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polymakeInterface.lib @ 5d51cc6

spielwiese

Last change on this file since 5d51cc6 was 5d51cc6, checked in by Hans Schoenemann <hannes@…>, 8 years ago
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1	///////////////////////////////////////////////////////////////////////////////
2	version="version polymakeInterface.lib 4.0.3.3 Oct_2016 ";
3	category = "Convex Geometry";
4	info="
5	LIBRARY: polymakeInterface.lib low level interface to polymake
6	AUTHORS: Yue Ren, email: ren@mathematik.uni-kl.de
7
8	PROCEDURES:
9	boundaryLatticePoints();
10	ehrhartPolynomialCoeff();
11	fVectorP();
12	facetVertexLatticeDistances();
13	facetWidth();
14	facetWidths();
15	gorensteinIndex();
16	gorensteinVector();
17	hStarVector();
18	hVector();
19	hilbertBasis();
20	interiorLatticePoints();
21	isBounded();
22	isCanonical();
23	isCompressed();
24	isGorenstein();
25	isLatticeEmpty();
26	isNormal();
27	isReflexive();
28	isSmooth();
29	isTerminal();
30	isVeryAmple();
31	latticeCodegree();
32	latticeDegree();
33	latticePoints();
34	latticeVolume();
35	maximalFace();
36	maximalValue();
37	minimalFace();
38	minimalValue();
39	minkowskiSum();
40	nBoundaryLatticePoints();
41	nHilbertBasis();
42	nInteriorLatticePoints();
43	nLatticePoints();
44	normalFan();
45	vertexAdjacencyGraph();
46	vertexEdgeGraph();
47	visual();
48	";
49
50	///////////////////////////////////////////////////////////////////////////////
51
52	proc boundaryLatticePoints()
53	"USAGE: boundaryLatticePoints(p); p polytope
54	ASSUME: isBounded(p)==1
55	RETURN: intmat, all lattice points on the relative boundary of p
56	EXAMPLE: example boundaryLatticePoints; shows an example
57	"
58	{
59
60	}
61	example
62	{
63	"EXAMPLE:"; echo = 2;
64	intmat M[3][3]=
65	1,2,-1,
66	1,-1,2,
67	1,-1,-1;
68	polytope p = polytopeViaPoints(M);
69	boundaryLatticePoints(p);
70	intmat N[2][3]=
71	1,2,0,
72	1,0,2;
73	polytope q = polytopeViaPoints(N);
74	boundaryLatticePoints(q);
75	}
76
77	proc ehrhartPolynomialCoeff()
78	"USAGE: ehrhartPolynomialCoeff(p); p polytope
79	ASSUME: isBounded(p)==1
80	RETURN: intvec, all lattice points on the relative boundary of p
81	EXAMPLE: example ehrhartPolynomialCoeff; shows an example
82	"
83	{
84
85	}
86	example
87	{
88	"EXAMPLE:"; echo = 2;
89	intmat M[6][4]=
90	1,1,1,2,
91	1,-1,-1,-2,
92	1,1,0,0,
93	1,-1,0,0,
94	1,0,1,0,
95	1,0,-1,0;
96	polytope p = polytopeViaPoints(M);
97	ehrhartPolynomialCoeff(p);
98	}
99
100	proc fVectorP()
101	"USAGE: fVectorP(p); p polytope
102	RETURN: intvec, the f-vector or p
103	EXAMPLE: example fVectorP; shows an example
104	"
105	{
106
107	}
108	example
109	{
110	"EXAMPLE:"; echo = 2;
111	intmat M[6][4]=
112	1,1,1,2,
113	1,-1,-1,-2,
114	1,1,0,0,
115	1,-1,0,0,
116	1,0,1,0,
117	1,0,-1,0;
118	polytope p = polytopeViaPoints(M);
119	fVectorP(p);
120	}
121
122	proc facetVertexLatticeDistances()
