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source: git/Singular/ipshell.cc @ 31a392

spielwiese

Last change on this file since 31a392 was cf21dd4, checked in by Frank Seelisch <seelisch@…>, 14 years ago
extends Z/2^m to m =32 resp. 64 (depending on platform) git-svn-id: file:///usr/local/Singular/svn/trunk@13035 2c84dea3-7e68-4137-9b89-c4e89433aadc
Property mode set to `100644`
File size: 128.3 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 <Singular/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.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.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	R->algring->qideal->m[0]=NULL;
2276	idDelete(&(R->algring->qideal));
2277	}
2278	else
2279	{
2280	WerrorS("not implemented yet.");
2281	}
2282	}
2283	}
2284	else
2285	{ // gf-char
2286	R->ch=fftable[is_gf_char];
2287	R->P=1;
2288	R->parameter=(char*)omAlloc0(1sizeof(char_ptr));
2289	R->parameter[0]=omStrDup((char*)((lists)(LL->m[1].Data()))->m[0].Data());
2290	}
2291	}
2292	}
2293	else
2294	{
2295	WerrorS("coefficient field must be described by `int` or `list`");
2296	goto rCompose_err;
2297	}
2298	rRenameVars(R);
2299	// ------------------------ Q-IDEAL ------------------------
2300	rComplete(R);
2301
2302	if (L->m[3].Typ()==IDEAL_CMD)
2303	{
2304	ideal q=(ideal)L->m[3].Data();
2305	if (q->m[0]!=NULL)
2306	{
2307	if (R->ch!=currRing->ch)
2308	{
2309	#if 0
2310	WerrorS("coefficient fields must be equal if q-ideal !=0");
2311	goto rCompose_err;
2312	#else
2313	ring orig_ring=currRing;
2314	rChangeCurrRing(R);
2315	int *perm=NULL;
2316	int *par_perm=NULL;
2317	int par_perm_size=0;
2318	nMapFunc nMap;
2319	BOOLEAN bo;
2320
2321	if ((nMap=nSetMap(orig_ring))==NULL)
2322	{
2323	if (rEqual(orig_ring,currRing))
2324	{
2325	nMap=nCopy;
2326	}
2327	else
2328	// Allow imap/fetch to be make an exception only for:
2329	if ( (rField_is_Q_a(orig_ring) && // Q(a..) -> Q(a..) \|\| Q \|\| Zp \|\| Zp(a)
2330	(rField_is_Q() \|\| rField_is_Q_a() \|\|
2331	(rField_is_Zp() \|\| rField_is_Zp_a())))
2332	\|\|
2333	(rField_is_Zp_a(orig_ring) && // Zp(a..) -> Zp(a..) \|\| Zp
2334	(rField_is_Zp(currRing, rInternalChar(orig_ring)) \|\|
2335	rField_is_Zp_a(currRing, rInternalChar(orig_ring)))) )
2336	{
2337	par_perm_size=rPar(orig_ring);
2338	BITSET save_test=test;
2339	naSetChar(rInternalChar(orig_ring),orig_ring);
2340	nSetChar(currRing);
2341	test=save_test;
2342	}
2343	else
2344	{
2345	WerrorS("coefficient fields must be equal if q-ideal !=0");
2346	goto rCompose_err;
2347	}
2348	}
2349	perm=(int )omAlloc0((orig_ring->N+1)sizeof(int));
2350	if (par_perm_size!=0)
2351	par_perm=(int )omAlloc0(par_perm_sizesizeof(int));
2352	int i;
2353	#if 0
2354	// use imap:
2355	maFindPerm(orig_ring->names,orig_ring->N,orig_ring->parameter,orig_ring->P,
2356	currRing->names,currRing->N,currRing->parameter, currRing->P,
2357	perm,par_perm, currRing->ch);
2358	#else
2359	// use fetch
2360	if ((rPar(orig_ring)>0) && (rPar(currRing)==0))
2361	{
2362	for(i=si_min(rPar(orig_ring),rVar(currRing))-1;i>=0;i--) par_perm[i]=i+1;
2363	}
2364	else if (par_perm_size!=0)
2365	for(i=si_min(rPar(orig_ring),rPar(currRing))-1;i>=0;i--) par_perm[i]=-(i+1);
2366	for(i=si_min(orig_ring->N,pVariables);i>0;i--) perm[i]=i;
2367	#endif
2368	ideal dest_id=idInit(IDELEMS(q),1);
2369	for(i=IDELEMS(q)-1; i>=0; i--)
2370	{
2371	dest_id->m[i]=pPermPoly(q->m[i],perm,orig_ring,nMap,
2372	par_perm,par_perm_size);
2373	// PrintS("map:");pWrite(dest_id->m[i]);PrintLn();
2374	pTest(dest_id->m[i]);
2375	}
2376	R->qideal=dest_id;
2377	if (perm!=NULL)
2378	omFreeSize((ADDRESS)perm,(orig_ring->N+1)*sizeof(int));
2379	if (par_perm!=NULL)
2380	omFreeSize((ADDRESS)par_perm,par_perm_size*sizeof(int));
2381	rChangeCurrRing(orig_ring);
2382	#endif
2383	}
2384	else
2385	R->qideal=idrCopyR(q,currRing,R);
2386	}
2387	}
2388	else
2389	{
2390	WerrorS("q-ideal must be given as `ideal`");
2391	goto rCompose_err;
2392	}
2393
2394
2395	// ---------------------------------------------------------------
2396	#ifdef HAVE_PLURAL
2397	if (L->nr==5)
2398	{
2399	if (nc_CallPlural((matrix)L->m[4].Data(),(matrix)L->m[5].Data(),NULL,NULL,R, true)) goto rCompose_err;
2400	// takes care about non-comm. quotient! i.e. calls "nc_SetupQuotient" due to last true
2401	}
2402	#endif
2403	return R;
2404
2405	rCompose_err:
2406	if (R->N>0)
2407	{
2408	int i;
2409	if (R->names!=NULL)
2410	{
2411	i=R->N-1;
2412	while (i>=0) { if (R->names[i]!=NULL) omFree(R->names[i]); i--; }
2413	omFree(R->names);
2414	}
2415	}
2416	if (R->order!=NULL) omFree(R->order);
2417	if (R->block0!=NULL) omFree(R->block0);
2418	if (R->block1!=NULL) omFree(R->block1);
2419	if (R->wvhdl!=NULL) omFree(R->wvhdl);
2420	omFree(R);
2421	return NULL;
2422	}
2423
2424	// from matpol.cc
2425
2426	/*2
2427	* compute the jacobi matrix of an ideal
2428	*/
2429	BOOLEAN mpJacobi(leftv res,leftv a)
2430	{
2431	int i,j;
2432	matrix result;
2433	ideal id=(ideal)a->Data();
2434
2435	result =mpNew(IDELEMS(id),pVariables);
2436	for (i=1; i<=IDELEMS(id); i++)
2437	{
2438	for (j=1; j<=pVariables; j++)
2439	{
2440	MATELEM(result,i,j) = pDiff(id->m[i-1],j);
2441	}
2442	}
2443	res->data=(char *)result;
2444	return FALSE;
2445	}
2446
2447	/*2
2448	* returns the Koszul-matrix of degree d of a vectorspace with dimension n
2449	* uses the first n entrees of id, if id <> NULL
2450	*/
2451	BOOLEAN mpKoszul(leftv res,leftv c/ip/, leftv b/in/, leftv id)
2452	{
2453	int n=(int)(long)b->Data();
2454	int d=(int)(long)c->Data();
2455	int k,l,sign,row,col;
2456	matrix result;
2457	ideal temp;
2458	BOOLEAN bo;
2459	poly p;
2460
2461	if ((d>n) \|\| (d<1) \|\| (n<1))
2462	{
2463	res->data=(char *)mpNew(1,1);
2464	return FALSE;
2465	}
2466	int choise = (int)omAlloc(d*sizeof(int));
2467	if (id==NULL)
2468	temp=idMaxIdeal(1);
2469	else
2470	temp=(ideal)id->Data();
2471
2472	k = binom(n,d);
2473	l = k*d;
2474	l /= n-d+1;
2475	result =mpNew(l,k);
2476	col = 1;
2477	idInitChoise(d,1,n,&bo,choise);
2478	while (!bo)
2479	{
2480	sign = 1;
2481	for (l=1;l<=d;l++)
2482	{
2483	if (choise[l-1]<=IDELEMS(temp))
2484	{
2485	p = pCopy(temp->m[choise[l-1]-1]);
2486	if (sign == -1) p = pNeg(p);
2487	sign *= -1;
2488	row = idGetNumberOfChoise(l-1,d,1,n,choise);
2489	MATELEM(result,row,col) = p;
2490	}
2491	}
2492	col++;
2493	idGetNextChoise(d,n,&bo,choise);
2494	}
2495	if (id==NULL) idDelete(&temp);
2496
2497	res->data=(char *)result;
2498	return FALSE;
2499	}
2500
2501	// from syz1.cc
2502	/*2
2503	* read out the Betti numbers from resolution
2504	* (interpreter interface)
2505	*/
2506	BOOLEAN syBetti2(leftv res, leftv u, leftv w)
2507	{
2508	syStrategy syzstr=(syStrategy)u->Data();
2509	BOOLEAN minim=(int)(long)w->Data();
2510	int row_shift=0;
2511	int add_row_shift=0;
2512	intvec *weights=NULL;
2513	intvec ww=(intvec )atGet(u,"isHomog",INTVEC_CMD);
2514	if (ww!=NULL)
2515	{
2516	weights=ivCopy(ww);
2517	add_row_shift = ww->min_in();
2518	(*weights) -= add_row_shift;
2519	}
2520	res->data=(void *)syBettiOfComputation(syzstr,minim,&row_shift,weights);
2521	//row_shift += add_row_shift;
2522	//Print("row_shift=%d, add_row_shift=%d\n",row_shift,add_row_shift);
2523	atSet(res,omStrDup("rowShift"),(void*)add_row_shift,INT_CMD);
2524	return FALSE;
2525	}
2526	BOOLEAN syBetti1(leftv res, leftv u)
2527	{
2528	sleftv tmp;
2529	memset(&tmp,0,sizeof(tmp));
2530	tmp.rtyp=INT_CMD;
2531	tmp.data=(void *)1;
2532	return syBetti2(res,u,&tmp);
2533	}
2534
2535	/*3
2536	* converts a resolution into a list of modules
2537	*/
2538	lists syConvRes(syStrategy syzstr,BOOLEAN toDel,int add_row_shift)
2539	{
2540	if ((syzstr->fullres==NULL) && (syzstr->minres==NULL))
2541	{
2542	if (syzstr->hilb_coeffs==NULL)
2543	{
2544	syzstr->fullres = syReorder(syzstr->res,syzstr->length,syzstr);
2545	}
2546	else
2547	{
2548	syzstr->minres = syReorder(syzstr->orderedRes,syzstr->length,syzstr);
2549	syKillEmptyEntres(syzstr->minres,syzstr->length);
2550	}
2551	}
2552	resolvente tr;
2553	int typ0=IDEAL_CMD;
2554	if (syzstr->minres!=NULL)
2555	tr = syzstr->minres;
2556	else
2557	tr = syzstr->fullres;
2558	resolvente trueres=NULL;
2559	intvec ** w=NULL;
2560	if (syzstr->length>0)
2561	{
2562	trueres=(resolvente)omAlloc0((syzstr->length)*sizeof(ideal));
2563	for (int i=(syzstr->length)-1;i>=0;i--)
2564	{
2565	if (tr[i]!=NULL)
2566	{
2567	trueres[i] = idCopy(tr[i]);
2568	}
2569	}
2570	if (idRankFreeModule(trueres[0]) > 0)
2571	typ0 = MODUL_CMD;
2572	if (syzstr->weights!=NULL)
2573	{
2574	w = (intvec*)omAlloc0((syzstr->length)sizeof(intvec*));
2575	for (int i=(syzstr->length)-1;i>=0;i--)
2576	{
2577	if (syzstr->weights[i]!=NULL) w[i] = ivCopy(syzstr->weights[i]);
2578	}
2579	}
2580	}
2581	lists li = liMakeResolv(trueres,syzstr->length,syzstr->list_length,typ0,
2582	w,add_row_shift);
2583	if (w != NULL) omFreeSize(w, (syzstr->length)sizeof(intvec));
2584	if (toDel) syKillComputation(syzstr);
2585	return li;
2586	}
2587
2588	/*3
2589	* converts a list of modules into a resolution
2590	*/
2591	syStrategy syConvList(lists li,BOOLEAN toDel)
2592	{
2593	int typ0;
2594	syStrategy result=(syStrategy)omAlloc0(sizeof(ssyStrategy));
2595
2596	resolvente fr = liFindRes(li,&(result->length),&typ0,&(result->weights));
2597	if (fr != NULL)
2598	{
2599
2600	result->fullres = (resolvente)omAlloc0((result->length+1)*sizeof(ideal));
2601	for (int i=result->length-1;i>=0;i--)
2602	{
2603	if (fr[i]!=NULL)
2604	result->fullres[i] = idCopy(fr[i]);
2605	}
2606	result->list_length=result->length;
2607	omFreeSize((ADDRESS)fr,(result->length)*sizeof(ideal));
2608	}
2609	else
2610	{
2611	omFreeSize(result, sizeof(ssyStrategy));
2612	result = NULL;
2613	}
2614	if (toDel) li->Clean();
2615	return result;
2616	}
2617
2618	/*3
2619	* converts a list of modules into a minimal resolution
2620	*/
2621	syStrategy syForceMin(lists li)
2622	{
2623	int typ0;
2624	syStrategy result=(syStrategy)omAlloc0(sizeof(ssyStrategy));
2625
2626	resolvente fr = liFindRes(li,&(result->length),&typ0);
2627	result->minres = (resolvente)omAlloc0((result->length+1)*sizeof(ideal));
2628	for (int i=result->length-1;i>=0;i--)
2629	{
2630	if (fr[i]!=NULL)
2631	result->minres[i] = idCopy(fr[i]);
2632	}
2633	omFreeSize((ADDRESS)fr,(result->length)*sizeof(ideal));
2634	return result;
2635	}
2636	// from weight.cc
2637	BOOLEAN kWeight(leftv res,leftv id)
2638	{
2639	ideal F=(ideal)id->Data();
2640	intvec * iv = new intvec(pVariables);
2641	polyset s;
2642	int sl, n, i;
2643	int *x;
2644
2645	res->data=(char *)iv;
2646	s = F->m;
2647	sl = IDELEMS(F) - 1;
2648	n = pVariables;
2649	double wNsqr = (double)2.0 / (double)n;
2650	wFunctional = wFunctionalBuch;
2651	x = (int * )omAlloc(2 * (n + 1) * sizeof(int));
2652	wCall(s, sl, x, wNsqr);
2653	for (i = n; i!=0; i--)
2654	(*iv)[i-1] = x[i + n + 1];
2655	omFreeSize((ADDRESS)x, 2 * (n + 1) * sizeof(int));
2656	return FALSE;
