Annotation of OpenXM_contrib/PHC/Ada/Root_Counts/Implift/set_structures_and_volumes.adb, Revision 1.1
1.1 ! maekawa 1: with Standard_Floating_Numbers; use Standard_Floating_Numbers;
! 2: with Standard_Complex_Numbers; use Standard_Complex_Numbers;
! 3: with Standard_Natural_Vectors;
! 4: with Standard_Complex_Vectors; use Standard_Complex_Vectors;
! 5: with Standard_Complex_Matrices; use Standard_Complex_Matrices;
! 6: with Standard_Complex_Linear_Solvers; use Standard_Complex_Linear_Solvers;
! 7: with Standard_Complex_Polynomials; use Standard_Complex_Polynomials;
! 8: with Standard_Complex_Poly_Randomizers; use Standard_Complex_Poly_Randomizers;
! 9: with Standard_Complex_Substitutors; use Standard_Complex_Substitutors;
! 10: with Standard_Complex_Laur_Systems; use Standard_Complex_Laur_Systems;
! 11: with Standard_Poly_Laur_Convertors; use Standard_Poly_Laur_Convertors;
! 12: with Arrays_of_Integer_Vector_Lists; use Arrays_of_Integer_Vector_Lists;
! 13: with Set_Structure;
! 14: with Random_Product_System;
! 15: with Random_Product_Start_Systems;
! 16: with Power_Lists; use Power_Lists;
! 17: with Volumes; use Volumes;
! 18: with Mixed_Homotopy_Continuation; use Mixed_Homotopy_Continuation;
! 19:
! 20: package body Set_Structures_and_Volumes is
! 21:
! 22: -- AUXILIARIES :
! 23:
! 24: procedure Build_RPS ( k,n : in natural; p : in Poly_Sys ) is
! 25:
! 26: -- DESCRIPTION :
! 27: -- If the set structure is empty, then a set structure will
! 28: -- be constructed for the first k polynomials of p;
! 29: -- the data in Random_Product_System will be build.
! 30:
! 31: begin
! 32: if Set_Structure.Empty
! 33: then declare
! 34: tmp : Poly_Sys(p'range);
! 35: t : Term;
! 36: cnst : Poly;
! 37: begin
! 38: tmp(1..k) := p(1..k);
! 39: t.dg := new Standard_Natural_Vectors.Vector'(1..n => 0);
! 40: t.cf := Create(1.0);
! 41: cnst := Create(t);
! 42: tmp(k+1..n) := (k+1..n => cnst);
! 43: Random_Product_Start_Systems.Build_Set_Structure(tmp);
! 44: Standard_Natural_Vectors.Clear
! 45: (Standard_Natural_Vectors.Link_to_Vector(t.dg));
! 46: Clear(cnst);
! 47: end;
! 48: end if;
! 49: Random_Product_System.Init(n);
! 50: Random_Product_Start_Systems.Build_Random_Product_System(n);
! 51: end Build_RPS;
! 52:
! 53: procedure Build_Elimination_Matrix
! 54: ( k,n : in natural; ind : in Standard_Natural_Vectors.Vector;
! 55: m : in out Matrix;
! 56: pivots : in out Standard_Natural_Vectors.Vector;
! 57: degenerate : out boolean ) is
! 58:
! 59: -- DESCRIPTION :
! 60: -- builds the elimination matrix m.
! 61:
! 62: -- ON ENTRY :
! 63: -- k the number of unknowns to be eliminated;
! 64: -- n the number of polynomials and unknowns;
! 65: -- ind entries in Random_Product_System;
! 66: -- ind(l) indicates lth hyperplane;
! 67:
! 68: -- ON RETURN :
! 69: -- m contains all k hyperplanes to use for elimination;
! 70: -- pivots if not degenerate, then m(i,pivots(i)) /= 0;
! 71: -- degenerate is true if the first k hyperplanes were inconsistent.
