ( tdg < 1 )
4110	{
4111	WerrorS("Last input parameter must be > 0!");
4112	return TRUE;
4113	}
4114	if ( n != pVariables )
4115	{
4116	Werror("Size of first input ideal must be equal to %d!",pVariables);
4117	return TRUE;
4118	}
4119	if ( m != (int)pow((double)tdg+1,(double)n) )
4120	{
4121	Werror("Size of second input ideal must be equal to %d!",
4122	(int)pow((double)tdg+1,(double)n));
4123	return TRUE;
4124	}
4125	if ( !(rField_is_Q() /* \|\|
4126	rField_is_R() \|\| rField_is_long_R() \|\|
4127	rField_is_long_C()*/ ) )
4128	{
4129	WerrorS("Ground field not implemented!");
4130	return TRUE;
4131	}
4132
4133	number tmp;
4134	number pevpoint= (number )omAlloc( n * sizeof( number ) );
4135	for ( i= 0; i < n; i++ )
4136	{
4137	pevpoint[i]=nInit(0);
4138	if ( (p->m)[i] )
4139	{
4140	tmp = pGetCoeff( (p->m)[i] );
4141	if ( nIsZero(tmp) \|\| nIsOne(tmp) \|\| nIsMOne(tmp) )
4142	{
4143	omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
4144	WerrorS("Elements of first input ideal must not be equal to -1, 0, 1!");
4145	return TRUE;
4146	}
4147	} else tmp= NULL;
4148	if ( !nIsZero(tmp) )
4149	{
4150	if ( !pIsConstant((p->m)[i]))
4151	{
4152	omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
4153	WerrorS("Elements of first input ideal must be numbers!");
4154	return TRUE;
4155	}
4156	pevpoint[i]= nCopy( tmp );
4157	}
4158	}
4159
4160	number wresults= (number )omAlloc( m * sizeof( number ) );
4161	for ( i= 0; i < m; i++ )
4162	{
4163	wresults[i]= nInit(0);
4164	if ( (w->m)[i] && !nIsZero(pGetCoeff((w->m)[i])) )
4165	{
4166	if ( !pIsConstant((w->m)[i]))
4167	{
4168	omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
4169	omFreeSize( (ADDRESS)wresults, m * sizeof( number ) );
4170	WerrorS("Elements of second input ideal must be numbers!");
4171	return TRUE;
4172	}
4173	wresults[i]= nCopy(pGetCoeff((w->m)[i]));
4174	}
4175	}
4176
4177	vandermonde vm( m, n, tdg, pevpoint, FALSE );
4178	number *ncpoly= vm.interpolateDense( wresults );
4179	// do not free ncpoly[]!!
4180	poly rpoly= vm.numvec2poly( ncpoly );
4181
4182	omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
4183	omFreeSize( (ADDRESS)wresults, m * sizeof( number ) );
4184
4185	res->data= (void*)rpoly;
4186	return FALSE;
4187	}
4188
4189	BOOLEAN nuUResSolve( leftv res, leftv args )
4190	{
4191	leftv v= args;
4192
4193	ideal gls;
4194	int imtype;
4195	int howclean;
4196
4197	// get ideal
4198	if ( v->Typ() != IDEAL_CMD )
4199	return TRUE;
4200	else gls= (ideal)(v->Data());
4201	v= v->next;
4202
4203	// get resultant matrix type to use (0,1)
4204	if ( v->Typ() != INT_CMD )
4205	return TRUE;
4206	else imtype= (int)(long)v->Data();
4207	v= v->next;
4208
4209	if (imtype==0)
4210	{
4211	ideal test_id=idInit(1,1);
4212	int j;
4213	for(j=IDELEMS(gls)-1;j>=0;j--)
4214	{
4215	if (gls->m[j]!=NULL)
4216	{
4217	test_id->m[0]=gls->m[j];
4218	intvec *dummy_w=idQHomWeight(test_id);
4219	if (dummy_w!=NULL)
4220	{
4221	WerrorS("Newton polytope not of expected dimension");
4222	delete dummy_w;
4223	return TRUE;
4224	}
4225	}
4226	}
4227	}
4228
4229	// get and set precision in digits ( > 0 )
4230	if ( v->Typ() != INT_CMD )
4231	return TRUE;
4232	else if ( !(rField_is_R()\|\|rField_is_long_R()\|\|rField_is_long_C()) )
4233	{
4234	unsigned long int ii=(unsigned long int)v->Data();
4235	setGMPFloatDigits( ii, ii );
4236	}
4237	v= v->next;
4238
4239	// get interpolation steps (0,1,2)
4240	if ( v->Typ() != INT_CMD )
4241	return TRUE;
4242	else howclean= (int)(long)v->Data();
4243
4244	uResultant::resMatType mtype= determineMType( imtype );
4245	int i,c,count;
4246	lists listofroots= NULL;
4247	lists emptylist;
4248	number smv= NULL;
4249	BOOLEAN interpolate_det= (mtype==uResultant::denseResMat)?TRUE:FALSE;
4250
4251	//emptylist= (lists)omAlloc( sizeof(slists) );
4252	//emptylist->Init( 0 );
4253
4254	//res->rtyp = LIST_CMD;
4255	//res->data= (void *)emptylist;
4256
4257	// check input ideal ( = polynomial system )
4258	if ( mprIdealCheck( gls, args->Name(), mtype ) != mprOk )
4259	{
4260	return TRUE;
