1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
|
/* ====================================================================== */
/* ========== ========== */
/* ========== P O L Y . C ========== */
/* ========== ========== */
/* ====================================================================== */
/*
* Coord get coordinates by reading them or converting weight input
* Rat rational functions
* Vertex computes Vertices and Faces
* Polynf normal form and symmetries
*/
#include "Global.h"
#include "LG.h"
#define OSL (42) /* opt_string's length */
FILE *inFILE, *outFILE;
void PrintUsage(char *c){
int i;
char *opt_string[OSL]={
"h print this information ",
"f use as filter ",
"g general output: ",
" P reflexive: numbers of (dual) points/vertices, Hodge numbers ",
" P not reflexive: numbers of points, vertices, equations ",
"p points of P ",
"v vertices of P ",
"e equations of P/vertices of P-dual",
"m pairing matrix between vertices and equations ",
"d points of P-dual (only if P reflexive) ",
"a all of the above except h,f ",
"l LG-`Hodge numbers' from single weight input ",
"r ignore non-reflexive input ",
"o ignore non-IP input ",
"q quick version of og, incompatible with other options",
"Q like 'q', with statistics on weights for 5d classification",
"D dual polytope as input (ref only)",
"n do not complete polytope or calculate Hodge numbers ",
"i incidence information ",
"s check for span property (only if P from CWS) ",
"I check for IP property ",
"S number of symmetries ",
"T upper triangular form ",
"N normal form ",
"t traced normal form computation ",
"V IP simplices among vertices of P*",
"P IP simplices among points of P* (with 1<=codim<=# when # is set)",
"Z lattice quotients for IP simplices",
"# #=1,2,3 fibers spanned by IP simplices with codim<=# ",
"## ##=11,22,33,(12,23): all (fibered) fibers with specified codim(s) ",
" when combined: ### = (##)# ",
"A affine normal form",
"B Barycenter and lattice volume [# ... points at deg #]",
"F print all facets",
"G Gorenstein: divisible by I>1",
"L like 'l' with Hodge data for twisted sectors",
"U simplicial facets in N-lattice",
"U1 Fano (simplicial and unimodular facets in N-lattice)",
"U5 5d fano from reflexive 4d projections (M lattice)",
"C1 conifold CY (unimodular or square 2-faces)",
"C2 conifold FANO (divisible by 2 & basic 2 faces)",
"E symmetries related to Einstein-Kaehler Metrics"};
puts("");
printf("This is '%s': computing data of a polytope P\n",c);
printf("Usage: %s [-<Option-string>] [in-file [out-file]]\n", c);
puts("");
printf("Options (concatenate any number of them into <Option-string>):\n");
for (i=0;i<OSL;i++) puts(opt_string[i]);
puts("");
puts("Input: degrees and weights `d1 w11 w12 ... d2 w21 w22 ...'");
puts(" or `d np' or `np d' (d=Dimension, np=#[points]) and");
puts(" (after newline) np*d coordinates");