! 72:
! 73: degen : boolean;
! 74:
! 75: begin
! 76: for i in ind'range loop -- build the matrix
! 77: declare
! 78: h : Vector(0..n) := Random_Product_System.Get_Hyperplane(i,ind(i));
! 79: begin
! 80: for j in 1..n loop
! 81: m(i,j) := h(j);
! 82: end loop;
! 83: m(i,n+1) := h(0);
! 84: end;
! 85: end loop;
! 86: diagonalize(m,k,n+1);
! 87: degen := false; -- check degeneracy
! 88: declare
! 89: eps : constant double_float := 10.0**(-10);
! 90: begin
! 91: for i in pivots'range loop
! 92: for j in 1..n loop
! 93: if AbsVal(m(i,j)) > eps
! 94: then pivots(i) := j;
! 95: end if;
! 96: exit when (pivots(i) /= 0);
! 97: end loop;
! 98: degen := (pivots(i) = 0);
! 99: exit when degen;
! 100: end loop;
! 101: end;
! 102: degenerate := degen;
! 103: end Build_Elimination_Matrix;
! 104:
! 105: procedure Eliminate ( k,n : in natural; p : in Poly_Sys; m : in Matrix;
! 106: pivots : in Standard_Natural_Vectors.Vector;
! 107: q : in out Poly_Sys ) is
! 108: -- DESCRIPTION :
! 109: -- eliminates k unknowns of the polynomial system p.
! 110:
! 111: -- ON ENTRY :
! 112: -- k the number of unknowns to be eliminated;
! 113: -- n the number of polynomials and unknowns;
! 114: -- p a polynomial system with random coefficients;
! 115: -- m the diagonalized matrix, to be used for elimination,
! 116: -- for i in m'range(1) : m(i,pivots(i)) /= 0;
! 117: -- pivots a vector indicating nonzero entries in m.
! 118:
! 119: -- ON RETURN :
! 120: -- q the reduced system.
! 121:
! 122: begin
! 123: Clear(q); Copy(p,q);
! 124: for i in pivots'range loop
! 125: declare
! 126: h : Vector(0..n-i+1);
! 127: piv : natural := pivots(i)-i+1;
! 128: begin
! 129: h(0) := m(i,n+1);
! 130: h(1..n-i+1) := (1..n-i+1 => Create(0.0));
! 131: h(piv) := m(i,pivots(i));
! 132: for j in piv+1..n-i+1 loop
! 133: h(j) := m(i,j+i-1);
! 134: end loop;
! 135: Substitute(piv,h,q);
! 136: end;
! 137: end loop;
! 138: end Eliminate;
! 139:
! 140: procedure Update ( sols : in out Solution_List; k,n : in natural;
! 141: m : in Matrix;
! 142: pivots : in Standard_Natural_Vectors.Vector ) is
! 143:
! 144: -- DESCRIPTION :
! 145: -- Based on the elimination matrix m, solution components for x1..xk
! 146: -- can be computed.
! 147:
! 148: -- ON ENTRY :
! 149: -- sols a list of solutions, with values for x(n-k+1)..x(n);
! 150: -- k the number of unknowns that have been eliminated;
! 151: -- n total number of unknowns;
! 152: -- m the elimination matrix;
! 153: -- pivots for i in pivots'range : m(i,pivots(i)) /= 0.
! 154:
! 155: -- ON RETURN :
! 156: -- sols the solution list with n-dimensional vectors.
