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source: git/Singular/ipshell.cc @ bf5ca41

spielwiese

Last change on this file since bf5ca41 was bf5ca41, checked in by Hans Schönemann <hannes@…>, 17 years ago
*hannes: avoid char -1,0,1,2 for Z/p^n git-svn-id: file:///usr/local/Singular/svn/trunk@9193 2c84dea3-7e68-4137-9b89-c4e89433aadc
Property mode set to `100644`
File size: 110.6 KB

Line
1	/****************************************
2	* Computer Algebra System SINGULAR *
3	****************************************/
4	/* $Id: ipshell.cc,v 1.138 2006-06-09 16:24:40 Singular Exp $ */
5	/*
6	* ABSTRACT:
7	*/
8
9	//#include <stdlib.h>
10	#include <stdio.h>
11	#include <string.h>
12	#include <ctype.h>
13	#include <math.h>
14
15	#include "mod2.h"
16	#include "tok.h"
17	#include "ipid.h"
18	#include "intvec.h"
19	#include "omalloc.h"
20	#include "febase.h"
21	#include "polys.h"
22	#include "prCopy.h"
23	#include "ideals.h"
24	#include "matpol.h"
25	#include "kstd1.h"
26	#include "ring.h"
27	#include "subexpr.h"
28	#include "maps.h"
29	#include "syz.h"
30	#include "numbers.h"
31	#include "modulop.h"
32	#include "lists.h"
33	#include "attrib.h"
34	#include "ipconv.h"
35	#include "silink.h"
36	#include "stairc.h"
37	#include "weight.h"
38	#include "semic.h"
39	#include "splist.h"
40	#include "spectrum.h"
41	#include "gnumpfl.h"
42	#include "mpr_base.h"
43	#include "ffields.h"
44	#include "clapsing.h"
45	#include "hutil.h"
46	#include "ipshell.h"
47	#ifdef HAVE_FACTORY
48	#define SI_DONT_HAVE_GLOBAL_VARS
49	#include <factory.h>
50	#endif
51
52	// define this if you want to use the fast_map routine for mapping ideals
53	#define FAST_MAP
54
55	#ifdef FAST_MAP
56	#include "fast_maps.h"
57	#endif
58
59	leftv iiCurrArgs=NULL;
60	int traceit = 0;
61	char *lastreserved=NULL;
62
63	int myynest = -1;
64
65	static BOOLEAN iiNoKeepRing=TRUE;
66
67	/0 implementation/
68
69	char * Tok2Cmdname(int tok)
70	{
71	int i = 0;
72	if (tok < 0)
73	{
74	return cmds[0].name;
75	}
76	if (tok==ANY_TYPE) return "any_type";
77	if (tok==NONE) return "nothing";
78	//if (tok==IFBREAK) return "if_break";
79	//if (tok==VECTOR_FROM_POLYS) return "vector_from_polys";
80	//if (tok==ORDER_VECTOR) return "ordering";
81	//if (tok==REF_VAR) return "ref";
82	//if (tok==OBJECT) return "object";
83	//if (tok==PRINT_EXPR) return "print_expr";
84	if (tok==IDHDL) return "identifier";
85	while (cmds[i].tokval!=0)
86	{
87	if ((cmds[i].tokval == tok)&&(cmds[i].alias==0))
88	{
89	return cmds[i].name;
90	}
91	i++;
92	}
93	return cmds[0].name;
94	}
95
96	char * iiTwoOps(int t)
97	{
98	if (t<127)
99	{
100	static char ch[2];
101	switch (t)
102	{
103	case '&':
104	return "and";
105	case '\|':
106	return "or";
107	default:
108	ch[0]=t;
109	ch[1]='\0';
110	return ch;
111	}
112	}
113	switch (t)
114	{
115	case COLONCOLON: return "::";
116	case DOTDOT: return "..";
117	//case PLUSEQUAL: return "+=";
118	//case MINUSEQUAL: return "-=";
119	case MINUSMINUS: return "--";
120	case PLUSPLUS: return "++";
121	case EQUAL_EQUAL: return "==";
122	case LE: return "<=";
123	case GE: return ">=";
124	case NOTEQUAL: return "<>";
125	default: return Tok2Cmdname(t);
126	}
127	}
128
129	static void list1(const char* s, idhdl h,BOOLEAN c, BOOLEAN fullname)
130	{
131	char buffer[22];
132	int l;
133	char buf2[128];
134
135	if(fullname) sprintf(buf2, "%s::%s", "", IDID(h));
136	else sprintf(buf2, "%s", IDID(h));
137
138	Print("%s%-20.20s [%d] ",s,buf2,IDLEV(h));
139	if (h == currRingHdl) PrintS("*");
140	PrintS(Tok2Cmdname((int)IDTYP(h)));
141
142	ipListFlag(h);
143	switch(IDTYP(h))
144	{
145	case INT_CMD: Print(" %d",IDINT(h)); break;
146	case INTVEC_CMD:Print(" (%d)",IDINTVEC(h)->length()); break;
147	case INTMAT_CMD:Print(" %d x %d",IDINTVEC(h)->rows(),IDINTVEC(h)->cols());
148	break;
149	case POLY_CMD:
150	case VECTOR_CMD:if (c)
151	{
152	PrintS(" ");wrp(IDPOLY(h));
153	if(IDPOLY(h) != NULL)
154	{
155	Print(", %d monomial(s)",pLength(IDPOLY(h)));
156	}
157	}
158	break;
159	case MODUL_CMD: Print(", rk %d", IDIDEAL(h)->rank);
160	case IDEAL_CMD: Print(", %u generator(s)",
161	IDELEMS(IDIDEAL(h)),IDIDEAL(h)->rank); break;
162	case MAP_CMD:
163	Print(" from %s",IDMAP(h)->preimage); break;
164	case MATRIX_CMD:Print(" %u x %u"
165	,MATROWS(IDMATRIX(h))
166	,MATCOLS(IDMATRIX(h))
167	);
168	break;
169	case PACKAGE_CMD:
170	PrintS(" (");
171	switch (IDPACKAGE(h)->language)
172	{
173	case LANG_SINGULAR: PrintS("S"); break;
174	case LANG_C: PrintS("C"); break;
175	case LANG_TOP: PrintS("T"); break;
176	case LANG_NONE: PrintS("N"); break;
177	default: PrintS("U");
178	}
179	if(IDPACKAGE(h)->libname!=NULL)
180	Print(",%s", IDPACKAGE(h)->libname);
181	PrintS(")");
182	break;
183	case PROC_CMD: if(strlen(IDPROC(h)->libname)>0)
184	Print(" from %s",IDPROC(h)->libname);
185	if(IDPROC(h)->is_static)
186	PrintS(" (static)");
187	break;
188	case STRING_CMD:
189	{
190	char *s;
191	l=strlen(IDSTRING(h));
192	memset(buffer,0,22);
193	strncpy(buffer,IDSTRING(h),si_min(l,20));
194	if ((s=strchr(buffer,'\n'))!=NULL)
195	{
196	*s='\0';
197	}
198	PrintS(" ");
199	PrintS(buffer);
200	if((s!=NULL) \|\|(l>20))
201	{
202	Print("..., %d char(s)",l);
203	}
204	break;
205	}
206	case LIST_CMD: Print(", size: %d",IDLIST(h)->nr+1);
207	break;
208	case QRING_CMD:
209	case RING_CMD:
210	if ((IDRING(h)==currRing) && (currRingHdl!=h))
211	PrintS("()"); / this is an alias to currRing */
212	#ifdef RDEBUG
213	if (traceit &TRACE_SHOW_RINGS)
214	Print(" <%x>",IDRING(h));
215	#endif
216	break;
217	/default: break;/
218	}
219	PrintLn();
220	}
221
222	void type_cmd(idhdl h)
223	{
224	BOOLEAN oldShortOut = FALSE;
225
226	if (currRing != NULL)
227	{
228	oldShortOut = currRing->ShortOut;
229	currRing->ShortOut = 1;
230	}
231	list1("// ",h,FALSE,FALSE);
232	if (IDTYP(h)!=INT_CMD)
233	{
234	sleftv expr;
235	memset(&expr,0,sizeof(expr));
236	expr.rtyp=IDHDL;
237	expr.name=IDID(h);
238	expr.data=(void *)h;
239	expr.Print();
240	}
241	if (currRing != NULL)
242	currRing->ShortOut = oldShortOut;
243	}
244
245	static void killlocals0(int v, idhdl * localhdl, const ring r)
246	{
247	idhdl h = *localhdl;
248	while (h!=NULL)
249	{
250	int vv;
251	//Print("consider %s, lev: %d:",IDID(h),IDLEV(h));
252	if ((vv=IDLEV(h))>0)
253	{
254	if (vv < v)
255	{
256	if (iiNoKeepRing)
257	{
258	//PrintS(" break\n");
259	return;
260	}
261	h = IDNEXT(h);
262	//PrintLn();
263	}
264	else if (vv >= v)
265	{
266	idhdl nexth = IDNEXT(h);
267	killhdl2(h,localhdl,r);
268	h = nexth;
269	//PrintS("kill\n");
270	}
271	}
272	else
273	{
274	h = IDNEXT(h);
275	//PrintLn();
276	}
277	}
278	}
279	#ifndef HAVE_NS
280	void killlocals(int v)
281	{
282	killlocals0(v,&IDROOT,currRing);
283
284	if ((iiRETURNEXPR_len > myynest)
285	&& ((iiRETURNEXPR[myynest].Typ()==RING_CMD)
286	\|\| (iiRETURNEXPR[myynest].Typ()==QRING_CMD)))
287	{
288	leftv h=&iiRETURNEXPR[myynest];
289	killlocals0(v,&(((ring)h->data)->idroot),(ring)h->data);
290	}
291
292	idhdl sh=currRingHdl;
293	ring sr=currRing;
294	BOOLEAN changed=FALSE;
295	idhdl h = IDROOT;
296
297	// Print("killlocals in %s\n",IDID(currPackHdl));
298	while (h!=NULL)
299	{
300	if (((IDTYP(h)==QRING_CMD) \|\| (IDTYP(h) == RING_CMD))
301	&& (IDRING(h)->idroot!=NULL))
302	{
303	if (IDRING(h)!=currRing) {changed=TRUE;rSetHdl(h);}
304	killlocals0(v,&(IDRING(h)->idroot),IDRING(h));
305	}
306	else if (IDTYP(h) == PACKAGE_CMD)
307	{
308	killlocals0(v,&(IDPACKAGE(h)->idroot),IDRING(h));
309	}
310	h = IDNEXT(h);
311	}
312	if (changed)
313	{
314	currRing=NULL;
315	currRingHdl=NULL;
316	if (sh!=NULL) rSetHdl(sh);
317	else if (sr!=NULL)
318	{
319	sh=rFindHdl(sr,NULL,NULL);
320	rSetHdl(sh);
321	}
322	}
323
324	if (myynest<=1) iiNoKeepRing=TRUE;
325	//Print("end killlocals >= %d\n",v);
326	//listall();
327	}
328	#endif
329	#ifdef HAVE_NS
330	void killlocals_rec(idhdl *root,int v, ring r)
331	{
332	idhdl h=*root;
333	while (h!=NULL)
334	{
335	if (IDLEV(h)>=v)
336	{
337	// Print("kill %s, lev %d for lev %d\n",IDID(h),IDLEV(h),v);
338	idhdl n=IDNEXT(h);
339	killhdl2(h,root,r);
340	h=n;
341	}
342	else if (IDTYP(h)==PACKAGE_CMD)
343	{
344	// Print("into pack %s, lev %d for lev %d\n",IDID(h),IDLEV(h),v);
345	if (IDPACKAGE(h)!=basePack)
346	killlocals_rec(&(IDRING(h)->idroot),v,r);
347	h=IDNEXT(h);
348	}
349	else if ((IDTYP(h)==RING_CMD)
350	\|\|(IDTYP(h)==QRING_CMD))
351	{
352	if (IDRING(h)->idroot!=NULL)
353	{
354	// Print("into ring %s, lev %d for lev %d\n",IDID(h),IDLEV(h),v);
355	killlocals_rec(&(IDRING(h)->idroot),v,IDRING(h));
356	}
357	h=IDNEXT(h);
358	}
359	else
360	{
361	// Print("skip %s lev %d for lev %d\n",IDID(h),IDLEV(h),v);
362	h=IDNEXT(h);
363	}
364	}
365	}
366	BOOLEAN killlocals_list(int v, lists L)
367	{
368	if (L==NULL) return FALSE;
369	BOOLEAN changed=FALSE;
370	int n=L->nr;
371	for(;n>=0;n--)
372	{
373	leftv h=&(L->m[n]);
374	void *d=h->data;
375	if (((h->rtyp==RING_CMD) \|\| (h->rtyp==QRING_CMD))
376	&& (((ring)d)->idroot!=NULL))
377	{
378	if (d!=currRing) {changed=TRUE;rChangeCurrRing((ring)d);}
379	killlocals0(v,&(((ring)h->data)->idroot),(ring)h->data);
380	}
381	else if (h->rtyp==LIST_CMD)
382	changed\|=killlocals_list(v,(lists)d);
383	}
384	return changed;
385	}
386	void killlocals(int v)
387	{
388	BOOLEAN changed=FALSE;
389	idhdl sh=currRingHdl;
390	ring cr=currRing;
391	if (sh!=NULL) changed=((IDLEV(sh)<v) \|\| (IDRING(sh)->ref>0));
392	//if (changed) Print("currRing=%s(%x), lev=%d,ref=%d\n",IDID(sh),IDRING(sh),IDLEV(sh),IDRING(sh)->ref);
393
394	killlocals_rec(&(basePack->idroot),v,currRing);
395
396	if (iiRETURNEXPR_len > myynest)
397	{
398	int t=iiRETURNEXPR[myynest].Typ();
399	if ((/iiRETURNEXPR[myynest].Typ()/ t==RING_CMD)
400	\|\| (/iiRETURNEXPR[myynest].Typ()/ t==QRING_CMD))
401	{
402	leftv h=&iiRETURNEXPR[myynest];
403	if (((ring)h->data)->idroot!=NULL)
404	killlocals0(v,&(((ring)h->data)->idroot),(ring)h->data);
405	}
406	else if (/iiRETURNEXPR[myynest].Typ()/ t==LIST_CMD)
407	{
408	leftv h=&iiRETURNEXPR[myynest];
409	changed \|=killlocals_list(v,(lists)h->data);
410	}
411	}
412	if (changed)
413	{
414	currRingHdl=rFindHdl(cr,NULL,NULL);
415	if (currRingHdl==NULL)
416	currRing=NULL;
417	else
418	rChangeCurrRing(cr);
419	}
420
421	if (myynest<=1) iiNoKeepRing=TRUE;
422	//Print("end killlocals >= %d\n",v);
423	//listall();
424	}
425	#endif
426
427	void list_cmd(int typ, const char* what, const char *prefix,BOOLEAN iterate, BOOLEAN fullname)
428	{
429	idhdl h,start;
430	BOOLEAN all = typ<0;
431	BOOLEAN really_all=FALSE;
432	BOOLEAN do_packages=FALSE;
433
434	if ( typ == -1 ) do_packages=TRUE;
435	if ( typ==0 )
436	{
437	if (strcmp(what,"all")==0)
438	{
439	really_all=TRUE;
440	#ifdef HAVE_NS
441	h=basePack->idroot;
442	#else
443	h=IDROOT;
444	#endif
445	}
446	else
447	{
448	h = ggetid(what);
449	if (h!=NULL)
450	{
451	if (iterate) list1(prefix,h,TRUE,fullname);
452	if ((IDTYP(h)==RING_CMD)
453	\|\| (IDTYP(h)==QRING_CMD)
454	#ifdef HAVE_NS
455	//\|\| (IDTYP(h)==PACKE_CMD)
456	#endif
457	)
458	{
459	h=IDRING(h)->idroot;
460	}
461	else if((IDTYP(h)==PACKAGE_CMD) \|\| (IDTYP(h)==POINTER_CMD))
462	{
463	//Print("list_cmd:package or pointer\n");
464	all=TRUE;typ=PROC_CMD;fullname=TRUE;really_all=TRUE;
465	h=IDPACKAGE(h)->idroot;
466	}
467	else
468	return;
469	}
470	else
471	{
472	Werror("%s is undefined",what);
473	return;
474	}
475	}
476	all=TRUE;
477	}
478	else if (RingDependend(typ))
479	{
480	h = currRing->idroot;
481	}
482	else
483	h = IDROOT;
484	start=h;
485	while (h!=NULL)
486	{
487	if ((all && (IDTYP(h)!=PROC_CMD) &&(IDTYP(h)!=PACKAGE_CMD))
488	\|\| (typ == IDTYP(h))
489	\|\| ((IDTYP(h)==QRING_CMD) && (typ==RING_CMD)))
490	{
491	list1(prefix,h,start==currRingHdl, fullname);
492	if (((IDTYP(h)==RING_CMD)\|\|(IDTYP(h)==QRING_CMD))
493	&& (really_all \|\| (all && (h==currRingHdl)))
494	&& ((IDLEV(h)==0)\|\|(IDLEV(h)==myynest)))
495	{
496	list_cmd(0,IDID(h),"// ",FALSE);
497	}
498	#ifdef HAVE_NS
499	if (IDTYP(h)==PACKAGE_CMD && really_all)
500	{
501	list_cmd(0,IDID(h),"// ",FALSE);
502	}
503	#endif /* HAVE_NS */
504	}
505	h = IDNEXT(h);
506	}
507	}
508
509	void test_cmd(int i)
510	{
511	int ii=(char)i;
512
513	if (i == (-32))
514	{
515	test = 0;
516	}
517	else
518	{
519	if (i<0)
520	{
521	ii= -i;
522	if (Sy_bit(ii) & kOptions)
523	{
524	Warn("Gerhard, use the option command");
525	test &= ~Sy_bit(ii);
526	}
527	else if (Sy_bit(ii) & validOpts)
528	test &= ~Sy_bit(ii);
529	}
530	else if (i<32)
531	{
532	if (Sy_bit(ii) & kOptions)
533	{
534	Warn("Gerhard, use the option command");
535	test \|= Sy_bit(ii);
536	}
537	else if (Sy_bit(ii) & validOpts)
538	test \|= Sy_bit(ii);
539	}
540	}
541	}
542
543	int exprlist_length(leftv v)
544	{
545	int rc = 0;
546	while (v!=NULL)
547	{
548	switch (v->Typ())
549	{
550	case INT_CMD:
551	case POLY_CMD:
552	case VECTOR_CMD:
553	case NUMBER_CMD:
554	rc++;
555	break;
556	case INTVEC_CMD:
557	case INTMAT_CMD:
558	rc += ((intvec *)(v->Data()))->length();
559	break;
560	case MATRIX_CMD:
561	case IDEAL_CMD:
562	case MODUL_CMD:
563	{
564	matrix mm = (matrix)(v->Data());
565	rc += mm->rows() * mm->cols();
566	}
567	break;
568	case LIST_CMD:
569	rc+=((lists)v->Data())->nr+1;
570	break;
571	default:
572	rc++;
573	}
574	v = v->next;
575	}
576	return rc;
577	}
578
579	#ifdef HAVE_RING2TOM
580	// avoid to test the "special" char: -1, 0, 1, 2
581	int Is2toM(int p) /* brute force !!!! */
582	{
583	if (p <= 2) return 0;
584	int test = p;
585	int i = 0;
586	while (p%2 == 0) {
587	p = p / 2;
588	i++;
589	}
590	if (p == 1) {
591	return i;
592	}
593	return 0;
594	}
595	#endif
596
597	int IsPrime(int p) /* brute force !!!! */
598	{
599	int i,j;
600	if (p == 0) return 0;
601	else if (p == 1) return 1/1/;
602	else if (p == 2) return p;
603	else if (p < 0) return (-IsPrime(-p));
604	else if (!(p & 1)) return IsPrime(p-1);
605	#ifdef HAVE_FACTORY
606	else if (p<=32749) // max. small prime in factory
607	{
608	int a=0;
609	int e=cf_getNumSmallPrimes()-1;
610	i=e/2;
611	do
612	{
613	if (p==(j=cf_getSmallPrime(i))) return p;
614	if (p<j) e=i-1;
615	else a=i+1;
616	i=a+(e-a)/2;
617	} while ( a<= e);
618	if (p>j) return j;
619	else return cf_getSmallPrime(i-1);
620	}
621	#endif
622	#ifdef HAVE_FACTORY
623	int end_i=cf_getNumSmallPrimes()-1;
624	#else
625	int end_i=p/2;
626	#endif
627	int end_p=(int)sqrt((double)p);
628	restart:
629	for (i=0; i<end_i; i++)
630	{
631	#ifdef HAVE_FACTORY
632	j=cf_getSmallPrime(i);
633	#else
634	if (i==0) j=2;
635	else j=2*i-1;
636	#endif
637	if ((p%j) == 0)
638	{
639	#ifdef HAVE_FACTORY
640	if (p<=32751) return IsPrime(p-2);
641	#endif
642	p-=2;
643	goto restart;
644	}
645	if (j > end_p) return p;
646	}
647	return p;
648	}
649
650	BOOLEAN iiWRITE(leftv res,leftv v)
651	{
652	sleftv vf;
653	if (iiConvert(v->Typ(),LINK_CMD,iiTestConvert(v->Typ(),LINK_CMD),v,&vf))