4261	}
4262
4263	uResultant * ures;
4264	rootContainer ** iproots;
4265	rootContainer ** muiproots;
4266	rootArranger * arranger;
4267
4268	// main task 1: setup of resultant matrix
4269	ures= new uResultant( gls, mtype );
4270	if ( ures->accessResMat()->initState() != resMatrixBase::ready )
4271	{
4272	WerrorS("Error occurred during matrix setup!");
4273	return TRUE;
4274	}
4275
4276	// if dense resultant, check if minor nonsingular
4277	if ( mtype == uResultant::denseResMat )
4278	{
4279	smv= ures->accessResMat()->getSubDet();
4280	#ifdef mprDEBUG_PROT
4281	PrintS("// Determinant of submatrix: ");nPrint(smv);PrintLn();
4282	#endif
4283	if ( nIsZero(smv) )
4284	{
4285	WerrorS("Unsuitable input ideal: Minor of resultant matrix is singular!");
4286	return TRUE;
4287	}
4288	}
4289
4290	// main task 2: Interpolate specialized resultant polynomials
4291	if ( interpolate_det )
4292	iproots= ures->interpolateDenseSP( false, smv );
4293	else
4294	iproots= ures->specializeInU( false, smv );
4295
4296	// main task 3: Interpolate specialized resultant polynomials
4297	if ( interpolate_det )
4298	muiproots= ures->interpolateDenseSP( true, smv );
4299	else
4300	muiproots= ures->specializeInU( true, smv );
4301
4302	#ifdef mprDEBUG_PROT
4303	c= iproots[0]->getAnzElems();
4304	for (i=0; i < c; i++) pWrite(iproots[i]->getPoly());
4305	c= muiproots[0]->getAnzElems();
4306	for (i=0; i < c; i++) pWrite(muiproots[i]->getPoly());
4307	#endif
4308
4309	// main task 4: Compute roots of specialized polys and match them up
4310	arranger= new rootArranger( iproots, muiproots, howclean );
4311	arranger->solve_all();
4312
4313	// get list of roots
4314	if ( arranger->success() )
4315	{
4316	arranger->arrange();
4317	listofroots= arranger->listOfRoots( gmp_output_digits );
4318	}
4319	else
4320	{
4321	WerrorS("Solver was unable to find any roots!");
4322	return TRUE;
4323	}
4324
4325	// free everything
4326	count= iproots[0]->getAnzElems();
4327	for (i=0; i < count; i++) delete iproots[i];
4328	omFreeSize( (ADDRESS) iproots, count * sizeof(rootContainer*) );
4329	count= muiproots[0]->getAnzElems();
4330	for (i=0; i < count; i++) delete muiproots[i];
4331	omFreeSize( (ADDRESS) muiproots, count * sizeof(rootContainer*) );
4332
4333	delete ures;
4334	delete arranger;
4335	nDelete( &smv );
4336
4337	res->data= (void *)listofroots;
4338
4339	//emptylist->Clean();
4340	// omFreeSize( (ADDRESS) emptylist, sizeof(slists) );
4341
4342	return FALSE;
4343	}
4344
4345	// from mpr_numeric.cc
4346	lists rootArranger::listOfRoots( const unsigned int oprec )
4347	{
4348	int i,j,tr;
4349	int count= roots[0]->getAnzRoots(); // number of roots
4350	int elem= roots[0]->getAnzElems(); // number of koordinates per root
4351
4352	lists listofroots= (lists)omAlloc( sizeof(slists) ); // must be done this way!
4353
4354	if ( found_roots )
4355	{
4356	listofroots->Init( count );
4357
4358	for (i=0; i < count; i++)
4359	{
4360	lists onepoint= (lists)omAlloc(sizeof(slists)); // must be done this way!
4361	onepoint->Init(elem);
4362	for ( j= 0; j < elem; j++ )
4363	{
4364	if ( !rField_is_long_C() )
4365	{
4366	onepoint->m[j].rtyp=STRING_CMD;
4367	onepoint->m[j].data=(void )complexToStr((roots[j])[i],oprec);
4368	}
4369	else
4370	{
4371	onepoint->m[j].rtyp=NUMBER_CMD;
4372	onepoint->m[j].data=(void *)nCopy((number)(roots[j]->getRoot(i)));
4373	}
4374	onepoint->m[j].next= NULL;
4375	onepoint->m[j].name= NULL;
4376	}
4377	listofroots->m[i].rtyp=LIST_CMD;
4378	listofroots->m[i].data=(void *)onepoint;
4379	listofroots->m[j].next= NULL;
4380	listofroots->m[j].name= NULL;
4381	}
4382
4383	}
4384	else
4385	{
4386	listofroots->Init( 0 );
4387	}
4388
4389	return listofroots;
4390	}
4391
4392	// from ring.cc
4393	void rSetHdl(idhdl h)
4394	{
4395	int i;
4396	ring rg = NULL;
4397	if (h!=NULL)
4398	{
4399	// Print(" new ring:%s (l:%d)\n",IDID(h),IDLEV(h));
4400	rg = IDRING(h);
4401	if (rg==NULL) return; //id <>NULL, ring==NULL
4402	omCheckAddrSize((ADDRESS)h,sizeof(idrec));
4403	if (IDID(h)) // OB: ????