! 157:
! 158: tmp,res,res_last : Solution_List;
! 159:
! 160: begin
! 161: tmp := sols;
! 162: while not Is_Null(tmp) loop
! 163: declare
! 164: sol : Solution(n-k) := Head_Of(tmp).all;
! 165: soln : Solution(n);
! 166: ind : natural;
! 167: begin
! 168: soln.t := Create(0.0);
! 169: soln.m := sol.m;
! 170: soln.v := (1..n => Create(0.0));
! 171: for i in 1..k loop
! 172: soln.v(pivots(i)) := -m(i,n+1);
! 173: end loop;
! 174: ind := 0;
! 175: for i in 1..n loop
! 176: if soln.v(i) = Create(0.0)
! 177: then ind := ind + 1;
! 178: soln.v(i) := sol.v(ind);
! 179: end if;
! 180: end loop;
! 181: for i in 1..k loop
! 182: ind := pivots(i);
! 183: for j in ind+1..n loop
! 184: soln.v(ind) := soln.v(ind) - m(i,j)*soln.v(j);
! 185: end loop;
! 186: soln.v(ind) := soln.v(ind) / m(i,ind);
! 187: end loop;
! 188: Append(res,res_last,soln);
! 189: end;
! 190: tmp := Tail_Of(tmp);
! 191: end loop;
! 192: Clear(sols); Copy(res,sols);
! 193: end Update;
! 194:
! 195: procedure Build_Indices ( l,k,n : in natural; p : in Poly_Sys;
! 196: acc : in out Standard_Natural_Vectors.Vector;
! 197: bb : in out natural ) is
! 198:
! 199: -- DESCRIPTION :
! 200: -- Builds the indices in the vector acc.
! 201:
! 202: -- ON ENTRY :
! 203: -- l index in the array acc;
! 204: -- k number of unknowns to eliminate;
! 205: -- n number of polynomials and unknowns;
! 206: -- p a polynomial system;
! 207: -- acc(1..l-1) contains entries indicating hyperplanes
! 208: -- in Random_Product_System.
! 209:
! 210: -- ON RETURN :
! 211: -- acc(1..l) contains entries indicating hyperplanes
! 212: -- in Random_Product_System;
! 213: -- bb the mixed Bezout BKK bound.
! 214:
! 215: begin
! 216: if l > k
! 217: then declare
! 218: degenerate : boolean;
! 219: m : Matrix(1..k,1..n+1);
! 220: pivots : Standard_Natural_Vectors.Vector(1..k);
! 221: begin
! 222: pivots := (1..k => 0);
! 223: Build_Elimination_Matrix(k,n,acc,m,pivots,degenerate);
! 224: if not degenerate
! 225: then declare
! 226: q : Poly_Sys(p'range);
! 227: begin
! 228: Eliminate(k,n,p,m,pivots,q);
! 229: bb := bb + Bezout_BKK(0,n-k,q);
! 230: Clear(q);
! 231: end;
! 232: end if;
! 233: end;
! 234: else for j in 1..Random_Product_System.Number_of_Hyperplanes(l) loop
! 235: acc(l) := j;
! 236: Build_Indices(l+1,k,n,p,acc,bb);
! 237: end loop;
! 238: end if;
! 239: end Build_Indices;
! 240:
! 241: procedure Build_Indices ( l,k,n : in natural; p : in Poly_Sys;
! 242: tv : in Tree_of_Vectors;
! 243: acc : in out Standard_Natural_Vectors.Vector;
! 244: bb : in out natural ) is
! 245:
! 246: -- DESCRIPTION :
! 247: -- Builds the indices in the vector acc.
! 248:
! 249: -- ON ENTRY :
! 250: -- l index in the array acc;
! 251: -- k number of unknowns to eliminate;
! 252: -- n number of polynomials and unknowns;
! 253: -- p a polynomial system;
! 254: -- tv the tree of degrees used to compute the mixed volume;
! 255: -- acc(1..l-1) contains entries indicating hyperplanes
! 256: -- in Random_Product_System.
! 257:
! 258: -- ON RETURN :
! 259: -- acc(1..l) contains entries indicating hyperplanes
! 260: -- in Random_Product_System;
! 261: -- bb the mixed Bezout BKK bound.