123	"USAGE: facetVertexLatticeDistances(p); p polytope
124	RETURN: intmat, encodes the lattice distances between vertices (columns) and facets (rows) of p.
125	EXAMPLE: example facetVertexLatticeDistances; shows an example
126	"
127	{
128
129	}
130	example
131	{
132	"EXAMPLE:"; echo = 2;
133	intmat M[4][3]=
134	1,2,0,
135	1,0,1,
136	1,2,1,
137	1,0,0;
138	polytope p = polytopeViaPoints(M);
139	facetVertexLatticeDistances(p);
140	}
141
142	proc facetWidth()
143	"USAGE: facetWidth(p); p polytope
144	ASSUME: isBounded(p)==1
145	RETURN: int, maximal integral width going over all facet normals
146	EXAMPLE: example facetWidth; shows an example
147	"
148	{
149
150	}
151	example
152	{
153	"EXAMPLE:"; echo = 2;
154	intmat M[4][3]=
155	1,2,0,
156	1,0,1,
157	1,2,1,
158	1,0,0;
159	polytope p = polytopeViaPoints(M);
160	facetWidth(p);
161	}
162
163	proc facetWidths()
164	"USAGE: facetWidths(p); p polytope
165	ASSUME: isBounded(p)==1
166	RETURN: intvec, vector with the integral widths of all facet normals
167	EXAMPLE: example facetWidths; shows an example
168	"
169	{
170
171	}
172	example
173	{
174	"EXAMPLE:"; echo = 2;
175	intmat M[4][3]=
176	1,2,0,
177	1,0,1,
178	1,2,1,
179	1,0,0;
180	polytope p = polytopeViaPoints(M);
181	facetWidths(p);
182	}
183
184	proc gorensteinIndex()
185	"USAGE: gorensteinIndex(p); p polytope
186	ASSUME: isGorenstein(p)==1
187	RETURN: int, a factor n such that n*p+v is reflexive for some translation v
188	NOTE: the translation v can be computed via gorensteinVector(p)
189	EXAMPLE: example gorensteinIndex; shows an example
190	"
191	{
192
193	}
194	example
195	{
196	"EXAMPLE:"; echo = 2;
197	intmat M[4][3]=1,1,0, 1,0,1, 1,0,0, 1,1,1;
198	polytope p = polytopeViaPoints(M);
199	gorensteinIndex(p);
200	}
201
202	proc gorensteinVector()
203	"USAGE: gorensteinVector(p); p polytope
204	ASSUME: isGorenstein(p)==1
205	RETURN: intvec, a vector v such that n*p+v is reflexive for some factor n
206	NOTE: the factor n can be computed via gorensteinIndex(p)
207	EXAMPLE: example gorensteinVector; shows an example
208	"
209	{
210
211	}
212	example
213	{
214	"EXAMPLE:"; echo = 2;
215	intmat M[4][3]=1,1,0, 1,0,1, 1,0,0, 1,1,1;
216	polytope p = polytopeViaPoints(M);
217	gorensteinVector(p);
218	}
219
220	proc hStarVector()
221	"USAGE: hStarVector(p); p polytope
222	RETURN: intvec, the h* vector of p
223	EXAMPLE: example hStarVector; shows an example
224	"
225	{
226
227	}
228	example
229	{
230	"EXAMPLE:"; echo = 2;
231	intmat
232	M[6][4]=
233	1,1,1,2,
234	1,-1,-1,-2,
235	1,1,0,0,
236	1,-1,0,0,
237	1,0,1,0,
238	1,0,-1,0;
239	polytope p = polytopeViaPoints(M);
240	hStarVector(p);
241	}
242
243	proc hVector()
244	"USAGE: hVector(p); p polytope
245	RETURN: intvec, the h vector of p
246	EXAMPLE: example hVector; shows an example
247	"
248	{
249
250	}
251	example
252	{
253	"EXAMPLE:"; echo = 2;