4404	omCheckAddr((ADDRESS)IDID(h));
4405	rTest(rg);
4406	}
4407
4408	// clean up history
4409	if (sLastPrinted.RingDependend())
4410	{
4411	sLastPrinted.CleanUp();
4412	memset(&sLastPrinted,0,sizeof(sleftv));
4413	}
4414
4415	// test for valid "currRing":
4416	if ((rg!=NULL) && (rg->idroot==NULL))
4417	{
4418	ring old=rg;
4419	rg=rAssure_HasComp(rg);
4420	if (old!=rg)
4421	{
4422	rKill(old);
4423	IDRING(h)=rg;
4424	}
4425	}
4426	/------------ change the global ring -----------------------/
4427	rChangeCurrRing(rg);
4428	currRingHdl = h;
4429	}
4430
4431	BOOLEAN rSleftvOrdering2Ordering(sleftv *ord, ring R)
4432	{
4433	int last = 0, o=0, n = 1, i=0, typ = 1, j;
4434	sleftv *sl = ord;
4435
4436	// determine nBlocks
4437	while (sl!=NULL)
4438	{
4439	intvec iv = (intvec )(sl->data);
4440	if (((iv)[1]==ringorder_c)\|\|((iv)[1]==ringorder_C))
4441	i++;
4442	else if ((*iv)[1]==ringorder_L)
4443	{
4444	R->bitmask=(*iv)[2];
4445	n--;
4446	}
4447	else if (((*iv)[1]!=ringorder_a)
4448	&& ((*iv)[1]!=ringorder_a64))
4449	o++;
4450	n++;
4451	sl=sl->next;
4452	}
4453	// check whether at least one real ordering
4454	if (o==0)
4455	{
4456	WerrorS("invalid combination of orderings");
4457	return TRUE;
4458	}
4459	// if no c/C ordering is given, increment n
4460	if (i==0) n++;
4461	else if (i != 1)
4462	{
4463	// throw error if more than one is given
4464	WerrorS("more than one ordering c/C specified");
4465	return TRUE;
4466	}
4467
4468	// initialize fields of R
4469	R->order=(int )omAlloc0(nsizeof(int));
4470	R->block0=(int )omAlloc0(nsizeof(int));
4471	R->block1=(int )omAlloc0(nsizeof(int));
4472	R->wvhdl=(int*)omAlloc0(nsizeof(int_ptr));
4473
4474	int weights=(int)omAlloc0((R->N+1)*sizeof(int));
4475
4476	// init order, so that rBlocks works correctly
4477	for (j=0; j < n-1; j++)
4478	R->order[j] = (int) ringorder_unspec;
4479	// set last _C order, if no c/C order was given
4480	if (i == 0) R->order[n-2] = ringorder_C;
4481
4482	/* init orders */
4483	sl=ord;
4484	n=-1;
4485	while (sl!=NULL)
4486	{
4487	intvec *iv;
4488	iv = (intvec *)(sl->data);
4489	if ((*iv)[1]!=ringorder_L)
4490	{
4491	n++;
4492
4493	/* the format of an ordering:
4494	* iv[0]: factor
4495	* iv[1]: ordering
4496	* iv[2..end]: weights
4497	*/
4498	R->order[n] = (*iv)[1];
4499	typ=1;
4500	switch ((*iv)[1])
4501	{
4502	case ringorder_ws:
4503	case ringorder_Ws:
4504	typ=-1;
4505	case ringorder_wp:
4506	case ringorder_Wp:
4507	R->wvhdl[n]=(int)omAlloc((iv->length()-1)sizeof(int));
4508	R->block0[n] = last+1;
4509	for (i=2; i<iv->length(); i++)
4510	{
4511	R->wvhdl[n][i-2] = (*iv)[i];
4512	last++;
4513	if (weights[last]==0) weights[last]=(iv)[i]typ;
4514	}
4515	R->block1[n] = last;
4516	break;
4517	case ringorder_ls:
4518	case ringorder_ds:
4519	case ringorder_Ds:
4520	case ringorder_rs:
4521	typ=-1;
4522	case ringorder_lp:
4523	case ringorder_dp:
4524	case ringorder_Dp:
4525	case ringorder_rp:
4526	R->block0[n] = last+1;
4527	if (iv->length() == 3) last+=(*iv)[2];
4528	else last += (*iv)[0];
4529	R->block1[n] = last;
4530	//if ((R->block0[n]>R->block1[n])
4531	//\|\| (R->block1[n]>rVar(R)))
4532	//{
4533	// R->block1[n]=rVar(R);
4534	// //WerrorS("ordering larger than number of variables");
4535	// break;
4536	//}
4537	if (rCheckIV(iv)) return TRUE;
4538	for(i=si_min(rVar(R),R->block1[n]);i>=R->block0[n];i--)
4539	{
4540	if (weights[i]==0) weights[i]=typ;
4541	}
4542	break;
4543	case ringorder_S:
4544	case ringorder_c:
4545	case ringorder_C:
4546	if (rCheckIV(iv)) return TRUE;
4547	break;
4548	case ringorder_aa:
4549	case ringorder_a:
4550	R->block0[n] = last+1;
4551	R->block1[n] = si_min(last+iv->length()-2 , rVar(R));
4552	R->wvhdl[n] = (int)omAlloc((iv->length()-1)sizeof(int));
4553	for (i=2; i<iv->length(); i++)
4554	{
4555	R->wvhdl[n][i-2]=(*iv)[i];
4556	last++;
4557	if (weights[last]==0) weights[last]=(iv)[i]typ;
4558	}
4559	last=R->block0[n]-1;
4560	break;