654	{
655	WerrorS("link expected");
656	return TRUE;
657	}
658	si_link l=(si_link)vf.Data();
659	if (vf.next == NULL)
660	{
661	WerrorS("write: need at least two arguments");
662	return TRUE;
663	}
664
665	BOOLEAN b=slWrite(l,vf.next); /* iiConvert preserves next */
666	if (b)
667	{
668	const char *s;
669	if ((l!=NULL)&&(l->name!=NULL)) s=l->name;
670	else s=sNoName;
671	Werror("cannot write to %s",s);
672	}
673	vf.CleanUp();
674	return b;
675	}
676
677	leftv iiMap(map theMap, char * what)
678	{
679	idhdl w,r;
680	leftv v;
681	int i;
682	nMapFunc nMap;
683
684	r=IDROOT->get(theMap->preimage,myynest);
685	#ifdef HAVE_NS
686	if ((currPack!=basePack)
687	&&((r==NULL) \|\| ((r->typ != RING_CMD) && (r->typ != QRING_CMD))))
688	r=basePack->idroot->get(theMap->preimage,myynest);
689	if ((r==NULL) && (currRingHdl!=NULL)
690	&& (strcmp(theMap->preimage,IDID(currRingHdl))==0))
691	{
692	r=currRingHdl;
693	}
694	#endif /* HAVE_NS */
695	if ((r!=NULL) && ((r->typ == RING_CMD) \|\| (r->typ== QRING_CMD)))
696	{
697	//if ((nMap=nSetMap(rInternalChar(IDRING(r)),
698	// IDRING(r)->parameter,
699	// rPar(IDRING(r)),
700	// IDRING(r)->minpoly)))
701	if ((nMap=nSetMap(IDRING(r)))==NULL)
702	{
703	if (rEqual(IDRING(r),currRing))
704	{
705	nMap=nCopy;
706	}
707	else
708	{
709	Werror("can not map from ground field of %s to current ground field",
710	theMap->preimage);
711	return NULL;
712	}
713	}
714	if (IDELEMS(theMap)<IDRING(r)->N)
715	{
716	theMap->m=(polyset)omReallocSize((ADDRESS)theMap->m,
717	IDELEMS(theMap)*sizeof(poly),
718	(IDRING(r)->N)*sizeof(poly));
719	for(i=IDELEMS(theMap);i<IDRING(r)->N;i++)
720	theMap->m[i]=NULL;
721	IDELEMS(theMap)=IDRING(r)->N;
722	}
723	if (what==NULL)
724	{
725	WerrorS("argument of a map must have a name");
726	}
727	else if ((w=IDRING(r)->idroot->get(what,myynest))!=NULL)
728	{
729	char *save_r=NULL;
730	v=(leftv)omAlloc0Bin(sleftv_bin);
731	sleftv tmpW;
732	memset(&tmpW,0,sizeof(sleftv));
733	tmpW.rtyp=IDTYP(w);
734	if (tmpW.rtyp==MAP_CMD)
735	{
736	tmpW.rtyp=IDEAL_CMD;
737	save_r=IDMAP(w)->preimage;
738	IDMAP(w)->preimage=0;
739	}
740	tmpW.data=IDDATA(w);
741	#ifdef FAST_MAP
742	if ((tmpW.rtyp==IDEAL_CMD) && (nMap==nCopy)
743	#ifdef HAVE_PLURAL
744	&& (!rIsPluralRing(currRing))
745	#endif
746	)
747	{
748	v->rtyp=IDEAL_CMD;
749	v->data=fast_map(IDIDEAL(w), IDRING(r), (ideal)theMap, currRing);
750	}
751	else
752	#endif
753	if (maApplyFetch(MAP_CMD,theMap,v,&tmpW,IDRING(r),NULL,NULL,0,nMap))
754	{
755	Werror("cannot map %s(%d)",Tok2Cmdname(w->typ),w->typ);
756	omFreeBin((ADDRESS)v, sleftv_bin);
757	if (save_r!=NULL) IDMAP(w)->preimage=save_r;
758	return NULL;
759	}
760	if (save_r!=NULL)
761	{
762	IDMAP(w)->preimage=save_r;
763	IDMAP((idhdl)v)->preimage=omStrDup(save_r);
764	v->rtyp=MAP_CMD;
765	}
766	return v;
767	}
768	else
769	{
770	Werror("%s undefined in %s",what,theMap->preimage);
771	}
772	}
773	else
774	{
775	Werror("cannot find preimage %s",theMap->preimage);
776	}
777	return NULL;
778	}
779
780	#ifdef OLD_RES
781	void iiMakeResolv(resolvente r, int length, int rlen, char * name, int typ0,
782	intvec ** weights)
783	{
784	lists L=liMakeResolv(r,length,rlen,typ0,weights);
785	int i=0;
786	idhdl h;
787	char * s=(char *)omAlloc(strlen(name)+5);
788
789	while (i<=L->nr)
790	{
791	sprintf(s,"%s(%d)",name,i+1);
792	if (i==0)
793	h=enterid(s,myynest,typ0,&(currRing->idroot), FALSE);
794	else
795	h=enterid(s,myynest,MODUL_CMD,&(currRing->idroot), FALSE);
796	if (h!=NULL)
797	{
798	h->data.uideal=(ideal)L->m[i].data;
799	h->attribute=L->m[i].attribute;
800	if (BVERBOSE(V_DEF_RES))
801	Print("//defining: %s as %d-th syzygy module\n",s,i+1);
802	}
803	else
804	{
805	idDelete((ideal *)&(L->m[i].data));
806	Warn("cannot define %s",s);
807	}
808	//L->m[i].data=NULL;
809	//L->m[i].rtyp=0;
810	//L->m[i].attribute=NULL;
811	i++;
812	}
813	omFreeSize((ADDRESS)L->m,(L->nr+1)*sizeof(sleftv));
814	omFreeBin((ADDRESS)L, slists_bin);
815	omFreeSize((ADDRESS)s,strlen(name)+5);
816	}
817	#endif
818
819	//resolvente iiFindRes(char * name, int * len, int *typ0)
820	//{
821	// char s=(char )omAlloc(strlen(name)+5);
822	// int i=-1;
823	// resolvente r;
824	// idhdl h;
825	//
826	// do
827	// {
828	// i++;
829	// sprintf(s,"%s(%d)",name,i+1);
830	// h=currRing->idroot->get(s,myynest);
831	// } while (h!=NULL);
832	// *len=i-1;
833	// if (*len<=0)
834	// {
835	// Werror("no objects %s(1),.. found",name);
836	// omFreeSize((ADDRESS)s,strlen(name)+5);
837	// return NULL;
838	// }
839	// r=(ideal )omAlloc(/(len+1)/ isizeof(ideal));
840	// memset(r,0,(len)sizeof(ideal));
841	// i=-1;
842	// *typ0=MODUL_CMD;
843	// while (i<(*len))
844	// {
845	// i++;
846	// sprintf(s,"%s(%d)",name,i+1);
847	// h=currRing->idroot->get(s,myynest);
848	// if (h->typ != MODUL_CMD)
849	// {
850	// if ((i!=0) \|\| (h->typ!=IDEAL_CMD))
851	// {
852	// Werror("%s is not of type module",s);
853	// omFreeSize((ADDRESS)r,(len)sizeof(ideal));
854	// omFreeSize((ADDRESS)s,strlen(name)+5);
855	// return NULL;
856	// }
857	// *typ0=IDEAL_CMD;
858	// }
859	// if ((i>0) && (idIs0(r[i-1])))
860	// {
861	// *len=i-1;
862	// break;
863	// }
864	// r[i]=IDIDEAL(h);
865	// }
866	// omFreeSize((ADDRESS)s,strlen(name)+5);
867	// return r;
868	//}
869
870	static resolvente iiCopyRes(resolvente r, int l)
871	{
872	int i;
873	resolvente res=(ideal )omAlloc0((l+1)sizeof(ideal));
874
875	for (i=0; i<l; i++)
876	res[i]=idCopy(r[i]);
877	return res;
878	}
879
880	BOOLEAN jjMINRES(leftv res, leftv v)
881	{
882	int len=0;
883	int typ0;
884	lists L=(lists)v->Data();
885	intvec weights=(intvec)atGet(v,"isHomog",INTVEC_CMD);
886	int add_row_shift = 0;
887	if (weights==NULL)
888	weights=(intvec*)atGet(&(L->m[0]),"isHomog",INTVEC_CMD);
889	if (weights!=NULL) add_row_shift=weights->min_in();
890	resolvente rr=liFindRes(L,&len,&typ0);
891	if (rr==NULL) return TRUE;
892	resolvente r=iiCopyRes(rr,len);
893
894	syMinimizeResolvente(r,len,0);
895	omFreeSize((ADDRESS)rr,len*sizeof(ideal));
896	len++;
897	res->data=(char *)liMakeResolv(r,len,-1,typ0,NULL,add_row_shift);
898	return FALSE;
899	}
900
901	BOOLEAN jjBETTI(leftv res, leftv u)
902	{
903	sleftv tmp;
904	memset(&tmp,0,sizeof(tmp));
905	tmp.rtyp=INT_CMD;
906	tmp.data=(void *)1;
907	if ((u->Typ()==IDEAL_CMD)
908	\|\| (u->Typ()==MODUL_CMD))
909	return jjBETTI2_ID(res,u,&tmp);
910	else
911	return jjBETTI2(res,u,&tmp);
912	}
913
914	BOOLEAN jjBETTI2_ID(leftv res, leftv u, leftv v)
915	{
916	lists l=(lists) omAllocBin(slists_bin);
917	l->Init(1);
918	l->m[0].rtyp=u->Typ();
919	l->m[0].data=u->Data();
920	l->m[0].attribute=u->attribute;
921	sleftv tmp2;
922	memset(&tmp2,0,sizeof(tmp2));
923	tmp2.rtyp=LIST_CMD;
924	tmp2.data=(void *)l;
925	BOOLEAN r=jjBETTI2(res,&tmp2,v);
926	l->m[0].data=NULL;
927	l->m[0].attribute=NULL;
928	l->m[0].rtyp=DEF_CMD;
929	l->Clean();
930	return r;
931	}
932
933	BOOLEAN jjBETTI2(leftv res, leftv u, leftv v)
934	{
935	resolvente r;
936	int len;
937	int reg,typ0;
938	lists l=(lists)u->Data();
939
940	intvec *weights=NULL;
941	int add_row_shift=0;
942	intvec ww=(intvec )atGet(&(l->m[0]),"isHomog",INTVEC_CMD);
943	if (ww!=NULL)
944	{
945	weights=ivCopy(ww);
946	add_row_shift = ww->min_in();
947	(*weights) -= add_row_shift;
948	}
949	//Print("attr:%x\n",weights);
950
951	r=liFindRes(l,&len,&typ0);
952	if (r==NULL) return TRUE;
953	res->data=(char *)syBetti(r,len,&reg,weights,(int)(long)v->Data());
954	omFreeSize((ADDRESS)r,(len)*sizeof(ideal));
955	atSet(res,omStrDup("rowShift"),(void*)add_row_shift,INT_CMD);
956	if (weights!=NULL) delete weights;
957	return FALSE;
958	}
959
960	int iiRegularity(lists L)
961	{
962	int len,reg,typ0;
963
964	resolvente r=liFindRes(L,&len,&typ0);
965
966	if (r==NULL)
967	return -2;
968	intvec * dummy=syBetti(r,len,&reg);
969	omFreeSize((ADDRESS)r,len*sizeof(ideal));
970	delete dummy;
971	return reg+1;
972	}
973
974	BOOLEAN iiDebugMarker=TRUE;
975	#define BREAK_LINE_LENGTH 80
976	void iiDebug()
977	{
978	Print("\n-- break point in %s --\n",VoiceName());
979	if (iiDebugMarker) VoiceBackTrack();
980	char * s;
981	iiDebugMarker=FALSE;
982	s = (char *)omAlloc(BREAK_LINE_LENGTH+4);
983	loop
984	{
985	memset(s,0,80);
986	fe_fgets_stdin("",s,BREAK_LINE_LENGTH);
987	if (s[BREAK_LINE_LENGTH-1]!='\0')
988	{
989	Print("line too long, max is %d chars\n",BREAK_LINE_LENGTH);
990	}
991	else
992	break;
993	}
994	if (*s=='\n')
995	{
996	iiDebugMarker=TRUE;
997	}
998	#if MDEBUG
999	else if(strncmp(s,"cont;",5)==0)
1000	{
1001	iiDebugMarker=TRUE;
1002	}
1003	#endif /* MDEBUG */
1004	else
1005	{
1006	strcat( s, "\n;~\n");
1007	newBuffer(s,BT_execute);
1008	}
1009	}
1010
1011	lists scIndIndset(ideal S, BOOLEAN all, ideal Q)
1012	{
1013	int i;
1014	indset save;
1015	lists res=(lists)omAlloc0Bin(slists_bin);
1016
1017	hexist = hInit(S, Q, &hNexist);
1018	if ((hNexist == 0) \|\| (hisModule!=0))
1019	{
1020	res->Init(0);
1021	return res;
1022	}
1023	save = ISet = (indset)omAlloc0Bin(indlist_bin);
1024	hMu = 0;
1025	hwork = (scfmon)omAlloc(hNexist * sizeof(scmon));
1026	hvar = (varset)omAlloc((pVariables + 1) * sizeof(int));
1027	hpure = (scmon)omAlloc((1 + (pVariables * pVariables)) * sizeof(Exponent_t));
1028	hrad = hexist;
1029	hNrad = hNexist;
1030	radmem = hCreate(pVariables - 1);
1031	hCo = pVariables + 1;
1032	hNvar = pVariables;
1033	hRadical(hrad, &hNrad, hNvar);
1034	hSupp(hrad, hNrad, hvar, &hNvar);
1035	if (hNvar)
1036	{
1037	hCo = hNvar;
1038	memset(hpure, 0, (pVariables + 1) * sizeof(Exponent_t));
1039	hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure);
1040	hLexR(hrad, hNrad, hvar, hNvar);
1041	hDimSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar);
1042	}
1043	if (hCo && (hCo < pVariables))
1044	{
1045	hIndMult(hpure, hNpure, hrad, hNrad, hvar, hNvar);
1046	}
1047	if (hMu!=0)
1048	{
1049	ISet = save;
1050	hMu2 = 0;
1051	if (all && (hCo+1 < pVariables))
1052	{
1053	JSet = (indset)omAlloc0Bin(indlist_bin);
1054	hIndAllMult(hpure, hNpure, hrad, hNrad, hvar, hNvar);
1055	i=hMu+hMu2;
1056	res->Init(i);
1057	if (hMu2 == 0)
1058	{
1059	omFreeBin((ADDRESS)JSet, indlist_bin);
1060	}
1061	}
1062	else
1063	{
1064	res->Init(hMu);
1065	}
1066	for (i=0;i<hMu;i++)
1067	{
1068	res->m[i].data = (void *)save->set;
1069	res->m[i].rtyp = INTVEC_CMD;
1070	ISet = save;
1071	save = save->nx;
1072	omFreeBin((ADDRESS)ISet, indlist_bin);
1073	}
1074	omFreeBin((ADDRESS)save, indlist_bin);
1075	if (hMu2 != 0)
1076	{
1077	save = JSet;
1078	for (i=hMu;i<hMu+hMu2;i++)
1079	{
1080	res->m[i].data = (void *)save->set;
1081	res->m[i].rtyp = INTVEC_CMD;
1082	JSet = save;
1083	save = save->nx;
1084	omFreeBin((ADDRESS)JSet, indlist_bin);
1085	}
1086	omFreeBin((ADDRESS)save, indlist_bin);
1087	}
1088	}
1089	else
1090	{
1091	res->Init(0);
1092	omFreeBin((ADDRESS)ISet, indlist_bin);
1093	}
1094	hKill(radmem, pVariables - 1);
1095	omFreeSize((ADDRESS)hpure, (1 + (pVariables * pVariables)) * sizeof(Exponent_t));
1096	omFreeSize((ADDRESS)hvar, (pVariables + 1) * sizeof(int));
1097	omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon));
1098	hDelete(hexist, hNexist);
1099	return res;
1100	}
1101
1102	int iiDeclCommand(leftv sy, leftv name, int lev,int t, idhdl* root,BOOLEAN isring, BOOLEAN init_b)
1103	{
1104	BOOLEAN res=FALSE;
1105	char *id = name->name;
1106
1107	memset(sy,0,sizeof(sleftv));
1108	if ((name->name==NULL)\|\|(isdigit(name->name[0])))
1109	{
1110	WerrorS("object to declare is not a name");
1111	res=TRUE;
1112	}
1113	else
1114	{
1115	//if (name->rtyp!=0)
1116	//{
1117	// Warn("`%s` is already in use",name->name);
1118	//}
1119	{
1120	sy->data = (char *)enterid(id,lev,t,root,init_b);
1121	}
1122	if (sy->data!=NULL)
1123	{
1124	sy->rtyp=IDHDL;
1125	currid=sy->name=IDID((idhdl)sy->data);
1126	// name->name=NULL; /* used in enterid */
1127	//sy->e = NULL;
1128	if (name->next!=NULL)
1129	{
1130	sy->next=(leftv)omAllocBin(sleftv_bin);
1131	res=iiDeclCommand(sy->next,name->next,lev,t,root, isring);
1132	}
1133	}
1134	else res=TRUE;
1135	}
1136	name->CleanUp();
1137	return res;
1138	}
1139
1140	BOOLEAN iiParameter(leftv p)
1141	{
1142	if (iiCurrArgs==NULL)
1143	{
1144	if (strcmp(p->name,"#")==0) return FALSE;
1145	Werror("not enough arguments for proc %s",VoiceName());
1146	p->CleanUp();
1147	return TRUE;
1148	}
1149	leftv h=iiCurrArgs;
1150	if (strcmp(p->name,"#")==0)
1151	{
1152	iiCurrArgs=NULL;
1153	}
1154	else
1155	{
1156	iiCurrArgs=h->next;
1157	h->next=NULL;
1158	}
1159	BOOLEAN res=iiAssign(p,h);
1160	h->CleanUp();
1161	omFreeBin((ADDRESS)h, sleftv_bin);
1162	return res;
1163	}
1164
1165	static BOOLEAN iiInternalExport (leftv v, int toLev)
1166	{
1167	idhdl h=(idhdl)v->data;
1168	//Print("iiInternalExport('%s',%d)%s\n", v->name, toLev,"");
1169	if (IDLEV(h)==0) Warn("`%s` is already global",IDID(h));
1170	else
1171	{
1172	h=IDROOT->get(v->name,toLev);
1173	idhdl *root=&IDROOT;
1174	if ((h==NULL)&&(currRing!=NULL))
1175	{
1176	h=currRing->idroot->get(v->name,toLev);
1177	root=&currRing->idroot;
1178	}
1179	BOOLEAN keepring=FALSE;
1180	if ((h!=NULL)&&(IDLEV(h)==toLev))
1181	{
1182	if (IDTYP(h)==v->Typ())
1183	{
1184	if (((IDTYP(h)==RING_CMD)\|\|(IDTYP(h)==QRING_CMD))
1185	&& (v->Data()==IDDATA(h)))
1186	{
1187	IDRING(h)->ref++;
1188	keepring=TRUE;
1189	IDLEV(h)=toLev;
1190	//WarnS("keepring");
1191	return FALSE;
1192	}
1193	if (BVERBOSE(V_REDEFINE))
1194	{
1195	Warn("redefining %s",IDID(h));
1196	}
1197	#ifdef USE_IILOCALRING
1198	if (iiLocalRing[0]==IDRING(h) && (!keepring)) iiLocalRing[0]=NULL;
1199	#else
1200	proclevel *p=procstack;
1201	while (p->next!=NULL) p=p->next;
1202	if ((p->cRing==IDRING(h)) && (!keepring))
1203	{
1204	p->cRing=NULL;
1205	p->cRingHdl=NULL;
1206	}
1207	#endif
1208	killhdl2(h,root,currRing);
1209	}
1210	else
1211	{
1212	return TRUE;
1213	}
1214	}
1215	h=(idhdl)v->data;
1216	IDLEV(h)=toLev;
1217	if (keepring) IDRING(h)->ref--;
1218	iiNoKeepRing=FALSE;
1219	//Print("export %s\n",IDID(h));
1220	}
1221	return FALSE;
1222	}
1223
1224	#ifdef HAVE_NS
1225	BOOLEAN iiInternalExport (leftv v, int toLev, idhdl roothdl)
1226	{
1227	idhdl h=(idhdl)v->data;
1228	if(h==NULL)
1229	{
1230	Warn("'%s': no such identifier\n", v->name);
1231	return FALSE;
1232	}
1233	package frompack=v->req_packhdl;
1234	if (frompack==NULL) frompack=currPack;
1235	package rootpack = IDPACKAGE(roothdl);
1236	// Print("iiInternalExport('%s',%d,%s->%s) typ:%d\n", v->name, toLev, IDID(currPackHdl),IDID(roothdl),v->Typ());
1237	if ((RingDependend(IDTYP(h)))
1238	\|\| ((IDTYP(h)==LIST_CMD)
1239	&& (lRingDependend(IDLIST(h)))
1240	)
1241	)
1242	{
1243	//Print("// ==> Ringdependent set nesting to 0\n");
1244	return (iiInternalExport(v, toLev));
1245	}
1246	else
1247	{
1248	IDLEV(h)=toLev;
1249	v->req_packhdl=rootpack;