! 262:
! 263: begin
! 264: if l > k
! 265: then declare
! 266: degenerate : boolean;
! 267: m : Matrix(1..k,1..n+1);
! 268: pivots : Standard_Natural_Vectors.Vector(1..k);
! 269: begin
! 270: pivots := (1..k => 0);
! 271: Build_Elimination_Matrix(k,n,acc,m,pivots,degenerate);
! 272: if not degenerate
! 273: then declare
! 274: q : Poly_Sys(p'range);
! 275: begin
! 276: Eliminate(k,n,p,m,pivots,q);
! 277: bb := bb + Bezout_BKK(0,n-k,q,tv);
! 278: Clear(q);
! 279: end;
! 280: end if;
! 281: end;
! 282: else for j in 1..Random_Product_System.Number_of_Hyperplanes(l) loop
! 283: acc(l) := j;
! 284: Build_Indices(l+1,k,n,p,tv,acc,bb);
! 285: end loop;
! 286: end if;
! 287: end Build_Indices;
! 288:
! 289: procedure Build_Indices2 ( l,k,n : in natural; p : in Poly_Sys;
! 290: tv : in out Tree_of_Vectors;
! 291: acc : in out Standard_Natural_Vectors.Vector;
! 292: bb : in out natural ) is
! 293:
! 294: -- DESCRIPTION :
! 295: -- Builds the indices in the vector acc.
! 296:
! 297: -- ON ENTRY :
! 298: -- l index in the array acc;
! 299: -- k number of unknowns to eliminate;
! 300: -- n number of polynomials and unknowns;
! 301: -- p a polynomial system;
! 302: -- acc(1..l-1) contains entries indicating hyperplanes
! 303: -- in Random_Product_System.
! 304:
! 305: -- ON RETURN :
! 306: -- tv the tree of degrees used to compute the mixed volume;
! 307: -- acc(1..l) contains entries indicating hyperplanes
! 308: -- in Random_Product_System;
! 309: -- bb the mixed Bezout BKK bound.
! 310:
! 311: begin
! 312: if l > k
! 313: then declare
! 314: degenerate : boolean;
! 315: m : Matrix(1..k,1..n+1);
! 316: pivots : Standard_Natural_Vectors.Vector(1..k);
! 317: begin
! 318: pivots := (1..k => 0);
! 319: Build_Elimination_Matrix(k,n,acc,m,pivots,degenerate);
! 320: if not degenerate
! 321: then declare
! 322: q : Poly_Sys(p'range);
! 323: qtv,tmp : Tree_of_Vectors;
! 324: mv : natural;
! 325: begin
! 326: Eliminate(k,n,p,m,pivots,q);
! 327: Bezout_BKK(0,n-k,q,qtv,mv);
! 328: bb := bb + mv;
! 329: tmp := qtv;
! 330: while not Is_Null(tmp) loop
! 331: declare
! 332: nd : node := Head_Of(tmp);
! 333: begin
! 334: if Is_In(tv,nd.d)
! 335: then Clear(nd);
! 336: else Construct(nd,tv);
! 337: end if;
! 338: end;
! 339: tmp := Tail_Of(tmp);
! 340: end loop;
! 341: Clear(q);
! 342: end;
! 343: end if;
! 344: end;
! 345: else for j in 1..Random_Product_System.Number_of_Hyperplanes(l) loop
! 346: acc(l) := j;
! 347: Build_Indices2(l+1,k,n,p,tv,acc,bb);
! 348: end loop;
! 349: end if;
! 350: end Build_Indices2;
! 351:
! 352: procedure Build_Indices
! 353: ( file : in file_type; p : in Poly_Sys; l,k,n : in natural;
! 354: acc : in out Standard_Natural_Vectors.Vector;
! 355: bb : in out natural;
! 356: sols,sols_last : in out Solution_List ) is
! 357:
! 358: -- DESCRIPTION :
! 359: -- Builds the indices in the vector acc.
! 360:
! 361: -- ON ENTRY :
! 362: -- file file to write intermediate results on;
! 363: -- p a polynomial system;
! 364: -- l index in the array acc;
! 365: -- k number of unknowns to eliminate;
! 366: -- n number of polynomials and unknowns;
! 367: -- acc(1..l-1) contains entries indicating hyperplanes
! 368: -- in Random_Product_System.