254	intmat
255	M[6][4]=
256	1,1,1,2,
257	1,-1,-1,-2,
258	1,1,0,0,
259	1,-1,0,0,
260	1,0,1,0,
261	1,0,-1,0;
262	polytope p = polytopeViaPoints(M);
263	hVector(p);
264	}
265
266	proc hilbertBasis()
267	"USAGE: hilbertBasis(c); c cone
268	RETURN: intmat, the Hilbert basis of c intersected with Z^n
269	EXAMPLE: example hilbertBasis; shows an example
270	"
271	{
272
273	}
274	example
275	{
276	"EXAMPLE:"; echo = 2;
277	intmat M[3][3]=
278	1,2,-1,
279	1,-1,2,
280	1,-1,-1;
281	cone c = coneViaPoints(M);
282	hilbertBasis(c);
283	}
284
285	proc interiorLatticePoints()
286	"USAGE: interiorLatticePoints(p); p polytope
287	ASSUME: isBounded(p)==1
288	RETURN: intmat, all lattice points in the relative interior of p
289	EXAMPLE: example interiorLatticePoints; shows an example
290	"
291	{
292
293	}
294	example
295	{
296	"EXAMPLE:"; echo = 2;
297	intmat M[3][3]=
298	1,2,-1,
299	1,-1,2,
300	1,-1,-1;
301	polytope p = polytopeViaPoints(M);
302	interiorLatticePoints(p);
303	intmat N[2][3]=
304	1,2,0,
305	1,0,2;
306	polytope q = polytopeViaPoints(N);
307	interiorLatticePoints(q);
308	}
309
310	proc isBounded()
311	"USAGE: isBounded(p); p polytope
312	RETURN: 1, if p is bounded; 0 otherwise
313	EXAMPLE: example isBounded; shows an example
314	"
315	{
316
317	}
318	example
319	{
320	"EXAMPLE:"; echo = 2;
321	intmat M[4][4]=
322	1,1,0,0,
323	1,0,1,0,
324	1,0,0,1,
325	1,-1,-1,-1;
326	polytope p = polytopeViaPoints(M);
327	isBounded(p);
328	M=
329	1,1,0,0,
330	1,0,1,0,
331	0,0,0,1,
332	1,-1,-1,-1;
333	p = polytopeViaPoints(M);
334	isBounded(p);
335	}
336
337	proc isCanonical()
338	"USAGE: isCanonical(p); p polytope
339	RETURN: 1, if p has exactly one interior lattice point; 0 otherwise
340	EXAMPLE: example isCanonical; shows an example
341	"
342	{
343
344	}
345	example
346	{
347	"EXAMPLE:"; echo = 2;
348	intmat M[6][4]=
349	1,1,1,2,
350	1,-1,-1,-2,
351	1,1,0,0,
352	1,-1,0,0,
353	1,0,1,0,
354	1,0,-1,0;
355	polytope p = polytopeViaPoints(M);
356	isCanonical(p);
357	isReflexive(p);
358	intmat N[3][3]=
359	1,2,0,
360	1,0,2,
361	1,-2,-2;
362	polytope q = polytopeViaPoints(N);
363	isCanonical(q);
364	}
365
366	proc isCompressed()
367	"USAGE: isCompressed(p); p polytope
368	RETURN: 1, if p has maximal facet width 1; 0 otherwise
369	EXAMPLE: example isCompressed; shows an example
370	"
371	{
372
373	}
374	example
375	{
376	"EXAMPLE:"; echo = 2;
377	intmat M[4][3]=
378	1,2,0,
379	1,0,1,
380	1,2,1,
381	1,0,0;
382	polytope p = polytopeViaPoints(M);
383	isCompressed(p);
384	intmat N[4][3]=
385	1,1,0,
386	1,0,1,
387	1,1,1,
388	1,0,0;
389	polytope q = polytopeViaPoints(N);
390	isCompressed(q);
391	}
392
393	proc isGorenstein()
394	"USAGE: isGorenstein(p); p polytope
395	RETURN: 1, if p is Gorenstein, i.e. reflexive modulo dilatation and translation; 0 otherwise
396	EXAMPLE: example isGorenstein; shows an example