1250	if (h==frompack->idroot)
1251	{
1252	frompack->idroot=h->next;
1253	}
1254	else
1255	{
1256	idhdl hh=frompack->idroot;
1257	while ((hh!=NULL) && (hh->next!=h))
1258	hh=hh->next;
1259	if ((hh!=NULL) && (hh->next==h))
1260	hh->next=h->next;
1261	else
1262	{
1263	Werror("`%s` not found",v->Name());
1264	return TRUE;
1265	}
1266	}
1267	h->next=rootpack->idroot;
1268	rootpack->idroot=h;
1269	}
1270	return FALSE;
1271	}
1272	#endif /* HAVE_NS */
1273
1274	BOOLEAN iiExport (leftv v, int toLev)
1275	{
1276	#ifdef HAVE_NS
1277	#ifndef NDEBUG
1278	checkall();
1279	#endif
1280	#endif
1281	BOOLEAN nok=FALSE;
1282	leftv r=v;
1283	while (v!=NULL)
1284	{
1285	if ((v->name==NULL)\|\|(v->rtyp==0)\|\|(v->e!=NULL))
1286	{
1287	WerrorS("cannot export");
1288	nok=TRUE;
1289	}
1290	else
1291	{
1292	if(iiInternalExport(v, toLev))
1293	{
1294	r->CleanUp();
1295	return TRUE;
1296	}
1297	}
1298	v=v->next;
1299	}
1300	r->CleanUp();
1301	#ifdef HAVE_NS
1302	#ifndef NDEBUG
1303	checkall();
1304	#endif
1305	#endif
1306	return nok;
1307	}
1308
1309	/assume root!=idroot/
1310	#ifdef HAVE_NS
1311	BOOLEAN iiExport (leftv v, int toLev, idhdl root)
1312	{
1313	#ifndef NDEBUG
1314	checkall();
1315	#endif
1316	// Print("iiExport1: pack=%s\n",IDID(root));
1317	package pack=IDPACKAGE(root);
1318	BOOLEAN nok=FALSE;
1319	leftv rv=v;
1320	while (v!=NULL)
1321	{
1322	if ((v->name==NULL)\|\|(v->rtyp==0)\|\|(v->e!=NULL)
1323	)
1324	{
1325	WerrorS("cannot export");
1326	nok=TRUE;
1327	}
1328	else
1329	{
1330	idhdl old=pack->idroot->get( v->name,toLev);
1331	if (old!=NULL)
1332	{
1333	if ((pack==currPack) && (old==(idhdl)v->data))
1334	{
1335	Warn("`%s` is already global",IDID(old));
1336	break;
1337	}
1338	else if (IDTYP(old)==v->Typ())
1339	{
1340	if (BVERBOSE(V_REDEFINE))
1341	{
1342	Warn("redefining %s",IDID(old));
1343	}
1344	v->name=omStrDup(v->name);
1345	killhdl2(old,&(pack->idroot),currRing);
1346	}
1347	else
1348	{
1349	rv->CleanUp();
1350	return TRUE;
1351	}
1352	}
1353	//Print("iiExport: pack=%s\n",IDID(root));
1354	if(iiInternalExport(v, toLev, root))
1355	{
1356	rv->CleanUp();
1357	return TRUE;
1358	}
1359	}
1360	v=v->next;
1361	}
1362	rv->CleanUp();
1363	#ifndef NDEBUG
1364	checkall();
1365	#endif
1366	return nok;
1367	}
1368	#endif
1369
1370	BOOLEAN iiCheckRing(int i)
1371	{
1372	if (currRingHdl==NULL)
1373	{
1374	#ifdef SIQ
1375	if (siq<=0)
1376	{
1377	#endif
1378	if (RingDependend(i))
1379	{
1380	WerrorS("no ring active");
1381	return TRUE;
1382	}
1383	#ifdef SIQ
1384	}
1385	#endif
1386	}
1387	return FALSE;
1388	}
1389
1390	poly iiHighCorner(ideal I, int ak)
1391	{
1392	int i;
1393	if(!idIsZeroDim(I)) return NULL; // not zero-dim.
1394	poly po=NULL;
1395	if (currRing->OrdSgn== -1)
1396	{
1397	scComputeHC(I,currQuotient,ak,po);
1398	if (po!=NULL)
1399	{
1400	pGetCoeff(po)=nInit(1);
1401	for (i=pVariables; i>0; i--)
1402	{
1403	if (pGetExp(po, i) > 0) pDecrExp(po,i);
1404	}
1405	pSetComp(po,ak);
1406	pSetm(po);
1407	}
1408	}
1409	else
1410	po=pOne();
1411	return po;
1412	}
1413
1414	#ifdef HAVE_NS
1415	void iiCheckPack(package &p)
1416	{
1417	if (p==basePack) return;
1418
1419	idhdl t=basePack->idroot;
1420
1421	while ((t!=NULL) && (IDTYP(t)!=PACKAGE_CMD) && (IDPACKAGE(t)!=p)) t=t->next;
1422
1423	if (t==NULL)
1424	{
1425	WarnS("package not found\n");
1426	p=basePack;
1427	}
1428	return;
1429	}
1430	#endif
1431
1432	idhdl rDefault(char *s)
1433	{
1434	idhdl tmp=NULL;
1435
1436	if (s!=NULL) tmp = enterid(s, myynest, RING_CMD, &IDROOT);
1437	if (tmp==NULL) return NULL;
1438
1439	if (ppNoether!=NULL) pDelete(&ppNoether);
1440	if (sLastPrinted.RingDependend())
1441	{
1442	sLastPrinted.CleanUp();
1443	memset(&sLastPrinted,0,sizeof(sleftv));
1444	}
1445
1446	ring r = IDRING(tmp);
1447
1448	r->ch = 32003;
1449	r->N = 3;
1450	/r->P = 0; Alloc0 in idhdl::set, ipid.cc/
1451	/names/
1452	r->names = (char *) omAlloc0(3 sizeof(char_ptr));
1453	r->names[0] = omStrDup("x");
1454	r->names[1] = omStrDup("y");
1455	r->names[2] = omStrDup("z");
1456	/weights: entries for 3 blocks: NULL/
1457	r->wvhdl = (int *)omAlloc0(3 sizeof(int_ptr));
1458	/order: dp,C,0/
1459	r->order = (int ) omAlloc(3 sizeof(int *));
1460	r->block0 = (int )omAlloc0(3 sizeof(int *));
1461	r->block1 = (int )omAlloc0(3 sizeof(int *));
1462	/* ringorder dp for the first block: var 1..3 */
1463	r->order[0] = ringorder_dp;
1464	r->block0[0] = 1;
1465	r->block1[0] = 3;
1466	/* ringorder C for the second block: no vars */
1467	r->order[1] = ringorder_C;
1468	/* the last block: everything is 0 */
1469	r->order[2] = 0;
1470	/polynomial ring/
1471	r->OrdSgn = 1;
1472
1473	/* complete ring intializations */
1474	rComplete(r);
1475	rSetHdl(tmp);
1476	return currRingHdl;
1477	}
1478
1479	idhdl rFindHdl(ring r, idhdl n, idhdl w)
1480	{
1481	idhdl h=rSimpleFindHdl(r,IDROOT,n);
1482	if (h!=NULL) return h;
1483	#ifdef HAVE_NS
1484	if (IDROOT!=basePack->idroot) h=rSimpleFindHdl(r,basePack->idroot,n);
1485	if (h!=NULL) return h;
1486	proclevel *p=procstack;
1487	while(p!=NULL)
1488	{
1489	if ((p->cPack!=basePack)
1490	&& (p->cPack!=currPack))
1491	h=rSimpleFindHdl(r,p->cPack->idroot,n);
1492	if (h!=NULL) return h;
1493	p=p->next;
1494	}
1495	idhdl tmp=basePack->idroot;
1496	while (tmp!=NULL)
1497	{
1498	if (IDTYP(tmp)==PACKAGE_CMD)
1499	h=rSimpleFindHdl(r,IDPACKAGE(tmp)->idroot,n);
1500	if (h!=NULL) return h;
1501	tmp=IDNEXT(tmp);
1502	}
1503	#endif
1504	return NULL;
1505	}
1506
1507	void rDecomposeCF(leftv h,const ring r,const ring R)
1508	{
1509	lists L=(lists)omAlloc0Bin(slists_bin);
1510	L->Init(4);
1511	h->rtyp=LIST_CMD;
1512	h->data=(void *)L;
1513	// 0: char/ cf - ring
1514	// 1: list (var)
1515	// 2: list (ord)
1516	// 3: qideal
1517	// ----------------------------------------
1518	// 0: char/ cf - ring
1519	L->m[0].rtyp=INT_CMD;
1520	L->m[0].data=(void *)r->ch;
1521	// ----------------------------------------
1522	// 1: list (var)
1523	lists LL=(lists)omAlloc0Bin(slists_bin);
1524	LL->Init(r->N);
1525	int i;
1526	for(i=0; i<r->N; i++)
1527	{
1528	LL->m[i].rtyp=STRING_CMD;
1529	LL->m[i].data=(void *)omStrDup(r->names[i]);
1530	}
1531	L->m[1].rtyp=LIST_CMD;
1532	L->m[1].data=(void *)LL;
1533	// ----------------------------------------
1534	// 2: list (ord)
1535	LL=(lists)omAlloc0Bin(slists_bin);
1536	i=rBlocks(r)-1;
1537	LL->Init(i);
1538	i--;
1539	lists LLL;
1540	for(; i>=0; i--)
1541	{
1542	intvec *iv;
1543	int j;
1544	LL->m[i].rtyp=LIST_CMD;
1545	LLL=(lists)omAlloc0Bin(slists_bin);
1546	LLL->Init(2);
1547	LLL->m[0].rtyp=STRING_CMD;
1548	LLL->m[0].data=(void *)omStrDup(rSimpleOrdStr(r->order[i]));
1549	if (r->block1[i]-r->block0[i] >=0 )
1550	{
1551	j=r->block1[i]-r->block0[i];
1552	if(r->order[i]==ringorder_M) j=(j+1)*(j+1)-1;
1553	iv=new intvec(j+1);
1554	if ((r->wvhdl!=NULL) && (r->wvhdl[i]!=NULL))
1555	{
1556	for(;j>=0; j--) (*iv)[j]=r->wvhdl[i][j];
1557	}
1558	else switch (r->order[i])
1559	{
1560	case ringorder_dp:
1561	case ringorder_Dp:
1562	case ringorder_ds:
1563	case ringorder_Ds:
1564	case ringorder_lp:
1565	for(;j>=0; j--) (*iv)[j]=1;
1566	break;
1567	default: /* do nothing */;
1568	}
1569	}
1570	else
1571	{
1572	iv=new intvec(1);
1573	}
1574	LLL->m[1].rtyp=INTVEC_CMD;
1575	LLL->m[1].data=(void *)iv;
1576	LL->m[i].data=(void *)LLL;
1577	}
1578	L->m[2].rtyp=LIST_CMD;
1579	L->m[2].data=(void *)LL;
1580	// ----------------------------------------
1581	// 3: qideal
1582	L->m[3].rtyp=IDEAL_CMD;
1583	if (R->minpoly==NULL)
1584	L->m[3].data=(void *)idInit(1,1);
1585	else
1586	{
1587	ideal I=idInit(1,1);
1588	L->m[3].data=(void *)I;
1589	I->m[0]=pOne();
1590	pSetCoeff(I->m[0],R->minpoly);
1591	}
1592	// ----------------------------------------
1593	}
1594	void rDecomposeC(leftv h,const ring R)
1595	/* field is R or C */
1596	{
1597	lists L=(lists)omAlloc0Bin(slists_bin);
1598	if (rField_is_long_C(R)) L->Init(3);
1599	else L->Init(2);
1600	h->rtyp=LIST_CMD;
1601	h->data=(void *)L;
1602	// 0: char/ cf - ring
1603	// 1: list (var)
1604	// 2: list (ord)
1605	// ----------------------------------------
1606	// 0: char/ cf - ring
1607	L->m[0].rtyp=INT_CMD;
1608	L->m[0].data=(void *)0;
1609	// ----------------------------------------
1610	// 1:
1611	lists LL=(lists)omAlloc0Bin(slists_bin);
1612	LL->Init(2);
1613	LL->m[0].rtyp=INT_CMD;
1614	LL->m[0].data=(void *)si_max(R->float_len,SHORT_REAL_LENGTH/2);
1615	LL->m[1].rtyp=INT_CMD;
1616	LL->m[1].data=(void *)si_max(R->float_len2,SHORT_REAL_LENGTH);
1617	L->m[1].rtyp=LIST_CMD;
1618	L->m[1].data=(void *)LL;
1619	// ----------------------------------------
1620	// 2: list (par)
1621	if (rField_is_long_C(R))
1622	{
1623	L->m[2].rtyp=STRING_CMD;
1624	L->m[2].data=(void *)omStrDup(R->parameter[0]);
1625	}
1626	// ----------------------------------------
1627	}
1628
1629	lists rDecompose(const ring r)
1630	{
1631	// sanity check: require currRing==r for rings with polynomial data
1632	if ((r!=currRing)
1633	&& ((r->minpoly!=NULL) \|\| (r->qideal!=NULL) \|\| (r->minideal!=NULL)
1634	#ifdef HAVE_PLURAL
1635	\|\| (rIsPluralRing(r))
1636	#endif
1637	))
1638	{
1639	WerrorS("ring with polynomial data must be the base ring or compatible");
1640	return NULL;
1641	}
1642	// 0: char/ cf - ring
1643	// 1: list (var)
1644	// 2: list (ord)
1645	// 3: qideal
1646	// possibly:
1647	// 4: C
1648	// 5: D
1649	lists L=(lists)omAlloc0Bin(slists_bin);
1650	if (rIsPluralRing(r))
1651	L->Init(6);
1652	else
1653	L->Init(4);
1654	// ----------------------------------------
1655	// 0: char/ cf - ring
1656	#if 1 /* TODO */
1657	if (rField_is_numeric(r))
1658	{
1659	rDecomposeC(&(L->m[0]),r);
1660	}
1661	else if (rIsExtension(r))
1662	{
1663	rDecomposeCF(&(L->m[0]),r->algring,r);
1664	if (L->m[0].rtyp==0)
1665	{
1666	omFreeBin(slists_bin,(void *)L);
1667	return NULL;
1668	}
1669	}
1670	else
1671	#endif
1672	{
1673	L->m[0].rtyp=INT_CMD;
1674	L->m[0].data=(void *)r->ch;
1675	}
1676	// ----------------------------------------
1677	// 1: list (var)
1678	lists LL=(lists)omAlloc0Bin(slists_bin);
1679	LL->Init(r->N);
1680	int i;
1681	for(i=0; i<r->N; i++)
1682	{
1683	LL->m[i].rtyp=STRING_CMD;
1684	LL->m[i].data=(void *)omStrDup(r->names[i]);
1685	}
1686	L->m[1].rtyp=LIST_CMD;
1687	L->m[1].data=(void *)LL;
1688	// ----------------------------------------
1689	// 2: list (ord)
1690	LL=(lists)omAlloc0Bin(slists_bin);
1691	i=rBlocks(r)-1;
1692	LL->Init(i);
1693	i--;
1694	lists LLL;
1695	for(; i>=0; i--)
1696	{
1697	intvec *iv;
1698	int j;
1699	LL->m[i].rtyp=LIST_CMD;
1700	LLL=(lists)omAlloc0Bin(slists_bin);
1701	LLL->Init(2);
1702	LLL->m[0].rtyp=STRING_CMD;
1703	LLL->m[0].data=(void *)omStrDup(rSimpleOrdStr(r->order[i]));
1704	if (r->block1[i]-r->block0[i] >=0 )
1705	{
1706	j=r->block1[i]-r->block0[i];
1707	iv=new intvec(j+1);
1708	if ((r->wvhdl!=NULL) && (r->wvhdl[i]!=NULL))
1709	{
1710	for(;j>=0; j--) (*iv)[j]=r->wvhdl[i][j];
1711	}
1712	else switch (r->order[i])
1713	{
1714	case ringorder_dp:
1715	case ringorder_Dp:
1716	case ringorder_ds:
1717	case ringorder_Ds:
1718	case ringorder_lp:
1719	for(;j>=0; j--) (*iv)[j]=1;
1720	break;
1721	default: /* do nothing */;
1722	}
1723	}
1724	else
1725	{
1726	iv=new intvec(1);
1727	}
1728	LLL->m[1].rtyp=INTVEC_CMD;
1729	LLL->m[1].data=(void *)iv;
1730	LL->m[i].data=(void *)LLL;
1731	}
1732	L->m[2].rtyp=LIST_CMD;
1733	L->m[2].data=(void *)LL;
1734	// ----------------------------------------
1735	// 3: qideal
1736	L->m[3].rtyp=IDEAL_CMD;
1737	if (r->qideal==NULL)
1738	L->m[3].data=(void *)idInit(1,1);
1739	else
1740	L->m[3].data=(void *)idCopy(r->qideal);
1741	// ----------------------------------------
1742	#ifdef HAVE_PLURAL
1743	if (rIsPluralRing(r))
1744	{
1745	L->m[4].rtyp=MATRIX_CMD;
1746	L->m[4].data=(void *)mpCopy(r->nc->C);
1747	L->m[5].rtyp=MATRIX_CMD;
1748	L->m[5].data=(void *)mpCopy(r->nc->D);
1749	}
1750	#endif
1751	return L;
1752	}
1753
1754	void rComposeC(lists L, ring R)
1755	/* field is R or C */
1756	{
1757	// ----------------------------------------
1758	// 0: char/ cf - ring
1759	if ((L->m[0].rtyp!=INT_CMD) \|\| (L->m[0].data!=(char *)0))
1760	{
1761	Werror("invald coeff. field description, expecting 0");
1762	return;
1763	}
1764	R->ch=-1;
1765	// ----------------------------------------
1766	// 1:
1767	if (L->m[1].rtyp!=LIST_CMD)
1768	Werror("invald coeff. field description, expecting precision list");
1769	lists LL=(lists)L->m[1].data;
1770	int r1=(int)(long)LL->m[0].data;
1771	int r2=(int)(long)LL->m[1].data;
1772	if ((r1<=SHORT_REAL_LENGTH)
1773	&& (r2=SHORT_REAL_LENGTH))
1774	{
1775	R->float_len=SHORT_REAL_LENGTH/2;
1776	R->float_len2=SHORT_REAL_LENGTH;
1777	}
1778	else
1779	{
1780	R->float_len=si_min(r1,32767);
1781	R->float_len2=si_min(r2,32767);
1782	}
1783	// ----------------------------------------
1784	// 2: list (par)
1785	if (L->nr==2)
1786	{
1787	R->P=1;
1788	if (L->m[2].rtyp!=STRING_CMD)
1789	{
1790	Werror("invald coeff. field description, expecting parameter name");
1791	return;
1792	}
1793	R->parameter=(char*)omAlloc0(R->Psizeof(char_ptr));
1794	R->parameter[0]=omStrDup((char *)L->m[2].data);
1795	}
1796	// ----------------------------------------
1797	}
1798	ring rCompose(const lists L)
1799	{
1800	if ((L->nr!=3)
1801	#ifdef HAVE_PLURAL
1802	&&(L->nr!=5)
1803	#endif
1804	)
1805	return NULL;
1806	// 0: char/ cf - ring
1807	// 1: list (var)
1808	// 2: list (ord)
1809	// 3: qideal
1810	// possibly:
1811	// 4: C
1812	// 5: D
1813	ring R=(ring) omAlloc0Bin(sip_sring_bin);
1814	if (L->m[0].Typ()==INT_CMD)
1815	{
1816	R->ch=(int)(long)L->m[0].Data();
1817	if (R->ch!=-1)
1818	{
1819	int l;
1820	if (((R->ch!=0) && (R->ch<2))
1821	#ifndef NV_OPS
1822	\|\| (R->ch > 32003)
1823	#endif
1824	\|\| ((l=IsPrime(R->ch))!=R->ch)
1825	)
1826	{
1827	Warn("%d is invalid characteristic of ground field. %d is used.", R->ch,l);
1828	R->ch=l;
1829	}
1830	}
1831	}
1832	else if (L->m[0].Typ()==LIST_CMD)
1833	{
1834	lists LL=(lists)L->m[0].Data();
1835	if (LL->nr<3)
1836	rComposeC(LL,R); /* R, long_R, long_C */
1837	else
1838	{
1839	R->algring=rCompose((lists)L->m[0].Data());
1840	if (R->algring==NULL)
1841	{
1842	WerrorS("could not create rational function coefficient field");
1843	goto rCompose_err;
1844	}
1845	if (R->algring->ch>0)
1846	R->ch= -R->algring->ch;
1847	else
1848	R->ch=1;
1849	R->P=R->algring->N;
1850	R->parameter=(char*)omAlloc0(R->Psizeof(char_ptr));
1851	int i;
1852	for(i=R->P-1;i>=0;i--)
1853	R->parameter[i]=omStrDup(R->algring->names[i]);
1854	if (R->algring->qideal!=NULL)
1855	{
1856	if (IDELEMS(R->algring->qideal)==1)
1857	{
1858	R->minpoly=pGetCoeff(R->algring->qideal->m[0]);
1859	omFreeBinAddr(R->algring->qideal->m[0]);
1860	R->algring->qideal->m[0]=NULL;
1861	idDelete(&(R->algring->qideal));
1862	}
1863	else
1864	{
1865	WerrorS("not implemented yet.");