2657	}
2658
2659	BOOLEAN kQHWeight(leftv res,leftv v)
2660	{
2661	res->data=(char *)idQHomWeight((ideal)v->Data());
2662	if (res->data==NULL)
2663	res->data=(char *)new intvec(pVariables);
2664	return FALSE;
2665	}
2666	/==============================================================/
2667	// from clapsing.cc
2668	#if 0
2669	BOOLEAN jjIS_SQR_FREE(leftv res, leftv u)
2670	{
2671	BOOLEAN b=singclap_factorize((poly)(u->CopyD()), &v, 0);
2672	res->data=(void *)b;
2673	}
2674	#endif
2675
2676	BOOLEAN jjRESULTANT(leftv res, leftv u, leftv v, leftv w)
2677	{
2678	res->data=singclap_resultant((poly)u->Data(),(poly)v->Data(), (poly)w->Data());
2679	return errorreported;
2680	}
2681	BOOLEAN jjCHARSERIES(leftv res, leftv u)
2682	{
2683	res->data=singclap_irrCharSeries((ideal)u->Data());
2684	return (res->data==NULL);
2685	}
2686
2687	// from semic.cc
2688	#ifdef HAVE_SPECTRUM
2689
2690	// ----------------------------------------------------------------------------
2691	// Initialize a spectrum deep from another spectrum
2692	// ----------------------------------------------------------------------------
2693
2694	void spectrum::copy_deep( const spectrum &spec )
2695	{
2696	mu = spec.mu;
2697	pg = spec.pg;
2698	n = spec.n;
2699
2700	copy_new( n );
2701
2702	for( int i=0; i<n; i++ )
2703	{
2704	s[i] = spec.s[i];
2705	w[i] = spec.w[i];
2706	}
2707	}
2708
2709	// ----------------------------------------------------------------------------
2710	// Initialize a spectrum deep from a singular lists
2711	// ----------------------------------------------------------------------------
2712
2713	void spectrum::copy_deep( lists l )
2714	{
2715	mu = (int)(long)(l->m[0].Data( ));
2716	pg = (int)(long)(l->m[1].Data( ));
2717	n = (int)(long)(l->m[2].Data( ));
2718
2719	copy_new( n );
2720
2721	intvec num = (intvec)l->m[3].Data( );
2722	intvec den = (intvec)l->m[4].Data( );
2723	intvec mul = (intvec)l->m[5].Data( );
2724
2725	for( int i=0; i<n; i++ )
2726	{
2727	s[i] = (Rational)((num)[i])/(Rational)((den)[i]);
2728	w[i] = (*mul)[i];
2729	}
2730	}
2731
2732	// ----------------------------------------------------------------------------
2733	// singular lists constructor for spectrum
2734	// ----------------------------------------------------------------------------
2735
2736	spectrum::spectrum( lists l )
2737	{
2738	copy_deep( l );
2739	}
2740
2741	// ----------------------------------------------------------------------------
2742	// generate a Singular lists from a spectrum
2743	// ----------------------------------------------------------------------------
2744
2745	lists spectrum::thelist( void )
2746	{
2747	lists L = (lists)omAllocBin( slists_bin);
2748
2749	L->Init( 6 );
2750
2751	intvec *num = new intvec( n );
2752	intvec *den = new intvec( n );
2753	intvec *mult = new intvec( n );
2754
2755	for( int i=0; i<n; i++ )
2756	{
2757	(*num) [i] = s[i].get_num_si( );
2758	(*den) [i] = s[i].get_den_si( );
2759	(*mult)[i] = w[i];
2760	}
2761
2762	L->m[0].rtyp = INT_CMD; // milnor number
2763	L->m[1].rtyp = INT_CMD; // geometrical genus
2764	L->m[2].rtyp = INT_CMD; // # of spectrum numbers
2765	L->m[3].rtyp = INTVEC_CMD; // numerators
2766	L->m[4].rtyp = INTVEC_CMD; // denomiantors
2767	L->m[5].rtyp = INTVEC_CMD; // multiplicities
2768
2769	L->m[0].data = (void*)mu;
2770	L->m[1].data = (void*)pg;
2771	L->m[2].data = (void*)n;
2772	L->m[3].data = (void*)num;
2773	L->m[4].data = (void*)den;
2774	L->m[5].data = (void*)mult;
2775
2776	return L;
2777	}
2778	// from spectrum.cc
2779	// ----------------------------------------------------------------------------
2780	// print out an error message for a spectrum list
2781	// ----------------------------------------------------------------------------
2782
2783	void list_error( semicState state )
2784	{
2785	switch( state )
2786	{
2787	case semicListTooShort:
2788	WerrorS( "the list is too short" );
2789	break;
2790	case semicListTooLong:
2791	WerrorS( "the list is too long" );
2792	break;
2793
2794	case semicListFirstElementWrongType:
2795	WerrorS( "first element of the list should be int" );
2796	break;
2797	case semicListSecondElementWrongType:
2798	WerrorS( "second element of the list should be int" );
2799	break;
2800	case semicListThirdElementWrongType:
2801	WerrorS( "third element of the list should be int" );
2802	break;
2803	case semicListFourthElementWrongType:
2804	WerrorS( "fourth element of the list should be intvec" );
2805	break;
2806	case semicListFifthElementWrongType:
2807	WerrorS( "fifth element of the list should be intvec" );
2808	break;
2809	case semicListSixthElementWrongType:
2810	WerrorS( "sixth element of the list should be intvec" );
2811	break;
2812
2813	case semicListNNegative:
2814	WerrorS( "first element of the list should be positive" );
2815	break;
2816	case semicListWrongNumberOfNumerators:
2817	WerrorS( "wrong number of numerators" );
2818	break;
2819	case semicListWrongNumberOfDenominators:
2820	WerrorS( "wrong number of denominators" );
2821	break;
2822	case semicListWrongNumberOfMultiplicities:
2823	WerrorS( "wrong number of multiplicities" );
2824	break;
2825
2826	case semicListMuNegative:
2827	WerrorS( "the Milnor number should be positive" );
2828	break;
2829	case semicListPgNegative:
2830	WerrorS( "the geometrical genus should be nonnegative" );
2831	break;
2832	case semicListNumNegative:
2833	WerrorS( "all numerators should be positive" );
2834	break;
2835	case semicListDenNegative:
2836	WerrorS( "all denominators should be positive" );
2837	break;
2838	case semicListMulNegative:
2839	WerrorS( "all multiplicities should be positive" );
2840	break;
2841
2842	case semicListNotSymmetric:
2843	WerrorS( "it is not symmetric" );
2844	break;
2845	case semicListNotMonotonous:
2846	WerrorS( "it is not monotonous" );
2847	break;
2848
2849	case semicListMilnorWrong:
2850	WerrorS( "the Milnor number is wrong" );
2851	break;
2852	case semicListPGWrong:
2853	WerrorS( "the geometrical genus is wrong" );
2854	break;
2855
2856	default:
2857	WerrorS( "unspecific error" );
2858	break;
2859	}
2860	}
2861	// ----------------------------------------------------------------------------
2862	// this is the main spectrum computation function
2863	// ----------------------------------------------------------------------------
2864
2865	spectrumState spectrumCompute( poly h,lists *L,int fast )
2866	{
2867	int i,j;
2868
2869	#ifdef SPECTRUM_DEBUG
2870	#ifdef SPECTRUM_PRINT
2871	#ifdef SPECTRUM_IOSTREAM
2872	cout << "spectrumCompute\n";
2873	if( fast==0 ) cout << " no optimization" << endl;
2874	if( fast==1 ) cout << " weight optimization" << endl;
2875	if( fast==2 ) cout << " symmetry optimization" << endl;
2876	#else
2877	fprintf( stdout,"spectrumCompute\n" );
2878	if( fast==0 ) fprintf( stdout," no optimization\n" );
2879	if( fast==1 ) fprintf( stdout," weight optimization\n" );
2880	if( fast==2 ) fprintf( stdout," symmetry optimization\n" );
2881	#endif
2882	#endif
2883	#endif
2884
2885	// ----------------------
2886	// check if h is zero
2887	// ----------------------
2888
2889	if( h==(poly)NULL )
2890	{
2891	return spectrumZero;
2892	}
2893
2894	// ----------------------------------
2895	// check if h has a constant term
2896	// ----------------------------------
2897
2898	if( hasConstTerm( h ) )
2899	{
2900	return spectrumBadPoly;
2901	}
2902
2903	// --------------------------------
2904	// check if h has a linear term
2905	// --------------------------------
2906
2907	if( hasLinearTerm( h ) )
2908	{
2909	*L = (lists)omAllocBin( slists_bin);
2910	(*L)->Init( 1 );
2911	(*L)->m[0].rtyp = INT_CMD; // milnor number
2912	/* (L)->m[0].data = (void)0;a -- done by Init */
2913
2914	return spectrumNoSingularity;
2915	}
2916
2917	// ----------------------------------
2918	// compute the jacobi ideal of (h)
2919	// ----------------------------------
2920
2921	ideal J = NULL;
2922	J = idInit( pVariables,1 );
2923
2924	#ifdef SPECTRUM_DEBUG
2925	#ifdef SPECTRUM_PRINT
2926	#ifdef SPECTRUM_IOSTREAM
2927	cout << "\n computing the Jacobi ideal...\n";
2928	#else
2929	fprintf( stdout,"\n computing the Jacobi ideal...\n" );
2930	#endif
2931	#endif
2932	#endif
2933
2934	for( i=0; i<pVariables; i++ )
2935	{
2936	J->m[i] = pDiff( h,i+1); //j );
2937
2938	#ifdef SPECTRUM_DEBUG
2939	#ifdef SPECTRUM_PRINT
2940	#ifdef SPECTRUM_IOSTREAM
2941	cout << " ";
2942	#else
2943	fprintf( stdout," " );
2944	#endif
2945	pWrite( J->m[i] );
2946	#endif
2947	#endif
2948	}
2949
2950	// --------------------------------------------
2951	// compute a standard basis stdJ of jac(h)
2952	// --------------------------------------------
2953
2954	#ifdef SPECTRUM_DEBUG
2955	#ifdef SPECTRUM_PRINT
2956	#ifdef SPECTRUM_IOSTREAM
2957	cout << endl;
2958	cout << " computing a standard basis..." << endl;
2959	#else
2960	fprintf( stdout,"\n" );
2961	fprintf( stdout," computing a standard basis...\n" );
2962	#endif
2963	#endif
2964	#endif
2965
2966	ideal stdJ = kStd(J,currQuotient,isNotHomog,NULL);
2967	idSkipZeroes( stdJ );
2968
2969	#ifdef SPECTRUM_DEBUG
2970	#ifdef SPECTRUM_PRINT
2971	for( i=0; i<IDELEMS(stdJ); i++ )
2972	{
2973	#ifdef SPECTRUM_IOSTREAM
2974	cout << " ";
2975	#else
2976	fprintf( stdout," " );
2977	#endif
2978
2979	pWrite( stdJ->m[i] );
2980	}
2981	#endif
2982	#endif
2983
2984	idDelete( &J );
2985
2986	// ------------------------------------------
2987	// check if the h has a singularity
2988	// ------------------------------------------
2989
2990	if( hasOne( stdJ ) )
2991	{
2992	// -------------------------------
2993	// h is smooth in the origin
2994	// return only the Milnor number
2995	// -------------------------------
2996
2997	*L = (lists)omAllocBin( slists_bin);
2998	(*L)->Init( 1 );
2999	(*L)->m[0].rtyp = INT_CMD; // milnor number
3000	/* (L)->m[0].data = (void)0;a -- done by Init */
3001
3002	return spectrumNoSingularity;
3003	}
3004
3005	// ------------------------------------------
3006	// check if the singularity h is isolated
3007	// ------------------------------------------
3008
3009	for( i=pVariables; i>0; i-- )
3010	{
3011	if( hasAxis( stdJ,i )==FALSE )
3012	{
3013	return spectrumNotIsolated;
3014	}
3015	}
3016
3017	// ------------------------------------------
3018	// compute the highest corner hc of stdJ
3019	// ------------------------------------------
3020
3021	#ifdef SPECTRUM_DEBUG
3022	#ifdef SPECTRUM_PRINT
3023	#ifdef SPECTRUM_IOSTREAM
3024	cout << "\n computing the highest corner...\n";
3025	#else
3026	fprintf( stdout,"\n computing the highest corner...\n" );
3027	#endif
3028	#endif
3029	#endif
3030
3031	poly hc = (poly)NULL;
3032
3033	scComputeHC( stdJ,currQuotient, 0,hc );
3034
3035	if( hc!=(poly)NULL )
3036	{
3037	pGetCoeff(hc) = nInit(1);
3038
3039	for( i=pVariables; i>0; i-- )
3040	{
3041	if( pGetExp( hc,i )>0 ) pDecrExp( hc,i );
3042	}
3043	pSetm( hc );