! 369:
! 370: -- ON RETURN :
! 371: -- acc(1..l) contains entries indicating hyperplanes
! 372: -- in Random_Product_System;
! 373: -- bb the mixed Bezout BKK bound;
! 374: -- sols the solutions of pi;
! 375: -- sols_last points to the last element of the list sols.
! 376:
! 377: begin
! 378: if l > k
! 379: then declare
! 380: degenerate : boolean;
! 381: m : Matrix(1..k,1..n+1);
! 382: pivots : Standard_Natural_Vectors.Vector(1..k);
! 383: begin
! 384: pivots := (1..k => 0);
! 385: Build_Elimination_Matrix(k,n,acc,m,pivots,degenerate);
! 386: if not degenerate
! 387: then declare
! 388: q : Poly_Sys(p'range);
! 389: begin
! 390: Eliminate(k,n,p,m,pivots,q);
! 391: declare
! 392: las : Laur_Sys(q'range);
! 393: qsols : Solution_List;
! 394: bkk : natural;
! 395: begin
! 396: las := Polynomial_to_Laurent_System(q);
! 397: Solve(file,las,bkk,qsols);
! 398: bb := bb + bkk;
! 399: Update(qsols,k,n,m,pivots);
! 400: Concat(sols,sols_last,qsols);
! 401: Clear(las); Shallow_Clear(qsols);
! 402: end;
! 403: Clear(q);
! 404: end;
! 405: end if;
! 406: end;
! 407: else for j in 1..Random_Product_System.Number_of_Hyperplanes(l) loop
! 408: acc(l) := j;
! 409: Build_Indices(file,p,l+1,k,n,acc,bb,sols,sols_last);
! 410: end loop;
! 411: end if;
! 412: end Build_Indices;
! 413:
! 414: procedure Build_Indices
! 415: ( file : in file_type; p : in Poly_Sys; l,k,n : in natural;
! 416: acc : in out Standard_Natural_Vectors.Vector;
! 417: tv : in Tree_of_Vectors; bb : in out natural;
! 418: sols,sols_last : in out Solution_List ) is
! 419:
! 420: -- DESCRIPTION :
! 421: -- Builds the indices in the vector acc.
! 422:
! 423: -- ON ENTRY :
! 424: -- file file to write intermediate results on;
! 425: -- p a polynomial system;
! 426: -- l index in the array acc;
! 427: -- k number of unknowns to eliminate;
! 428: -- n number of polynomials and unknowns;
! 429: -- acc(1..l-1) contains entries indicating hyperplanes
! 430: -- in Random_Product_System;
! 431: -- tv the tree containing useful directions;
! 432:
! 433: -- ON RETURN :
! 434: -- acc(1..l) contains entries indicating hyperplanes
! 435: -- in Random_Product_System;
! 436: -- bb the mixed Bezout BKK bound;
! 437: -- sols the solutions of pi;
! 438: -- sols_last points to the last element of the list sols.