4561	case ringorder_a64:
4562	{
4563	R->block0[n] = last+1;
4564	R->block1[n] = si_min(last+iv->length()-2 , rVar(R));
4565	R->wvhdl[n] = (int)omAlloc((iv->length()-1)sizeof(int64));
4566	int64 w=(int64 )R->wvhdl[n];
4567	for (i=2; i<iv->length(); i++)
4568	{
4569	w[i-2]=(*iv)[i];
4570	last++;
4571	if (weights[last]==0) weights[last]=(iv)[i]typ;
4572	}
4573	last=R->block0[n]-1;
4574	break;
4575	}
4576	case ringorder_M:
4577	{
4578	int Mtyp=rTypeOfMatrixOrder(iv);
4579	if (Mtyp==0) return TRUE;
4580	if (Mtyp==-1) typ = -1;
4581
4582	R->wvhdl[n] =( int )omAlloc((iv->length()-1)sizeof(int));
4583	for (i=2; i<iv->length();i++)
4584	R->wvhdl[n][i-2]=(*iv)[i];
4585
4586	R->block0[n] = last+1;
4587	last += (int)sqrt((double)(iv->length()-2));
4588	R->block1[n] = last;
4589	for(i=si_min(rVar(R),R->block1[n]);i>=R->block0[n];i--)
4590	{
4591	if (weights[i]==0) weights[i]=typ;
4592	}
4593	break;
4594	}
4595
4596	case ringorder_no:
4597	R->order[n] = ringorder_unspec;
4598	return TRUE;
4599
4600	default:
4601	Werror("Internal Error: Unknown ordering %d", (*iv)[1]);
4602	R->order[n] = ringorder_unspec;
4603	return TRUE;
4604	}
4605	}
4606	sl=sl->next;
4607	}
4608
4609	// check for complete coverage
4610	if ((R->order[n]==ringorder_c) \|\| (R->order[n]==ringorder_C)) n--;
4611	if (R->block1[n] != R->N)
4612	{
4613	if (((R->order[n]==ringorder_dp) \|\|
4614	(R->order[n]==ringorder_ds) \|\|
4615	(R->order[n]==ringorder_Dp) \|\|
4616	(R->order[n]==ringorder_Ds) \|\|
4617	(R->order[n]==ringorder_rp) \|\|
4618	(R->order[n]==ringorder_rs) \|\|
4619	(R->order[n]==ringorder_lp) \|\|
4620	(R->order[n]==ringorder_ls))
4621	&&
4622	R->block0[n] <= R->N)
4623	{
4624	R->block1[n] = R->N;
4625	}
4626	else
4627	{
4628	Werror("mismatch of number of vars (%d) and ordering (%d vars)",
4629	R->N,R->block1[n]);
4630	return TRUE;
4631	}
4632	}
4633	// find OrdSgn:
4634	R->OrdSgn = 1;
4635	for(i=1;i<=R->N;i++)
4636	{ if (weights[i]<0) { R->OrdSgn=-1;break; }}
4637	omFree(weights);
4638	return FALSE;
4639	}
4640
4641	BOOLEAN rSleftvList2StringArray(sleftv* sl, char** p)
4642	{
4643
4644	while(sl!=NULL)
4645	{
4646	if (sl->Name() == sNoName)
4647	{
4648	if (sl->Typ()==POLY_CMD)
4649	{
4650	sleftv s_sl;
4651	iiConvert(POLY_CMD,ANY_TYPE,-1,sl,&s_sl);
4652	if (s_sl.Name() != sNoName)
4653	*p = omStrDup(s_sl.Name());
4654	else
4655	*p = NULL;
4656	sl->next = s_sl.next;
4657	s_sl.next = NULL;
4658	s_sl.CleanUp();
4659	if (*p == NULL) return TRUE;
4660	}
4661	else
4662	return TRUE;
4663	}
4664	else
4665	*p = omStrDup(sl->Name());
4666	p++;
4667	sl=sl->next;
4668	}
4669	return FALSE;
4670	}
4671
4672	#ifdef HAVE_RINGS
4673	char ring_warn_done=0;
4674	#endif
4675
4676	////////////////////
4677	//
4678	// rInit itself:
4679	//
4680	// INPUT: s: name, pn: ch & parameter (names), rv: variable (names)
4681	// ord: ordering
4682	// RETURN: currRingHdl on success
4683	// NULL on error
4684	// NOTE: * makes new ring to current ring, on success
4685	// * considers input sleftv's as read-only
4686	//idhdl rInit(char s, sleftv pn, sleftv* rv, sleftv* ord)
4687	ring rInit(sleftv* pn, sleftv* rv, sleftv* ord)
4688	{
4689	int ch;
4690	#ifdef HAVE_RINGS
4691	unsigned int ringtype = 0;
4692	int_number ringflaga = NULL;
4693	unsigned int ringflagb = 1;
4694	#endif
4695	int float_len=0;
4696	int float_len2=0;
4697	ring R = NULL;
4698	idhdl tmp = NULL;
4699	BOOLEAN ffChar=FALSE;
4700	int typ = 1;
4701
4702	/* ch -------------------------------------------------------*/
4703	// get ch of ground field
4704	int numberOfAllocatedBlocks;
4705
4706	if (pn->Typ()==INT_CMD)
4707	{
4708	ch=(int)(long)pn->Data();
4709	}
4710	else if ((pn->name != NULL)
4711	&& ((strcmp(pn->name,"real")==0) \|\| (strcmp(pn->name,"complex")==0)))
4712	{
4713	BOOLEAN complex_flag=(strcmp(pn->name,"complex")==0);
4714	ch=-1;
4715	if ((pn->next!=NULL) && (pn->next->Typ()==INT_CMD))
4716	{
4717	float_len=(int)(long)pn->next->Data();