397	"
398	{
399
400	}
401	example
402	{
403	"EXAMPLE:"; echo = 2;
404	intmat M[4][3]=
405	1,1,0,
406	1,0,1,
407	1,0,0,
408	1,1,1;
409	polytope p = polytopeViaPoints(M);
410	isGorenstein(p);
411	intmat N[3][3]=
412	1,2,0,
413	1,0,2,
414	1,-2,-2;
415	polytope q = polytopeViaPoints(N);
416	isGorenstein(q);
417	}
418
419	proc isLatticeEmpty()
420	"USAGE: isLatticeEmpty(p); p polytope
421	RETURN: 1, if p contains no lattice points other than the vertices; 0 otherwise
422	EXAMPLE: example isLatticeEmpty; shows an example
423	"
424	{
425
426	}
427	example
428	{
429	"EXAMPLE:"; echo = 2;
430	intmat M[4][3]=
431	1,1,0,
432	1,1,1,
433	1,0,1,
434	1,0,0;
435	polytope p = polytopeViaPoints(M);
436	isLatticeEmpty(p);
437	intmat N[4][3]=
438	1,1,0,
439	1,2,1,
440	1,0,1,
441	1,0,0;
442	polytope q = polytopeViaPoints(N);
443	isLatticeEmpty(q);
444	}
445
446	proc isNormal()
447	"USAGE: isNormal(p); p polytope
448	RETURN: 1, if the projective toric variety defined by p is projectively normal; 0 otherwise
449	EXAMPLE: example isNormal; shows an example
450	"
451	{
452
453	}
454	example
455	{
456	"EXAMPLE:"; echo = 2;
457	intmat M[6][4]=
458	1,1,1,2,
459	1,-1,-1,-2,
460	1,1,0,0,
461	1,-1,0,0,
462	1,0,1,0,
463	1,0,-1,0;
464	polytope p = polytopeViaPoints(M);
465	isNormal(p);
466	}
467
468	proc isReflexive()
469	"USAGE: isReflexive(p); p polytope
470	RETURN: 1, if p is reflexive; 0 otherwise
471	EXAMPLE: example isReflexive; shows an example
472	"
473	{
474
475	}
476	example
477	{
478	"EXAMPLE:"; echo = 2;
479	intmat M[4][4]=
480	1,1,0,0,
481	1,0,1,0,
482	1,0,0,1,
483	1,-1,-1,-1;
484	polytope p = polytopeViaPoints(M);
485	isReflexive(p);
486	intmat N[4][4]=
487	1,2,0,0,
488	1,0,2,0,
489	1,0,0,2,
490	1,-2,-2,-2;
491	polytope q = polytopeViaPoints(M);
492	isReflexive(q);
493	}
494
495	proc isSmooth()
496	"USAGE: isSmooth(c); c cone
497	isSmooth(f); f fan
498	isSmooth(p); p polytope
499	RETURN: 1, if the input is smooth; 0 otherwise
500	EXAMPLE: example isSmooth; shows an example
501	"
502	{
503
504	}
505	example
506	{
507	"EXAMPLE:"; echo = 2;
508	intmat M1[2][2]=
509	1,0,
510	0,1;
511	cone c1 = coneViaPoints(M1);
512	isSmooth(c1);
513	intmat M2[3][3]=
514	1,0,
515	1,2;
516	cone c2 = coneViaPoints(M2);
517	fan F1 = emptyFan(2);
518	insertCone(F1,c1);
519	isSmooth(F1);
520	fan F2 = emptyFan(3);
521	insertCone(F2,c2);
522	isSmooth(F2);
523	intmat Mp[3][3]=
524	1,-2,-3,
525	1,1,0,
526	1,0,1;
527	polytope p = polytopeViaPoints(Mp);
528	isSmooth(p);
529	fan F = normalFan(p);
530	isSmooth(F);
531	intmat Mq[4][3]=
532	1,2,0,
533	1,0,1,
534	1,2,1,
535	1,0,0;
536	polytope q = polytopeViaPoints(Mq);
537	isSmooth(q);
538	}
539
540	proc isTerminal()
541	"USAGE: isTerminal(p); p polytope
542	RETURN: 1, if p has exactly one interior lattice point and all other lattice points are vertices; 0 otherwise