! 439:
! 440: begin
! 441: if l > k
! 442: then declare
! 443: degenerate : boolean;
! 444: m : Matrix(1..k,1..n+1);
! 445: pivots : Standard_Natural_Vectors.Vector(1..k);
! 446: begin
! 447: pivots := (1..k => 0);
! 448: Build_Elimination_Matrix(k,n,acc,m,pivots,degenerate);
! 449: if not degenerate
! 450: then declare
! 451: q : Poly_Sys(p'range);
! 452: begin
! 453: Eliminate(k,n,p,m,pivots,q);
! 454: declare
! 455: las : Laur_Sys(q'range);
! 456: qsols : Solution_List;
! 457: bkk : natural;
! 458: begin
! 459: las := Polynomial_to_Laurent_System(q);
! 460: Solve(file,las,tv,bkk,qsols);
! 461: bb := bb + bkk;
! 462: Update(qsols,k,n,m,pivots);
! 463: Concat(sols,sols_last,qsols);
! 464: Clear(las); Shallow_Clear(qsols);
! 465: end;
! 466: Clear(q);
! 467: end;
! 468: end if;
! 469: end;
! 470: else for j in 1..Random_Product_System.Number_of_Hyperplanes(l) loop
! 471: acc(l) := j;
! 472: Build_Indices(file,p,l+1,k,n,acc,tv,bb,sols,sols_last);
! 473: end loop;
! 474: end if;
! 475: end Build_Indices;
! 476:
! 477: -- TARGET ROUTINES :
! 478:
! 479: function Bezout_BKK ( k,n : natural; p : Poly_Sys ) return natural is
! 480:
! 481: res : natural;
! 482:
! 483: begin
! 484: if k = 0
! 485: then declare
! 486: adl : Array_of_Lists(p'range) := Create(p);
! 487: begin
! 488: res := Mixed_Volume(n,adl);
! 489: Deep_Clear(adl);
! 490: end;
! 491: elsif k = n
! 492: then if Set_Structure.Empty
! 493: then Random_Product_Start_Systems.Build_Set_Structure(p);
! 494: res := Set_Structure.B;
! 495: Set_Structure.Clear;
! 496: else res := Set_Structure.B;
! 497: end if;
! 498: else Build_RPS(k,n,p);
! 499: declare
! 500: acc : Standard_Natural_Vectors.Vector(1..k);
! 501: q : Poly_Sys(1..n-k);
! 502: begin
! 503: acc := (1..k => 0); res := 0;
! 504: for i in q'range loop
! 505: q(i) := Complex_Randomize1(p(i+k));
! 506: end loop;
! 507: Build_Indices(1,k,n,q,acc,res);
! 508: Clear(q);
! 509: end;
! 510: Random_Product_System.Clear;
! 511: end if;
! 512: return res;
! 513: end Bezout_BKK;
! 514:
! 515: function Bezout_BKK ( k,n : natural; p : Poly_Sys; tv : Tree_of_Vectors )
! 516: return natural is
! 517: res : natural;
! 518:
! 519: begin
! 520: if k = 0
! 521: then declare
! 522: adl : Array_of_Lists(p'range) := Create(p);
! 523: begin
! 524: res := Mixed_Volume(n,adl,tv);
! 525: Deep_Clear(adl);
! 526: end;
! 527: elsif k = n
! 528: then if Set_Structure.Empty
! 529: then Random_Product_Start_Systems.Build_Set_Structure(p);
! 530: res := Set_Structure.B;
! 531: Set_Structure.Clear;
! 532: else res := Set_Structure.B;
! 533: end if;
! 534: else Build_RPS(k,n,p);
! 535: declare
! 536: acc : Standard_Natural_Vectors.Vector(1..k);
! 537: q : Poly_Sys(1..n-k);
! 538: begin
! 539: acc := (1..k => 0); res := 0;
! 540: for i in q'range loop
! 541: q(i) := Complex_Randomize1(p(i+k));
! 542: end loop;
! 543: Build_Indices(1,k,n,q,tv,acc,res);
! 544: Clear(q);
! 545: end;
! 546: Random_Product_System.Clear;
! 547: end if;
! 548: return res;
! 549: end Bezout_BKK;
! 550:
! 551: procedure Bezout_BKK ( k,n : in natural; p : in Poly_Sys;
! 552: tv : in out Tree_of_Vectors; bb : out natural ) is
! 553: res : natural;
! 554:
! 555: begin
! 556: if k = 0
! 557: then declare
! 558: adl : Array_of_Lists(p'range) := Create(p);
! 559: begin