3044	}
3045	else
3046	{
3047	return spectrumNoHC;
3048	}
3049
3050	#ifdef SPECTRUM_DEBUG
3051	#ifdef SPECTRUM_PRINT
3052	#ifdef SPECTRUM_IOSTREAM
3053	cout << " ";
3054	#else
3055	fprintf( stdout," " );
3056	#endif
3057	pWrite( hc );
3058	#endif
3059	#endif
3060
3061	// ----------------------------------------
3062	// compute the Newton polygon nph of h
3063	// ----------------------------------------
3064
3065	#ifdef SPECTRUM_DEBUG
3066	#ifdef SPECTRUM_PRINT
3067	#ifdef SPECTRUM_IOSTREAM
3068	cout << "\n computing the newton polygon...\n";
3069	#else
3070	fprintf( stdout,"\n computing the newton polygon...\n" );
3071	#endif
3072	#endif
3073	#endif
3074
3075	newtonPolygon nph( h );
3076
3077	#ifdef SPECTRUM_DEBUG
3078	#ifdef SPECTRUM_PRINT
3079	cout << nph;
3080	#endif
3081	#endif
3082
3083	// -----------------------------------------------
3084	// compute the weight corner wc of (stdj,nph)
3085	// -----------------------------------------------
3086
3087	#ifdef SPECTRUM_DEBUG
3088	#ifdef SPECTRUM_PRINT
3089	#ifdef SPECTRUM_IOSTREAM
3090	cout << "\n computing the weight corner...\n";
3091	#else
3092	fprintf( stdout,"\n computing the weight corner...\n" );
3093	#endif
3094	#endif
3095	#endif
3096
3097	poly wc = ( fast==0 ? pCopy( hc ) :
3098	( fast==1 ? computeWC( nph,(Rational)pVariables ) :
3099	/* fast==2 */computeWC( nph,((Rational)pVariables)/(Rational)2 ) ) );
3100
3101	#ifdef SPECTRUM_DEBUG
3102	#ifdef SPECTRUM_PRINT
3103	#ifdef SPECTRUM_IOSTREAM
3104	cout << " ";
3105	#else
3106	fprintf( stdout," " );
3107	#endif
3108	pWrite( wc );
3109	#endif
3110	#endif
3111
3112	// -------------
3113	// compute NF
3114	// -------------
3115
3116	#ifdef SPECTRUM_DEBUG
3117	#ifdef SPECTRUM_PRINT
3118	#ifdef SPECTRUM_IOSTREAM
3119	cout << "\n computing NF...\n" << endl;
3120	#else
3121	fprintf( stdout,"\n computing NF...\n" );
3122	#endif
3123	#endif
3124	#endif
3125
3126	spectrumPolyList NF( &nph );
3127
3128	computeNF( stdJ,hc,wc,&NF );
3129
3130	#ifdef SPECTRUM_DEBUG
3131	#ifdef SPECTRUM_PRINT
3132	cout << NF;
3133	#ifdef SPECTRUM_IOSTREAM
3134	cout << endl;
3135	#else
3136	fprintf( stdout,"\n" );
3137	#endif
3138	#endif
3139	#endif
3140
3141	// ----------------------------
3142	// compute the spectrum of h
3143	// ----------------------------
3144
3145	return NF.spectrum( L,fast );
3146	}
3147
3148	// ----------------------------------------------------------------------------
3149	// this procedure is called from the interpreter
3150	// ----------------------------------------------------------------------------
3151	// first = polynomial
3152	// result = list of spectrum numbers
3153	// ----------------------------------------------------------------------------
3154
3155	BOOLEAN spectrumProc( leftv result,leftv first )
3156	{
3157	spectrumState state = spectrumOK;
3158
3159	// -------------------
3160	// check consistency
3161	// -------------------
3162
3163	// check for a local ring
3164
3165	if( !ringIsLocal( ) )
3166	{
3167	WerrorS( "only works for local orderings" );
3168	state = spectrumWrongRing;
3169	}
3170
3171	// no quotient rings are allowed
3172
3173	else if( currRing->qideal != NULL )
3174	{
3175	WerrorS( "does not work in quotient rings" );
3176	state = spectrumWrongRing;
3177	}
3178	else
3179	{
3180	lists L = (lists)NULL;
3181	int flag = 1; // weight corner optimization is safe
3182
3183	state = spectrumCompute( (poly)first->Data( ),&L,flag );
3184
3185	if( state==spectrumOK )
3186	{
3187	result->rtyp = LIST_CMD;
3188	result->data = (char*)L;
3189	}
3190	else
3191	{
3192	spectrumPrintError(state);
3193	}
3194	}
3195
3196	return (state!=spectrumOK);
3197	}
3198
3199	// ----------------------------------------------------------------------------
3200	// this procedure is called from the interpreter
3201	// ----------------------------------------------------------------------------
3202	// first = polynomial
3203	// result = list of spectrum numbers
3204	// ----------------------------------------------------------------------------
3205
3206	BOOLEAN spectrumfProc( leftv result,leftv first )
3207	{
3208	spectrumState state = spectrumOK;
3209
3210	// -------------------
3211	// check consistency
3212	// -------------------
3213
3214	// check for a local polynomial ring
3215
3216	if( currRing->OrdSgn != -1 )
3217	// ?? HS: the test above is also true for k[x][[y]], k[[x]][y]
3218	// or should we use:
3219	//if( !ringIsLocal( ) )
3220	{
3221	WerrorS( "only works for local orderings" );
3222	state = spectrumWrongRing;
3223	}
3224	else if( currRing->qideal != NULL )
3225	{
3226	WerrorS( "does not work in quotient rings" );
3227	state = spectrumWrongRing;
3228	}
3229	else
3230	{
3231	lists L = (lists)NULL;
3232	int flag = 2; // symmetric optimization
3233
3234	state = spectrumCompute( (poly)first->Data( ),&L,flag );
3235
3236	if( state==spectrumOK )
3237	{
3238	result->rtyp = LIST_CMD;
3239	result->data = (char*)L;
3240	}
3241	else
3242	{
3243	spectrumPrintError(state);
3244	}
3245	}
3246
3247	return (state!=spectrumOK);
3248	}
3249
3250	// ----------------------------------------------------------------------------
3251	// check if a list is a spectrum
3252	// check for:
3253	// list has 6 elements
3254	// 1st element is int (mu=Milnor number)
3255	// 2nd element is int (pg=geometrical genus)
3256	// 3rd element is int (n =number of different spectrum numbers)
3257	// 4th element is intvec (num=numerators)
3258	// 5th element is intvec (den=denomiantors)
3259	// 6th element is intvec (mul=multiplicities)
3260	// exactly n numerators
3261	// exactly n denominators
3262	// exactly n multiplicities
3263	// mu>0
3264	// pg>=0
3265	// n>0
3266	// num>0
3267	// den>0
3268	// mul>0
3269	// symmetriy with respect to numberofvariables/2
3270	// monotony
3271	// mu = sum of all multiplicities
3272	// pg = sum of all multiplicities where num/den<=1
3273	// ----------------------------------------------------------------------------
3274
3275	semicState list_is_spectrum( lists l )
3276	{
3277	// -------------------
3278	// check list length
3279	// -------------------
3280
3281	if( l->nr < 5 )
3282	{
3283	return semicListTooShort;
3284	}
3285	else if( l->nr > 5 )
3286	{
3287	return semicListTooLong;
3288	}
3289
3290	// -------------
3291	// check types
3292	// -------------
3293
3294	if( l->m[0].rtyp != INT_CMD )
3295	{
3296	return semicListFirstElementWrongType;
3297	}
3298	else if( l->m[1].rtyp != INT_CMD )
3299	{
3300	return semicListSecondElementWrongType;
3301	}
3302	else if( l->m[2].rtyp != INT_CMD )
3303	{
3304	return semicListThirdElementWrongType;
3305	}
3306	else if( l->m[3].rtyp != INTVEC_CMD )
3307	{
3308	return semicListFourthElementWrongType;
3309	}
3310	else if( l->m[4].rtyp != INTVEC_CMD )
3311	{
3312	return semicListFifthElementWrongType;
3313	}
3314	else if( l->m[5].rtyp != INTVEC_CMD )
3315	{
3316	return semicListSixthElementWrongType;
3317	}
3318
3319	// -------------------------
3320	// check number of entries
3321	// -------------------------
3322
3323	int mu = (int)(long)(l->m[0].Data( ));
3324	int pg = (int)(long)(l->m[1].Data( ));
3325	int n = (int)(long)(l->m[2].Data( ));
3326
3327	if( n <= 0 )
3328	{
3329	return semicListNNegative;
3330	}
3331
3332	intvec num = (intvec)l->m[3].Data( );
3333	intvec den = (intvec)l->m[4].Data( );
3334	intvec mul = (intvec)l->m[5].Data( );
3335
3336	if( n != num->length( ) )
3337	{
3338	return semicListWrongNumberOfNumerators;
3339	}
3340	else if( n != den->length( ) )
3341	{
3342	return semicListWrongNumberOfDenominators;
3343	}
3344	else if( n != mul->length( ) )
3345	{
3346	return semicListWrongNumberOfMultiplicities;
3347	}
3348
3349	// --------
3350	// values
3351	// --------
3352
3353	if( mu <= 0 )
3354	{
3355	return semicListMuNegative;
3356	}
3357	if( pg < 0 )
3358	{
3359	return semicListPgNegative;
3360	}
3361
3362	int i;
3363
3364	for( i=0; i<n; i++ )
3365	{
3366	if( (*num)[i] <= 0 )
3367	{
3368	return semicListNumNegative;
3369	}
3370	if( (*den)[i] <= 0 )
3371	{
3372	return semicListDenNegative;
3373	}
3374	if( (*mul)[i] <= 0 )
3375	{
3376	return semicListMulNegative;
3377	}
3378	}
3379
3380	// ----------------
3381	// check symmetry
3382	// ----------------
3383
3384	int j;
3385
3386	for( i=0, j=n-1; i<=j; i++,j-- )
3387	{
3388	if( (num)[i] != pVariables((den)[i]) - (num)[j] \|\|
3389	(den)[i] != (den)[j] \|\|
3390	(mul)[i] != (mul)[j] )
3391	{
3392	return semicListNotSymmetric;
3393	}
3394	}
3395
3396	// ----------------
3397	// check monotony
3398	// ----------------
3399
3400	for( i=0, j=1; i<n/2; i++,j++ )
3401	{
3402	if( (num)[i](den)[j] >= (num)[j](den)[i] )
3403	{
3404	return semicListNotMonotonous;
3405	}
3406	}
3407
3408	// ---------------------
3409	// check Milnor number
3410	// ---------------------
3411
3412	for( mu=0, i=0; i<n; i++ )
3413	{
3414	mu += (*mul)[i];
3415	}
3416
3417	if( mu != (int)(long)(l->m[0].Data( )) )
3418	{
3419	return semicListMilnorWrong;
3420	}
3421
3422	// -------------------------
3423	// check geometrical genus
3424	// -------------------------
3425
3426	for( pg=0, i=0; i<n; i++ )
3427	{
3428	if( (num)[i]<=(den)[i] )
3429	{
3430	pg += (*mul)[i];
3431	}
3432	}
3433
3434	if( pg != (int)(long)(l->m[1].Data( )) )
3435	{
3436	return semicListPGWrong;
3437	}
3438
3439	return semicOK;
3440	}
3441
3442	// ----------------------------------------------------------------------------
3443	// this procedure is called from the interpreter
3444	// ----------------------------------------------------------------------------
3445	// first = list of spectrum numbers
3446	// second = list of spectrum numbers
3447	// result = sum of the two lists
3448	// ----------------------------------------------------------------------------
3449
3450	BOOLEAN spaddProc( leftv result,leftv first,leftv second )
3451	{
3452	semicState state;
3453
3454	// -----------------
3455	// check arguments
3456	// -----------------
3457
3458	lists l1 = (lists)first->Data( );
3459	lists l2 = (lists)second->Data( );
3460
3461	if( (state=list_is_spectrum( l1 )) != semicOK )
3462	{
3463	WerrorS( "first argument is not a spectrum:" );
3464	list_error( state );
3465	}
3466	else if( (state=list_is_spectrum( l2 )) != semicOK )
3467	{
3468	WerrorS( "second argument is not a spectrum:" );
3469	list_error( state );
3470	}
3471	else
3472	{
3473	spectrum s1( l1 );
3474	spectrum s2( l2 );
3475	spectrum sum( s1+s2 );
3476
3477	result->rtyp = LIST_CMD;
3478	result->data = (char*)(sum.thelist( ));
3479	}
3480
3481	return (state!=semicOK);
3482	}
3483
3484	// ----------------------------------------------------------------------------
3485	// this procedure is called from the interpreter
3486	// ----------------------------------------------------------------------------
3487	// first = list of spectrum numbers
3488	// second = integer