543	EXAMPLE: example isTerminal; shows an example
544	"
545	{
546
547	}
548	example
549	{
550	"EXAMPLE:"; echo = 2;
551	intmat M[6][4]=
552	1,1,1,2,
553	1,-1,-1,-2,
554	1,1,0,0,
555	1,-1,0,0,
556	1,0,1,0,
557	1,0,-1,0;
558	polytope p = polytopeViaPoints(M);
559	isTerminal(p);
560	isReflexive(p);
561	intmat N[6][4]=
562	1,1,1,2,
563	1,-1,-1,-2,
564	1,1,1,0,
565	1,-1,-1,0,
566	1,-1,1,0,
567	1,1,-1,0;
568	polytope q = polytopeViaPoints(N);
569	isTerminal(q);
570	isCanonical(q);
571	}
572
573	proc isVeryAmple()
574	"USAGE: isVeryAmple(p); p polytope
575	RETURN: 1, if p is very ample; 0 otherwise
576	EXAMPLE: example isVeryAmple; shows an example
577	"
578	{
579
580	}
581	example
582	{
583	"EXAMPLE:"; echo = 2;
584	intmat M[3][3]=
585	1,1,0,
586	1,0,1,
587	1,-1,-1;
588	polytope p = polytopeViaPoints(M);
589	isVeryAmple(p);
590	intmat N[3][4]=
591	1,1,0,0,
592	1,0,1,0,
593	1,1,1,2;
594	polytope q = polytopeViaPoints(N);
595	isVeryAmple(q);
596	}
597
598	proc latticeCodegree()
599	"USAGE: latticeCodegree(p); p polytope
600	RETURN: int, the smalles number n such that n*p has a relative interior lattice point
601	NOTE: dimension(p)+1==latticeDegree(p)+latticeCodegree(p)
602	EXAMPLE: example latticeCodegree; shows an example
603	"
604	{
605
606	}
607	example
608	{
609	"EXAMPLE:"; echo = 2;
610	intmat M[4][3]=
611	1,1,0,
612	1,1,1,
613	1,0,1,
614	1,0,0;
615	polytope p = polytopeViaPoints(M);
616	latticeCodegree(p);
617	intmat N[4][4]=
618	1,1,0,0,
619	1,0,1,0,
620	1,0,0,1,
621	1,0,0,0;
622	polytope q = polytopeViaPoints(N);
623	latticeCodegree(q);
624	}
625
626	proc latticeDegree()
627	"USAGE: latticeDegree(p); p polytope
628	RETURN: int, the degree of the Ehrhart polynomial of p
629	NOTE: dimension(p)+1==latticeDegree(p)+latticeCodegree(p)
630	EXAMPLE: example latticeDegree; shows an example
631	"
632	{
633
634	}
635	example
636	{
637	"EXAMPLE:"; echo = 2;
638	intmat M[4][3]=
639	1,1,0,
640	1,1,1,
641	1,0,1,
642	1,0,0;
643	polytope p = polytopeViaPoints(M);
644	latticeDegree(p);
645	intmat N[4][4]=
646	1,1,0,0,
647	1,0,1,0,
648	1,0,0,1,
649	1,0,0,0;
650	polytope q = polytopeViaPoints(N);
651	latticeDegree(q);
652	}
653
654	proc latticePoints()
655	"USAGE: latticePoints(p); p polytope
656	ASSUME: isBounded(p)==1
657	RETURN: intmat, all lattice points in p
658	EXAMPLE: example latticePoints; shows an example
659	"
660	{
661
662	}
663	example
664	{
665	"EXAMPLE:"; echo = 2;
666	intmat M[3][3]=
667	1,2,-1,
668	1,-1,2,
669	1,-1,-1;
670	polytope p = polytopeViaPoints(M);
671	latticePoints(p);
672	intmat N[2][3]=
673	1,2,0,
674	1,0,2;
675	polytope q = polytopeViaPoints(N);
676	latticePoints(q);
677	}
678
679	proc latticeVolume()
680	"USAGE: latticeVolume(p); p polytope
681	ASSUME: isBounded(p)==1
682	RETURN: int, the lattice volume of p
683	EXAMPLE: example latticeVolume; shows an example
684	"
685	{
686