puts("Output: as specified by options");
}
typedef struct {int p[SYM_Nmax][VERT_Nmax];} VPermList;
int main (int narg, char* fn[]){
int n=0, k, FilterFlag=0, lg=0, s=0, i=0, m=0, p=0, v=0, e=0, d=0, t=0, z=0,
S=0, N=0, I=0, r=0, nc=0, g=0, D=0, IP, R, Tr, T=0, PS=0, VS=0, CD=0, ZS=1,
A=0, B=0, G=0, F=0, U=0, dd=0, Einstein=0, o=0, q=0, Q=0;
char c;
CWS *CW=(CWS *) malloc(sizeof(CWS));
Weight W;
VertexNumList V;
EqList *E = (EqList *) malloc(sizeof(EqList));
EqList *DE = (EqList *) malloc(sizeof(EqList));
BaHo BH;
VaHo VH;
PolyPointList *_P = (PolyPointList *) malloc(sizeof(PolyPointList)),
*_DP = (PolyPointList *) malloc(sizeof(PolyPointList));
FaceInfo *FI=NULL;
PairMat *PM = (PairMat *) malloc(sizeof(PairMat)),
*DPM = (PairMat *) malloc(sizeof(PairMat));
C5stats C5S;
if((CW==NULL)||(E==NULL)||(_P==NULL)||(DE==NULL)||(_DP==NULL)
||(PM==NULL)||(DPM==NULL)) {
puts("Allocation failure: Reduce dimensions!"); exit(0);}
CW->nw=0;
while(narg > ++n) {
if(fn[n][0]!='-') break;
k=0;
while ((c=fn[n][++k])!='\0'){
if(c=='A') A=1;
else if(c=='B') B=1;
else if(c=='F') F=1;
else if(c=='G') G=1;
else if(c=='L') lg=2;
else if(c=='U') U=1;
else if(c=='C') U=2;
else if(c=='E') Einstein=1;
else if(c=='h') { PrintUsage(fn[0]); exit(0);}
else if(c=='f') FilterFlag=1;
else if(c=='g') g=1;
else if(c=='l') lg=1;
else if(c=='s') s=1;
else if(c=='i') i=1;
else if(c=='I') I=1;
else if(c=='m') m=1;
else if(c=='p') p=1;
else if(c=='v') v=1;
else if(c=='e') e=1;
else if(c=='d') d=1;
else if(c=='t') t=1;
else if(c=='S') S=1;
else if(c=='N') N=1;
else if(c=='T') T=1;
else if(c=='r') r=1;
else if(c=='o') o=1;
else if(c=='q') q=1;
else if(c=='Q') Q=1;
else if(c=='n') nc=1;
else if(c=='P') PS=1;
else if(c=='V') VS=1;
else if(c=='Z') ZS=-1;
else if(c=='z') z=1;
else if(c=='D') D=1;
else if(('0'<=c)&&(c<='9')) CD=10*CD+c-'0';
else if(c=='a') {g=1; m=1; p=1; v=1; e=1; d=1; }
else {printf("Unknown option '-%c'; use -h for help\n",c); exit(0);}}}
n--;
if(s+i+I+m+p+v+e+d+t+S+N+T+PS+VS+CD+G+A+B+F+z==0) g=1;
VH.sts=(lg==2);
if ((U==1)&&(CD==1)&&(s+i+I+m+p+v+e+d+t+S+N+T+PS+VS+G+A+B+F+z==0)) g=1;
if(g+lg+p+d+PS+CD==0) nc=1; /* don't need completion of points */
if((T==1)&&(B+U+lg+g+s+i+I+m+p+v+e+d+t+S+N+PS+VS+(1-ZS)==0)){ puts(
"\n-T: Please specify desired output, e.g. via -v or -p \n");exit(0);}
if(FilterFlag) {inFILE=NULL; outFILE=stdout;}
else {
if (narg > ++n) inFILE=fopen(fn[n],"r");
else inFILE=stdin;
if (inFILE==NULL){printf("Input file %s not found!\n",fn[n]);exit(0);}
if (narg > ++n) outFILE=fopen(fn[n],"w");
else outFILE=stdout; }
if(U) {dd=CD; CD=0; if((U==2)||(dd==5)) nc=0;}
if(i){
FI=(FaceInfo *) malloc(sizeof(FaceInfo));
if (FI==NULL) {puts("Unable to allocate space for FaceInfo FI"); exit(0);}}
if(Q) Initialize_C5S(&C5S, POLY_Dmax); // Initialize statistics
if(Einstein) Einstein_Metric(CW,_P,&V,E);