4718	float_len2=float_len;
4719	pn=pn->next;
4720	if ((pn->next!=NULL) && (pn->next->Typ()==INT_CMD))
4721	{
4722	float_len2=(int)(long)pn->next->Data();
4723	pn=pn->next;
4724	}
4725	}
4726	if ((pn->next==NULL) && complex_flag)
4727	{
4728	pn->next=(leftv)omAlloc0Bin(sleftv_bin);
4729	pn->next->name=omStrDup("i");
4730	}
4731	}
4732	#ifdef HAVE_RINGS
4733	else if ((pn->name != NULL) && (strcmp(pn->name, "integer") == 0))
4734	{
4735	ringflaga = (int_number) omAlloc(sizeof(mpz_t));
4736	mpz_init_set_si(ringflaga, 0);
4737	if ((pn->next!=NULL) && (pn->next->Typ()==INT_CMD))
4738	{
4739	mpz_set_ui(ringflaga, (int)(long) pn->next->Data());
4740	pn=pn->next;
4741	if ((pn->next!=NULL) && (pn->next->Typ()==INT_CMD))
4742	{
4743	ringflagb = (long) pn->next->Data();
4744	pn=pn->next;
4745	}
4746	while ((pn->next!=NULL) && (pn->next->Typ()==INT_CMD))
4747	{
4748	mpz_mul_ui(ringflaga, ringflaga, (int)(long) pn->next->Data());
4749	pn=pn->next;
4750	}
4751	}
4752	if ((mpz_cmp_ui(ringflaga, 1) == 0) && (mpz_cmp_ui(ringflaga, 0) < 0))
4753	{
4754	Werror("Wrong ground ring specification (module is 1)");
4755	goto rInitError;
4756	}
4757	if (ringflagb < 1)
4758	{
4759	Werror("Wrong ground ring specification (exponent smaller than 1");
4760	goto rInitError;
4761	}
4762	// module is 0 ---> integers
4763	if (mpz_cmp_ui(ringflaga, 0) == 0)
4764	{
4765	ch = 0;
4766	ringtype = 4;
4767	}
4768	// we have an exponent
4769	else if (ringflagb > 1)
4770	{
4771	ch = ringflagb;
4772	if ((mpz_cmp_ui(ringflaga, 2) == 0) && (ringflagb <= 8*sizeof(NATNUMBER)))
4773	{
4774	/* this branch should be active for ringflagb = 2..32 resp. 2..64,
4775	depending on the size of a long on the respective platform */
4776	ringtype = 1; // Use Z/2^ch
4777	}
4778	else
4779	{
4780	ringtype = 3;
4781	}
4782	}
4783	// just a module m > 1
4784	else
4785	{
4786	ringtype = 2;
4787	ch = mpz_get_ui(ringflaga);
4788	}
4789	}
4790	#endif
4791	else
4792	{
4793	Werror("Wrong ground field specification");
4794	goto rInitError;
4795	}
4796	pn=pn->next;
4797
4798	#ifdef HAVE_RINGS
4799	if ((ringtype > 0)&&(ring_warn_done==0))
4800	{
4801	WarnS("You are using coefficient rings which are not fields.");
4802	WarnS("Please note that only limited functionality is available");
4803	WarnS("for these coefficients.");
4804	WarnS("");
4805	WarnS("The following commands are meant to work:");
4806	WarnS("- basic polynomial arithmetic");
4807	WarnS("- std");
4808	WarnS("- syz");
4809	WarnS("- lift");
4810	WarnS("- reduce");
4811	ring_warn_done=1;
4812	}
4813	#endif
4814
4815	int l, last;
4816	sleftv * sl;
4817	/every entry in the new ring is initialized to 0/
4818
4819	/* characteristic -----------------------------------------------*/
4820	/* input: 0 ch=0 : Q parameter=NULL ffChar=FALSE float_len
4821	* 0 1 : Q(a,...) *names FALSE
4822	* 0 -1 : R NULL FALSE 0
4823	* 0 -1 : R NULL FALSE prec. >6
4824	* 0 -1 : C *names FALSE prec. 0..?
4825	* p p : Fp NULL FALSE
4826	* p -p : Fp(a) *names FALSE
4827	* q q : GF(q=p^n) *names TRUE
4828	*/
4829	if ((ch!=-1)
4830	#ifdef HAVE_RINGS
4831	&& (ringtype == 0)
4832	#endif
4833	)
4834	{
4835	int l = 0;
4836
4837	if (((ch!=0) && (ch<2))
4838	#ifndef NV_OPS
4839	\|\| (ch > 32003)
4840	#endif
4841	)
4842	{
4843	Warn("%d is invalid characteristic of ground field. 32003 is used.", ch);
4844	ch=32003;
4845	}
4846	// load fftable, if necessary
4847	if (pn!=NULL)
4848	{
4849	while ((ch!=fftable[l]) && (fftable[l])) l++;
4850	if (fftable[l]==0) ch = IsPrime(ch);
4851	else
4852	{
4853	char m[1]={(char )sNoName};
4854	nfSetChar(ch,m);
4855	if (errorreported) goto rInitError;
4856	else ffChar=TRUE;
4857	}
4858	}
4859	else
4860	{
4861	ch = IsPrime(ch);
4862	}
4863	}
4864	// allocated ring and set ch
4865	R = (ring) omAlloc0Bin(sip_sring_bin);
4866	R->ch = ch;
4867	#ifdef HAVE_RINGS
4868	R->ringtype = ringtype;
4869	R->ringflaga = ringflaga;