687	}
688	example
689	{
690	"EXAMPLE:"; echo = 2;
691	intmat M[4][3]=
692	1,1,0,
693	1,1,1,
694	1,0,1,
695	1,0,0;
696	polytope p = polytopeViaPoints(M);
697	latticeVolume(p);
698	intmat N[4][3]=
699	1,1,0,
700	1,2,1,
701	1,0,1,
702	1,0,0;
703	polytope q = polytopeViaPoints(N);
704	latticeVolume(q);
705	intmat W[4][4]=
706	1,1,0,0,
707	1,0,1,0,
708	1,0,0,1,
709	1,0,0,0;
710	polytope r = polytopeViaPoints(W);
711	latticeVolume(r);
712	}
713
714	proc maximalFace()
715	"USAGE: maximalFace(p,v); p polytope, v intvec
716	ASSUME: v lies in the negative dual tail cone of p
717	RETURN: intmat, vertices of the face of p on which the linear form v is maximal
718	NOTE: the maximal face is independent of the first coordinate of v
719	since p is considered as a polytope in the plane (first coordinate) = 1.
720	EXAMPLE: example maximalFace; shows an example
721	"
722	{
723
724	}
725	example
726	{
727	"EXAMPLE:"; echo = 2;
728	intmat M[3][3]=
729	1,1,0,
730	1,0,1,
731	1,-1,-1;
732	intvec v = 0,1,1;
733	polytope p = polytopeViaPoints(M);
734	maximalFace(p,v);
735	intvec w = -5,1,1;
736	maximalFace(p,w);
737	}
738
739	proc maximalValue()
740	"USAGE: maximalValue(p,v); p polytope, v intvec
741	ASSUME: v lies in the negative dual tail cone of p
742	RETURN: intmat, vertices of the face of p on which the linear form v is maximal
743	NOTE: first coordinate of v corresponds to a shift of the maximal value
744	since p is considered as a polytope in the plane (first coordinate) = 1.
745	EXAMPLE: example maximalValue; shows an example
746	"
747	{
748
749	}
750	example
751	{
752	"EXAMPLE:"; echo = 2;
753	intmat M[3][3]=
754	1,1,0,
755	1,0,1,
756	1,-1,-1;
757	intvec v = 0,1,1;
758	polytope p = polytopeViaPoints(M);
759	maximalValue(p,v);
760	intvec w = -5,1,1;
761	maximalValue(p,w);
762	}
763
764	proc minimalFace()
765	"USAGE: minimalFace(p,v); p polytope, v intvec
766	ASSUME: v lies in the dual tail cone of p
767	RETURN: intmat, vertices of the face of p on which the linear form v is minimal
768	NOTE: the minimal face is independent of the first coordinate of v
769	since p is considered as a polytope in the plane (first coordinate) = 1.
770	EXAMPLE: example minimalFace; shows an example
771	"
772	{
773
774	}
775	example
776	{
777	"EXAMPLE:"; echo = 2;
778	intmat M[3][3]=
779	1,1,0,
780	1,0,1,
781	1,-1,-1;
782	intvec v = 0,-1,-1;
783	polytope p = polytopeViaPoints(M);
784	minimalFace(p,v);
785	intvec w = 5,-1,-1;
786	minimalFace(p,w);
787	}
788
789	proc minimalValue()
790	"USAGE: minimalValue(p,v); p polytope, v intvec
791	ASSUME: v lies in the negative dual tail cone of p
792	RETURN: intmat, vertices of the face of p on which the linear form v is minimal
793	NOTE: first coordinate of v corresponds to a shift of the minimal value
794	since p is considered as a polytope in the plane (first coordinate) = 1.