1866	}
1867	}
1868	}
1869	}
1870	else
1871	{
1872	WerrorS("coefficient field must be described by `int` or `list`");
1873	goto rCompose_err;
1874	}
1875	// ------------------------- VARS ---------------------------
1876	if (L->m[1].Typ()==LIST_CMD)
1877	{
1878	lists v=(lists)L->m[1].Data();
1879	R->N = v->nr+1;
1880	R->names = (char *)omAlloc0(R->N sizeof(char_ptr));
1881	int i;
1882	for(i=0;i<R->N;i++)
1883	{
1884	if (v->m[i].Typ()==STRING_CMD)
1885	R->names[i]=omStrDup((char *)v->m[i].Data());
1886	else if (v->m[i].Typ()==POLY_CMD)
1887	{
1888	poly p=(poly)v->m[i].Data();
1889	int nr=pIsPurePower(p);
1890	if (nr>0)
1891	R->names[i]=omStrDup(currRing->names[nr-1]);
1892	else
1893	{
1894	Werror("var name %d must be a string or a ring variable",i+1);
1895	goto rCompose_err;
1896	}
1897	}
1898	else
1899	{
1900	Werror("var name %d must be `string`",i+1);
1901	goto rCompose_err;
1902	}
1903	}
1904	}
1905	else
1906	{
1907	WerrorS("variable must be given as `list`");
1908	goto rCompose_err;
1909	}
1910	rNameCheck(R);
1911	// ------------------------ ORDER ------------------------------
1912	if (L->m[2].Typ()==LIST_CMD)
1913	{
1914	lists v=(lists)L->m[2].Data();
1915	int n= v->nr+2;
1916	int j;
1917	// initialize fields of R
1918	R->order=(int )omAlloc0(nsizeof(int));
1919	R->block0=(int )omAlloc0(nsizeof(int));
1920	R->block1=(int )omAlloc0(nsizeof(int));
1921	R->wvhdl=(int*)omAlloc0(nsizeof(int_ptr));
1922	// init order, so that rBlocks works correctly
1923	for (j=0; j < n-1; j++)
1924	R->order[j] = (int) ringorder_unspec;
1925	// orderings
1926	R->OrdSgn=1;
1927	for(j=0;j<n-1;j++)
1928	{
1929	// todo: a(..), M
1930	if (v->m[j].Typ()!=LIST_CMD)
1931	{
1932	WerrorS("ordering must be list of lists");
1933	goto rCompose_err;
1934	}
1935	lists vv=(lists)v->m[j].Data();
1936	if ((vv->nr!=1)
1937	\|\| (vv->m[0].Typ()!=STRING_CMD)
1938	\|\| ((vv->m[1].Typ()!=INTVEC_CMD) && (vv->m[1].Typ()!=INT_CMD)))
1939	{
1940	WerrorS("ordering name must be a (string,intvec)");
1941	goto rCompose_err;
1942	}
1943	R->order[j]=rOrderName(omStrDup((char*)vv->m[0].Data())); // assume STRING
1944	if (j==0) R->block0[0]=1;
1945	else
1946	{
1947	int jj=j-1;
1948	while((jj>=0)
1949	&& ((R->order[jj]== ringorder_a)
1950	\|\| (R->order[jj]== ringorder_aa)
1951	\|\| (R->order[jj]== ringorder_c)
1952	\|\| (R->order[jj]== ringorder_C)
1953	))
1954	{
1955	//Print("jj=%, skip %s\n",rSimpleOrdStr(R->order[jj]));
1956	jj--;
1957	}
1958	if (jj<0) R->block0[j]=1;
1959	else R->block0[j]=R->block1[jj]+1;
1960	}
1961	intvec *iv;
1962	if (vv->m[1].Typ()==INT_CMD)
1963	iv=new intvec((int)(long)vv->m[1].Data(),(int)(long)vv->m[1].Data());
1964	else
1965	iv=ivCopy((intvec*)vv->m[1].Data()); //assume INTVEC
1966	R->block1[j]=si_max(R->block0[j],R->block0[j]+iv->length()-1);
1967	//Print("block %d from %d to %d\n",j,R->block0[j], R->block1[j]);
1968	int i;
1969	switch (R->order[j])
1970	{
1971	case ringorder_ws:
1972	case ringorder_Ws:
1973	R->OrdSgn=-1;
1974	case ringorder_aa:
1975	case ringorder_a:
1976	case ringorder_wp:
1977	case ringorder_Wp:
1978	R->wvhdl[j] =( int )omAlloc((iv->length())sizeof(int));
1979	for (i=0; i<iv->length();i++) R->wvhdl[j][i]=(*iv)[i];
1980	break;
1981	case ringorder_ls:
1982	case ringorder_ds:
1983	case ringorder_Ds:
1984	R->OrdSgn=-1;
1985	case ringorder_lp:
1986	case ringorder_dp:
1987	case ringorder_Dp:
1988	case ringorder_rp:
1989	break;
1990	case ringorder_S:
1991	break;
1992	case ringorder_c:
1993	case ringorder_C:
1994	R->block1[j]=R->block0[j]-1;
1995	break;
1996	case ringorder_M:
1997	// todo
1998	break;
1999	case 0:
2000	case ringorder_unspec:
2001	break;
2002	}
2003	}
2004	// sanity check
2005	j=n-2;
2006	if ((R->order[j]==ringorder_c)
2007	\|\| (R->order[j]==ringorder_C)
2008	\|\| (R->order[j]==ringorder_unspec)) j--;
2009	if (R->block1[j] != R->N)
2010	{
2011	if (((R->order[j]==ringorder_dp) \|\|
2012	(R->order[j]==ringorder_ds) \|\|
2013	(R->order[j]==ringorder_Dp) \|\|
2014	(R->order[j]==ringorder_Ds) \|\|
2015	(R->order[j]==ringorder_rp) \|\|
2016	(R->order[j]==ringorder_lp) \|\|
2017	(R->order[j]==ringorder_ls))
2018	&&
2019	R->block0[j] <= R->N)
2020	{
2021	R->block1[j] = R->N;
2022	}
2023	else
2024	{
2025	Werror("ordering incomplete: size (%d) should be %d",R->block1[j],R->N);
2026	goto rCompose_err;
2027	}
2028	}
2029	}
2030	else
2031	{
2032	WerrorS("ordering must be given as `list`");
2033	goto rCompose_err;
2034	}
2035	// ------------------------ Q-IDEAL ------------------------
2036	rComplete(R);
2037
2038	if (L->m[3].Typ()==IDEAL_CMD)
2039	{
2040	ideal q=(ideal)L->m[3].Data();
2041	if (q->m[0]!=NULL)
2042	R->qideal=idrCopyR(q,currRing,R);
2043	}
2044	else
2045	{
2046	WerrorS("q-ideal must be given as `ideal`");
2047	goto rCompose_err;
2048	}
2049
2050
2051	// ---------------------------------------------------------------
2052	#ifdef HAVE_PLURAL
2053	if (L->nr==5)
2054	{
2055	if (nc_CallPlural((matrix)L->m[4].Data(),(matrix)L->m[5].Data(),
2056	NULL,NULL,R))
2057	goto rCompose_err;
2058	}
2059	#endif
2060	return R;
2061
2062	rCompose_err:
2063	if (R->N>0)
2064	{
2065	int i;
2066	if (R->names!=NULL)
2067	{
2068	i=R->N-1;
2069	while (i>=0) { if (R->names[i]!=NULL) omFree(R->names[i]); i--; }
2070	omFree(R->names);
2071	}
2072	}
2073	if (R->order!=NULL) omFree(R->order);
2074	if (R->block0!=NULL) omFree(R->block0);
2075	if (R->block1!=NULL) omFree(R->block1);
2076	if (R->wvhdl!=NULL) omFree(R->wvhdl);
2077	omFree(R);
2078	return NULL;
2079	}
2080
2081	// from matpol.cc
2082
2083	/*2
2084	* compute the jacobi matrix of an ideal
2085	*/
2086	BOOLEAN mpJacobi(leftv res,leftv a)
2087	{
2088	int i,j;
2089	matrix result;
2090	ideal id=(ideal)a->Data();
2091
2092	result =mpNew(IDELEMS(id),pVariables);
2093	for (i=1; i<=IDELEMS(id); i++)
2094	{
2095	for (j=1; j<=pVariables; j++)
2096	{
2097	MATELEM(result,i,j) = pDiff(id->m[i-1],j);
2098	}
2099	}
2100	res->data=(char *)result;
2101	return FALSE;
2102	}
2103
2104	/*2
2105	* returns the Koszul-matrix of degree d of a vectorspace with dimension n
2106	* uses the first n entrees of id, if id <> NULL
2107	*/
2108	BOOLEAN mpKoszul(leftv res,leftv c/ip/, leftv b/in/, leftv id)
2109	{
2110	int n=(int)(long)b->Data();
2111	int d=(int)(long)c->Data();
2112	int k,l,sign,row,col;
2113	matrix result;
2114	ideal temp;
2115	BOOLEAN bo;
2116	poly p;
2117
2118	if ((d>n) \|\| (d<1) \|\| (n<1))
2119	{
2120	res->data=(char *)mpNew(1,1);
2121	return FALSE;
2122	}
2123	int choise = (int)omAlloc(d*sizeof(int));
2124	if (id==NULL)
2125	temp=idMaxIdeal(1);
2126	else
2127	temp=(ideal)id->Data();
2128
2129	k = binom(n,d);
2130	l = k*d;
2131	l /= n-d+1;
2132	result =mpNew(l,k);
2133	col = 1;
2134	idInitChoise(d,1,n,&bo,choise);
2135	while (!bo)
2136	{
2137	sign = 1;
2138	for (l=1;l<=d;l++)
2139	{
2140	if (choise[l-1]<=IDELEMS(temp))
2141	{
2142	p = pCopy(temp->m[choise[l-1]-1]);
2143	if (sign == -1) p = pNeg(p);
2144	sign *= -1;
2145	row = idGetNumberOfChoise(l-1,d,1,n,choise);
2146	MATELEM(result,row,col) = p;
2147	}
2148	}
2149	col++;
2150	idGetNextChoise(d,n,&bo,choise);
2151	}
2152	if (id==NULL) idDelete(&temp);
2153
2154	res->data=(char *)result;
2155	return FALSE;
2156	}
2157
2158	// from syz1.cc
2159	/*2
2160	* read out the Betti numbers from resolution
2161	* (interpreter interface)
2162	*/
2163	BOOLEAN syBetti2(leftv res, leftv u, leftv w)
2164	{
2165	syStrategy syzstr=(syStrategy)u->Data();
2166	BOOLEAN minim=(int)(long)w->Data();
2167	int row_shift=0;
2168	int add_row_shift=0;
2169	intvec *weights=NULL;
2170	intvec ww=(intvec )atGet(u,"isHomog",INTVEC_CMD);
2171	if (ww!=NULL)
2172	{
2173	weights=ivCopy(ww);
2174	add_row_shift = ww->min_in();
2175	(*weights) -= add_row_shift;
2176	}
2177	res->data=(void *)syBettiOfComputation(syzstr,minim,&row_shift,weights);
2178	//row_shift += add_row_shift;
2179	//Print("row_shift=%d, add_row_shift=%d\n",row_shift,add_row_shift);
2180	atSet(res,omStrDup("rowShift"),(void*)add_row_shift,INT_CMD);
2181	return FALSE;
2182	}
2183	BOOLEAN syBetti1(leftv res, leftv u)
2184	{
2185	sleftv tmp;
2186	memset(&tmp,0,sizeof(tmp));
2187	tmp.rtyp=INT_CMD;
2188	tmp.data=(void *)1;
2189	return syBetti2(res,u,&tmp);
2190	}
2191
2192	/*3
2193	* converts a resolution into a list of modules
2194	*/
2195	lists syConvRes(syStrategy syzstr,BOOLEAN toDel,int add_row_shift)
2196	{
2197	if ((syzstr->fullres==NULL) && (syzstr->minres==NULL))
2198	{
2199	if (syzstr->hilb_coeffs==NULL)
2200	{
2201	syzstr->fullres = syReorder(syzstr->res,syzstr->length,syzstr);
2202	}
2203	else
2204	{
2205	syzstr->minres = syReorder(syzstr->orderedRes,syzstr->length,syzstr);
2206	syKillEmptyEntres(syzstr->minres,syzstr->length);
2207	}
2208	}
2209	resolvente tr;
2210	int typ0=IDEAL_CMD;
2211	if (syzstr->minres!=NULL)
2212	tr = syzstr->minres;
2213	else
2214	tr = syzstr->fullres;
2215	resolvente trueres=NULL;
2216	intvec ** w=NULL;
2217	if (syzstr->length>0)
2218	{
2219	trueres=(resolvente)omAlloc0((syzstr->length)*sizeof(ideal));
2220	for (int i=(syzstr->length)-1;i>=0;i--)
2221	{
2222	if (tr[i]!=NULL)
2223	{
2224	trueres[i] = idCopy(tr[i]);
2225	}
2226	}
2227	if (idRankFreeModule(trueres[0]) > 0)
2228	typ0 = MODUL_CMD;
2229	if (syzstr->weights!=NULL)
2230	{
2231	w = (intvec*)omAlloc0((syzstr->length)sizeof(intvec*));
2232	for (int i=(syzstr->length)-1;i>=0;i--)
2233	{
2234	if (syzstr->weights[i]!=NULL) w[i] = ivCopy(syzstr->weights[i]);
2235	}
2236	}
2237	}
2238	lists li = liMakeResolv(trueres,syzstr->length,syzstr->list_length,typ0,
2239	w,add_row_shift);
2240	if (w != NULL) omFreeSize(w, (syzstr->length)sizeof(intvec));
2241	if (toDel) syKillComputation(syzstr);
2242	return li;
2243	}
2244
2245	/*3
2246	* converts a list of modules into a resolution
2247	*/
2248	syStrategy syConvList(lists li,BOOLEAN toDel)
2249	{
2250	int typ0;
2251	syStrategy result=(syStrategy)omAlloc0(sizeof(ssyStrategy));
2252
2253	resolvente fr = liFindRes(li,&(result->length),&typ0,&(result->weights));
2254	if (fr != NULL)
2255	{
2256
2257	result->fullres = (resolvente)omAlloc0((result->length+1)*sizeof(ideal));
2258	for (int i=result->length-1;i>=0;i--)
2259	{
2260	if (fr[i]!=NULL)
2261	result->fullres[i] = idCopy(fr[i]);
2262	}
2263	result->list_length=result->length;
2264	omFreeSize((ADDRESS)fr,(result->length)*sizeof(ideal));
2265	}
2266	else
2267	{
2268	omFreeSize(result, sizeof(ssyStrategy));
2269	result = NULL;
2270	}
2271	if (toDel) li->Clean();
2272	return result;
2273	}
2274
2275	/*3
2276	* converts a list of modules into a minimal resolution
2277	*/
2278	syStrategy syForceMin(lists li)
2279	{
2280	int typ0;
2281	syStrategy result=(syStrategy)omAlloc0(sizeof(ssyStrategy));
2282
2283	resolvente fr = liFindRes(li,&(result->length),&typ0);
2284	result->minres = (resolvente)omAlloc0((result->length+1)*sizeof(ideal));
2285	for (int i=result->length-1;i>=0;i--)
2286	{
2287	if (fr[i]!=NULL)
2288	result->minres[i] = idCopy(fr[i]);
2289	}
2290	omFreeSize((ADDRESS)fr,(result->length)*sizeof(ideal));
2291	return result;
2292	}
2293	// from weight.cc
2294	BOOLEAN kWeight(leftv res,leftv id)
2295	{
2296	ideal F=(ideal)id->Data();
2297	intvec * iv = new intvec(pVariables);
2298	polyset s;
2299	int sl, n, i;
2300	int *x;
2301
2302	res->data=(char *)iv;
2303	s = F->m;
2304	sl = IDELEMS(F) - 1;
2305	n = pVariables;
2306	wNsqr = (double)2.0 / (double)n;
2307	wFunctional = wFunctionalBuch;
2308	x = (int * )omAlloc(2 * (n + 1) * sizeof(int));
2309	wCall(s, sl, x);
2310	for (i = n; i!=0; i--)
2311	(*iv)[i-1] = x[i + n + 1];
2312	omFreeSize((ADDRESS)x, 2 * (n + 1) * sizeof(int));
2313	return FALSE;
2314	}
2315
2316	BOOLEAN kQHWeight(leftv res,leftv v)
2317	{
2318	res->data=(char *)idQHomWeight((ideal)v->Data());
2319	if (res->data==NULL)
2320	res->data=(char *)new intvec(pVariables);
2321	return FALSE;
2322	}
2323	/==============================================================/
2324	// from clapsing.cc
2325	#if 0
2326	BOOLEAN jjIS_SQR_FREE(leftv res, leftv u)
2327	{
2328	BOOLEAN b=singclap_factorize((poly)(u->Data()), &v, 0);
2329	res->data=(void *)b;
2330	}
2331	#endif
2332
2333	BOOLEAN jjRESULTANT(leftv res, leftv u, leftv v, leftv w)
2334	{
2335	res->data=singclap_resultant((poly)u->Data(),(poly)v->Data(), (poly)w->Data());
2336	return errorreported;
2337	}
2338	BOOLEAN jjCHARSERIES(leftv res, leftv u)
2339	{
2340	res->data=singclap_irrCharSeries((ideal)u->Data());
2341	return (res->data==NULL);
2342	}
2343
2344	// from semic.cc
2345	#ifdef HAVE_SPECTRUM
2346
2347	// ----------------------------------------------------------------------------
2348	// Initialize a spectrum deep from another spectrum
2349	// ----------------------------------------------------------------------------
2350
2351	void spectrum::copy_deep( const spectrum &spec )
2352	{
2353	mu = spec.mu;
2354	pg = spec.pg;
2355	n = spec.n;
2356
2357	copy_new( n );
2358
2359	for( int i=0; i<n; i++ )
2360	{
2361	s[i] = spec.s[i];
2362	w[i] = spec.w[i];
2363	}
2364	}
2365
2366	// ----------------------------------------------------------------------------
2367	// Initialize a spectrum deep from a singular lists
2368	// ----------------------------------------------------------------------------
2369
2370	void spectrum::copy_deep( lists l )
2371	{
2372	mu = (int)(long)(l->m[0].Data( ));
2373	pg = (int)(long)(l->m[1].Data( ));
2374	n = (int)(long)(l->m[2].Data( ));
2375
2376	copy_new( n );
2377
2378	intvec num = (intvec)l->m[3].Data( );
2379	intvec den = (intvec)l->m[4].Data( );
2380	intvec mul = (intvec)l->m[5].Data( );
2381
2382	for( int i=0; i<n; i++ )
2383	{
2384	s[i] = (Rational)((num)[i])/(Rational)((den)[i]);
2385	w[i] = (*mul)[i];
2386	}
2387	}
2388
2389	// ----------------------------------------------------------------------------
2390	// singular lists constructor for spectrum
2391	// ----------------------------------------------------------------------------
2392
2393	spectrum::spectrum( lists l )
2394	{
2395	copy_deep( l );
2396	}
2397
2398	// ----------------------------------------------------------------------------
2399	// generate a Singular lists from a spectrum
2400	// ----------------------------------------------------------------------------
2401
2402	lists spectrum::thelist( void )
2403	{
2404	lists L = (lists)omAllocBin( slists_bin);
2405
2406	L->Init( 6 );
2407
2408	intvec *num = new intvec( n );
2409	intvec *den = new intvec( n );
2410	intvec *mult = new intvec( n );
2411
2412	for( int i=0; i<n; i++ )
2413	{
2414	(*num) [i] = s[i].get_num_si( );
2415	(*den) [i] = s[i].get_den_si( );
2416	(*mult)[i] = w[i];
2417	}
2418
2419	L->m[0].rtyp = INT_CMD; // milnor number
2420	L->m[1].rtyp = INT_CMD; // geometrical genus
2421	L->m[2].rtyp = INT_CMD; // # of spectrum numbers