4870	R->ringflagb = ringflagb;
4871	#endif
4872	if (ch == -1)
4873	{
4874	R->float_len= si_min(float_len,32767);
4875	R->float_len2= si_min(float_len2,32767);
4876	}
4877
4878	/* parameter -------------------------------------------------------*/
4879	if (pn!=NULL)
4880	{
4881	R->P=pn->listLength();
4882	//if ((ffChar\|\| (ch == 1)) && (R->P > 1))
4883	if ((R->P > 1) && (ffChar \|\| (ch == -1)))
4884	{
4885	WerrorS("too many parameters");
4886	goto rInitError;
4887	}
4888	R->parameter=(char*)omAlloc0(R->Psizeof(char_ptr));
4889	if (rSleftvList2StringArray(pn, R->parameter))
4890	{
4891	WerrorS("parameter expected");
4892	goto rInitError;
4893	}
4894	if (ch>1 && !ffChar) R->ch=-ch;
4895	else if (ch==0) R->ch=1;
4896	}
4897	else if (ffChar)
4898	{
4899	WerrorS("need one parameter");
4900	goto rInitError;
4901	}
4902	/* post-processing of field description */
4903	// we have short reals, but no short complex
4904	if ((R->ch == - 1)
4905	&& (R->parameter !=NULL)
4906	&& (R->float_len < SHORT_REAL_LENGTH))
4907	{
4908	R->float_len = SHORT_REAL_LENGTH;
4909	R->float_len2 = SHORT_REAL_LENGTH;
4910	}
4911
4912	/* names and number of variables-------------------------------------*/
4913	{
4914	int l=rv->listLength();
4915	#if SIZEOF_SHORT == 2
4916	#define MAX_SHORT 0x7fff
4917	#endif
4918	if (l>MAX_SHORT)
4919	{
4920	Werror("too many ring variables(%d), max is %d",l,MAX_SHORT);
4921	goto rInitError;
4922	}
4923	R->N = l; /rv->listLength();/
4924	}
4925	R->names = (char *)omAlloc0(R->N sizeof(char_ptr));
4926	if (rSleftvList2StringArray(rv, R->names))
4927	{
4928	WerrorS("name of ring variable expected");
4929	goto rInitError;
4930	}
4931
4932	/* check names and parameters for conflicts ------------------------- */
4933	rRenameVars(R); // conflicting variables will be renamed
4934	/* ordering -------------------------------------------------------------*/
4935	if (rSleftvOrdering2Ordering(ord, R))
4936	goto rInitError;
4937
4938	// Complete the initialization
4939	if (rComplete(R,1))
4940	goto rInitError;
4941
4942	rTest(R);
4943
4944	// try to enter the ring into the name list
4945	// need to clean up sleftv here, before this ring can be set to
4946	// new currRing or currRing can be killed beacuse new ring has
4947	// same name
4948	if (pn != NULL) pn->CleanUp();
4949	if (rv != NULL) rv->CleanUp();
4950	if (ord != NULL) ord->CleanUp();
4951	//if ((tmp = enterid(s, myynest, RING_CMD, &IDROOT))==NULL)
4952	// goto rInitError;
4953
4954	//memcpy(IDRING(tmp),R,sizeof(*R));
4955	// set current ring
4956	//omFreeBin(R, ip_sring_bin);
4957	//return tmp;
4958	return R;
4959
4960	// error case:
4961	rInitError:
4962	if (R != NULL) rDelete(R);
4963	if (pn != NULL) pn->CleanUp();
4964	if (rv != NULL) rv->CleanUp();
4965	if (ord != NULL) ord->CleanUp();
4966	return NULL;
4967	}
4968
4969	ring rSubring(ring org_ring, sleftv* rv)
4970	{
4971	ring R = rCopy0(org_ring);
4972	int perm=(int )omAlloc0((org_ring->N+1)*sizeof(int));
4973	int last = 0, o=0, n = rBlocks(org_ring), i=0, typ = 1, j;
4974
4975	/* names and number of variables-------------------------------------*/
4976	{
4977	int l=rv->listLength();
4978	if (l>MAX_SHORT)
4979	{
4980	Werror("too many ring variables(%d), max is %d",l,MAX_SHORT);
4981	goto rInitError;
4982	}
4983	R->N = l; /rv->listLength();/
4984	}
4985	omFree(R->names);
4986	R->names = (char *)omAlloc0(R->N sizeof(char_ptr));
4987	if (rSleftvList2StringArray(rv, R->names))
4988	{
4989	WerrorS("name of ring variable expected");
4990	goto rInitError;
4991	}
4992
4993	/* check names for subring in org_ring ------------------------- */
4994	{
4995	i=0;
4996
4997	for(j=0;j<R->N;j++)
4998	{
4999	for(;i<org_ring->N;i++)
5000	{
5001	if (strcmp(org_ring->names[i],R->names[j])==0)
5002	{
5003	perm[i+1]=j+1;
5004	break;
5005	}
5006	}
5007	if (i>org_ring->N)
5008	{
5009	Werror("variable %d (%s) not in basering",j+1,R->names[j]);
5010	break;
5011	}