3489	// result = the multiple of the first list by the second factor
3490	// ----------------------------------------------------------------------------
3491
3492	BOOLEAN spmulProc( leftv result,leftv first,leftv second )
3493	{
3494	semicState state;
3495
3496	// -----------------
3497	// check arguments
3498	// -----------------
3499
3500	lists l = (lists)first->Data( );
3501	int k = (int)(long)second->Data( );
3502
3503	if( (state=list_is_spectrum( l ))!=semicOK )
3504	{
3505	WerrorS( "first argument is not a spectrum" );
3506	list_error( state );
3507	}
3508	else if( k < 0 )
3509	{
3510	WerrorS( "second argument should be positive" );
3511	state = semicMulNegative;
3512	}
3513	else
3514	{
3515	spectrum s( l );
3516	spectrum product( k*s );
3517
3518	result->rtyp = LIST_CMD;
3519	result->data = (char*)product.thelist( );
3520	}
3521
3522	return (state!=semicOK);
3523	}
3524
3525	// ----------------------------------------------------------------------------
3526	// this procedure is called from the interpreter
3527	// ----------------------------------------------------------------------------
3528	// first = list of spectrum numbers
3529	// second = list of spectrum numbers
3530	// result = semicontinuity index
3531	// ----------------------------------------------------------------------------
3532
3533	BOOLEAN semicProc3 ( leftv res,leftv u,leftv v,leftv w )
3534	{
3535	semicState state;
3536	BOOLEAN qh=(((int)(long)w->Data())==1);
3537
3538	// -----------------
3539	// check arguments
3540	// -----------------
3541
3542	lists l1 = (lists)u->Data( );
3543	lists l2 = (lists)v->Data( );
3544
3545	if( (state=list_is_spectrum( l1 ))!=semicOK )
3546	{
3547	WerrorS( "first argument is not a spectrum" );
3548	list_error( state );
3549	}
3550	else if( (state=list_is_spectrum( l2 ))!=semicOK )
3551	{
3552	WerrorS( "second argument is not a spectrum" );
3553	list_error( state );
3554	}
3555	else
3556	{
3557	spectrum s1( l1 );
3558	spectrum s2( l2 );
3559
3560	res->rtyp = INT_CMD;
3561	if (qh)
3562	res->data = (void*)(s1.mult_spectrumh( s2 ));
3563	else
3564	res->data = (void*)(s1.mult_spectrum( s2 ));
3565	}
3566
3567	// -----------------
3568	// check status
3569	// -----------------
3570
3571	return (state!=semicOK);
3572	}
3573	BOOLEAN semicProc ( leftv res,leftv u,leftv v )
3574	{
3575	sleftv tmp;
3576	memset(&tmp,0,sizeof(tmp));
3577	tmp.rtyp=INT_CMD;
3578	/* tmp.data = (void )0; -- done by memset /
3579
3580	return semicProc3(res,u,v,&tmp);
3581	}
3582	// from splist.cc
3583	// ----------------------------------------------------------------------------
3584	// Compute the spectrum of a spectrumPolyList
3585	// ----------------------------------------------------------------------------
3586
3587	spectrumState spectrumPolyList::spectrum( lists *L,int fast )
3588	{
3589	spectrumPolyNode **node = &root;
3590	spectrumPolyNode *search;
3591
3592	poly f,tmp;
3593	int found,cmp;
3594
3595	Rational smax( ( fast==0 ? 0 : pVariables ),
3596	( fast==2 ? 2 : 1 ) );
3597
3598	Rational weight_prev( 0,1 );
3599
3600	int mu = 0; // the milnor number
3601	int pg = 0; // the geometrical genus
3602	int n = 0; // number of different spectral numbers
3603	int z = 0; // number of spectral number equal to smax
3604
3605	int k = 0;
3606
3607	while( (node)!=(spectrumPolyNode)NULL &&
3608	( fast==0 \|\| (*node)->weight<=smax ) )
3609	{
3610	// ---------------------------------------
3611	// determine the first normal form which
3612	// contains the monomial node->mon
3613	// ---------------------------------------
3614
3615	found = FALSE;
3616	search = *node;
3617
3618	while( search!=(spectrumPolyNode*)NULL && found==FALSE )
3619	{
3620	if( search->nf!=(poly)NULL )
3621	{
3622	f = search->nf;
3623
3624	do
3625	{
3626	// --------------------------------
3627	// look for (*node)->mon in f
3628	// --------------------------------
3629
3630	cmp = pCmp( (*node)->mon,f );
3631
3632	if( cmp<0 )
3633	{
3634	f = pNext( f );
3635	}
3636	else if( cmp==0 )
3637	{
3638	// -----------------------------
3639	// we have found a normal form
3640	// -----------------------------
3641
3642	found = TRUE;
3643
3644	// normalize coefficient
3645
3646	number inv = nInvers( pGetCoeff( f ) );
3647	pMult_nn( search->nf,inv );
3648	nDelete( &inv );
3649
3650	// exchange normal forms
3651
3652	tmp = (*node)->nf;
3653	(*node)->nf = search->nf;
3654	search->nf = tmp;
3655	}
3656	}
3657	while( cmp<0 && f!=(poly)NULL );
3658	}
3659	search = search->next;
3660	}
3661
3662	if( found==FALSE )
3663	{
3664	// ------------------------------------------------
3665	// the weight of node->mon is a spectrum number
3666	// ------------------------------------------------
3667
3668	mu++;
3669
3670	if( (*node)->weight<=(Rational)1 ) pg++;
3671	if( (*node)->weight==smax ) z++;
3672	if( (*node)->weight>weight_prev ) n++;
3673
3674	weight_prev = (*node)->weight;
3675	node = &((*node)->next);
3676	}
3677	else
3678	{
3679	// -----------------------------------------------
3680	// determine all other normal form which contain
3681	// the monomial node->mon
3682	// replace for node->mon its normal form
3683	// -----------------------------------------------
3684
3685	while( search!=(spectrumPolyNode*)NULL )
3686	{
3687	if( search->nf!=(poly)NULL )
3688	{
3689	f = search->nf;
3690
3691	do
3692	{
3693	// --------------------------------
3694	// look for (*node)->mon in f
3695	// --------------------------------
3696
3697	cmp = pCmp( (*node)->mon,f );
3698
3699	if( cmp<0 )
3700	{
3701	f = pNext( f );
3702	}
3703	else if( cmp==0 )
3704	{
3705	search->nf = pSub( search->nf,
3706	ppMult_nn( (*node)->nf,pGetCoeff( f ) ) );
3707	pNorm( search->nf );
3708	}
3709	}
3710	while( cmp<0 && f!=(poly)NULL );
3711	}
3712	search = search->next;
3713	}
3714	delete_node( node );
3715	}
3716
3717	}
3718
3719	// --------------------------------------------------------
3720	// fast computation exploits the symmetry of the spectrum
3721	// --------------------------------------------------------
3722
3723	if( fast==2 )
3724	{
3725	mu = 2*mu - z;
3726	n = ( z > 0 ? 2n - 1 : 2n );
3727	}
3728
3729	// --------------------------------------------------------
3730	// compute the spectrum numbers with their multiplicities
3731	// --------------------------------------------------------
3732
3733	intvec *nom = new intvec( n );
3734	intvec *den = new intvec( n );
3735	intvec *mult = new intvec( n );
3736
3737	int count = 0;
3738	int multiplicity = 1;
3739
3740	for( search=root; search!=(spectrumPolyNode*)NULL &&
3741	( fast==0 \|\| search->weight<=smax );
3742	search=search->next )
3743	{
3744	if( search->next==(spectrumPolyNode*)NULL \|\|
3745	search->weight<search->next->weight )
3746	{
3747	(*nom) [count] = search->weight.get_num_si( );
3748	(*den) [count] = search->weight.get_den_si( );
3749	(*mult)[count] = multiplicity;
3750
3751	multiplicity=1;
3752	count++;
3753	}
3754	else
3755	{
3756	multiplicity++;
3757	}
3758	}
3759
3760	// --------------------------------------------------------
3761	// fast computation exploits the symmetry of the spectrum
3762	// --------------------------------------------------------
3763
3764	if( fast==2 )
3765	{
3766	int n1,n2;
3767	for( n1=0, n2=n-1; n1<n2; n1++, n2-- )
3768	{
3769	(nom) [n2] = pVariables(den)[n1]-(nom)[n1];
3770	(den) [n2] = (den)[n1];
3771	(mult)[n2] = (mult)[n1];
3772	}
3773	}
3774
3775	// -----------------------------------
3776	// test if the spectrum is symmetric
3777	// -----------------------------------
3778
3779	if( fast==0 \|\| fast==1 )
3780	{
3781	int symmetric=TRUE;
3782
3783	for( int n1=0, n2=n-1 ; n1<n2 && symmetric==TRUE; n1++, n2-- )
3784	{
3785	if( (mult)[n1]!=(mult)[n2] \|\|
3786	(den) [n1]!= (den)[n2] \|\|
3787	(nom)[n1]+(nom)[n2]!=pVariables(den) [n1] )
3788	{
3789	symmetric = FALSE;
3790	}
3791	}
3792
3793	if( symmetric==FALSE )
3794	{
3795	// ---------------------------------------------
3796	// the spectrum is not symmetric => degenerate
3797	// principal part
3798	// ---------------------------------------------
3799
3800	*L = (lists)omAllocBin( slists_bin);
3801	(*L)->Init( 1 );
3802	(*L)->m[0].rtyp = INT_CMD; // milnor number
3803	(L)->m[0].data = (void)mu;
3804
3805	return spectrumDegenerate;
3806	}
3807	}
3808
3809	*L = (lists)omAllocBin( slists_bin);
3810
3811	(*L)->Init( 6 );
3812
3813	(*L)->m[0].rtyp = INT_CMD; // milnor number
3814	(*L)->m[1].rtyp = INT_CMD; // geometrical genus
3815	(*L)->m[2].rtyp = INT_CMD; // number of spectrum values
3816	(*L)->m[3].rtyp = INTVEC_CMD; // nominators
3817	(*L)->m[4].rtyp = INTVEC_CMD; // denomiantors
3818	(*L)->m[5].rtyp = INTVEC_CMD; // multiplicities
3819
3820	(L)->m[0].data = (void)mu;
3821	(L)->m[1].data = (void)pg;
3822	(L)->m[2].data = (void)n;
3823	(L)->m[3].data = (void)nom;
3824	(L)->m[4].data = (void)den;
3825	(L)->m[5].data = (void)mult;
3826
3827	return spectrumOK;
3828	}
3829
3830	#endif
3831
3832	//from mpr_inout.cc
3833	extern void nPrint(number n);
3834
3835	BOOLEAN loNewtonP( leftv res, leftv arg1 )
3836	{
3837	res->data= (void*)loNewtonPolytope( (ideal)arg1->Data() );
3838	return FALSE;
3839	}
3840
3841	BOOLEAN loSimplex( leftv res, leftv args )
3842	{
3843	if ( !(rField_is_long_R()) )
3844	{
3845	WerrorS("Ground field not implemented!");
3846	return TRUE;
3847	}
3848
3849	simplex * LP;
3850	matrix m;
3851
3852	leftv v= args;
3853	if ( v->Typ() != MATRIX_CMD ) // 1: matrix
3854	return TRUE;
3855	else
3856	m= (matrix)(v->CopyD());
3857
3858	LP = new simplex(MATROWS(m),MATCOLS(m));
3859	LP->mapFromMatrix(m);
3860
3861	v= v->next;
3862	if ( v->Typ() != INT_CMD ) // 2: m = number of constraints
3863	return TRUE;
3864	else
3865	LP->m= (int)(long)(v->Data());
3866
3867	v= v->next;
3868	if ( v->Typ() != INT_CMD ) // 3: n = number of variables
3869	return TRUE;
3870	else
3871	LP->n= (int)(long)(v->Data());
3872
3873	v= v->next;
3874	if ( v->Typ() != INT_CMD ) // 4: m1 = number of <= constraints
3875	return TRUE;
3876	else
3877	LP->m1= (int)(long)(v->Data());
3878
3879	v= v->next;
3880	if ( v->Typ() != INT_CMD ) // 5: m2 = number of >= constraints
3881	return TRUE;
3882	else
3883	LP->m2= (int)(long)(v->Data());
3884
3885	v= v->next;
3886	if ( v->Typ() != INT_CMD ) // 6: m3 = number of == constraints
3887	return TRUE;
3888	else
3889	LP->m3= (int)(long)(v->Data());
3890
3891	#ifdef mprDEBUG_PROT
3892	Print("m (constraints) %d\n",LP->m);
3893	Print("n (columns) %d\n",LP->n);
3894	Print("m1 (<=) %d\n",LP->m1);
3895	Print("m2 (>=) %d\n",LP->m2);
3896	Print("m3 (==) %d\n",LP->m3);
3897	#endif
3898
3899	LP->compute();
3900
3901	lists lres= (lists)omAlloc( sizeof(slists) );
3902	lres->Init( 6 );
3903
3904	lres->m[0].rtyp= MATRIX_CMD; // output matrix
3905	lres->m[0].data=(void*)LP->mapToMatrix(m);
3906
3907	lres->m[1].rtyp= INT_CMD; // found a solution?