2422	L->m[3].rtyp = INTVEC_CMD; // numerators
2423	L->m[4].rtyp = INTVEC_CMD; // denomiantors
2424	L->m[5].rtyp = INTVEC_CMD; // multiplicities
2425
2426	L->m[0].data = (void*)mu;
2427	L->m[1].data = (void*)pg;
2428	L->m[2].data = (void*)n;
2429	L->m[3].data = (void*)num;
2430	L->m[4].data = (void*)den;
2431	L->m[5].data = (void*)mult;
2432
2433	return L;
2434	}
2435	// from spectrum.cc
2436	// ----------------------------------------------------------------------------
2437	// print out an error message for a spectrum list
2438	// ----------------------------------------------------------------------------
2439
2440	void list_error( semicState state )
2441	{
2442	switch( state )
2443	{
2444	case semicListTooShort:
2445	WerrorS( "the list is too short" );
2446	break;
2447	case semicListTooLong:
2448	WerrorS( "the list is too long" );
2449	break;
2450
2451	case semicListFirstElementWrongType:
2452	WerrorS( "first element of the list should be int" );
2453	break;
2454	case semicListSecondElementWrongType:
2455	WerrorS( "second element of the list should be int" );
2456	break;
2457	case semicListThirdElementWrongType:
2458	WerrorS( "third element of the list should be int" );
2459	break;
2460	case semicListFourthElementWrongType:
2461	WerrorS( "fourth element of the list should be intvec" );
2462	break;
2463	case semicListFifthElementWrongType:
2464	WerrorS( "fifth element of the list should be intvec" );
2465	break;
2466	case semicListSixthElementWrongType:
2467	WerrorS( "sixth element of the list should be intvec" );
2468	break;
2469
2470	case semicListNNegative:
2471	WerrorS( "first element of the list should be positive" );
2472	break;
2473	case semicListWrongNumberOfNumerators:
2474	WerrorS( "wrong number of numerators" );
2475	break;
2476	case semicListWrongNumberOfDenominators:
2477	WerrorS( "wrong number of denominators" );
2478	break;
2479	case semicListWrongNumberOfMultiplicities:
2480	WerrorS( "wrong number of multiplicities" );
2481	break;
2482
2483	case semicListMuNegative:
2484	WerrorS( "the Milnor number should be positive" );
2485	break;
2486	case semicListPgNegative:
2487	WerrorS( "the geometrical genus should be nonnegative" );
2488	break;
2489	case semicListNumNegative:
2490	WerrorS( "all numerators should be positive" );
2491	break;
2492	case semicListDenNegative:
2493	WerrorS( "all denominators should be positive" );
2494	break;
2495	case semicListMulNegative:
2496	WerrorS( "all multiplicities should be positive" );
2497	break;
2498
2499	case semicListNotSymmetric:
2500	WerrorS( "it is not symmetric" );
2501	break;
2502	case semicListNotMonotonous:
2503	WerrorS( "it is not monotonous" );
2504	break;
2505
2506	case semicListMilnorWrong:
2507	WerrorS( "the Milnor number is wrong" );
2508	break;
2509	case semicListPGWrong:
2510	WerrorS( "the geometrical genus is wrong" );
2511	break;
2512
2513	default:
2514	WerrorS( "unspecific error" );
2515	break;
2516	}
2517	}
2518	// ----------------------------------------------------------------------------
2519	// this is the main spectrum computation function
2520	// ----------------------------------------------------------------------------
2521
2522	spectrumState spectrumCompute( poly h,lists *L,int fast )
2523	{
2524	int i,j;
2525
2526	#ifdef SPECTRUM_DEBUG
2527	#ifdef SPECTRUM_PRINT
2528	#ifdef SPECTRUM_IOSTREAM
2529	cout << "spectrumCompute\n";
2530	if( fast==0 ) cout << " no optimization" << endl;
2531	if( fast==1 ) cout << " weight optimization" << endl;
2532	if( fast==2 ) cout << " symmetry optimization" << endl;
2533	#else
2534	fprintf( stdout,"spectrumCompute\n" );
2535	if( fast==0 ) fprintf( stdout," no optimization\n" );
2536	if( fast==1 ) fprintf( stdout," weight optimization\n" );
2537	if( fast==2 ) fprintf( stdout," symmetry optimization\n" );
2538	#endif
2539	#endif
2540	#endif
2541
2542	// ----------------------
2543	// check if h is zero
2544	// ----------------------
2545
2546	if( h==(poly)NULL )
2547	{
2548	return spectrumZero;
2549	}
2550
2551	// ----------------------------------
2552	// check if h has a constant term
2553	// ----------------------------------
2554
2555	if( hasConstTerm( h ) )
2556	{
2557	return spectrumBadPoly;
2558	}
2559
2560	// --------------------------------
2561	// check if h has a linear term
2562	// --------------------------------
2563
2564	if( hasLinearTerm( h ) )
2565	{
2566	*L = (lists)omAllocBin( slists_bin);
2567	(*L)->Init( 1 );
2568	(*L)->m[0].rtyp = INT_CMD; // milnor number
2569	/* (L)->m[0].data = (void)0;a -- done by Init */
2570
2571	return spectrumNoSingularity;
2572	}
2573
2574	// ----------------------------------
2575	// compute the jacobi ideal of (h)
2576	// ----------------------------------
2577
2578	ideal J = NULL;
2579	J = idInit( pVariables,1 );
2580
2581	#ifdef SPECTRUM_DEBUG
2582	#ifdef SPECTRUM_PRINT
2583	#ifdef SPECTRUM_IOSTREAM
2584	cout << "\n computing the Jacobi ideal...\n";
2585	#else
2586	fprintf( stdout,"\n computing the Jacobi ideal...\n" );
2587	#endif
2588	#endif
2589	#endif
2590
2591	for( i=0; i<pVariables; i++ )
2592	{
2593	J->m[i] = pDiff( h,i+1); //j );
2594
2595	#ifdef SPECTRUM_DEBUG
2596	#ifdef SPECTRUM_PRINT
2597	#ifdef SPECTRUM_IOSTREAM
2598	cout << " ";
2599	#else
2600	fprintf( stdout," " );
2601	#endif
2602	pWrite( J->m[i] );
2603	#endif
2604	#endif
2605	}
2606
2607	// --------------------------------------------
2608	// compute a standard basis stdJ of jac(h)
2609	// --------------------------------------------
2610
2611	#ifdef SPECTRUM_DEBUG
2612	#ifdef SPECTRUM_PRINT
2613	#ifdef SPECTRUM_IOSTREAM
2614	cout << endl;
2615	cout << " computing a standard basis..." << endl;
2616	#else
2617	fprintf( stdout,"\n" );
2618	fprintf( stdout," computing a standard basis...\n" );
2619	#endif
2620	#endif
2621	#endif
2622
2623	ideal stdJ = kStd(J,currQuotient,isNotHomog,NULL);
2624	idSkipZeroes( stdJ );
2625
2626	#ifdef SPECTRUM_DEBUG
2627	#ifdef SPECTRUM_PRINT
2628	for( i=0; i<IDELEMS(stdJ); i++ )
2629	{
2630	#ifdef SPECTRUM_IOSTREAM
2631	cout << " ";
2632	#else
2633	fprintf( stdout," " );
2634	#endif
2635
2636	pWrite( stdJ->m[i] );
2637	}
2638	#endif
2639	#endif
2640
2641	idDelete( &J );
2642
2643	// ------------------------------------------
2644	// check if the h has a singularity
2645	// ------------------------------------------
2646
2647	if( hasOne( stdJ ) )
2648	{
2649	// -------------------------------
2650	// h is smooth in the origin
2651	// return only the Milnor number
2652	// -------------------------------
2653
2654	*L = (lists)omAllocBin( slists_bin);
2655	(*L)->Init( 1 );
2656	(*L)->m[0].rtyp = INT_CMD; // milnor number
2657	/* (L)->m[0].data = (void)0;a -- done by Init */
2658
2659	return spectrumNoSingularity;
2660	}
2661
2662	// ------------------------------------------
2663	// check if the singularity h is isolated
2664	// ------------------------------------------
2665
2666	for( i=pVariables; i>0; i-- )
2667	{
2668	if( hasAxis( stdJ,i )==FALSE )
2669	{
2670	return spectrumNotIsolated;
2671	}
2672	}
2673
2674	// ------------------------------------------
2675	// compute the highest corner hc of stdJ
2676	// ------------------------------------------
2677
2678	#ifdef SPECTRUM_DEBUG
2679	#ifdef SPECTRUM_PRINT
2680	#ifdef SPECTRUM_IOSTREAM
2681	cout << "\n computing the highest corner...\n";
2682	#else
2683	fprintf( stdout,"\n computing the highest corner...\n" );
2684	#endif
2685	#endif
2686	#endif
2687
2688	poly hc = (poly)NULL;
2689
2690	scComputeHC( stdJ,currQuotient, 0,hc );
2691
2692	if( hc!=(poly)NULL )
2693	{
2694	pGetCoeff(hc) = nInit(1);
2695
2696	for( i=pVariables; i>0; i-- )
2697	{
2698	if( pGetExp( hc,i )>0 ) pDecrExp( hc,i );
2699	}
2700	pSetm( hc );
2701	}
2702	else
2703	{
2704	return spectrumNoHC;
2705	}
2706
2707	#ifdef SPECTRUM_DEBUG
2708	#ifdef SPECTRUM_PRINT
2709	#ifdef SPECTRUM_IOSTREAM
2710	cout << " ";
2711	#else
2712	fprintf( stdout," " );
2713	#endif
2714	pWrite( hc );
2715	#endif
2716	#endif
2717
2718	// ----------------------------------------
2719	// compute the Newton polygon nph of h
2720	// ----------------------------------------
2721
2722	#ifdef SPECTRUM_DEBUG
2723	#ifdef SPECTRUM_PRINT
2724	#ifdef SPECTRUM_IOSTREAM
2725	cout << "\n computing the newton polygon...\n";
2726	#else
2727	fprintf( stdout,"\n computing the newton polygon...\n" );
2728	#endif
2729	#endif
2730	#endif
2731
2732	newtonPolygon nph( h );
2733
2734	#ifdef SPECTRUM_DEBUG
2735	#ifdef SPECTRUM_PRINT
2736	cout << nph;
2737	#endif
2738	#endif
2739
2740	// -----------------------------------------------
2741	// compute the weight corner wc of (stdj,nph)
2742	// -----------------------------------------------
2743
2744	#ifdef SPECTRUM_DEBUG
2745	#ifdef SPECTRUM_PRINT
2746	#ifdef SPECTRUM_IOSTREAM
2747	cout << "\n computing the weight corner...\n";
2748	#else
2749	fprintf( stdout,"\n computing the weight corner...\n" );
2750	#endif
2751	#endif
2752	#endif
2753
2754	poly wc = ( fast==0 ? pCopy( hc ) :
2755	( fast==1 ? computeWC( nph,(Rational)pVariables ) :
2756	/* fast==2 */computeWC( nph,((Rational)pVariables)/(Rational)2 ) ) );
2757
2758	#ifdef SPECTRUM_DEBUG
2759	#ifdef SPECTRUM_PRINT
2760	#ifdef SPECTRUM_IOSTREAM
2761	cout << " ";
2762	#else
2763	fprintf( stdout," " );
2764	#endif
2765	pWrite( wc );
2766	#endif
2767	#endif
2768
2769	// -------------
2770	// compute NF
2771	// -------------
2772
2773	#ifdef SPECTRUM_DEBUG
2774	#ifdef SPECTRUM_PRINT
2775	#ifdef SPECTRUM_IOSTREAM
2776	cout << "\n computing NF...\n" << endl;
2777	#else
2778	fprintf( stdout,"\n computing NF...\n" );
2779	#endif
2780	#endif
2781	#endif
2782
2783	spectrumPolyList NF( &nph );
2784
2785	computeNF( stdJ,hc,wc,&NF );
2786
2787	#ifdef SPECTRUM_DEBUG
2788	#ifdef SPECTRUM_PRINT
2789	cout << NF;
2790	#ifdef SPECTRUM_IOSTREAM
2791	cout << endl;
2792	#else
2793	fprintf( stdout,"\n" );
2794	#endif
2795	#endif
2796	#endif
2797
2798	// ----------------------------
2799	// compute the spectrum of h
2800	// ----------------------------
2801
2802	return NF.spectrum( L,fast );
2803	}
2804
2805	// ----------------------------------------------------------------------------
2806	// this procedure is called from the interpreter
2807	// ----------------------------------------------------------------------------
2808	// first = polynomial
2809	// result = list of spectrum numbers
2810	// ----------------------------------------------------------------------------
2811
2812	BOOLEAN spectrumProc( leftv result,leftv first )
2813	{
2814	spectrumState state = spectrumOK;
2815
2816	// -------------------
2817	// check consistency
2818	// -------------------
2819
2820	// check for a local ring
2821
2822	if( !ringIsLocal( ) )
2823	{
2824	WerrorS( "only works for local orderings" );
2825	state = spectrumWrongRing;
2826	}
2827
2828	// no quotient rings are allowed
2829
2830	else if( currRing->qideal != NULL )
2831	{
2832	WerrorS( "does not work in quotient rings" );
2833	state = spectrumWrongRing;
2834	}
2835	else
2836	{
2837	lists L = (lists)NULL;
2838	int flag = 1; // weight corner optimization is safe
2839
2840	state = spectrumCompute( (poly)first->Data( ),&L,flag );
2841
2842	if( state==spectrumOK )
2843	{
2844	result->rtyp = LIST_CMD;
2845	result->data = (char*)L;
2846	}
2847	else
2848	{
2849	spectrumPrintError(state);
2850	}
2851	}
2852
2853	return (state!=spectrumOK);
2854	}
2855
2856	// ----------------------------------------------------------------------------
2857	// this procedure is called from the interpreter
2858	// ----------------------------------------------------------------------------
2859	// first = polynomial
2860	// result = list of spectrum numbers
2861	// ----------------------------------------------------------------------------
2862
2863	BOOLEAN spectrumfProc( leftv result,leftv first )
2864	{
2865	spectrumState state = spectrumOK;
2866
2867	// -------------------
2868	// check consistency
2869	// -------------------
2870
2871	// check for a local polynomial ring
2872
2873	if( currRing->OrdSgn != -1 )
2874	// ?? HS: the test above is also true for k[x][[y]], k[[x]][y]
2875	// or should we use:
2876	//if( !ringIsLocal( ) )
2877	{
2878	WerrorS( "only works for local orderings" );
2879	state = spectrumWrongRing;
2880	}
2881	else if( currRing->qideal != NULL )
2882	{
2883	WerrorS( "does not work in quotient rings" );
2884	state = spectrumWrongRing;
2885	}
2886	else
2887	{
2888	lists L = (lists)NULL;
2889	int flag = 2; // symmetric optimization
2890
2891	state = spectrumCompute( (poly)first->Data( ),&L,flag );
2892
2893	if( state==spectrumOK )
2894	{
2895	result->rtyp = LIST_CMD;
2896	result->data = (char*)L;
2897	}
2898	else
2899	{
2900	spectrumPrintError(state);
2901	}
2902	}
2903
2904	return (state!=spectrumOK);
2905	}
2906
2907	// ----------------------------------------------------------------------------
2908	// check if a list is a spectrum
2909	// check for:
2910	// list has 6 elements
2911	// 1st element is int (mu=Milnor number)
2912	// 2nd element is int (pg=geometrical genus)
2913	// 3rd element is int (n =number of different spectrum numbers)
2914	// 4th element is intvec (num=numerators)
2915	// 5th element is intvec (den=denomiantors)
2916	// 6th element is intvec (mul=multiplicities)
2917	// exactly n numerators
2918	// exactly n denominators
2919	// exactly n multiplicities
2920	// mu>0
2921	// pg>=0
2922	// n>0
2923	// num>0
2924	// den>0
2925	// mul>0
2926	// symmetriy with respect to numberofvariables/2
2927	// monotony
2928	// mu = sum of all multiplicities
2929	// pg = sum of all multiplicities where num/den<=1
2930	// ----------------------------------------------------------------------------
2931
2932	semicState list_is_spectrum( lists l )
2933	{
2934	// -------------------
2935	// check list length
2936	// -------------------
2937
2938	if( l->nr < 5 )
2939	{
2940	return semicListTooShort;
2941	}
2942	else if( l->nr > 5 )
2943	{
2944	return semicListTooLong;
2945	}
2946
2947	// -------------
2948	// check types
2949	// -------------
2950
2951	if( l->m[0].rtyp != INT_CMD )
2952	{
2953	return semicListFirstElementWrongType;
2954	}
2955	else if( l->m[1].rtyp != INT_CMD )
2956	{
2957	return semicListSecondElementWrongType;
2958	}
2959	else if( l->m[2].rtyp != INT_CMD )
2960	{
2961	return semicListThirdElementWrongType;
2962	}
2963	else if( l->m[3].rtyp != INTVEC_CMD )
2964	{
2965	return semicListFourthElementWrongType;
2966	}
2967	else if( l->m[4].rtyp != INTVEC_CMD )
2968	{
2969	return semicListFifthElementWrongType;
2970	}
2971	else if( l->m[5].rtyp != INTVEC_CMD )
2972	{
2973	return semicListSixthElementWrongType;
2974	}
2975
2976	// -------------------------
2977	// check number of entries
