Annotation of OpenXM_contrib/PHC/Ada/Root_Counts/Symmetry/faces_of_symmetric_polytopes.adb, Revision 1.1
1.1 ! maekawa 1: with Permutations,Permute_Operations; use Permutations,Permute_Operations;
! 2: with Lists_of_Integer_Vectors; use Lists_of_Integer_Vectors;
! 3: with Permutations_of_Faces; use Permutations_of_Faces;
! 4:
! 5: package body Faces_of_Symmetric_Polytopes is
! 6:
! 7: -- ON FACES : group * faces -> invariant subgroup
! 8:
! 9: function Stabilizer ( v : List_of_Permutations; f : Face )
! 10: return List_of_Permutations is
! 11:
! 12: tmp,res,res_last : List_of_Permutations;
! 13:
! 14: begin
! 15: tmp := v;
! 16: while not Is_Null(tmp) loop
! 17: declare
! 18: p : constant Permutation := Permutation(Head_Of(tmp).all);
! 19: pf : Face := Permute(f,p);
! 20: begin
! 21: if Is_Equal(f,pf)
! 22: then Append(res,res_last,p);
! 23: end if;
! 24: Deep_Clear(pf);
! 25: end;
! 26: tmp := Tail_Of(tmp);
! 27: end loop;
! 28: return res;
! 29: end Stabilizer;
! 30:
! 31: function Stabilizer_Lifted ( v : List_of_Permutations; f : Face )
! 32: return List_of_Permutations is
! 33:
! 34: tmp,res,res_last : List_of_Permutations;
! 35:
! 36: begin
! 37: tmp := v;
! 38: while not Is_Null(tmp) loop
! 39: declare
! 40: p : constant Permutation := Permutation(Head_Of(tmp).all);
! 41: pf : Face := Permute_Lifted(f,p);
! 42: begin
! 43: if Is_Equal(f,pf)
! 44: then Append(res,res_last,p);
! 45: end if;
! 46: Deep_Clear(pf);
! 47: end;
! 48: tmp := Tail_Of(tmp);
! 49: end loop;
! 50: return res;
! 51: end Stabilizer_Lifted;
! 52:
! 53: -- ON FACES : group * faces -> invariant faces
! 54:
! 55: function Invariant_Faces ( v : List_of_Permutations;
! 56: f : Faces ) return Faces is
! 57:
! 58: tmpf,res,res_last : Faces;
! 59: tmpv : List_of_Permutations;
! 60: inva : boolean;
! 61:
! 62: begin
! 63: tmpf := f;
! 64: while not Is_Null(tmpf) loop
! 65: inva := false;
! 66: declare
! 67: ff : Face := Head_Of(tmpf);
! 68: cf : Face;
! 69: begin
! 70: tmpv := v;
! 71: while not Is_Null(tmpv) loop
! 72: inva := Invariant(ff,Permutation(Head_Of(tmpv).all));
! 73: exit when not inva;
! 74: tmpv := Tail_Of(tmpv);
! 75: end loop;
! 76: if inva
! 77: then Copy(ff,cf); Append(res,res_last,cf);
! 78: end if;
! 79: end;
! 80: tmpf := Tail_Of(tmpf);
! 81: end loop;
! 82: return res;
! 83: end Invariant_Faces;
! 84:
! 85: function Invariant_Lifted_Faces ( v : List_of_Permutations;
! 86: f : Faces ) return Faces is
! 87:
! 88: tmpf,res,res_last : Faces;
! 89: tmpv : List_of_Permutations;
! 90: inva : boolean;
! 91:
! 92: begin
! 93: tmpf := f;
! 94: while not Is_Null(tmpf) loop
! 95: inva := false;
! 96: declare
! 97: ff : Face := Head_Of(tmpf);
! 98: cf : Face;
! 99: begin
! 100: tmpv := v;
! 101: while not Is_Null(tmpv) loop
! 102: inva := Invariant_Lifted(ff,Permutation(Head_Of(tmpv).all));
! 103: exit when not inva;
! 104: tmpv := Tail_Of(tmpv);
! 105: end loop;
! 106: if inva
! 107: then Copy(ff,cf); Append(res,res_last,cf);
! 108: end if;
! 109: end;
! 110: tmpf := Tail_Of(tmpf);
! 111: end loop;
! 112: return res;
! 113: end Invariant_Lifted_Faces;
! 114:
! 115: -- ON FACES : group * faces -> generated faces
! 116:
! 117: function Generated_Faces ( v : List_of_Permutations; f : Faces )
! 118: return Faces is
! 119:
! 120: tmp,res,res_last : Faces;
! 121:
! 122: begin
! 123: return res;
! 124: end Generated_Faces;
! 125:
! 126: function Generated_Lifted_Faces
! 127: ( v : List_of_Permutations; f : Faces )
! 128: return Faces is
! 129:
! 130: tmp,res,res_last : Faces;
! 131:
! 132: begin
! 133: return res;
! 134: end Generated_Lifted_Faces;
! 135:
! 136: -- ON FACES : group * faces -> generating faces
! 137:
! 138: function Generating_Faces ( f : Faces ) return Faces is
! 139:
! 140: tmp,res,res_last : Faces;
! 141: lf : Face;
! 142:
! 143: begin
! 144: tmp := f;
! 145: while not Is_Null(tmp) loop
! 146: lf := Head_Of(tmp);
! 147: if not Permutable(lf,res)
! 148: then Append(res,res_last,lf);
! 149: end if;
! 150: tmp := Tail_Of(tmp);
! 151: end loop;
! 152: return res;
! 153: end Generating_Faces;
! 154:
! 155: function Generating_Lifted_Faces ( f : Faces ) return Faces is
! 156:
! 157: tmp,res,res_last : Faces;
! 158: lf : Face;
! 159:
! 160: begin
! 161: tmp := f;
! 162: while not Is_Null(tmp) loop
! 163: lf := Head_Of(tmp);
! 164: if not Permutable_Lifted(lf,res)
! 165: then Append(res,res_last,lf);
! 166: end if;
! 167: tmp := Tail_Of(tmp);
! 168: end loop;
! 169: return res;
! 170: end Generating_Lifted_Faces;
! 171:
! 172: function Generating_Faces ( v : List_of_Permutations; f : Faces )
! 173: return Faces is
! 174:
! 175: tmp,res,res_last : Faces;
! 176: tmpv : List_of_Permutations;
! 177: found : boolean;
! 178: lf : Face;
! 179:
! 180: begin
! 181: tmp := f;
! 182: while not Is_Null(tmp) loop
! 183: lf := Head_Of(tmp);
! 184: tmpv := v;
! 185: while not Is_Null(tmpv) loop
! 186: declare
! 187: pv : constant Permutation := Permutation(Head_Of(tmpv).all);
! 188: begin
! 189: found := Is_In(res,Permute(lf,pv));
! 190: end;
! 191: exit when found;
! 192: tmpv := Tail_Of(tmpv);
! 193: end loop;
! 194: if not found
! 195: then Append(res,res_last,lf);
! 196: end if;
! 197: tmp := Tail_Of(tmp);
! 198: end loop;
! 199: return res;
! 200: end Generating_Faces;
! 201:
! 202: function Generating_Lifted_Faces ( v : List_of_Permutations; f : Faces )
! 203: return Faces is
! 204:
! 205: tmp,res,res_last : Faces;
! 206: tmpv : List_of_Permutations;
! 207: found : boolean;
! 208: lf : Face;
! 209:
! 210: begin
! 211: tmp := f;
! 212: while not Is_Null(tmp) loop
! 213: lf := Head_Of(tmp);
! 214: tmpv := v;
! 215: while not Is_Null(tmpv) loop
! 216: declare
! 217: pv : constant Permutation := Permutation(Head_Of(tmpv).all);
! 218: begin
! 219: found := Is_In(res,Permute_Lifted(lf,pv));
! 220: end;
! 221: exit when found;
! 222: tmpv := Tail_Of(tmpv);
! 223: end loop;
! 224: if not found
! 225: then Append(res,res_last,lf);
! 226: end if;
! 227: tmp := Tail_Of(tmp);
! 228: end loop;
! 229: return res;
! 230: end Generating_Lifted_Faces;
! 231:
! 232: -- ON TUPLES OF FACES : group * faces -> invariant faces
! 233:
! 234: function Invariant_Faces ( v : List_of_Permutations;
! 235: af : Array_of_Faces ) return Array_of_Faces is
! 236:
! 237: res : Array_of_Faces(af'range);
! 238:
! 239: begin
! 240: for i in res'range loop
! 241: res(i) := Invariant_Faces(v,af(i));
! 242: end loop;
! 243: return res;
! 244: end Invariant_Faces;
! 245:
! 246: function Invariant_Lifted_Faces
! 247: ( v : List_of_Permutations; af : Array_of_Faces )
! 248: return Array_of_Faces is
! 249:
! 250: res : Array_of_Faces(af'range);
! 251:
! 252: begin
! 253: for i in res'range loop
! 254: res(i) := Invariant_Lifted_Faces(v,af(i));
! 255: end loop;
! 256: return res;
! 257: end Invariant_Lifted_Faces;
! 258:
! 259: -- ON TUPLES OF FACES : group * faces -> generators of faces
! 260:
! 261: function Generating_Faces ( af : Array_of_Faces ) return Array_of_Faces is
! 262:
! 263: res,res_last : Array_of_Faces(af'range);
! 264: tmp : Faces;
! 265: lf : Face;
! 266: found : boolean;
! 267:
! 268: begin
! 269: for i in af'range loop
! 270: tmp := af(i);
! 271: while not Is_Null(tmp) loop
! 272: lf := Head_Of(tmp);
! 273: for j in res'range loop
! 274: found := Permutable(lf,res(j));
! 275: exit when found;
! 276: end loop;