3908	lres->m[1].data=(void*)LP->icase;
3909
3910	lres->m[2].rtyp= INTVEC_CMD;
3911	lres->m[2].data=(void*)LP->posvToIV();
3912
3913	lres->m[3].rtyp= INTVEC_CMD;
3914	lres->m[3].data=(void*)LP->zrovToIV();
3915
3916	lres->m[4].rtyp= INT_CMD;
3917	lres->m[4].data=(void*)LP->m;
3918
3919	lres->m[5].rtyp= INT_CMD;
3920	lres->m[5].data=(void*)LP->n;
3921
3922	res->data= (void*)lres;
3923
3924	return FALSE;
3925	}
3926
3927	BOOLEAN nuMPResMat( leftv res, leftv arg1, leftv arg2 )
3928	{
3929	ideal gls = (ideal)(arg1->Data());
3930	int imtype= (int)(long)arg2->Data();
3931
3932	uResultant::resMatType mtype= determineMType( imtype );
3933
3934	// check input ideal ( = polynomial system )
3935	if ( mprIdealCheck( gls, arg1->Name(), mtype, true ) != mprOk )
3936	{
3937	return TRUE;
3938	}
3939
3940	uResultant *resMat= new uResultant( gls, mtype, false );
3941	if (resMat!=NULL)
3942	{
3943	res->rtyp = MODUL_CMD;
3944	res->data= (void*)resMat->accessResMat()->getMatrix();
3945	if (!errorreported) delete resMat;
3946	}
3947	return errorreported;
3948	}
3949
3950	BOOLEAN nuLagSolve( leftv res, leftv arg1, leftv arg2, leftv arg3 )
3951	{
3952
3953	poly gls;
3954	gls= (poly)(arg1->Data());
3955	int howclean= (int)(long)arg3->Data();
3956
3957	if ( !(rField_is_R() \|\|
3958	rField_is_Q() \|\|
3959	rField_is_long_R() \|\|
3960	rField_is_long_C()) )
3961	{
3962	WerrorS("Ground field not implemented!");
3963	return TRUE;
3964	}
3965
3966	if ( !(rField_is_R()\|\|rField_is_long_R()\|\|rField_is_long_C()) )
3967	{
3968	unsigned long int ii = (unsigned long int)arg2->Data();
3969	setGMPFloatDigits( ii, ii );
3970	}
3971
3972	if ( gls == NULL \|\| pIsConstant( gls ) )
3973	{
3974	WerrorS("Input polynomial is constant!");
3975	return TRUE;
3976	}
3977
3978	int ldummy;
3979	int deg= pLDeg( gls, &ldummy, currRing );
3980	// int deg= pDeg( gls );
3981	int len= pLength( gls );
3982	int i,vpos=0;
3983	poly piter;
3984	lists elist;
3985	lists rlist;
3986
3987	elist= (lists)omAlloc( sizeof(slists) );
3988	elist->Init( 0 );
3989
3990	if ( pVariables > 1 )
3991	{
3992	piter= gls;
3993	for ( i= 1; i <= pVariables; i++ )
3994	if ( pGetExp( piter, i ) )
3995	{
3996	vpos= i;
3997	break;
3998	}
3999	while ( piter )
4000	{
4001	for ( i= 1; i <= pVariables; i++ )
4002	if ( (vpos != i) && (pGetExp( piter, i ) != 0) )
4003	{
4004	WerrorS("The input polynomial must be univariate!");
4005	return TRUE;
4006	}
4007	pIter( piter );
4008	}
4009	}
4010
4011	rootContainer * roots= new rootContainer();
4012	number * pcoeffs= (number )omAlloc( (deg+1) sizeof( number ) );
4013	piter= gls;
4014	for ( i= deg; i >= 0; i-- )
4015	{
4016	//if ( piter ) Print("deg %d, pDeg(piter) %d\n",i,pTotaldegree(piter));
4017	if ( piter && pTotaldegree(piter) == i )
4018	{
4019	pcoeffs[i]= nCopy( pGetCoeff( piter ) );
4020	//nPrint( pcoeffs[i] );PrintS(" ");
4021	pIter( piter );
4022	}
4023	else
4024	{
4025	pcoeffs[i]= nInit(0);
4026	}
4027	}
4028
4029	#ifdef mprDEBUG_PROT
4030	for (i=deg; i >= 0; i--)
4031	{
4032	nPrint( pcoeffs[i] );PrintS(" ");
4033	}
4034	PrintLn();
4035	#endif
4036
4037	roots->fillContainer( pcoeffs, NULL, 1, deg, rootContainer::onepoly, 1 );
4038	roots->solver( howclean );
4039
4040	int elem= roots->getAnzRoots();
4041	char *out;
4042	char *dummy;
4043	int j;
4044
4045	rlist= (lists)omAlloc( sizeof(slists) );
4046	rlist->Init( elem );
4047
4048	if (rField_is_long_C())
4049	{
4050	for ( j= 0; j < elem; j++ )
4051	{
4052	rlist->m[j].rtyp=NUMBER_CMD;
4053	rlist->m[j].data=(void *)nCopy((number)(roots->getRoot(j)));
4054	//rlist->m[j].data=(void *)(number)(roots->getRoot(j));
4055	}
4056	}
4057	else
4058	{
4059	for ( j= 0; j < elem; j++ )
4060	{
4061	dummy = complexToStr( (*roots)[j], gmp_output_digits );
4062	rlist->m[j].rtyp=STRING_CMD;
4063	rlist->m[j].data=(void *)dummy;
4064	}
4065	}
4066
4067	elist->Clean();
4068	//omFreeSize( (ADDRESS) elist, sizeof(slists) );
4069
4070	// this is (via fillContainer) the same data as in root
4071	//for ( i= deg; i >= 0; i-- ) nDelete( &pcoeffs[i] );
4072	//omFreeSize( (ADDRESS) pcoeffs, (deg+1) * sizeof( number ) );
4073
4074	delete roots;
4075
4076	res->rtyp= LIST_CMD;
4077	res->data= (void*)rlist;
4078
4079	return FALSE;
4080	}
4081
4082	BOOLEAN nuVanderSys( leftv res, leftv arg1, leftv arg2, leftv arg3)
4083	{
4084	int i;
4085	ideal p,w;
4086	p= (ideal)arg1->Data();
4087	w= (ideal)arg2->Data();
4088
4089	// w[0] = f(p^0)
4090	// w[1] = f(p^1)
4091	// ...
4092	// p can be a vector of numbers (multivariate polynom)
4093	// or one number (univariate polynom)
4094	// tdg = deg(f)
4095
4096	int n= IDELEMS( p );
4097	int m= IDELEMS( w );
4098	int tdg= (int)(long)arg3->Data();
4099
4100	res->data= (void*)NULL;
4101
4102	// check the input
4103	if ( tdg < 1 )
4104	{
4105	WerrorS("Last input parameter must be > 0!");
4106	return TRUE;
4107	}
4108	if ( n != pVariables )
4109	{
4110	Werror("Size of first input ideal must be equal to %d!",pVariables);
4111	return TRUE;
4112	}
4113	if ( m != (int)pow((double)tdg+1,(double)n) )
4114	{
4115	Werror("Size of second input ideal must be equal to %d!",
4116	(int)pow((double)tdg+1,(double)n));
4117	return TRUE;
4118	}
4119	if ( !(rField_is_Q() /* \|\|
4120	rField_is_R() \|\| rField_is_long_R() \|\|
4121	rField_is_long_C()*/ ) )
4122	{
4123	WerrorS("Ground field not implemented!");
4124	return TRUE;
4125	}
4126
4127	number tmp;
4128	number pevpoint= (number )omAlloc( n * sizeof( number ) );
4129	for ( i= 0; i < n; i++ )
4130	{
4131	pevpoint[i]=nInit(0);
4132	if ( (p->m)[i] )
4133	{
4134	tmp = pGetCoeff( (p->m)[i] );
4135	if ( nIsZero(tmp) \|\| nIsOne(tmp) \|\| nIsMOne(tmp) )
4136	{
4137	omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
4138	WerrorS("Elements of first input ideal must not be equal to -1, 0, 1!");
4139	return TRUE;
4140	}
4141	} else tmp= NULL;
4142	if ( !nIsZero(tmp) )
4143	{
4144	if ( !pIsConstant((p->m)[i]))
4145	{
4146	omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
4147	WerrorS("Elements of first input ideal must be numbers!");
4148	return TRUE;
4149	}
4150	pevpoint[i]= nCopy( tmp );
4151	}
4152	}
4153
4154	number wresults= (number )omAlloc( m * sizeof( number ) );
4155	for ( i= 0; i < m; i++ )
4156	{
4157	wresults[i]= nInit(0);
4158	if ( (w->m)[i] && !nIsZero(pGetCoeff((w->m)[i])) )
4159	{
4160	if ( !pIsConstant((w->m)[i]))
4161	{
4162	omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
4163	omFreeSize( (ADDRESS)wresults, m * sizeof( number ) );
4164	WerrorS("Elements of second input ideal must be numbers!");
4165	return TRUE;
4166	}
4167	wresults[i]= nCopy(pGetCoeff((w->m)[i]));
4168	}
4169	}
4170
4171	vandermonde vm( m, n, tdg, pevpoint, FALSE );
4172	number *ncpoly= vm.interpolateDense( wresults );
4173	// do not free ncpoly[]!!