2978	// -------------------------
2979
2980	int mu = (int)(long)(l->m[0].Data( ));
2981	int pg = (int)(long)(l->m[1].Data( ));
2982	int n = (int)(long)(l->m[2].Data( ));
2983
2984	if( n <= 0 )
2985	{
2986	return semicListNNegative;
2987	}
2988
2989	intvec num = (intvec)l->m[3].Data( );
2990	intvec den = (intvec)l->m[4].Data( );
2991	intvec mul = (intvec)l->m[5].Data( );
2992
2993	if( n != num->length( ) )
2994	{
2995	return semicListWrongNumberOfNumerators;
2996	}
2997	else if( n != den->length( ) )
2998	{
2999	return semicListWrongNumberOfDenominators;
3000	}
3001	else if( n != mul->length( ) )
3002	{
3003	return semicListWrongNumberOfMultiplicities;
3004	}
3005
3006	// --------
3007	// values
3008	// --------
3009
3010	if( mu <= 0 )
3011	{
3012	return semicListMuNegative;
3013	}
3014	if( pg < 0 )
3015	{
3016	return semicListPgNegative;
3017	}
3018
3019	int i;
3020
3021	for( i=0; i<n; i++ )
3022	{
3023	if( (*num)[i] <= 0 )
3024	{
3025	return semicListNumNegative;
3026	}
3027	if( (*den)[i] <= 0 )
3028	{
3029	return semicListDenNegative;
3030	}
3031	if( (*mul)[i] <= 0 )
3032	{
3033	return semicListMulNegative;
3034	}
3035	}
3036
3037	// ----------------
3038	// check symmetry
3039	// ----------------
3040
3041	int j;
3042
3043	for( i=0, j=n-1; i<=j; i++,j-- )
3044	{
3045	if( (num)[i] != pVariables((den)[i]) - (num)[j] \|\|
3046	(den)[i] != (den)[j] \|\|
3047	(mul)[i] != (mul)[j] )
3048	{
3049	return semicListNotSymmetric;
3050	}
3051	}
3052
3053	// ----------------
3054	// check monotony
3055	// ----------------
3056
3057	for( i=0, j=1; i<n/2; i++,j++ )
3058	{
3059	if( (num)[i](den)[j] >= (num)[j](den)[i] )
3060	{
3061	return semicListNotMonotonous;
3062	}
3063	}
3064
3065	// ---------------------
3066	// check Milnor number
3067	// ---------------------
3068
3069	for( mu=0, i=0; i<n; i++ )
3070	{
3071	mu += (*mul)[i];
3072	}
3073
3074	if( mu != (int)(long)(l->m[0].Data( )) )
3075	{
3076	return semicListMilnorWrong;
3077	}
3078
3079	// -------------------------
3080	// check geometrical genus
3081	// -------------------------
3082
3083	for( pg=0, i=0; i<n; i++ )
3084	{
3085	if( (num)[i]<=(den)[i] )
3086	{
3087	pg += (*mul)[i];
3088	}
3089	}
3090
3091	if( pg != (int)(long)(l->m[1].Data( )) )
3092	{
3093	return semicListPGWrong;
3094	}
3095
3096	return semicOK;
3097	}
3098
3099	// ----------------------------------------------------------------------------
3100	// this procedure is called from the interpreter
3101	// ----------------------------------------------------------------------------
3102	// first = list of spectrum numbers
3103	// second = list of spectrum numbers
3104	// result = sum of the two lists
3105	// ----------------------------------------------------------------------------
3106
3107	BOOLEAN spaddProc( leftv result,leftv first,leftv second )
3108	{
3109	semicState state;
3110
3111	// -----------------
3112	// check arguments
3113	// -----------------
3114
3115	lists l1 = (lists)first->Data( );
3116	lists l2 = (lists)second->Data( );
3117
3118	if( (state=list_is_spectrum( l1 )) != semicOK )
3119	{
3120	WerrorS( "first argument is not a spectrum:" );
3121	list_error( state );
3122	}
3123	else if( (state=list_is_spectrum( l2 )) != semicOK )
3124	{
3125	WerrorS( "second argument is not a spectrum:" );
3126	list_error( state );
3127	}
3128	else
3129	{
3130	spectrum s1( l1 );
3131	spectrum s2( l2 );
3132	spectrum sum( s1+s2 );
3133
3134	result->rtyp = LIST_CMD;
3135	result->data = (char*)(sum.thelist( ));
3136	}
3137
3138	return (state!=semicOK);
3139	}
3140
3141	// ----------------------------------------------------------------------------
3142	// this procedure is called from the interpreter
3143	// ----------------------------------------------------------------------------
3144	// first = list of spectrum numbers
3145	// second = integer
3146	// result = the multiple of the first list by the second factor
3147	// ----------------------------------------------------------------------------
3148
3149	BOOLEAN spmulProc( leftv result,leftv first,leftv second )
3150	{
3151	semicState state;
3152
3153	// -----------------
3154	// check arguments
3155	// -----------------
3156
3157	lists l = (lists)first->Data( );
3158	int k = (int)(long)second->Data( );
3159
3160	if( (state=list_is_spectrum( l ))!=semicOK )
3161	{
3162	WerrorS( "first argument is not a spectrum" );
3163	list_error( state );
3164	}
3165	else if( k < 0 )
3166	{
3167	WerrorS( "second argument should be positive" );
3168	state = semicMulNegative;
3169	}
3170	else
3171	{
3172	spectrum s( l );
3173	spectrum product( k*s );
3174
3175	result->rtyp = LIST_CMD;
3176	result->data = (char*)product.thelist( );
3177	}
3178
3179	return (state!=semicOK);
3180	}
3181
3182	// ----------------------------------------------------------------------------
3183	// this procedure is called from the interpreter
3184	// ----------------------------------------------------------------------------
3185	// first = list of spectrum numbers
3186	// second = list of spectrum numbers
3187	// result = semicontinuity index
3188	// ----------------------------------------------------------------------------
3189
3190	BOOLEAN semicProc3 ( leftv res,leftv u,leftv v,leftv w )
3191	{
3192	semicState state;
3193	BOOLEAN qh=(((int)(long)w->Data())==1);
3194
3195	// -----------------
3196	// check arguments
3197	// -----------------
3198
3199	lists l1 = (lists)u->Data( );
3200	lists l2 = (lists)v->Data( );
3201
3202	if( (state=list_is_spectrum( l1 ))!=semicOK )
3203	{
3204	WerrorS( "first argument is not a spectrum" );
3205	list_error( state );
3206	}
3207	else if( (state=list_is_spectrum( l2 ))!=semicOK )
3208	{
3209	WerrorS( "second argument is not a spectrum" );
3210	list_error( state );
3211	}
3212	else
3213	{
3214	spectrum s1( l1 );
3215	spectrum s2( l2 );
3216
3217	res->rtyp = INT_CMD;
3218	if (qh)
3219	res->data = (void*)(s1.mult_spectrumh( s2 ));
3220	else
3221	res->data = (void*)(s1.mult_spectrum( s2 ));
3222	}
3223
3224	// -----------------
3225	// check status
3226	// -----------------
3227
3228	return (state!=semicOK);
3229	}
3230	BOOLEAN semicProc ( leftv res,leftv u,leftv v )
3231	{
3232	sleftv tmp;
3233	memset(&tmp,0,sizeof(tmp));
3234	tmp.rtyp=INT_CMD;
3235	/* tmp.data = (void )0; -- done by memset /
3236
3237	return semicProc3(res,u,v,&tmp);
3238	}
3239	// from splist.cc
3240	// ----------------------------------------------------------------------------
3241	// Compute the spectrum of a spectrumPolyList
3242	// ----------------------------------------------------------------------------
3243
3244	spectrumState spectrumPolyList::spectrum( lists *L,int fast )
3245	{
3246	spectrumPolyNode **node = &root;
3247	spectrumPolyNode *search;
3248
3249	poly f,tmp;
3250	int found,cmp;
3251
3252	Rational smax( ( fast==0 ? 0 : pVariables ),
3253	( fast==2 ? 2 : 1 ) );
3254
3255	Rational weight_prev( 0,1 );
3256
3257	int mu = 0; // the milnor number
3258	int pg = 0; // the geometrical genus
3259	int n = 0; // number of different spectral numbers
3260	int z = 0; // number of spectral number equal to smax
3261
3262	int k = 0;
3263
3264	while( (node)!=(spectrumPolyNode)NULL &&
3265	( fast==0 \|\| (*node)->weight<=smax ) )
3266	{
3267	// ---------------------------------------
3268	// determine the first normal form which
3269	// contains the monomial node->mon
3270	// ---------------------------------------
3271
3272	found = FALSE;
3273	search = *node;
3274
3275	while( search!=(spectrumPolyNode*)NULL && found==FALSE )
3276	{
3277	if( search->nf!=(poly)NULL )
3278	{
3279	f = search->nf;
3280
3281	do
3282	{
3283	// --------------------------------
3284	// look for (*node)->mon in f
3285	// --------------------------------
3286
3287	cmp = pCmp( (*node)->mon,f );
3288
3289	if( cmp<0 )
3290	{
3291	f = pNext( f );
3292	}
3293	else if( cmp==0 )
3294	{
3295	// -----------------------------
3296	// we have found a normal form
3297	// -----------------------------
3298
3299	found = TRUE;
3300
3301	// normalize coefficient
3302
3303	number inv = nInvers( pGetCoeff( f ) );
3304	pMult_nn( search->nf,inv );
3305	nDelete( &inv );
3306
3307	// exchange normal forms
3308
3309	tmp = (*node)->nf;
3310	(*node)->nf = search->nf;
3311	search->nf = tmp;
3312	}
3313	}
3314	while( cmp<0 && f!=(poly)NULL );
3315	}
3316	search = search->next;
3317	}
3318
3319	if( found==FALSE )
3320	{
3321	// ------------------------------------------------
3322	// the weight of node->mon is a spectrum number
3323	// ------------------------------------------------
3324
3325	mu++;
3326
3327	if( (*node)->weight<=(Rational)1 ) pg++;
3328	if( (*node)->weight==smax ) z++;
3329	if( (*node)->weight>weight_prev ) n++;
3330
3331	weight_prev = (*node)->weight;
3332	node = &((*node)->next);
3333	}
3334	else
3335	{
3336	// -----------------------------------------------
3337	// determine all other normal form which contain
3338	// the monomial node->mon
3339	// replace for node->mon its normal form
3340	// -----------------------------------------------
3341
3342	while( search!=(spectrumPolyNode*)NULL )
3343	{
3344	if( search->nf!=(poly)NULL )
3345	{
3346	f = search->nf;
3347
3348	do
3349	{
3350	// --------------------------------
3351	// look for (*node)->mon in f
3352	// --------------------------------
3353
3354	cmp = pCmp( (*node)->mon,f );
3355
3356	if( cmp<0 )
3357	{
3358	f = pNext( f );
3359	}
3360	else if( cmp==0 )
3361	{
3362	search->nf = pSub( search->nf,
3363	ppMult_nn( (*node)->nf,pGetCoeff( f ) ) );
3364	pNorm( search->nf );
3365	}
3366	}
3367	while( cmp<0 && f!=(poly)NULL );
3368	}
3369	search = search->next;
3370	}
3371	delete_node( node );
3372	}
3373
3374	}
3375
3376	// --------------------------------------------------------
3377	// fast computation exploits the symmetry of the spectrum
3378	// --------------------------------------------------------
3379
3380	if( fast==2 )
3381	{
3382	mu = 2*mu - z;
3383	n = ( z > 0 ? 2n - 1 : 2n );
3384	}
3385
3386	// --------------------------------------------------------
3387	// compute the spectrum numbers with their multiplicities
3388	// --------------------------------------------------------
3389
3390	intvec *nom = new intvec( n );
3391	intvec *den = new intvec( n );
3392	intvec *mult = new intvec( n );
3393
3394	int count = 0;
3395	int multiplicity = 1;
3396
3397	for( search=root; search!=(spectrumPolyNode*)NULL &&
3398	( fast==0 \|\| search->weight<=smax );
3399	search=search->next )
3400	{
3401	if( search->next==(spectrumPolyNode*)NULL \|\|
3402	search->weight<search->next->weight )
3403	{
3404	(*nom) [count] = search->weight.get_num_si( );
3405	(*den) [count] = search->weight.get_den_si( );
3406	(*mult)[count] = multiplicity;
3407
3408	multiplicity=1;
3409	count++;
3410	}
3411	else
3412	{
3413	multiplicity++;
3414	}
3415	}
3416
3417	// --------------------------------------------------------
3418	// fast computation exploits the symmetry of the spectrum
3419	// --------------------------------------------------------
3420
3421	if( fast==2 )
3422	{
3423	int n1,n2;
3424	for( n1=0, n2=n-1; n1<n2; n1++, n2-- )
3425	{
3426	(nom) [n2] = pVariables(den)[n1]-(nom)[n1];
3427	(den) [n2] = (den)[n1];
3428	(mult)[n2] = (mult)[n1];
3429	}
3430	}
3431
3432	// -----------------------------------
3433	// test if the spectrum is symmetric
3434	// -----------------------------------
3435
3436	if( fast==0 \|\| fast==1 )
3437	{
3438	int symmetric=TRUE;
3439
3440	for( int n1=0, n2=n-1 ; n1<n2 && symmetric==TRUE; n1++, n2-- )
3441	{
3442	if( (mult)[n1]!=(mult)[n2] \|\|
3443	(den) [n1]!= (den)[n2] \|\|
3444	(nom)[n1]+(nom)[n2]!=pVariables(den) [n1] )
3445	{
3446	symmetric = FALSE;
3447	}
3448	}
3449
3450	if( symmetric==FALSE )
3451	{
3452	// ---------------------------------------------
3453	// the spectrum is not symmetric => degenerate
3454	// principal part
3455	// ---------------------------------------------
3456
3457	*L = (lists)omAllocBin( slists_bin);
3458	(*L)->Init( 1 );
3459	(*L)->m[0].rtyp = INT_CMD; // milnor number
3460	(L)->m[0].data = (void)mu;
3461
3462	return spectrumDegenerate;
3463	}
3464	}
3465
3466	*L = (lists)omAllocBin( slists_bin);
3467
3468	(*L)->Init( 6 );
3469
3470	(*L)->m[0].rtyp = INT_CMD; // milnor number
3471	(*L)->m[1].rtyp = INT_CMD; // geometrical genus
3472	(*L)->m[2].rtyp = INT_CMD; // number of spectrum values
3473	(*L)->m[3].rtyp = INTVEC_CMD; // nominators
3474	(*L)->m[4].rtyp = INTVEC_CMD; // denomiantors
3475	(*L)->m[5].rtyp = INTVEC_CMD; // multiplicities
3476
3477	(L)->m[0].data = (void)mu;
3478	(L)->m[1].data = (void)pg;
3479	(L)->m[2].data = (void)n;
3480	(L)->m[3].data = (void)nom;
3481	(L)->m[4].data = (void)den;
3482	(L)->m[5].data = (void)mult;
3483
3484	return spectrumOK;
3485	}
3486
3487	#endif
3488
3489	//from mpr_inout.cc
3490	extern void nPrint(number n);
3491
3492	BOOLEAN loNewtonP( leftv res, leftv arg1 )
3493	{
3494	res->data= (void*)loNewtonPolytope( (ideal)arg1->Data() );
3495	return FALSE;
3496	}
3497
3498	BOOLEAN loSimplex( leftv res, leftv args )
3499	{
3500	if ( !(rField_is_long_R()) )
3501	{
3502	WerrorS("Ground field not implemented!");
3503	return TRUE;
3504	}
3505
3506	simplex * LP;
3507	matrix m;
3508
3509	leftv v= args;
3510	if ( v->Typ() != MATRIX_CMD ) // 1: matrix
3511	return TRUE;
3512	else
3513	m= (matrix)(v->CopyD());
3514
3515	LP = new simplex(MATROWS(m),MATCOLS(m));
3516	LP->mapFromMatrix(m);
3517
3518	v= v->next;
3519	if ( v->Typ() != INT_CMD ) // 2: m = number of constraints
3520	return TRUE;
3521	else
3522	LP->m= (int)(long)(v->Data());
3523
3524	v= v->next;
3525	if ( v->Typ() != INT_CMD ) // 3: n = number of variables
3526	return TRUE;
3527	else
3528	LP->n= (int)(long)(v->Data());
3529
3530	v= v->next;
3531	if ( v->Typ() != INT_CMD ) // 4: m1 = number of <= constraints
3532	return TRUE;
3533	else
3534	LP->m1= (int)(long)(v->Data());
3535
3536	v= v->next;
3537	if ( v->Typ() != INT_CMD ) // 5: m2 = number of >= constraints
3538	return TRUE;
3539	else
3540	LP->m2= (int)(long)(v->Data());
3541
3542	v= v->next;
3543	if ( v->Typ() != INT_CMD ) // 6: m3 = number of == constraints
3544	return TRUE;
3545	else
3546	LP->m3= (int)(long)(v->Data());
3547
3548	#ifdef mprDEBUG_PROT
3549	Print("m (constraints) %d\n",LP->m);
3550	Print("n (columns) %d\n",LP->n);
3551	Print("m1 (<=) %d\n",LP->m1);
3552	Print("m2 (>=) %d\n",LP->m2);
3553	Print("m3 (==) %d\n",LP->m3);
3554	#endif
3555
3556	LP->compute();
3557
3558	lists lres= (lists)omAlloc( sizeof(slists) );
3559	lres->Init( 6 );
3560
3561	lres->m[0].rtyp= MATRIX_CMD; // output matrix
3562	lres->m[0].data=(void*)LP->mapToMatrix(m);
3563
3564	lres->m[1].rtyp= INT_CMD; // found a solution?