5012	}
5013	}
5014	//Print("perm=");
5015	//for(i=1;i<org_ring->N;i++) Print("v%d -> v%d\n",i,perm[i]);
5016	/* ordering -------------------------------------------------------------*/
5017
5018	for(i=0;i<n;i++)
5019	{
5020	int min_var=-1;
5021	int max_var=-1;
5022	for(j=R->block0[i];j<=R->block1[i];j++)
5023	{
5024	if (perm[j]>0)
5025	{
5026	if (min_var==-1) min_var=perm[j];
5027	max_var=perm[j];
5028	}
5029	}
5030	if (min_var!=-1)
5031	{
5032	//Print("block %d: old %d..%d, now:%d..%d\n",
5033	// i,R->block0[i],R->block1[i],min_var,max_var);
5034	R->block0[i]=min_var;
5035	R->block1[i]=max_var;
5036	if (R->wvhdl[i]!=NULL)
5037	{
5038	omFree(R->wvhdl[i]);
5039	R->wvhdl[i]=(int)omAlloc0((max_var-min_var+1)sizeof(int));
5040	for(j=org_ring->block0[i];j<=org_ring->block1[i];j++)
5041	{
5042	if (perm[j]>0)
5043	{
5044	R->wvhdl[i][perm[j]-R->block0[i]]=
5045	org_ring->wvhdl[i][j-org_ring->block0[i]];
5046	//Print("w%d=%d (orig_w%d)\n",perm[j],R->wvhdl[i][perm[j]-R->block0[i]],j);
5047	}
5048	}
5049	}
5050	}
5051	else
5052	{
5053	if(R->block0[i]>0)
5054	{
5055	//Print("skip block %d\n",i);
5056	R->order[i]=ringorder_unspec;
5057	if (R->wvhdl[i] !=NULL) omFree(R->wvhdl[i]);
5058	R->wvhdl[i]=NULL;
5059	}
5060	//else Print("keep block %d\n",i);
5061	}
5062	}
5063	i=n-1;
5064	while(i>0)
5065	{
5066	// removed unneded blocks
5067	if(R->order[i-1]==ringorder_unspec)
5068	{
5069	for(j=i;j<=n;j++)
5070	{
5071	R->order[j-1]=R->order[j];
5072	R->block0[j-1]=R->block0[j];
5073	R->block1[j-1]=R->block1[j];
5074	if (R->wvhdl[j-1] !=NULL) omFree(R->wvhdl[j-1]);
5075	R->wvhdl[j-1]=R->wvhdl[j];
5076	}
5077	R->order[n]=ringorder_unspec;
5078	n--;
5079	}
5080	i--;
5081	}
5082	n=rBlocks(org_ring)-1;
5083	while (R->order[n]==0) n--;
5084	while (R->order[n]==ringorder_unspec) n--;
5085	if ((R->order[n]==ringorder_c) \|\| (R->order[n]==ringorder_C)) n--;
5086	if (R->block1[n] != R->N)
5087	{
5088	if (((R->order[n]==ringorder_dp) \|\|
5089	(R->order[n]==ringorder_ds) \|\|
5090	(R->order[n]==ringorder_Dp) \|\|
5091	(R->order[n]==ringorder_Ds) \|\|
5092	(R->order[n]==ringorder_rp) \|\|
5093	(R->order[n]==ringorder_rs) \|\|
5094	(R->order[n]==ringorder_lp) \|\|
5095	(R->order[n]==ringorder_ls))
5096	&&
5097	R->block0[n] <= R->N)
5098	{
5099	R->block1[n] = R->N;
5100	}
5101	else
5102	{
5103	Werror("mismatch of number of vars (%d) and ordering (%d vars) in block %d",
5104	R->N,R->block1[n],n);
5105	return NULL;
5106	}
5107	}
5108	omFree(perm);
5109	// find OrdSgn:
5110	R->OrdSgn = org_ring->OrdSgn; // IMPROVE!
5111	//for(i=1;i<=R->N;i++)
5112	//{ if (weights[i]<0) { R->OrdSgn=-1;break; }}
5113	//omFree(weights);
5114	// Complete the initialization
5115	if (rComplete(R,1))
5116	goto rInitError;
5117
5118	rTest(R);
5119
5120	if (rv != NULL) rv->CleanUp();
5121
5122	return R;
5123
5124	// error case:
5125	rInitError:
5126	if (R != NULL) rDelete(R);
5127	if (rv != NULL) rv->CleanUp();
5128	return NULL;
5129	}
5130
5131	void rKill(ring r)
5132	{
5133	if ((r->ref<=0)&&(r->order!=NULL))
5134	{
5135	#ifdef RDEBUG
5136	if (traceit &TRACE_SHOW_RINGS) Print("kill ring %lx\n",(long)r);
5137	#endif
5138	if (r->qideal!=NULL)
5139	{
5140	id_Delete(&r->qideal, r);
5141	r->qideal = NULL;
5142	}
5143	int i=1;
5144	int j;
5145	int *pi=r->order;
5146	#ifdef USE_IILOCALRING
5147	for (j=0;j<iiRETURNEXPR_len;j++)
5148	{
5149	if (iiLocalRing[j]==r)
5150	{
5151	if (j<myynest) Warn("killing the basering for level %d",j);
5152	iiLocalRing[j]=NULL;
5153	}
5154	}
5155	#else /* USE_IILOCALRING */
5156	//#endif /* USE_IILOCALRING */
5157	{
5158	proclevel * nshdl = procstack;
5159	int lev=myynest-1;
5160
5161	for(; nshdl != NULL; nshdl = nshdl->next)
5162	{
5163	if (nshdl->cRing==r)
5164	{
5165	Warn("killing the basering for level %d",lev);
5166	nshdl->cRing=NULL;
5167	nshdl->cRingHdl=NULL;
5168	}
5169	}
5170	}
5171	#endif /* USE_IILOCALRING */
5172	// any variables depending on r ?