4174	poly rpoly= vm.numvec2poly( ncpoly );
4175
4176	omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
4177	omFreeSize( (ADDRESS)wresults, m * sizeof( number ) );
4178
4179	res->data= (void*)rpoly;
4180	return FALSE;
4181	}
4182
4183	BOOLEAN nuUResSolve( leftv res, leftv args )
4184	{
4185	leftv v= args;
4186
4187	ideal gls;
4188	int imtype;
4189	int howclean;
4190
4191	// get ideal
4192	if ( v->Typ() != IDEAL_CMD )
4193	return TRUE;
4194	else gls= (ideal)(v->Data());
4195	v= v->next;
4196
4197	// get resultant matrix type to use (0,1)
4198	if ( v->Typ() != INT_CMD )
4199	return TRUE;
4200	else imtype= (int)(long)v->Data();
4201	v= v->next;
4202
4203	if (imtype==0)
4204	{
4205	ideal test_id=idInit(1,1);
4206	int j;
4207	for(j=IDELEMS(gls)-1;j>=0;j--)
4208	{
4209	if (gls->m[j]!=NULL)
4210	{
4211	test_id->m[0]=gls->m[j];
4212	intvec *dummy_w=idQHomWeight(test_id);
4213	if (dummy_w!=NULL)
4214	{
4215	WerrorS("Newton polytope not of expected dimension");
4216	delete dummy_w;
4217	return TRUE;
4218	}
4219	}
4220	}
4221	}
4222
4223	// get and set precision in digits ( > 0 )
4224	if ( v->Typ() != INT_CMD )
4225	return TRUE;
4226	else if ( !(rField_is_R()\|\|rField_is_long_R()\|\|rField_is_long_C()) )
4227	{
4228	unsigned long int ii=(unsigned long int)v->Data();
4229	setGMPFloatDigits( ii, ii );
4230	}
4231	v= v->next;
4232
4233	// get interpolation steps (0,1,2)
4234	if ( v->Typ() != INT_CMD )
4235	return TRUE;
4236	else howclean= (int)(long)v->Data();
4237
4238	uResultant::resMatType mtype= determineMType( imtype );
4239	int i,c,count;
4240	lists listofroots= NULL;
4241	lists emptylist;
4242	number smv= NULL;
4243	BOOLEAN interpolate_det= (mtype==uResultant::denseResMat)?TRUE:FALSE;
4244
4245	//emptylist= (lists)omAlloc( sizeof(slists) );
4246	//emptylist->Init( 0 );
4247
4248	//res->rtyp = LIST_CMD;
4249	//res->data= (void *)emptylist;
4250
4251	// check input ideal ( = polynomial system )
4252	if ( mprIdealCheck( gls, args->Name(), mtype ) != mprOk )
4253	{
4254	return TRUE;
4255	}
4256
4257	uResultant * ures;
4258	rootContainer ** iproots;
4259	rootContainer ** muiproots;
4260	rootArranger * arranger;
4261
4262	// main task 1: setup of resultant matrix
4263	ures= new uResultant( gls, mtype );
4264	if ( ures->accessResMat()->initState() != resMatrixBase::ready )
4265	{
4266	WerrorS("Error occurred during matrix setup!");
4267	return TRUE;
4268	}
4269
4270	// if dense resultant, check if minor nonsingular
4271	if ( mtype == uResultant::denseResMat )
4272	{
4273	smv= ures->accessResMat()->getSubDet();
4274	#ifdef mprDEBUG_PROT
4275	PrintS("// Determinant of submatrix: ");nPrint(smv);PrintLn();
4276	#endif
4277	if ( nIsZero(smv) )
4278	{
4279	WerrorS("Unsuitable input ideal: Minor of resultant matrix is singular!");
4280	return TRUE;
4281	}
4282	}
4283
4284	// main task 2: Interpolate specialized resultant polynomials
4285	if ( interpolate_det )
4286	iproots= ures->interpolateDenseSP( false, smv );
4287	else
4288	iproots= ures->specializeInU( false, smv );
4289
4290	// main task 3: Interpolate specialized resultant polynomials
4291	if ( interpolate_det )
4292	muiproots= ures->interpolateDenseSP( true, smv );
4293	else
4294	muiproots= ures->specializeInU( true, smv );
4295
4296	#ifdef mprDEBUG_PROT
4297	c= iproots[0]->getAnzElems();
4298	for (i=0; i < c; i++) pWrite(iproots[i]->getPoly());
4299	c= muiproots[0]->getAnzElems();
4300	for (i=0; i < c; i++) pWrite(muiproots[i]->getPoly());
4301	#endif
4302
4303	// main task 4: Compute roots of specialized polys and match them up
4304	arranger= new rootArranger( iproots, muiproots, howclean );
4305	arranger->solve_all();
4306
4307	// get list of roots
4308	if ( arranger->success() )
4309	{
4310	arranger->arrange();
4311	listofroots= arranger->listOfRoots( gmp_output_digits );
4312	}
4313	else
4314	{
4315	WerrorS("Solver was unable to find any roots!");
4316	return TRUE;
4317	}
4318
4319	// free everything
4320	count= iproots[0]->getAnzElems();
4321	for (i=0; i < count; i++) delete iproots[i];
4322	omFreeSize( (ADDRESS) iproots, count * sizeof(rootContainer*) );
4323	count= muiproots[0]->getAnzElems();
4324	for (i=0; i < count; i++) delete muiproots[i];
4325	omFreeSize( (ADDRESS) muiproots, count * sizeof(rootContainer*) );
4326
4327	delete ures;
4328	delete arranger;
4329	nDelete( &smv );
4330
4331	res->data= (void *)listofroots;
4332
4333	//emptylist->Clean();
4334	// omFreeSize( (ADDRESS) emptylist, sizeof(slists) );
4335
4336	return FALSE;
4337	}
4338
4339	// from mpr_numeric.cc
4340	lists rootArranger::listOfRoots( const unsigned int oprec )
4341	{
4342	int i,j,tr;
4343	int count= roots[0]->getAnzRoots(); // number of roots
4344	int elem= roots[0]->getAnzElems(); // number of koordinates per root
4345
4346	lists listofroots= (lists)omAlloc( sizeof(slists) ); // must be done this way!
4347
4348	if ( found_roots )
4349	{
4350	listofroots->Init( count );
4351
4352	for (i=0; i < count; i++)
4353	{
4354	lists onepoint= (lists)omAlloc(sizeof(slists)); // must be done this way!
4355	onepoint->Init(elem);
4356	for ( j= 0; j < elem; j++ )
4357	{
4358	if ( !rField_is_long_C() )
4359	{
4360	onepoint->m[j].rtyp=STRING_CMD;
4361	onepoint->m[j].data=(void )complexToStr((roots[j])[i],oprec);
4362	}
4363	else
4364	{
4365	onepoint->m[j].rtyp=NUMBER_CMD;
4366	onepoint->m[j].data=(void *)nCopy((number)(roots[j]->getRoot(i)));
4367	}
4368	onepoint->m[j].next= NULL;
4369	onepoint->m[j].name= NULL;
4370	}
4371	listofroots->m[i].rtyp=LIST_CMD;
4372	listofroots->m[i].data=(void *)onepoint;
4373	listofroots->m[j].next= NULL;
4374	listofroots->m[j].name= NULL;
4375	}
4376
4377	}
4378	else
4379	{
4380	listofroots->Init( 0 );
4381	}
4382
4383	return listofroots;
4384	}
4385
4386	// from ring.cc
4387	void rSetHdl(idhdl h)
4388	{
4389	int i;
4390	ring rg = NULL;
4391	if (h!=NULL)
4392	{
4393	// Print(" new ring:%s (l:%d)\n",IDID(h),IDLEV(h));
4394	rg = IDRING(h);
4395	if (rg==NULL) return; //id <>NULL, ring==NULL
4396	omCheckAddrSize((ADDRESS)h,sizeof(idrec));
4397	if (IDID(h)) // OB: ????
4398	omCheckAddr((ADDRESS)IDID(h));
4399	rTest(rg);
4400	}
4401
4402	// clean up history
4403	if (sLastPrinted.RingDependend())
4404	{
4405	sLastPrinted.CleanUp();
4406	memset(&sLastPrinted,0,sizeof(sleftv));
4407	}
4408
4409	// test for valid "currRing":
4410	if ((rg!=NULL) && (rg->idroot==NULL))
4411	{
4412	ring old=rg;
4413	rg=rAssure_HasComp(rg);
4414	if (old!=rg)
4415	{
4416	rKill(old);
4417	IDRING(h)=rg;
4418	}
4419	}
4420	/------------ change the global ring -----------------------/
4421	rChangeCurrRing(rg);
4422	currRingHdl = h;
4423	}
4424
4425	BOOLEAN rSleftvOrdering2Ordering(sleftv *ord, ring R)
4426	{
4427	int last = 0, o=0, n = 1, i=0, typ = 1, j;
4428	sleftv *sl = ord;
4429
4430	// determine nBlocks
4431	while (sl!=NULL)
4432	{
4433	intvec iv = (intvec )(sl->data);
4434	if (((iv)[1]==ringorder_c)\|\|((iv)[1]==ringorder_C))
4435	i++;
4436	else if ((*iv)[1]==ringorder_L)
4437	{
4438	R->bitmask=(*iv)[2];
4439	n--;
4440	}
4441	else if (((*iv)[1]!=ringorder_a)
4442	&& ((*iv)[1]!=ringorder_a64))
4443	o++;
4444	n++;
4445	sl=sl->next;
4446	}
4447	// check whether at least one real ordering
4448	if (o==0)
4449	{
4450	WerrorS("invalid combination of orderings");
4451	return TRUE;
4452	}
4453	// if no c/C ordering is given, increment n
4454	if (i==0) n++;
4455	else if (i != 1)
4456	{
4457	// throw error if more than one is given
4458	WerrorS("more than one ordering c/C specified");
4459	return TRUE;
4460	}
4461
4462	// initialize fields of R
4463	R->order=(int )omAlloc0(nsizeof(int));
4464	R->block0=(int )omAlloc0(nsizeof(int));
4465	R->block1=(int )omAlloc0(nsizeof(int));
4466	R->wvhdl=(int*)omAlloc0(nsizeof(int_ptr));
4467
4468	int weights=(int)omAlloc0((R->N+1)*sizeof(int));
4469
4470	// init order, so that rBlocks works correctly
4471	for (j=0; j < n-1; j++)
4472	R->order[j] = (int) ringorder_unspec;
4473	// set last _C order, if no c/C order was given
4474	if (i == 0) R->order[n-2] = ringorder_C;
4475
4476	/* init orders */
4477	sl=ord;
4478	n=-1;
4479	while (sl!=NULL)
4480	{
4481	intvec *iv;
4482	iv = (intvec *)(sl->data);
4483	if ((*iv)[1]!=ringorder_L)
4484	{
4485	n++;
4486
4487	/* the format of an ordering:
4488	* iv[0]: factor
4489	* iv[1]: ordering
4490	* iv[2..end]: weights
4491	*/
4492	R->order[n] = (*iv)[1];
4493	typ=1;
4494	switch ((*iv)[1])
4495	{
4496	case ringorder_ws:
4497	case ringorder_Ws:
4498	typ=-1;
4499	case ringorder_wp:
4500	case ringorder_Wp:
4501	R->wvhdl[n]=(int)omAlloc((iv->length()-1)sizeof(int));
4502	R->block0[n] = last+1;
4503	for (i=2; i<iv->length(); i++)
4504	{
4505	R->wvhdl[n][i-2] = (*iv)[i];
4506	last++;
4507	if (weights[last]==0) weights[last]=(iv)[i]typ;
4508	}
4509	R->block1[n] = last;
4510	break;
4511	case ringorder_ls:
4512	case ringorder_ds:
4513	case ringorder_Ds:
4514	case ringorder_rs:
4515	typ=-1;
4516	case ringorder_lp:
4517	case ringorder_dp:
4518	case ringorder_Dp:
4519	case ringorder_rp:
4520	R->block0[n] = last+1;
4521	if (iv->length() == 3) last+=(*iv)[2];
4522	else last += (*iv)[0];
4523	R->block1[n] = last;
4524	//if ((R->block0[n]>R->block1[n])
4525	//\|\| (R->block1[n]>rVar(R)))
4526	//{
4527	// R->block1[n]=rVar(R);
4528	// //WerrorS("ordering larger than number of variables");
4529	// break;
4530	//}
4531	if (rCheckIV(iv)) return TRUE;
4532	for(i=si_min(rVar(R),R->block1[n]);i>=R->block0[n];i--)
4533	{
4534	if (weights[i]==0) weights[i]=typ;
4535	}
4536	break;
4537	case ringorder_S:
4538	case ringorder_c:
4539	case ringorder_C:
4540	if (rCheckIV(iv)) return TRUE;
4541	break;
4542	case ringorder_aa:
4543	case ringorder_a:
4544	R->block0[n] = last+1;
4545	R->block1[n] = si_min(last+iv->length()-2 , rVar(R));
4546	R->wvhdl[n] = (int)omAlloc((iv->length()-1)sizeof(int));