3565	lres->m[1].data=(void*)LP->icase;
3566
3567	lres->m[2].rtyp= INTVEC_CMD;
3568	lres->m[2].data=(void*)LP->posvToIV();
3569
3570	lres->m[3].rtyp= INTVEC_CMD;
3571	lres->m[3].data=(void*)LP->zrovToIV();
3572
3573	lres->m[4].rtyp= INT_CMD;
3574	lres->m[4].data=(void*)LP->m;
3575
3576	lres->m[5].rtyp= INT_CMD;
3577	lres->m[5].data=(void*)LP->n;
3578
3579	res->data= (void*)lres;
3580
3581	return FALSE;
3582	}
3583
3584	BOOLEAN nuMPResMat( leftv res, leftv arg1, leftv arg2 )
3585	{
3586	ideal gls = (ideal)(arg1->Data());
3587	int imtype= (int)(long)arg2->Data();
3588
3589	uResultant::resMatType mtype= determineMType( imtype );
3590
3591	// check input ideal ( = polynomial system )
3592	if ( mprIdealCheck( gls, arg1->Name(), mtype, true ) != mprOk )
3593	{
3594	return TRUE;
3595	}
3596
3597	uResultant *resMat= new uResultant( gls, mtype, false );
3598
3599	res->rtyp = MODUL_CMD;
3600	res->data= (void*)resMat->accessResMat()->getMatrix();
3601
3602	delete resMat;
3603
3604	return FALSE;
3605	}
3606
3607	BOOLEAN nuLagSolve( leftv res, leftv arg1, leftv arg2, leftv arg3 )
3608	{
3609
3610	poly gls;
3611	gls= (poly)(arg1->Data());
3612	int howclean= (int)(long)arg3->Data();
3613
3614	if ( !(rField_is_R() \|\|
3615	rField_is_Q() \|\|
3616	rField_is_long_R() \|\|
3617	rField_is_long_C()) )
3618	{
3619	WerrorS("Ground field not implemented!");
3620	return TRUE;
3621	}
3622
3623	if ( !(rField_is_R()\|\|rField_is_long_R()\|\|rField_is_long_C()) )
3624	{
3625	unsigned long int ii = (unsigned long int)arg2->Data();
3626	setGMPFloatDigits( ii, ii );
3627	}
3628
3629	if ( gls == NULL \|\| pIsConstant( gls ) )
3630	{
3631	WerrorS("Input polynomial is constant!");
3632	return TRUE;
3633	}
3634
3635	int ldummy;
3636	int deg= pLDeg( gls, &ldummy, currRing );
3637	// int deg= pDeg( gls );
3638	int len= pLength( gls );
3639	int i,vpos;
3640	poly piter;
3641	lists elist;
3642	lists rlist;
3643
3644	elist= (lists)omAlloc( sizeof(slists) );
3645	elist->Init( 0 );
3646
3647	if ( pVariables > 1 )
3648	{
3649	piter= gls;
3650	for ( i= 1; i <= pVariables; i++ )
3651	if ( pGetExp( piter, i ) )
3652	{
3653	vpos= i;
3654	break;
3655	}
3656	while ( piter )
3657	{
3658	for ( i= 1; i <= pVariables; i++ )
3659	if ( (vpos != i) && (pGetExp( piter, i ) != 0) )
3660	{
3661	WerrorS("The input polynomial must be univariate!");
3662	return TRUE;
3663	}
3664	pIter( piter );
3665	}
3666	}
3667
3668	rootContainer * roots= new rootContainer();
3669	number * pcoeffs= (number )omAlloc( (deg+1) sizeof( number ) );
3670	piter= gls;
3671	for ( i= deg; i >= 0; i-- )
3672	{
3673	//if ( piter ) Print("deg %d, pDeg(piter) %d\n",i,pTotaldegree(piter));
3674	if ( piter && pTotaldegree(piter) == i )
3675	{
3676	pcoeffs[i]= nCopy( pGetCoeff( piter ) );
3677	//nPrint( pcoeffs[i] );PrintS(" ");
3678	pIter( piter );
3679	}
3680	else
3681	{
3682	pcoeffs[i]= nInit(0);
3683	}
3684	}
3685
3686	#ifdef mprDEBUG_PROT
3687	for (i=deg; i >= 0; i--)
3688	{
3689	nPrint( pcoeffs[i] );PrintS(" ");
3690	}
3691	PrintLn();
3692	#endif
3693
3694	roots->fillContainer( pcoeffs, NULL, 1, deg, rootContainer::onepoly, 1 );
3695	roots->solver( howclean );
3696
3697	int elem= roots->getAnzRoots();
3698	char *out;
3699	char *dummy;
3700	int j;
3701
3702	rlist= (lists)omAlloc( sizeof(slists) );
3703	rlist->Init( elem );
3704
3705	if (rField_is_long_C())
3706	{
3707	for ( j= 0; j < elem; j++ )
3708	{
3709	rlist->m[j].rtyp=NUMBER_CMD;
3710	rlist->m[j].data=(void *)nCopy((number)(roots->getRoot(j)));
3711	//rlist->m[j].data=(void *)(number)(roots->getRoot(j));
3712	}
3713	}
3714	else
3715	{
3716	for ( j= 0; j < elem; j++ )
3717	{
3718	dummy = complexToStr( (*roots)[j], gmp_output_digits );
3719	rlist->m[j].rtyp=STRING_CMD;
3720	rlist->m[j].data=(void *)dummy;
3721	}
3722	}
3723
3724	elist->Clean();
3725	//omFreeSize( (ADDRESS) elist, sizeof(slists) );
3726
3727	// this is (via fillContainer) the same data as in root
3728	//for ( i= deg; i >= 0; i-- ) nDelete( &pcoeffs[i] );
3729	//omFreeSize( (ADDRESS) pcoeffs, (deg+1) * sizeof( number ) );
3730
3731	delete roots;
3732
3733	res->rtyp= LIST_CMD;
3734	res->data= (void*)rlist;
3735
3736	return FALSE;
3737	}
3738
3739	BOOLEAN nuVanderSys( leftv res, leftv arg1, leftv arg2, leftv arg3)
3740	{
3741	int i;
3742	ideal p,w;
3743	p= (ideal)arg1->Data();
3744	w= (ideal)arg2->Data();
3745
3746	// w[0] = f(p^0)
3747	// w[1] = f(p^1)
3748	// ...
3749	// p can be a vector of numbers (multivariate polynom)
3750	// or one number (univariate polynom)
3751	// tdg = deg(f)
3752
3753	int n= IDELEMS( p );
3754	int m= IDELEMS( w );
3755	int tdg= (int)(long)arg3->Data();
3756
3757	res->data= (void*)NULL;
3758
3759	// check the input
3760	if ( tdg < 1 )
3761	{
3762	WerrorS("Last input parameter must be > 0!");
3763	return TRUE;
3764	}
3765	if ( n != pVariables )
3766	{
3767	Werror("Size of first input ideal must be equal to %d!",pVariables);
3768	return TRUE;
3769	}
3770	if ( m != (int)pow((double)tdg+1,(double)n) )
3771	{
3772	Werror("Size of second input ideal must be equal to %d!",
3773	(int)pow((double)tdg+1,(double)n));
3774	return TRUE;
3775	}
3776	if ( !(rField_is_Q() /* \|\|
3777	rField_is_R() \|\| rField_is_long_R() \|\|
3778	rField_is_long_C()*/ ) )
3779	{
3780	WerrorS("Ground field not implemented!");
3781	return TRUE;
3782	}
3783
3784	number tmp;
3785	number pevpoint= (number )omAlloc( n * sizeof( number ) );
3786	for ( i= 0; i < n; i++ )
3787	{
3788	pevpoint[i]=nInit(0);
3789	if ( (p->m)[i] )
3790	{
3791	tmp = pGetCoeff( (p->m)[i] );
3792	if ( nIsZero(tmp) \|\| nIsOne(tmp) \|\| nIsMOne(tmp) )
3793	{
3794	omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
3795	WerrorS("Elements of first input ideal must not be equal to -1, 0, 1!");
3796	return TRUE;
3797	}
3798	} else tmp= NULL;
3799	if ( !nIsZero(tmp) )
3800	{
3801	if ( !pIsConstant((p->m)[i]))
3802	{
3803	omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
3804	WerrorS("Elements of first input ideal must be numbers!");
3805	return TRUE;
3806	}
3807	pevpoint[i]= nCopy( tmp );
3808	}
3809	}
3810
3811	number wresults= (number )omAlloc( m * sizeof( number ) );
3812	for ( i= 0; i < m; i++ )
3813	{
3814	wresults[i]= nInit(0);
3815	if ( (w->m)[i] && !nIsZero(pGetCoeff((w->m)[i])) )
3816	{
3817	if ( !pIsConstant((w->m)[i]))
3818	{
3819	omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
3820	omFreeSize( (ADDRESS)wresults, m * sizeof( number ) );
3821	WerrorS("Elements of second input ideal must be numbers!");
3822	return TRUE;
3823	}
3824	wresults[i]= nCopy(pGetCoeff((w->m)[i]));
3825	}
3826	}
3827
3828	vandermonde vm( m, n, tdg, pevpoint, FALSE );
3829	number *ncpoly= vm.interpolateDense( wresults );
3830	// do not free ncpoly[]!!
3831	poly rpoly= vm.numvec2poly( ncpoly );
3832
3833	omFreeSize( (ADDRESS)pevpoint, n * sizeof( number ) );
3834	omFreeSize( (ADDRESS)wresults, m * sizeof( number ) );
3835
3836	res->data= (void*)rpoly;
3837	return FALSE;
3838	}
3839
3840	BOOLEAN nuUResSolve( leftv res, leftv args )
3841	{
3842	leftv v= args;
3843
3844	ideal gls;
3845	int imtype;
3846	int howclean;
3847
3848	// get ideal
3849	if ( v->Typ() != IDEAL_CMD )
3850	return TRUE;
3851	else gls= (ideal)(v->Data());
3852	v= v->next;
3853
3854	// get resultant matrix type to use (0,1)
3855	if ( v->Typ() != INT_CMD )
3856	return TRUE;
3857	else imtype= (int)(long)v->Data();
3858	v= v->next;
3859
3860	if (imtype==0)
3861	{
3862	ideal test_id=idInit(1,1);
3863	int j;
3864	for(j=IDELEMS(gls)-1;j>=0;j--)
3865	{
3866	if (gls->m[j]!=NULL)
3867	{
3868	test_id->m[0]=gls->m[j];
3869	intvec *dummy_w=idQHomWeight(test_id);
3870	if (dummy_w!=NULL)
3871	{
3872	WerrorS("Newton polytope not of expected dimension");
3873	delete dummy_w;
3874	return TRUE;
3875	}
3876	}
3877	}
3878	}
3879
3880	// get and set precision in digits ( > 0 )
3881	if ( v->Typ() != INT_CMD )
3882	return TRUE;
3883	else if ( !(rField_is_R()\|\|rField_is_long_R()\|\|rField_is_long_C()) )
3884	{
3885	unsigned long int ii=(unsigned long int)v->Data();
3886	setGMPFloatDigits( ii, ii );
3887	}
3888	v= v->next;
3889
3890	// get interpolation steps (0,1,2)
3891	if ( v->Typ() != INT_CMD )
3892	return TRUE;
3893	else howclean= (int)(long)v->Data();
3894
3895	uResultant::resMatType mtype= determineMType( imtype );
3896	int i,c,count;
3897	lists listofroots= NULL;
3898	lists emptylist;
3899	number smv= NULL;
3900	BOOLEAN interpolate_det= (mtype==uResultant::denseResMat)?TRUE:FALSE;
3901
3902	//emptylist= (lists)omAlloc( sizeof(slists) );
3903	//emptylist->Init( 0 );
3904
3905	//res->rtyp = LIST_CMD;
3906	//res->data= (void *)emptylist;
3907
3908	// check input ideal ( = polynomial system )
3909	if ( mprIdealCheck( gls, args->Name(), mtype ) != mprOk )
3910	{
3911	return TRUE;
3912	}
3913
3914	uResultant * ures;
3915	rootContainer ** iproots;
3916	rootContainer ** muiproots;
3917	rootArranger * arranger;
3918
3919	// main task 1: setup of resultant matrix
3920	ures= new uResultant( gls, mtype );
3921	if ( ures->accessResMat()->initState() != resMatrixBase::ready )
3922	{
3923	WerrorS("Error occurred during matrix setup!");
3924	return TRUE;
3925	}
3926
3927	// if dense resultant, check if minor nonsingular
3928	if ( mtype == uResultant::denseResMat )
3929	{
3930	smv= ures->accessResMat()->getSubDet();
3931	#ifdef mprDEBUG_PROT
3932	PrintS("// Determinant of submatrix: ");nPrint(smv);PrintLn();
3933	#endif
3934	if ( nIsZero(smv) )
3935	{
3936	WerrorS("Unsuitable input ideal: Minor of resultant matrix is singular!");
3937	return TRUE;
3938	}
3939	}
3940
3941	// main task 2: Interpolate specialized resultant polynomials
3942	if ( interpolate_det )
3943	iproots= ures->interpolateDenseSP( false, smv );
3944	else
3945	iproots= ures->specializeInU( false, smv );
3946
3947	// main task 3: Interpolate specialized resultant polynomials
3948	if ( interpolate_det )
3949	muiproots= ures->interpolateDenseSP( true, smv );
3950	else
3951	muiproots= ures->specializeInU( true, smv );
3952
3953	#ifdef mprDEBUG_PROT
3954	c= iproots[0]->getAnzElems();
3955	for (i=0; i < c; i++) pWrite(iproots[i]->getPoly());
3956	c= muiproots[0]->getAnzElems();
3957	for (i=0; i < c; i++) pWrite(muiproots[i]->getPoly());
3958	#endif
3959
3960	// main task 4: Compute roots of specialized polys and match them up
3961	arranger= new rootArranger( iproots, muiproots, howclean );
3962	arranger->solve_all();
3963
3964	// get list of roots
3965	if ( arranger->success() )
3966	{
3967	arranger->arrange();
3968	listofroots= arranger->listOfRoots( gmp_output_digits );
3969	}
3970	else
3971	{
3972	WerrorS("Solver was unable to find any roots!");
3973	return TRUE;
3974	}
3975
3976	// free everything
3977	count= iproots[0]->getAnzElems();
3978	for (i=0; i < count; i++) delete iproots[i];
3979	omFreeSize( (ADDRESS) iproots, count * sizeof(rootContainer*) );
3980	count= muiproots[0]->getAnzElems();
3981	for (i=0; i < count; i++) delete muiproots[i];
3982	omFreeSize( (ADDRESS) muiproots, count * sizeof(rootContainer*) );
3983
3984	delete ures;
3985	delete arranger;
3986	nDelete( &smv );
3987
3988	res->data= (void *)listofroots;
3989
3990	//emptylist->Clean();
3991	// omFreeSize( (ADDRESS) emptylist, sizeof(slists) );
3992
3993	return FALSE;
3994	}
3995
3996	// from mpr_numeric.cc
3997	lists rootArranger::listOfRoots( const unsigned int oprec )
3998	{
3999	int i,j,tr;
4000	int count= roots[0]->getAnzRoots(); // number of roots
4001	int elem= roots[0]->getAnzElems(); // number of koordinates per root
4002
4003	lists listofroots= (lists)omAlloc( sizeof(slists) ); // must be done this way!
4004
4005	if ( found_roots )
4006	{
4007	listofroots->Init( count );
4008
4009	for (i=0; i < count; i++)
4010	{
4011	lists onepoint= (lists)omAlloc(sizeof(slists)); // must be done this way!
4012	onepoint->Init(elem);
4013	for ( j= 0; j < elem; j++ )
4014	{
4015	if ( !rField_is_long_C() )
4016	{
4017	onepoint->m[j].rtyp=STRING_CMD;
4018	onepoint->m[j].data=(void )complexToStr((roots[j])[i],oprec);
4019	}
4020	else
4021	{
4022	onepoint->m[j].rtyp=NUMBER_CMD;
4023	onepoint->m[j].data=(void *)nCopy((number)(roots[j]->getRoot(i)));
4024	}
4025	onepoint->m[j].next= NULL;
4026	onepoint->m[j].name= NULL;
4027	}
4028	listofroots->m[i].rtyp=LIST_CMD;
4029	listofroots->m[i].data=(void *)onepoint;
4030	listofroots->m[j].next= NULL;
4031	listofroots->m[j].name= NULL;
4032	}
4033
4034	}
4035	else
4036	{
4037	listofroots->Init( 0 );
4038	}
4039
4040	return listofroots;
4041	}
4042
4043	#ifdef PDEBUG
4044
4045	#if (OM_TRACK > 2) && defined(OM_TRACK_CUSTOM)
4046
4047	void p_SetRingOfPoly(poly p, ring r)
4048	{
4049	while (p != NULL)
4050	{
4051	p_SetRingOfLm(p, r);
4052	pIter(p);
4053	}
4054	}
4055
4056	void p_SetRingOfIdeal(ideal id, ring r)
4057	{
4058	if (id == NULL) return;
4059
4060	int i, n = id->ncols*id->nrows;
4061
4062	for (i=0; i<n; i++)
4063	{
4064	p_SetRingOfPoly(id->m[i], r);
4065	}
4066	}
4067
4068	void p_SetRingOfList(lists L, ring r)
4069	{
4070	int i;
4071	for (i=0; i<L->nr; i++)
4072	{
4073	p_SetRingOfLeftv(&(L->m[i]), r);
4074	}
4075	}
4076
4077	void p_SetRingOfCommand(command cmd, ring r)
4078	{
4079	if (cmd->op == PROC_CMD && cmd->argc == 2)
4080	p_SetRingOfLeftv(&(cmd->arg2), r);
4081	else if (cmd->argc > 0)
4082	{
4083	p_SetRingOfLeftv(&(cmd->arg1), r);
4084	if (cmd->argc > 1)
4085	{
4086	p_SetRingOfLeftv(&(cmd->arg2), r);
4087	if (cmd->argc > 2)
4088	p_SetRingOfLeftv(&(cmd->arg3), r);
4089	}
4090	}
4091	}
4092
4093	void p_SetRingOfLeftv(leftv l, ring r)
4094	{
4095	while (l != NULL)
4096	{
4097	switch(l->rtyp)
4098	{
4099	case POLY_CMD:
4100	case VECTOR_CMD:
4101	p_SetRingOfPoly((poly) l->data, r);
4102	break;
4103
4104	case IDEAL_CMD:
4105	case MODUL_CMD:
4106	case MATRIX_CMD:
4107	case MAP_CMD:
4108	p_SetRingOfIdeal((ideal) l->data, r);
4109	break;
4110
4111	case LIST_CMD:
4112	p_SetRingOfList((lists) l->data, r);
4113	break;
4114
4115	case COMMAND:
4116	p_SetRingOfCommand((command)l->data, r);
4117	default:
4118	break;
4119	}
4120	l = l->next;
4121	}
4122	}
4123	#endif // (OM_TRACK > 2) && defined(OM_TRACK_CUSTOM)
4124
4125	#endif // PDEBUG
4126
4127	// from ring.cc
4128	void rSetHdl(idhdl h)
4129	{
4130	int i;
4131	ring rg = NULL;
4132	if (h!=NULL)
4133	{
4134	// Print(" new ring:%s (l:%d)\n",IDID(h),IDLEV(h));
4135	rg = IDRING(h);
4136	omCheckAddrSize((ADDRESS)h,sizeof(idrec));
4137	if (IDID(h)) // OB: ????