! 277: if not found
! 278: then Append(res(i),res_last(i),lf);
! 279: end if;
! 280: tmp := Tail_Of(tmp);
! 281: end loop;
! 282: end loop;
! 283: return res;
! 284: end Generating_Faces;
! 285:
! 286: function Generating_Lifted_Faces
! 287: ( af : Array_of_Faces ) return Array_of_Faces is
! 288:
! 289: res,res_last : Array_of_Faces(af'range);
! 290: tmp : Faces;
! 291: lf : Face;
! 292: found : boolean;
! 293:
! 294: begin
! 295: for i in af'range loop
! 296: tmp := af(i);
! 297: while not Is_Null(tmp) loop
! 298: lf := Head_Of(tmp);
! 299: for j in res'range loop
! 300: found := Permutable_Lifted(lf,res(j));
! 301: exit when found;
! 302: end loop;
! 303: if not found
! 304: then Append(res(i),res_last(i),lf);
! 305: end if;
! 306: tmp := Tail_Of(tmp);
! 307: end loop;
! 308: end loop;
! 309: return res;
! 310: end Generating_Lifted_Faces;
! 311:
! 312: function Generating_Faces
! 313: ( v : List_of_Permutations; af : Array_of_Faces )
! 314: return Array_of_Faces is
! 315:
! 316: res : Array_of_Faces(af'range);
! 317:
! 318: begin
! 319: for i in res'range loop
! 320: res(i) := Generating_Faces(v,af(i));
! 321: end loop;
! 322: return res;
! 323: end Generating_Faces;
! 324:
! 325: function Generating_Lifted_Faces
! 326: ( v : List_of_Permutations; af : Array_of_Faces )
! 327: return Array_of_Faces is
! 328:
! 329: res : Array_of_Faces(af'range);
! 330:
! 331: begin
! 332: for i in res'range loop
! 333: res(i) := Generating_Lifted_Faces(v,af(i));
! 334: end loop;
! 335: return res;
! 336: end Generating_Lifted_Faces;
! 337:
! 338: function Generating_Faces
! 339: ( v,w : List_of_Permutations; af : Array_of_Faces )
! 340: return Array_of_Faces is
! 341:
! 342: res,res_last : Array_of_Faces(af'range);
! 343: tmp : Faces;
! 344: lf : Face;
! 345: found : boolean;
! 346: tmpv,tmpw : List_of_Permutations;
! 347:
! 348: begin
! 349: for i in af'range loop
! 350: tmp := af(i);
! 351: while not Is_Null(tmp) loop
! 352: lf := Head_Of(tmp);
! 353: tmpv := v; tmpw := w;
! 354: while not Is_Null(tmpv) loop
! 355: declare
! 356: pv : constant Permutation := Permutation(Head_Of(tmpv).all);
! 357: pw : constant Permutation := Permutation(Head_Of(tmpw).all);
! 358: begin
! 359: found := Is_In(res(pw(i)),Permute(lf,pv));
! 360: end;
! 361: exit when found;
! 362: tmpv := Tail_Of(tmpv); tmpw := Tail_Of(tmpw);
! 363: end loop;
! 364: if not found
! 365: then Append(res(i),res_last(i),lf);
! 366: end if;
! 367: tmp := Tail_Of(tmp);
! 368: end loop;
! 369: end loop;
! 370: return res;
! 371: end Generating_Faces;
! 372:
! 373: function Generating_Lifted_Faces
! 374: ( v,w : List_of_Permutations; af : Array_of_Faces )
! 375: return Array_of_Faces is
! 376:
! 377: res,res_last : Array_of_Faces(af'range);
! 378: tmp : Faces;
! 379: lf : Face;
! 380: found : boolean;
! 381: tmpv,tmpw : List_of_Permutations;
! 382:
! 383: begin
! 384: for i in af'range loop
! 385: tmp := af(i);
! 386: while not Is_Null(tmp) loop
! 387: lf := Head_Of(tmp);
! 388: tmpv := v; tmpw := w;
! 389: while not Is_Null(tmpv) loop
! 390: declare
! 391: pv : constant Permutation := Permutation(Head_Of(tmpv).all);
! 392: pw : constant Permutation := Permutation(Head_Of(tmpw).all);
! 393: begin
! 394: found := Is_In(res(pw(i)),Permute_Lifted(lf,pv));
! 395: end;
! 396: exit when found;
! 397: tmpv := Tail_Of(tmpv); tmpw := Tail_Of(tmpw);
! 398: end loop;
! 399: if not found
! 400: then Append(res(i),res_last(i),lf);
! 401: end if;
! 402: tmp := Tail_Of(tmp);
! 403: end loop;
! 404: end loop;
! 405: return res;
! 406: end Generating_Lifted_Faces;
! 407:
! 408: end Faces_of_Symmetric_Polytopes;
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