795	EXAMPLE: example minimalValue; shows an example
796	"
797	{
798
799	}
800	example
801	{
802	"EXAMPLE:"; echo = 2;
803	intmat M[3][3]=
804	1,1,0,
805	1,0,1,
806	1,-1,-1;
807	intvec v = 0,-1,-1;
808	polytope p = polytopeViaPoints(M);
809	minimalValue(p,v);
810	intvec w = 5,-1,-1;
811	minimalValue(p,w);
812	}
813
814	proc minkowskiSum()
815	"USAGE: minkowskiSum(c,d); c cone, d cone
816	minkowskiSum(c,q); c cone, q polytope
817	minkowskiSum(p,d); p polytope, d cone
818	minkowskiSum(p,q); p polytope, q polytope
819	ASSUME: input arguments have the same ambient dimension
820	RETURN: cone, if both inputs are cones; polytope, otherwise
821	the minkowski sum of the two input arguments
822	EXAMPLE: example minkowskiSum; shows an example
823	"
824	{
825
826	}
827	example
828	{
829	"EXAMPLE:"; echo = 2;
830	intmat M[3][4]=
831	1,1,0,0,
832	1,0,1,0,
833	1,0,0,0;
834	intmat N[3][4]=
835	1,0,0,1,
836	1,-1,-1,-1,
837	1,0,0,0;
838	polytope p = polytopeViaPoints(M);
839	polytope q = polytopeViaPoints(N);
840	vertices(minkowskiSum(p,q));
841	}
842
843	proc nBoundaryLatticePoints()
844	"USAGE: nBoundaryLatticePoints(p); p polytope
845	ASSUME: isBounded(p)==1
846	RETURN: int, the number of lattice points in the relative boundary of p
847	EXAMPLE: example nBoundaryLatticePoints; shows an example
848	"
849	{
850
851	}
852	example
853	{
854	"EXAMPLE:"; echo = 2;
855	intmat M[3][3]=
856	1,2,-1,
857	1,-1,2,
858	1,-1,-1;
859	polytope p = polytopeViaPoints(M);
860	nBoundaryLatticePoints(p);
861	intmat N[2][3]=
862	1,2,0,
863	1,0,2;
864	polytope q = polytopeViaPoints(N);
865	nBoundaryLatticePoints(q);
866	}
867
868	proc nHilbertBasis()
869	"USAGE: nHilbertBasis(c); c cone
870	RETURN: int, the number of elements in the Hilbert basis of c intersected with Z^n
871	EXAMPLE: example nHilbertBasis; shows an example
872	"
873	{
874
875	}
876	example
877	{
878	"EXAMPLE:"; echo = 2;
879	intmat M[3][3]=
880	1,2,-1,
881	1,-1,2,
882	1,-1,-1;
883	cone c = coneViaPoints(M);
884	nHilbertBasis(c);
885	}
886
887	proc nInteriorLatticePoints()
888	"USAGE: nInteriorLatticePoints(p); p polytope
889	ASSUME: isBounded(p)==1
890	RETURN: int, the number of lattice points in the relative interior of p
891	EXAMPLE: example nInteriorLatticePoints; shows an example
892	"
893	{
894
895	}
896	example
897	{
898	"EXAMPLE:"; echo = 2;
899	intmat M[3][3]=
900	1,2,-1,
901	1,-1,2,
902	1,-1,-1;
903	polytope p = polytopeViaPoints(M);
904	nInteriorLatticePoints(p);
905	intmat N[2][3]=
906	1,2,0,
907	1,0,2;
908	polytope q = polytopeViaPoints(N);
909	nInteriorLatticePoints(q);
910	}
911
912	proc nLatticePoints()
913	"USAGE: nLatticePoints(p); p polytope
914	ASSUME: isBounded(p)==1
915	RETURN: intmat, the number of lattice points in p
916	EXAMPLE: example nLatticePoints; shows an example
917	"
918	{
919
920	}
921	example
922	{