4138	omCheckAddr((ADDRESS)IDID(h));
4139	rTest(rg);
4140	}
4141
4142	// clean up history
4143	if (sLastPrinted.RingDependend())
4144	{
4145	sLastPrinted.CleanUp();
4146	memset(&sLastPrinted,0,sizeof(sleftv));
4147	}
4148
4149	/------------ change the global ring -----------------------/
4150	rChangeCurrRing(rg);
4151	currRingHdl = h;
4152	}
4153
4154	BOOLEAN rSleftvOrdering2Ordering(sleftv *ord, ring R)
4155	{
4156	int last = 0, o=0, n = 1, i=0, typ = 1, j;
4157	sleftv *sl = ord;
4158
4159	// determine nBlocks
4160	while (sl!=NULL)
4161	{
4162	intvec iv = (intvec )(sl->data);
4163	if (((iv)[1]==ringorder_c)\|\|((iv)[1]==ringorder_C)) i++;
4164	else if ((*iv)[1]==ringorder_L)
4165	{
4166	R->bitmask=(*iv)[2];
4167	n--;
4168	}
4169	else if (((*iv)[1]!=ringorder_a)
4170	&& ((*iv)[1]!=ringorder_a64)) o++;
4171	n++;
4172	sl=sl->next;
4173	}
4174	// check whether at least one real ordering
4175	if (o==0)
4176	{
4177	WerrorS("invalid combination of orderings");
4178	return TRUE;
4179	}
4180	// if no c/C ordering is given, increment n
4181	if (i==0) n++;
4182	else if (i != 1)
4183	{
4184	// throw error if more than one is given
4185	WerrorS("more than one ordering c/C specified");
4186	return TRUE;
4187	}
4188
4189	// initialize fields of R
4190	R->order=(int )omAlloc0(nsizeof(int));
4191	R->block0=(int )omAlloc0(nsizeof(int));
4192	R->block1=(int )omAlloc0(nsizeof(int));
4193	R->wvhdl=(int*)omAlloc0(nsizeof(int_ptr));
4194
4195	// init order, so that rBlocks works correctly
4196	for (j=0; j < n-1; j++)
4197	R->order[j] = (int) ringorder_unspec;
4198	// set last _C order, if no c/C order was given
4199	if (i == 0) R->order[n-2] = ringorder_C;
4200
4201	/* init orders */
4202	sl=ord;
4203	n=-1;
4204	while (sl!=NULL)
4205	{
4206	intvec *iv;
4207	iv = (intvec *)(sl->data);
4208	if ((*iv)[1]!=ringorder_L)
4209	{
4210	n++;
4211
4212	/* the format of an ordering:
4213	* iv[0]: factor
4214	* iv[1]: ordering
4215	* iv[2..end]: weights
4216	*/
4217	R->order[n] = (*iv)[1];
4218	switch ((*iv)[1])
4219	{
4220	case ringorder_ws:
4221	case ringorder_Ws:
4222	typ=-1;
4223	case ringorder_wp:
4224	case ringorder_Wp:
4225	R->wvhdl[n]=(int)omAlloc((iv->length()-1)sizeof(int));
4226	for (i=2; i<iv->length(); i++)
4227	R->wvhdl[n][i-2] = (*iv)[i];
4228	R->block0[n] = last+1;
4229	last += iv->length()-2;
4230	R->block1[n] = last;
4231	break;
4232	case ringorder_ls:
4233	case ringorder_ds:
4234	case ringorder_Ds:
4235	typ=-1;
4236	case ringorder_lp:
4237	case ringorder_dp:
4238	case ringorder_Dp:
4239	case ringorder_rp:
4240	R->block0[n] = last+1;
4241	if (iv->length() == 3) last+=(*iv)[2];
4242	else last += (*iv)[0];
4243	R->block1[n] = last;
4244	if (rCheckIV(iv)) return TRUE;
4245	break;
4246	case ringorder_S:
4247	case ringorder_c:
4248	case ringorder_C:
4249	if (rCheckIV(iv)) return TRUE;
4250	break;
4251	case ringorder_aa:
4252	case ringorder_a:
4253	R->block0[n] = last+1;
4254	R->block1[n] = si_min(last+iv->length()-2 , R->N);
4255	R->wvhdl[n] = (int)omAlloc((iv->length()-1)sizeof(int));
4256	for (i=2; i<iv->length(); i++)
4257	{
4258	R->wvhdl[n][i-2]=(*iv)[i];
4259	if ((*iv)[i]<0) typ=-1;
4260	}
4261	break;
4262	case ringorder_a64:
4263	{
4264	R->block0[n] = last+1;
4265	R->block1[n] = si_min(last+iv->length()-2 , R->N);
4266	R->wvhdl[n] = (int)omAlloc((iv->length()-1)sizeof(int64));
4267	int64 w=(int64 )R->wvhdl[n];
4268	for (i=2; i<iv->length(); i++)
4269	{
4270	w[i-2]=(*iv)[i];
4271	if ((*iv)[i]<0) typ=-1;
4272	}
4273	break;
4274	}
4275	case ringorder_M:
4276	{
4277	int Mtyp=rTypeOfMatrixOrder(iv);
4278	if (Mtyp==0) return TRUE;
4279	if (Mtyp==-1) typ = -1;
4280
4281	R->wvhdl[n] =( int )omAlloc((iv->length()-1)sizeof(int));
4282	for (i=2; i<iv->length();i++)
4283	R->wvhdl[n][i-2]=(*iv)[i];
4284
4285	R->block0[n] = last+1;
4286	last += (int)sqrt((double)(iv->length()-2));
4287	R->block1[n] = last;
4288	break;
4289	}
4290
4291	case ringorder_no:
4292	R->order[n] = ringorder_unspec;
4293	return TRUE;
4294
4295	default:
4296	Werror("Internal Error: Unknown ordering %d", (*iv)[1]);
4297	R->order[n] = ringorder_unspec;
4298	return TRUE;
4299	}
4300	}
4301	sl=sl->next;
4302	}
4303
4304	// check for complete coverage
4305	if ((R->order[n]==ringorder_c) \|\| (R->order[n]==ringorder_C)) n--;
4306	if (R->block1[n] != R->N)
4307	{
4308	if (((R->order[n]==ringorder_dp) \|\|
4309	(R->order[n]==ringorder_ds) \|\|
4310	(R->order[n]==ringorder_Dp) \|\|
4311	(R->order[n]==ringorder_Ds) \|\|
4312	(R->order[n]==ringorder_rp) \|\|
4313	(R->order[n]==ringorder_lp) \|\|
4314	(R->order[n]==ringorder_ls))
4315	&&
4316	R->block0[n] <= R->N)
4317	{
4318	R->block1[n] = R->N;
4319	}
4320	else
4321	{
4322	Werror("mismatch of number of vars (%d) and ordering (%d vars)",
4323	R->N,R->block1[n]);
4324	return TRUE;
4325	}
4326	}
4327	R->OrdSgn = typ;
4328	return FALSE;
4329	}
4330
4331	BOOLEAN rSleftvList2StringArray(sleftv* sl, char** p)
4332	{
4333
4334	while(sl!=NULL)
4335	{
4336	if (sl->Name() == sNoName)
4337	{
4338	if (sl->Typ()==POLY_CMD)
4339	{
4340	sleftv s_sl;
4341	iiConvert(POLY_CMD,ANY_TYPE,-1,sl,&s_sl);
4342	if (s_sl.Name() != sNoName)
4343	*p = omStrDup(s_sl.Name());
4344	else
4345	*p = NULL;
4346	sl->next = s_sl.next;
4347	s_sl.next = NULL;
4348	s_sl.CleanUp();
4349	if (*p == NULL) return TRUE;
4350	}
4351	else
4352	return TRUE;
4353	}
4354	else
4355	*p = omStrDup(sl->Name());
4356	p++;
4357	sl=sl->next;
4358	}
4359	return FALSE;
4360	}
4361
4362	////////////////////
4363	//
4364	// rInit itself:
4365	//
4366	// INPUT: s: name, pn: ch & parameter (names), rv: variable (names)
4367	// ord: ordering
4368	// RETURN: currRingHdl on success
4369	// NULL on error
4370	// NOTE: * makes new ring to current ring, on success
4371	// * considers input sleftv's as read-only
4372	//idhdl rInit(char s, sleftv pn, sleftv* rv, sleftv* ord)
4373	ring rInit(sleftv* pn, sleftv* rv, sleftv* ord)
4374	{
4375	int ch;
4376	#ifdef HAVE_RING2TOM
4377	int cring = 0;
4378	#endif
4379	int float_len=0;
4380	int float_len2=0;
4381	ring R = NULL;
4382	idhdl tmp = NULL;
4383	BOOLEAN ffChar=FALSE;
4384	int typ = 1;
4385
4386	/* ch -------------------------------------------------------*/
4387	// get ch of ground field
4388	int numberOfAllocatedBlocks;
4389
4390	if (pn->Typ()==INT_CMD)
4391	{
4392	ch=(int)(long)pn->Data();
4393	}
4394	else if ((pn->name != NULL)
4395	&& ((strcmp(pn->name,"real")==0) \|\| (strcmp(pn->name,"complex")==0)))
4396	{
4397	BOOLEAN complex_flag=(strcmp(pn->name,"complex")==0);
4398	ch=-1;
4399	if ((pn->next!=NULL) && (pn->next->Typ()==INT_CMD))
4400	{
4401	float_len=(int)(long)pn->next->Data();
4402	float_len2=float_len;
4403	pn=pn->next;
4404	if ((pn->next!=NULL) && (pn->next->Typ()==INT_CMD))
4405	{
4406	float_len2=(int)(long)pn->next->Data();
4407	pn=pn->next;
4408	}
4409	}
4410	if ((pn->next==NULL) && complex_flag)
4411	{
4412	pn->next=(leftv)omAlloc0Bin(sleftv_bin);
4413	pn->next->name=omStrDup("i");
4414	}
4415	}
4416	else
4417	{
4418	Werror("Wrong ground field specification");
4419	goto rInitError;
4420	}
4421	pn=pn->next;
4422
4423	int l, last;
4424	sleftv * sl;
4425	/every entry in the new ring is initialized to 0/
4426
4427	/* characteristic -----------------------------------------------*/
4428	/* input: 0 ch=0 : Q parameter=NULL ffChar=FALSE float_len
4429	* 0 1 : Q(a,...) *names FALSE
4430	* 0 -1 : R NULL FALSE 0
4431	* 0 -1 : R NULL FALSE prec. >6
4432	* 0 -1 : C *names FALSE prec. 0..?
4433	* p p : Fp NULL FALSE
4434	* p -p : Fp(a) *names FALSE
4435	* q q : GF(q=p^n) *names TRUE
4436	*/
4437	if (ch!=-1)
4438	{
4439	int l = 0;
4440
4441	if (((ch!=0) && (ch<2))
4442	#ifndef NV_OPS
4443	\|\| (ch > 32003)
4444	#endif
4445	)
4446	{
4447	Warn("%d is invalid characteristic of ground field. 32003 is used.", ch);
4448	ch=32003;
4449	}
4450	// load fftable, if necessary
4451	if (pn!=NULL)
4452	{
4453	while ((ch!=fftable[l]) && (fftable[l])) l++;
4454	if (fftable[l]==0) ch = IsPrime(ch);
4455	else
4456	{
4457	char m[1]={(char )sNoName};
4458	nfSetChar(ch,m);
4459	if (errorreported) goto rInitError;
4460	else ffChar=TRUE;
4461	}
4462	}
4463	else {
4464	#ifdef HAVE_RING2TOM
4465	int blupp = Is2toM(ch);
4466	if (blupp != 0) {
4467	cring = 1; // Use Z/2^ch
4468	ch = blupp;
4469	Print("Beta: using Z/2^%d", ch);
4470	PrintLn();
4471	}
4472	else
4473	#endif
4474	ch = IsPrime(ch);
4475	}
4476	}
4477	// allocated ring and set ch
4478	R = (ring) omAlloc0Bin(sip_sring_bin);
4479	R->ch = ch;
4480	#ifdef HAVE_RING2TOM
4481	R->cring = cring;
4482	#endif
4483	if (ch == -1)
4484	{
4485	R->float_len= si_min(float_len,32767);
4486	R->float_len2= si_min(float_len2,32767);
4487	}
4488
4489	/* parameter -------------------------------------------------------*/
4490	if (pn!=NULL)
4491	{
4492	R->P=pn->listLength();
4493	//if ((ffChar\|\| (ch == 1)) && (R->P > 1))
4494	if ((R->P > 1) && (ffChar \|\| (ch == -1)))
4495	{
4496	WerrorS("too many parameters");
4497	goto rInitError;
4498	}
4499	R->parameter=(char*)omAlloc0(R->Psizeof(char_ptr));
4500	if (rSleftvList2StringArray(pn, R->parameter))
4501	{
4502	WerrorS("parameter expected");
4503	goto rInitError;
4504	}
4505	if (ch>1 && !ffChar) R->ch=-ch;
4506	else if (ch==0) R->ch=1;
4507	}
4508	else if (ffChar)
4509	{
4510	WerrorS("need one parameter");
4511	goto rInitError;
4512	}
4513	/* post-processing of field description */
4514	// we have short reals, but no short complex
4515	if ((R->ch == - 1)
4516	&& (R->parameter !=NULL)
4517	&& (R->float_len < SHORT_REAL_LENGTH))
4518	{
4519	R->float_len = SHORT_REAL_LENGTH;
4520	R->float_len2 = SHORT_REAL_LENGTH;
4521	}
4522
4523	/* names and number of variables-------------------------------------*/
4524	{
4525	int l=rv->listLength();
4526	#if SIZEOF_SHORT == 2
4527	#define MAX_SHORT 0x7fff
4528	#endif
4529	if (l>MAX_SHORT)
4530	{
4531	Werror("too many ring variables(%d), max is %d",l,MAX_SHORT);
4532	goto rInitError;
4533	}
4534	R->N = l; /rv->listLength();/
4535	}
4536	R->names = (char *)omAlloc0(R->N sizeof(char_ptr));
4537	if (rSleftvList2StringArray(rv, R->names))
4538	{
4539	WerrorS("name of ring variable expected");
4540	goto rInitError;
4541	}
4542
4543	/* check names and parameters for conflicts ------------------------- */
4544	{
4545	int i,j;
4546	for(i=0;i<R->P; i++)
4547	{
4548	for(j=0;j<R->N;j++)
4549	{
4550	if (strcmp(R->parameter[i],R->names[j])==0)
4551	{
4552	Werror("parameter %d conflicts with variable %d",i+1,j+1);
4553	goto rInitError;
4554	}
4555	}
4556	}
4557	}
4558	rNameCheck(R);
4559	/* ordering -------------------------------------------------------------*/
4560	if (rSleftvOrdering2Ordering(ord, R))
4561	goto rInitError;
4562
4563	// Complete the initialization
4564	if (rComplete(R,1))
4565	goto rInitError;
4566
4567	rTest(R);
4568
4569	// try to enter the ring into the name list
4570	// need to clean up sleftv here, before this ring can be set to
4571	// new currRing or currRing can be killed beacuse new ring has
4572	// same name
4573	if (pn != NULL) pn->CleanUp();
4574	if (rv != NULL) rv->CleanUp();
4575	if (ord != NULL) ord->CleanUp();
4576	//if ((tmp = enterid(s, myynest, RING_CMD, &IDROOT))==NULL)
4577	// goto rInitError;
4578
4579	//memcpy(IDRING(tmp),R,sizeof(*R));
4580	// set current ring
4581	//omFreeBin(R, ip_sring_bin);
4582	//return tmp;
4583	return R;
4584
4585	// error case:
4586	rInitError:
4587	if (R != NULL) rDelete(R);
4588	if (pn != NULL) pn->CleanUp();
4589	if (rv != NULL) rv->CleanUp();
4590	if (ord != NULL) ord->CleanUp();
4591	return NULL;
4592	}
4593
4594	void rKill(ring r)
4595	{
4596	if ((r->ref<=0)&&(r->order!=NULL))
4597	{
4598	#ifdef RDEBUG
4599	if (traceit &TRACE_SHOW_RINGS) Print("kill ring %x\n",r);
4600	#endif
4601	if (r==currRing)
4602	{
4603	if (r->qideal!=NULL)
4604	{
4605	idDelete(&r->qideal);
4606	r->qideal=NULL;
4607	currQuotient=NULL;
4608	}
4609	if (ppNoether!=NULL) pDelete(&ppNoether);
4610	if (sLastPrinted.RingDependend())
4611	{
4612	sLastPrinted.CleanUp();
4613	}
4614	if ((myynest>0) && (iiRETURNEXPR[myynest].RingDependend()))
4615	{
4616	WerrorS("return value depends on local ring variable (export missing ?)");
4617	iiRETURNEXPR[myynest].CleanUp();
4618	}
4619	currRing=NULL;
4620	currRingHdl=NULL;
4621	}
4622	else if (r->qideal!=NULL)
4623	{
4624	id_Delete(&r->qideal, r);
4625	r->qideal = NULL;
4626	}
4627	int i=1;
4628	int j;
4629	int *pi=r->order;
4630	#ifdef USE_IILOCALRING
4631	for (j=0;j<iiRETURNEXPR_len;j++)
4632	{
4633	if (iiLocalRing[j]==r)
4634	{
4635	if (j<myynest) Warn("killing the basering for level %d",j);
4636	iiLocalRing[j]=NULL;
4637	}
4638	}
4639	#else /* USE_IILOCALRING */
4640	//#endif /* USE_IILOCALRING */
4641	{
4642	proclevel * nshdl = procstack;
4643	int lev=myynest-1;
4644
4645	for(; nshdl != NULL; nshdl = nshdl->next)
4646	{
4647	if (nshdl->cRing==r)
4648	{
4649	Warn("killing the basering for level %d",lev);
4650	nshdl->cRing=NULL;
4651	nshdl->cRingHdl=NULL;
4652	}
4653	}
4654	}
4655	#endif /* USE_IILOCALRING */
4656
4657	/* nKillChar(r); will be called from inside of rDelete */
4658	rDelete(r);
4659	return;
4660	}
4661	r->ref--;
4662	}
4663
4664	void rKill(idhdl h)
4665	{
4666	ring r = IDRING(h);
4667	int ref=0;
4668	if (r!=NULL)
4669	{
4670	ref=r->ref;
4671	rKill(r);
4672	}
4673	if (h==currRingHdl)
4674	{
4675	if (ref<=0) { currRing=NULL; currRingHdl=NULL;}
4676	else
4677	{
4678	currRingHdl=rFindHdl(r,currRingHdl,NULL);
4679	}
4680	}
4681	}
4682
4683	idhdl rSimpleFindHdl(ring r, idhdl root, idhdl n=NULL)
4684	{
4685	//idhdl next_best=NULL;
4686	idhdl h=root;
4687	while (h!=NULL)
4688	{
4689	if (((IDTYP(h)==RING_CMD)\|\|(IDTYP(h)==QRING_CMD))
4690	&& (h!=n)
4691	&& (IDRING(h)==r)
4692	)
4693	{
4694	// if (IDLEV(h)==myynest)
4695	// return h;
4696	// if ((IDLEV(h)==0) \|\| (next_best==NULL))
4697	// next_best=h;
4698	// else if (IDLEV(next_best)<IDLEV(h))
4699	// next_best=h;
4700	return h;
4701	}
4702	h=IDNEXT(h);
4703	}
4704	//return next_best;
4705	return NULL;
4706	}

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