while(lg ? Read_W_PP(&W,_P) : Read_CWS_PP(CW,_P)) {
if(q||Q) {
FaceInfo FI;
if(!QuickAnalysis(_P, &BH, &FI)) {if(Q) C5S.n_nonIP++; continue;} //non-IP
Print_CWH(CW, &BH);
if(Q) Update_C5S(&BH, FI.nf, CW->W[0], &C5S);
continue;}
if(T) {
if (CW->nw) {
puts("Please do not use weight input with the -T option"); continue;}
else Make_Poly_UTriang(_P);}
R=0;
if ((IP=Find_Equations(_P,&V,E))){
if (D){
int k;
*_DP=*_P;
R=EL_to_PPL(E, _P, &_P->n);
VNL_to_DEL(_DP, &V, E);
for (k=0;k<_P->np;k++) V.v[k]=k;
V.nv=_P->np; }
else R=EL_to_PPL(E, _DP, &_P->n);}
else if (o&&!IP) continue;
if (D&&!R) {fprintf(outFILE,"Input not reflexive!\n"); continue;}
if (r&&!R) continue;
Sort_VL(&V);
Make_VEPM(_P,&V,E,*PM);
if(!nc) {
if(D||!(lg||CW->nw)) Complete_Poly(*PM,E,V.nv,_P);
if(R&&!(D&&(lg||CW->nw))) {
if(0==Transpose_PM(*PM, *DPM, V.nv, E->ne))
{ fprintf(stderr,"Transpose_PM failed because #eq=%d > VERT_Nmax\n",
E->ne);exit(0);}
VNL_to_DEL(_P, &V, DE);
Complete_Poly(*DPM,DE,E->ne,_DP);}}
if (U==1) {
if(dd==5) {if(!Fano5d(_P,&V,E)) continue;}
else if(!SimpUnimod(_P,&V,E,dd)) continue; }
if (U==2) {
VNL_to_DEL(_P,&V,DE);
if(!ConifoldSing(_P,&V,E,_DP,DE,dd)) continue;}
if(g){
if(!R||nc) {BH.mp=_P->np; BH.mv=V.nv; BH.np=0; BH.nv=E->ne;}
else RC_Calc_BaHo(_P,&V,E,_DP,&BH);
if(lg) {
if ((Tr=Trans_Check(W))) LGO_VaHo(&W,&VH);
Write_WH(&W, &BH, &VH, R, Tr, _P, &V, E); }
else Print_CWH(CW, &BH); }
if(s&&CW->nw) if(!Span_Check(E,&(CW->B),&_P->n))
fprintf(outFILE,"No Span\n");
if(I && !IP) fprintf(outFILE,"No IP\n");
if(p) Print_PPL(_P,"Points of P");
if(v) Print_VL(_P, &V, "Vertices of P");
if(e) Print_EL(E, &_P->n, R,
(R ? "Vertices of P-dual <-> Equations of P" : "Equations of P"));
if(i){Make_Incidence(_P,&V,E,FI); Print_FaceInfo(_P->n,FI);}
if(m) Print_Matrix(*PM, E->ne, V.nv,
"Pairing matrix of vertices and equations of P");
if(d&&(_DP->np>E->ne)) Print_PPL(_DP, "Points of P-dual");
if(S||N||t){
int SymNum /*, VPMSymNum*/; Long NF[POLY_Dmax][VERT_Nmax];
VPermList *VP = (VPermList*) malloc(sizeof(VPermList));
assert(VP!=NULL);
/* VPMSymNum=*/ Make_Poly_Sym_NF(_P, &V, E, &SymNum, VP->p, NF, t, S, N);
free(VP);}
if(R&&(PS||VS||CD)) IP_Simplices(_DP, (!D)*E->ne, PS*ZS, VS*ZS, CD);
if(G) {
char divi[99]; Long g=Divisibility_Index(_P,&V);
if(g>1){sprintf(divi,"divisible by factor=%ld",g); Print_VL(_P,&V,divi);}}
if(B) {
Long vB[POLY_Dmax],Z; int j;
Long vol=LatVol_Barycent(_P,&V,vB,&Z); printf("vol=%ld, baricent=(",vol);
for(j=0;j<_P->n;j++) printf("%s%ld",j?",":"",vB[j]);
printf(")/%ld\n",Z); if(CD) IPs_degD(_P,&V,E,CD);}
if(F) {
int j, cc;
Long VM[POLY_Dmax][VERT_Nmax];
for (j=0; j<E->ne; j++){
Make_Facet(_P, &V, E, j, VM, &cc);
Print_Matrix(VM,_P->n-1,cc,"");} }
if(A) {
Long ANF[POLY_Dmax][VERT_Nmax];
Make_ANF(_P,&V,E,ANF);
Print_Matrix(ANF, _P->n, V.nv,"Affine normal form");}
fflush(outFILE); }
if(Q) Print_C5S(&C5S);
return 0;
}
|