4547	for (i=2; i<iv->length(); i++)
4548	{
4549	R->wvhdl[n][i-2]=(*iv)[i];
4550	last++;
4551	if (weights[last]==0) weights[last]=(iv)[i]typ;
4552	}
4553	last=R->block0[n]-1;
4554	break;
4555	case ringorder_a64:
4556	{
4557	R->block0[n] = last+1;
4558	R->block1[n] = si_min(last+iv->length()-2 , rVar(R));
4559	R->wvhdl[n] = (int)omAlloc((iv->length()-1)sizeof(int64));
4560	int64 w=(int64 )R->wvhdl[n];
4561	for (i=2; i<iv->length(); i++)
4562	{
4563	w[i-2]=(*iv)[i];
4564	last++;
4565	if (weights[last]==0) weights[last]=(iv)[i]typ;
4566	}
4567	last=R->block0[n]-1;
4568	break;
4569	}
4570	case ringorder_M:
4571	{
4572	int Mtyp=rTypeOfMatrixOrder(iv);
4573	if (Mtyp==0) return TRUE;
4574	if (Mtyp==-1) typ = -1;
4575
4576	R->wvhdl[n] =( int )omAlloc((iv->length()-1)sizeof(int));
4577	for (i=2; i<iv->length();i++)
4578	R->wvhdl[n][i-2]=(*iv)[i];
4579
4580	R->block0[n] = last+1;
4581	last += (int)sqrt((double)(iv->length()-2));
4582	R->block1[n] = last;
4583	for(i=si_min(rVar(R),R->block1[n]);i>=R->block0[n];i--)
4584	{
4585	if (weights[i]==0) weights[i]=typ;
4586	}
4587	break;
4588	}
4589
4590	case ringorder_no:
4591	R->order[n] = ringorder_unspec;
4592	return TRUE;
4593
4594	default:
4595	Werror("Internal Error: Unknown ordering %d", (*iv)[1]);
4596	R->order[n] = ringorder_unspec;
4597	return TRUE;
4598	}
4599	}
4600	sl=sl->next;
4601	}
4602
4603	// check for complete coverage
4604	if ((R->order[n]==ringorder_c) \|\| (R->order[n]==ringorder_C)) n--;
4605	if (R->block1[n] != R->N)
4606	{
4607	if (((R->order[n]==ringorder_dp) \|\|
4608	(R->order[n]==ringorder_ds) \|\|
4609	(R->order[n]==ringorder_Dp) \|\|
4610	(R->order[n]==ringorder_Ds) \|\|
4611	(R->order[n]==ringorder_rp) \|\|
4612	(R->order[n]==ringorder_rs) \|\|
4613	(R->order[n]==ringorder_lp) \|\|
4614	(R->order[n]==ringorder_ls))
4615	&&
4616	R->block0[n] <= R->N)
4617	{
4618	R->block1[n] = R->N;
4619	}
4620	else
4621	{
4622	Werror("mismatch of number of vars (%d) and ordering (%d vars)",
4623	R->N,R->block1[n]);
4624	return TRUE;
4625	}
4626	}
4627	// find OrdSgn:
4628	R->OrdSgn = 1;
4629	for(i=1;i<=R->N;i++)
4630	{ if (weights[i]<0) { R->OrdSgn=-1;break; }}
4631	omFree(weights);
4632	return FALSE;
4633	}
4634
4635	BOOLEAN rSleftvList2StringArray(sleftv* sl, char** p)
4636	{
4637
4638	while(sl!=NULL)
4639	{
4640	if (sl->Name() == sNoName)
4641	{
4642	if (sl->Typ()==POLY_CMD)
4643	{
4644	sleftv s_sl;
4645	iiConvert(POLY_CMD,ANY_TYPE,-1,sl,&s_sl);
4646	if (s_sl.Name() != sNoName)
4647	*p = omStrDup(s_sl.Name());
4648	else
4649	*p = NULL;
4650	sl->next = s_sl.next;
4651	s_sl.next = NULL;
4652	s_sl.CleanUp();
4653	if (*p == NULL) return TRUE;
4654	}
4655	else
4656	return TRUE;
4657	}
4658	else
4659	*p = omStrDup(sl->Name());
4660	p++;
4661	sl=sl->next;
4662	}
4663	return FALSE;
4664	}
4665
4666	////////////////////
4667	//
4668	// rInit itself:
4669	//
4670	// INPUT: s: name, pn: ch & parameter (names), rv: variable (names)
4671	// ord: ordering
4672	// RETURN: currRingHdl on success
4673	// NULL on error
4674	// NOTE: * makes new ring to current ring, on success
4675	// * considers input sleftv's as read-only
4676	//idhdl rInit(char s, sleftv pn, sleftv* rv, sleftv* ord)
4677	ring rInit(sleftv* pn, sleftv* rv, sleftv* ord)
4678	{
4679	int ch;
4680	#ifdef HAVE_RINGS
4681	unsigned int ringtype = 0;
4682	int_number ringflaga = NULL;
4683	unsigned int ringflagb = 1;
4684	#endif
4685	int float_len=0;
4686	int float_len2=0;
4687	ring R = NULL;
4688	idhdl tmp = NULL;
4689	BOOLEAN ffChar=FALSE;
4690	int typ = 1;
4691
4692	/* ch -------------------------------------------------------*/
4693	// get ch of ground field
4694	int numberOfAllocatedBlocks;
4695
4696	if (pn->Typ()==INT_CMD)
4697	{
4698	ch=(int)(long)pn->Data();
4699	}
4700	else if ((pn->name != NULL)
4701	&& ((strcmp(pn->name,"real")==0) \|\| (strcmp(pn->name,"complex")==0)))
4702	{
4703	BOOLEAN complex_flag=(strcmp(pn->name,"complex")==0);
4704	ch=-1;
4705	if ((pn->next!=NULL) && (pn->next->Typ()==INT_CMD))
4706	{
4707	float_len=(int)(long)pn->next->Data();
4708	float_len2=float_len;
4709	pn=pn->next;
4710	if ((pn->next!=NULL) && (pn->next->Typ()==INT_CMD))
4711	{
4712	float_len2=(int)(long)pn->next->Data();
4713	pn=pn->next;
4714	}
4715	}
4716	if ((pn->next==NULL) && complex_flag)
4717	{
4718	pn->next=(leftv)omAlloc0Bin(sleftv_bin);
4719	pn->next->name=omStrDup("i");
4720	}
4721	}
4722	#ifdef HAVE_RINGS
4723	else if ((pn->name != NULL) && (strcmp(pn->name, "integer") == 0))
4724	{
4725	ringflaga = (int_number) omAlloc(sizeof(mpz_t));
4726	mpz_init_set_si(ringflaga, 0);
4727	if ((pn->next!=NULL) && (pn->next->Typ()==INT_CMD))
4728	{
4729	mpz_set_ui(ringflaga, (int)(long) pn->next->Data());
4730	pn=pn->next;
4731	if ((pn->next!=NULL) && (pn->next->Typ()==INT_CMD))
4732	{
4733	ringflagb = (long) pn->next->Data();
4734	pn=pn->next;
4735	}
4736	while ((pn->next!=NULL) && (pn->next->Typ()==INT_CMD))
4737	{
4738	mpz_mul_ui(ringflaga, ringflaga, (int)(long) pn->next->Data());
4739	pn=pn->next;
4740	}
4741	}
4742	if ((mpz_cmp_ui(ringflaga, 1) == 0) && (mpz_cmp_ui(ringflaga, 0) < 0))
4743	{
4744	Werror("Wrong ground ring specification (module is 1)");
4745	goto rInitError;
4746	}
4747	if (ringflagb < 1)
4748	{
4749	Werror("Wrong ground ring specification (exponent smaller than 1");
4750	goto rInitError;
4751	}
4752	// module is 0 ---> integers
4753	if (mpz_cmp_ui(ringflaga, 0) == 0)
4754	{
4755	ch = 0;
4756	ringtype = 4;
4757	}
4758	// we have an exponent
4759	else if (ringflagb > 1)
4760	{
4761	ch = ringflagb;
4762	if ((mpz_cmp_ui(ringflaga, 2) == 0) && (ringflagb <= 8*sizeof(NATNUMBER)))
4763	{
4764	/* this branch should be active for ringflagb = 2..32 resp. 2..64,
4765	depending on the size of a long on the respective platform */
4766	ringtype = 1; // Use Z/2^ch
4767	}
4768	else
4769	{
4770	ringtype = 3;
4771	}
4772	}
4773	// just a module m > 1
4774	else
4775	{
4776	ringtype = 2;
4777	ch = mpz_get_ui(ringflaga);
4778	}
4779	}
4780	#endif
4781	else
4782	{
4783	Werror("Wrong ground field specification");
4784	goto rInitError;
4785	}
4786	pn=pn->next;
4787
4788	#ifdef HAVE_RINGS
4789	if (ringtype > 0)
4790	{
4791	WarnS("You are using coefficient rings which are not fields.");
4792	WarnS("Please note that only limited functionality is available");
4793	WarnS("for these coefficients.");
4794	WarnS("");
4795	WarnS("The following commands are meant to work:");
4796	WarnS("- basic polynomial arithmetic");
4797	WarnS("- std");
4798	WarnS("- syz");
4799	WarnS("- lift");
4800	WarnS("- reduce");
4801	}
4802	#endif
4803
4804	int l, last;
4805	sleftv * sl;
4806	/every entry in the new ring is initialized to 0/
4807
4808	/* characteristic -----------------------------------------------*/
4809	/* input: 0 ch=0 : Q parameter=NULL ffChar=FALSE float_len
4810	* 0 1 : Q(a,...) *names FALSE
4811	* 0 -1 : R NULL FALSE 0
4812	* 0 -1 : R NULL FALSE prec. >6
4813	* 0 -1 : C *names FALSE prec. 0..?
4814	* p p : Fp NULL FALSE
4815	* p -p : Fp(a) *names FALSE
4816	* q q : GF(q=p^n) *names TRUE
4817	*/
4818	if ((ch!=-1)
4819	#ifdef HAVE_RINGS
4820	&& (ringtype == 0)
4821	#endif
4822	)
4823	{
4824	int l = 0;
4825
4826	if (((ch!=0) && (ch<2))
4827	#ifndef NV_OPS
4828	\|\| (ch > 32003)
4829	#endif
4830	)
4831	{
4832	Warn("%d is invalid characteristic of ground field. 32003 is used.", ch);
4833	ch=32003;
4834	}
4835	// load fftable, if necessary
4836	if (pn!=NULL)
4837	{
4838	while ((ch!=fftable[l]) && (fftable[l])) l++;
4839	if (fftable[l]==0) ch = IsPrime(ch);
4840	else
4841	{
4842	char m[1]={(char )sNoName};
4843	nfSetChar(ch,m);
4844	if (errorreported) goto rInitError;
4845	else ffChar=TRUE;
4846	}
4847	}
4848	else
4849	{
4850	ch = IsPrime(ch);
4851	}
4852	}
4853	// allocated ring and set ch
4854	R = (ring) omAlloc0Bin(sip_sring_bin);
4855	R->ch = ch;
4856	#ifdef HAVE_RINGS
4857	R->ringtype = ringtype;
4858	R->ringflaga = ringflaga;
4859	R->ringflagb = ringflagb;
4860	#endif
4861	if (ch == -1)
4862	{
4863	R->float_len= si_min(float_len,32767);
4864	R->float_len2= si_min(float_len2,32767);
4865	}
4866
4867	/* parameter -------------------------------------------------------*/
4868	if (pn!=NULL)
4869	{
4870	R->P=pn->listLength();
4871	//if ((ffChar\|\| (ch == 1)) && (R->P > 1))
4872	if ((R->P > 1) && (ffChar \|\| (ch == -1)))
4873	{
4874	WerrorS("too many parameters");
4875	goto rInitError;
4876	}
4877	R->parameter=(char*)omAlloc0(R->Psizeof(char_ptr));
4878	if (rSleftvList2StringArray(pn, R->parameter))
4879	{
4880	WerrorS("parameter expected");
4881	goto rInitError;
4882	}
4883	if (ch>1 && !ffChar) R->ch=-ch;
4884	else if (ch==0) R->ch=1;
4885	}
4886	else if (ffChar)
4887	{
4888	WerrorS("need one parameter");
4889	goto rInitError;
4890	}
4891	/* post-processing of field description */
4892	// we have short reals, but no short complex
4893	if ((R->ch == - 1)
4894	&& (R->parameter !=NULL)
4895	&& (R->float_len < SHORT_REAL_LENGTH))
4896	{
4897	R->float_len = SHORT_REAL_LENGTH;
4898	R->float_len2 = SHORT_REAL_LENGTH;
4899	}
4900
4901	/* names and number of variables-------------------------------------*/
4902	{
4903	int l=rv->listLength();
4904	#if SIZEOF_SHORT == 2
4905	#define MAX_SHORT 0x7fff
4906	#endif
4907	if (l>MAX_SHORT)
4908	{
4909	Werror("too many ring variables(%d), max is %d",l,MAX_SHORT);
4910	goto rInitError;
4911	}
4912	R->N = l; /rv->listLength();/
4913	}
4914	R->names = (char *)omAlloc0(R->N sizeof(char_ptr));
4915	if (rSleftvList2StringArray(rv, R->names))
4916	{
4917	WerrorS("name of ring variable expected");
4918	goto rInitError;
4919	}
4920
4921	/* check names and parameters for conflicts ------------------------- */
4922	rRenameVars(R); // conflicting variables will be renamed
4923	/* ordering -------------------------------------------------------------*/