923	"EXAMPLE:"; echo = 2;
924	intmat M[3][3]=
925	1,2,-1,
926	1,-1,2,
927	1,-1,-1;
928	polytope p = polytopeViaPoints(M);
929	nLatticePoints(p);
930	intmat N[2][3]=
931	1,2,0,
932	1,0,2;
933	polytope q = polytopeViaPoints(N);
934	nLatticePoints(q);
935	}
936
937	proc normalFan()
938	"USAGE: normalFan(p); p polytope
939	RETURN: fan, the normal fan of p
940	EXAMPLE: example normalFan; shows an example
941	"
942	{
943
944	}
945	example
946	{
947	"EXAMPLE:"; echo = 2;
948	intmat M[6][4] =
949	1,1,0,0,
950	1,0,1,0,
951	1,0,-1,0,
952	1,0,0,1,
953	1,0,0,-1,
954	1,-1,0,0;
955	polytope p = polytopeViaPoints(M);
956	normalFan(p);
957	}
958
959	proc vertexAdjacencyGraph()
960	"USAGE: vertexAdjacencyGraph(p); p polytope
961	RETURN: list, the first entry is a bigintmat containing all vertices as row vectors, and therefore assigning all vertices an integer.
962	the second entry is a list of intvecs representing the adjacency graph of the vertices of p,
963	the intvec in position i contains all vertices j which are connected to vertex i via an edge of p.
964	EXAMPLE: example vertexAdjacencyGraph; shows an example
965	"
966	{
967
968	}
969	example
970	{
971	"EXAMPLE:"; echo = 2;
972	intmat M[6][4] =
973	1,1,0,0,
974	1,0,1,0,
975	1,0,-1,0,
976	1,0,0,1,
977	1,0,0,-1,
978	1,-1,0,0;
979	polytope p = polytopeViaPoints(M);
980	vertexAdjacencyGraph(p);
981	}
982
983	proc vertexEdgeGraph()
984	"USAGE: vertexEdgeGraph(p); p polytope
985	RETURN: list, the first entry is a bigintmat containing all vertices as row vectors, and therefore assigning all vertices an integer.
986	the second entry is a list of intvecs representing the edge graph of the vertices of p,
987	each intvec represents an edge of p connecting vertex i with vertex j.
988	EXAMPLE: example vertexEdgeGraph; shows an example
989	"
990	{
991
992	}
993	example
994	{
995	"EXAMPLE:"; echo = 2;
996	intmat M[6][4] =
997	1,1,0,0,
998	1,0,1,0,
999	1,0,-1,0,
1000	1,0,0,1,
1001	1,0,0,-1,
1002	1,-1,0,0;
1003	polytope p = polytopeViaPoints(M);
1004	vertexEdgeGraph(p);
1005	}
1006
1007
1008	proc visual()
1009	"USAGE: visual(f); f fan
1010	visual(p); p polytope
1011	ASSUME: ambientDimension(f) resp ambientDimension(p) less or equal 3
1012	RETURN: none
1013	EXAMPLE: example visual; shows an example
1014	"
1015	{
1016
1017	}
1018	example
1019	{
1020	"EXAMPLE:"; echo = 2;
1021	intmat M[6][4] =
1022	1,1,0,0,
1023	1,0,1,0,
1024	1,0,-1,0,
1025	1,0,0,1,
1026	1,0,0,-1,
1027	1,-1,0,0;
1028	polytope p = polytopeViaPoints(M);
1029	// visual(p);
1030	fan f = normalFan(p);
1031	// visual(f);
1032	}
1033
1034
1035	static proc mod_init()
1036	{
1037	intvec save=option(get);
1038	option(noredefine);
1039	LIB "customstd.so";
1040	LIB "gfanlib.so";
1041	LIB "polymake.so";
1042	option(set,save);
1043	}

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