5173	while (r->idroot!=NULL)
5174	{
5175	killhdl2(r->idroot,&(r->idroot),r);
5176	}
5177	if (r==currRing)
5178	{
5179	// all dependend stuff is done, clean global vars:
5180	if (r->qideal!=NULL)
5181	{
5182	currQuotient=NULL;
5183	}
5184	if (ppNoether!=NULL) pDelete(&ppNoether);
5185	if (sLastPrinted.RingDependend())
5186	{
5187	sLastPrinted.CleanUp();
5188	}
5189	if ((myynest>0) && (iiRETURNEXPR[myynest].RingDependend()))
5190	{
5191	WerrorS("return value depends on local ring variable (export missing ?)");
5192	iiRETURNEXPR[myynest].CleanUp();
5193	}
5194	currRing=NULL;
5195	currRingHdl=NULL;
5196	}
5197
5198	/* nKillChar(r); will be called from inside of rDelete */
5199	rDelete(r);
5200	return;
5201	}
5202	r->ref--;
5203	}
5204
5205	void rKill(idhdl h)
5206	{
5207	ring r = IDRING(h);
5208	int ref=0;
5209	if (r!=NULL)
5210	{
5211	ref=r->ref;
5212	rKill(r);
5213	}
5214	if (h==currRingHdl)
5215	{
5216	if (ref<=0) { currRing=NULL; currRingHdl=NULL;}
5217	else
5218	{
5219	currRingHdl=rFindHdl(r,currRingHdl,NULL);
5220	}
5221	}
5222	}
5223
5224	idhdl rSimpleFindHdl(ring r, idhdl root, idhdl n=NULL)
5225	{
5226	//idhdl next_best=NULL;
5227	idhdl h=root;
5228	while (h!=NULL)
5229	{
5230	if (((IDTYP(h)==RING_CMD)\|\|(IDTYP(h)==QRING_CMD))
5231	&& (h!=n)
5232	&& (IDRING(h)==r)
5233	)
5234	{
5235	// if (IDLEV(h)==myynest)
5236	// return h;
5237	// if ((IDLEV(h)==0) \|\| (next_best==NULL))
5238	// next_best=h;
5239	// else if (IDLEV(next_best)<IDLEV(h))
5240	// next_best=h;
5241	return h;
5242	}
5243	h=IDNEXT(h);
5244	}
5245	//return next_best;
5246	return NULL;
5247	}
5248
5249	extern BOOLEAN jjPROC(leftv res, leftv u, leftv v);
5250	ideal kGroebner(ideal F, ideal Q)
5251	{
5252	//test\|=Sy_bit(OPT_PROT);
5253	idhdl save_ringhdl=currRingHdl;
5254	ideal resid;
5255	idhdl new_ring=NULL;
5256	if ((currRingHdl==NULL) \|\| (IDRING(currRingHdl)!=currRing))
5257	{
5258	currRingHdl=enterid(omStrDup(" GROEBNERring"),0,RING_CMD,&IDROOT,FALSE);
5259	new_ring=currRingHdl;
5260	IDRING(currRingHdl)=currRing;
5261	}
5262	sleftv v; memset(&v,0,sizeof(v)); v.rtyp=IDEAL_CMD; v.data=(char *) F;
5263	idhdl h=ggetid("groebner");
5264	sleftv u; memset(&u,0,sizeof(u)); u.rtyp=IDHDL; u.data=(char *) h;
5265	u.name=IDID(h);
5266
5267	sleftv res; memset(&res,0,sizeof(res));
5268	if(jjPROC(&res,&u,&v))
5269	{
5270	resid=kStd(F,Q,testHomog,NULL);
5271	}
5272	else
5273	{
5274	//printf("typ:%d\n",res.rtyp);
5275	resid=(ideal)(res.data);
5276	}
5277	// cleanup GROEBNERring, save_ringhdl, u,v,(res )
5278	if (new_ring!=NULL)
5279	{
5280	idhdl h=IDROOT;
5281	if (h==new_ring) IDROOT=h->next;
5282	else
5283	{
5284	while ((h!=NULL) &&(h->next!=new_ring)) h=h->next;
5285	if (h!=NULL) h->next=h->next->next;
5286	}
5287	if (h!=NULL) omFreeSize(h,sizeof(*h));
5288	}
5289	currRingHdl=save_ringhdl;
5290	u.CleanUp();
5291	v.CleanUp();
5292	return resid;
5293	}
5294
5295	void jjINT_S_TO_ID(int n,int *e, leftv res)
5296	{
5297	if (n==0) n=1;
5298	ideal l=idInit(n,1);
5299	int i;
5300	poly p;
5301	for(i=pVariables;i>0;i--)
5302	{
5303	if (e[i]>0)
5304	{
5305	n--;
5306	p=pOne();
5307	pSetExp(p,i,1);
5308	pSetm(p);
5309	l->m[n]=p;
5310	if (n==0) break;
5311	}
5312	}
5313	res->data=(char*)l;
5314	omFreeSize((ADDRESS)e,(pVariables+1)*sizeof(int));
5315	}
5316	BOOLEAN jjVARIABLES_P(leftv res, leftv u)
5317	{
5318	int e=(int )omAlloc0((pVariables+1)*sizeof(int));
5319	int n=pGetVariables((poly)u->Data(),e);
5320	jjINT_S_TO_ID(n,e,res);
5321	return FALSE;
5322	}
5323
5324	BOOLEAN jjVARIABLES_ID(leftv res, leftv u)
5325	{
5326	int e=(int )omAlloc0((pVariables+1)*sizeof(int));
5327	ideal I=(ideal)u->Data();
5328	int i;
5329	int n=0;
5330	for(i=I->nrows*I->ncols-1;i>=0;i--)
5331	{
5332	n=pGetVariables(I->m[i],e);
5333	}
5334	jjINT_S_TO_ID(n,e,res);
5335	return FALSE;
5336	}

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