4924	if (rSleftvOrdering2Ordering(ord, R))
4925	goto rInitError;
4926
4927	// Complete the initialization
4928	if (rComplete(R,1))
4929	goto rInitError;
4930
4931	rTest(R);
4932
4933	// try to enter the ring into the name list
4934	// need to clean up sleftv here, before this ring can be set to
4935	// new currRing or currRing can be killed beacuse new ring has
4936	// same name
4937	if (pn != NULL) pn->CleanUp();
4938	if (rv != NULL) rv->CleanUp();
4939	if (ord != NULL) ord->CleanUp();
4940	//if ((tmp = enterid(s, myynest, RING_CMD, &IDROOT))==NULL)
4941	// goto rInitError;
4942
4943	//memcpy(IDRING(tmp),R,sizeof(*R));
4944	// set current ring
4945	//omFreeBin(R, ip_sring_bin);
4946	//return tmp;
4947	return R;
4948
4949	// error case:
4950	rInitError:
4951	if (R != NULL) rDelete(R);
4952	if (pn != NULL) pn->CleanUp();
4953	if (rv != NULL) rv->CleanUp();
4954	if (ord != NULL) ord->CleanUp();
4955	return NULL;
4956	}
4957
4958	ring rSubring(ring org_ring, sleftv* rv)
4959	{
4960	ring R = rCopy0(org_ring);
4961	int perm=(int )omAlloc0((org_ring->N+1)*sizeof(int));
4962	int last = 0, o=0, n = rBlocks(org_ring), i=0, typ = 1, j;
4963
4964	/* names and number of variables-------------------------------------*/
4965	{
4966	int l=rv->listLength();
4967	if (l>MAX_SHORT)
4968	{
4969	Werror("too many ring variables(%d), max is %d",l,MAX_SHORT);
4970	goto rInitError;
4971	}
4972	R->N = l; /rv->listLength();/
4973	}
4974	omFree(R->names);
4975	R->names = (char *)omAlloc0(R->N sizeof(char_ptr));
4976	if (rSleftvList2StringArray(rv, R->names))
4977	{
4978	WerrorS("name of ring variable expected");
4979	goto rInitError;
4980	}
4981
4982	/* check names for subring in org_ring ------------------------- */
4983	{
4984	i=0;
4985
4986	for(j=0;j<R->N;j++)
4987	{
4988	for(;i<org_ring->N;i++)
4989	{
4990	if (strcmp(org_ring->names[i],R->names[j])==0)
4991	{
4992	perm[i+1]=j+1;
4993	break;
4994	}
4995	}
4996	if (i>org_ring->N)
4997	{
4998	Werror("variable %d (%s) not in basering",j+1,R->names[j]);
4999	break;
5000	}
5001	}
5002	}
5003	//Print("perm=");
5004	//for(i=1;i<org_ring->N;i++) Print("v%d -> v%d\n",i,perm[i]);
5005	/* ordering -------------------------------------------------------------*/
5006
5007	for(i=0;i<n;i++)
5008	{
5009	int min_var=-1;
5010	int max_var=-1;
5011	for(j=R->block0[i];j<=R->block1[i];j++)
5012	{
5013	if (perm[j]>0)
5014	{
5015	if (min_var==-1) min_var=perm[j];
5016	max_var=perm[j];
5017	}
5018	}
5019	if (min_var!=-1)
5020	{
5021	//Print("block %d: old %d..%d, now:%d..%d\n",
5022	// i,R->block0[i],R->block1[i],min_var,max_var);
5023	R->block0[i]=min_var;
5024	R->block1[i]=max_var;
5025	if (R->wvhdl[i]!=NULL)
5026	{
5027	omFree(R->wvhdl[i]);
5028	R->wvhdl[i]=(int)omAlloc0((max_var-min_var+1)sizeof(int));
5029	for(j=org_ring->block0[i];j<=org_ring->block1[i];j++)
5030	{
5031	if (perm[j]>0)
5032	{
5033	R->wvhdl[i][perm[j]-R->block0[i]]=
5034	org_ring->wvhdl[i][j-org_ring->block0[i]];
5035	//Print("w%d=%d (orig_w%d)\n",perm[j],R->wvhdl[i][perm[j]-R->block0[i]],j);
5036	}
5037	}
5038	}
5039	}
5040	else
5041	{
5042	if(R->block0[i]>0)
5043	{
5044	//Print("skip block %d\n",i);
5045	R->order[i]=ringorder_unspec;
5046	if (R->wvhdl[i] !=NULL) omFree(R->wvhdl[i]);
5047	R->wvhdl[i]=NULL;
5048	}
5049	//else Print("keep block %d\n",i);
5050	}
5051	}
5052	i=n-1;
5053	while(i>0)
5054	{
5055	// removed unneded blocks
5056	if(R->order[i-1]==ringorder_unspec)
5057	{
5058	for(j=i;j<=n;j++)
5059	{
5060	R->order[j-1]=R->order[j];
5061	R->block0[j-1]=R->block0[j];
5062	R->block1[j-1]=R->block1[j];
5063	if (R->wvhdl[j-1] !=NULL) omFree(R->wvhdl[j-1]);
5064	R->wvhdl[j-1]=R->wvhdl[j];
5065	}
5066	R->order[n]=ringorder_unspec;
5067	n--;
5068	}
5069	i--;
5070	}
5071	n=rBlocks(org_ring)-1;
5072	while (R->order[n]==0) n--;
5073	while (R->order[n]==ringorder_unspec) n--;
5074	if ((R->order[n]==ringorder_c) \|\| (R->order[n]==ringorder_C)) n--;
5075	if (R->block1[n] != R->N)
5076	{
5077	if (((R->order[n]==ringorder_dp) \|\|
5078	(R->order[n]==ringorder_ds) \|\|
5079	(R->order[n]==ringorder_Dp) \|\|
5080	(R->order[n]==ringorder_Ds) \|\|
5081	(R->order[n]==ringorder_rp) \|\|
5082	(R->order[n]==ringorder_rs) \|\|
5083	(R->order[n]==ringorder_lp) \|\|
5084	(R->order[n]==ringorder_ls))
5085	&&
5086	R->block0[n] <= R->N)
5087	{
5088	R->block1[n] = R->N;
5089	}
5090	else
5091	{
5092	Werror("mismatch of number of vars (%d) and ordering (%d vars) in block %d",
5093	R->N,R->block1[n],n);
5094	return NULL;
5095	}
5096	}
5097	omFree(perm);
5098	// find OrdSgn:
5099	R->OrdSgn = org_ring->OrdSgn; // IMPROVE!
5100	//for(i=1;i<=R->N;i++)
5101	//{ if (weights[i]<0) { R->OrdSgn=-1;break; }}
5102	//omFree(weights);
5103	// Complete the initialization
5104	if (rComplete(R,1))
5105	goto rInitError;
5106
5107	rTest(R);
5108
5109	if (rv != NULL) rv->CleanUp();
5110
5111	return R;
5112
5113	// error case:
5114	rInitError:
5115	if (R != NULL) rDelete(R);
5116	if (rv != NULL) rv->CleanUp();
5117	return NULL;
5118	}
5119
5120	void rKill(ring r)
5121	{
5122	if ((r->ref<=0)&&(r->order!=NULL))
5123	{
5124	#ifdef RDEBUG
5125	if (traceit &TRACE_SHOW_RINGS) Print("kill ring %lx\n",(long)r);
5126	#endif
5127	if (r->qideal!=NULL)
5128	{
5129	id_Delete(&r->qideal, r);
5130	r->qideal = NULL;
5131	}
5132	int i=1;
5133	int j;
5134	int *pi=r->order;
5135	#ifdef USE_IILOCALRING
5136	for (j=0;j<iiRETURNEXPR_len;j++)
5137	{
5138	if (iiLocalRing[j]==r)
5139	{
5140	if (j<myynest) Warn("killing the basering for level %d",j);
5141	iiLocalRing[j]=NULL;
5142	}
5143	}
5144	#else /* USE_IILOCALRING */
5145	//#endif /* USE_IILOCALRING */
5146	{
5147	proclevel * nshdl = procstack;
5148	int lev=myynest-1;
5149
5150	for(; nshdl != NULL; nshdl = nshdl->next)
5151	{
5152	if (nshdl->cRing==r)
5153	{
5154	Warn("killing the basering for level %d",lev);
5155	nshdl->cRing=NULL;
5156	nshdl->cRingHdl=NULL;
5157	}
5158	}
5159	}
5160	#endif /* USE_IILOCALRING */
5161	// any variables depending on r ?
5162	while (r->idroot!=NULL)
5163	{
5164	killhdl2(r->idroot,&(r->idroot),r);
5165	}
5166	if (r==currRing)
5167	{
5168	// all dependend stuff is done, clean global vars:
5169	if (r->qideal!=NULL)
5170	{
5171	currQuotient=NULL;
5172	}
5173	if (ppNoether!=NULL) pDelete(&ppNoether);
5174	if (sLastPrinted.RingDependend())
5175	{
5176	sLastPrinted.CleanUp();
5177	}
5178	if ((myynest>0) && (iiRETURNEXPR[myynest].RingDependend()))
5179	{
5180	WerrorS("return value depends on local ring variable (export missing ?)");
5181	iiRETURNEXPR[myynest].CleanUp();
5182	}
5183	currRing=NULL;
5184	currRingHdl=NULL;
5185	}
5186
5187	/* nKillChar(r); will be called from inside of rDelete */
5188	rDelete(r);
5189	return;
5190	}
5191	r->ref--;
5192	}
5193
5194	void rKill(idhdl h)
5195	{
5196	ring r = IDRING(h);
5197	int ref=0;
5198	if (r!=NULL)
5199	{
5200	ref=r->ref;
5201	rKill(r);
5202	}
5203	if (h==currRingHdl)
5204	{
5205	if (ref<=0) { currRing=NULL; currRingHdl=NULL;}
5206	else
5207	{
5208	currRingHdl=rFindHdl(r,currRingHdl,NULL);
5209	}
5210	}
5211	}
5212
5213	idhdl rSimpleFindHdl(ring r, idhdl root, idhdl n=NULL)
5214	{
5215	//idhdl next_best=NULL;
5216	idhdl h=root;
5217	while (h!=NULL)
5218	{
5219	if (((IDTYP(h)==RING_CMD)\|\|(IDTYP(h)==QRING_CMD))
5220	&& (h!=n)
5221	&& (IDRING(h)==r)
5222	)
5223	{
5224	// if (IDLEV(h)==myynest)
5225	// return h;
5226	// if ((IDLEV(h)==0) \|\| (next_best==NULL))
5227	// next_best=h;
5228	// else if (IDLEV(next_best)<IDLEV(h))
5229	// next_best=h;
5230	return h;
5231	}
5232	h=IDNEXT(h);
5233	}
5234	//return next_best;
5235	return NULL;
5236	}
5237
5238	extern BOOLEAN jjPROC(leftv res, leftv u, leftv v);
5239	ideal kGroebner(ideal F, ideal Q)
5240	{
5241	//test\|=Sy_bit(OPT_PROT);
5242	idhdl save_ringhdl=currRingHdl;
5243	ideal resid;
5244	idhdl new_ring=NULL;
5245	if ((currRingHdl==NULL) \|\| (IDRING(currRingHdl)!=currRing))
5246	{
5247	currRingHdl=enterid(omStrDup(" GROEBNERring"),0,RING_CMD,&IDROOT,FALSE);
5248	new_ring=currRingHdl;
5249	IDRING(currRingHdl)=currRing;
5250	}
5251	sleftv v; memset(&v,0,sizeof(v)); v.rtyp=IDEAL_CMD; v.data=(char *) F;
5252	idhdl h=ggetid("groebner");
5253	sleftv u; memset(&u,0,sizeof(u)); u.rtyp=IDHDL; u.data=(char *) h;
5254	u.name=IDID(h);
5255
5256	sleftv res; memset(&res,0,sizeof(res));
5257	if(jjPROC(&res,&u,&v))
5258	{
5259	resid=kStd(F,Q,testHomog,NULL);
5260	}
5261	else
5262	{
5263	//printf("typ:%d\n",res.rtyp);
5264	resid=(ideal)(res.data);
5265	}
5266	// cleanup GROEBNERring, save_ringhdl, u,v,(res )
5267	if (new_ring!=NULL)
5268	{
5269	idhdl h=IDROOT;
5270	if (h==new_ring) IDROOT=h->next;
5271	else
5272	{
5273	while ((h!=NULL) &&(h->next!=new_ring)) h=h->next;
5274	if (h!=NULL) h->next=h->next->next;
5275	}
5276	if (h!=NULL) omFreeSize(h,sizeof(*h));
5277	}
5278	currRingHdl=save_ringhdl;
5279	u.CleanUp();
5280	v.CleanUp();
5281	return resid;
5282	}
5283
5284	void jjINT_S_TO_ID(int n,int *e, leftv res)
5285	{
5286	if (n==0) n=1;
5287	ideal l=idInit(n,1);
5288	int i;
5289	poly p;
5290	for(i=pVariables;i>0;i--)
5291	{
5292	if (e[i]>0)
5293	{
5294	n--;
5295	p=pOne();
5296	pSetExp(p,i,1);
5297	pSetm(p);
5298	l->m[n]=p;
5299	if (n==0) break;
5300	}
5301	}
5302	res->data=(char*)l;
5303	omFreeSize((ADDRESS)e,(pVariables+1)*sizeof(int));
5304	}
5305	BOOLEAN jjVARIABLES_P(leftv res, leftv u)
5306	{
5307	int e=(int )omAlloc0((pVariables+1)*sizeof(int));
5308	int n=pGetVariables((poly)u->Data(),e);
5309	jjINT_S_TO_ID(n,e,res);
5310	return FALSE;
5311	}
5312
5313	BOOLEAN jjVARIABLES_ID(leftv res, leftv u)
5314	{
5315	int e=(int )omAlloc0((pVariables+1)*sizeof(int));
5316	ideal I=(ideal)u->Data();
5317	int i;
5318	int n=0;
5319	for(i=I->nrows*I->ncols-1;i>=0;i--)
5320	{
5321	n=pGetVariables(I->m[i],e);
5322	}
5323	jjINT_S_TO_ID(n,e,res);
5324	return FALSE;
5325	}

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