! 560: Mixed_Volume(n,adl,tv,res);
! 561: Deep_Clear(adl);
! 562: end;
! 563: elsif k = n
! 564: then if Set_Structure.Empty
! 565: then Random_Product_Start_Systems.Build_Set_Structure(p);
! 566: res := Set_Structure.B;
! 567: Set_Structure.Clear;
! 568: else res := Set_Structure.B;
! 569: end if;
! 570: else Build_RPS(k,n,p);
! 571: declare
! 572: acc : Standard_Natural_Vectors.Vector(1..k);
! 573: q : Poly_Sys(1..n-k);
! 574: begin
! 575: acc := (1..k => 0); res := 0;
! 576: for i in q'range loop
! 577: q(i) := Complex_Randomize1(p(i+k));
! 578: end loop;
! 579: Build_Indices2(1,k,n,q,tv,acc,res);
! 580: Clear(q);
! 581: end;
! 582: Random_Product_System.Clear;
! 583: end if;
! 584: bb := res;
! 585: end Bezout_BKK;
! 586:
! 587: procedure Mixed_Solve
! 588: ( file : in file_type; k,n : in natural; p : in Poly_Sys;
! 589: bb : out natural;
! 590: g : in out Poly_Sys; sols : in out Solution_List ) is
! 591: begin
! 592: if k = 0
! 593: then declare
! 594: l : Laur_Sys(g'range);
! 595: tmp : Solution_List;
! 596: begin
! 597: l := Polynomial_to_Laurent_System(g);
! 598: Solve(file,l,bb,sols);
! 599: tmp := sols;
! 600: while not Is_Null(tmp) loop
! 601: Head_Of(tmp).t := Create(0.0);
! 602: tmp := Tail_Of(tmp);
! 603: end loop;
! 604: Clear(l);
! 605: end;
! 606: elsif k = n
! 607: then Random_Product_Start_Systems.Construct(p,g,sols);
! 608: bb := Length_Of(sols);
! 609: else Build_RPS(k,n,p);
! 610: declare
! 611: acc : Standard_Natural_Vectors.Vector(1..k);
! 612: q : Poly_Sys(1..n-k);
! 613: rq : Poly_Sys(p'range);
! 614: sols_last : Solution_List;
! 615: res : natural;
! 616: begin
! 617: acc := (1..k => 0); res := 0;
! 618: for i in q'range loop
! 619: q(i) := g(i+k);
! 620: end loop;
! 621: Build_Indices(file,q,1,k,n,acc,res,sols,sols_last);
! 622: bb := res;
! 623: rq := Random_Product_System.Polynomial_System;
! 624: g(1..k) := rq(1..k);
! 625: end;
! 626: Random_Product_System.Clear;
! 627: end if;
! 628: end Mixed_Solve;
! 629:
! 630: procedure Mixed_Solve
! 631: ( file : in file_type; k,n : in natural; p : in Poly_Sys;
! 632: tv : in Tree_of_Vectors; bb : out natural;
! 633: g : in out Poly_Sys; sols : in out Solution_List ) is
! 634: begin
! 635: if k = 0
! 636: then declare
! 637: l : Laur_Sys(g'range);
! 638: tmp : Solution_List;
! 639: begin
! 640: l := Polynomial_to_Laurent_System(g);
! 641: Solve(file,l,tv,bb,sols);
! 642: tmp := sols;
! 643: while not Is_Null(tmp) loop
! 644: Head_Of(tmp).t := Create(0.0);
! 645: tmp := Tail_Of(tmp);
! 646: end loop;
! 647: Clear(l);
! 648: end;
! 649: elsif k = n
! 650: then Random_Product_Start_Systems.Construct(p,g,sols);
! 651: bb := Length_Of(sols);
! 652: else Build_RPS(k,n,p);
! 653: declare
! 654: acc : Standard_Natural_Vectors.Vector(1..k);
! 655: q : Poly_Sys(1..n-k);
! 656: rq : Poly_Sys(p'range);
! 657: sols_last : Solution_List;
! 658: res : natural;
! 659: begin
! 660: acc := (1..k => 0); res := 0;
! 661: for i in q'range loop
! 662: q(i) := g(i+k);
! 663: end loop;
! 664: Build_Indices(file,q,1,k,n,acc,tv,res,sols,sols_last);
! 665: bb := res;
! 666: rq := Random_Product_System.Polynomial_System;
! 667: g(1..k) := rq(1..k);
! 668: end;
! 669: Random_Product_System.Clear;
! 670: end if;
! 671: end Mixed_Solve;
! 672:
! 673: end Set_Structures_and_Volumes;
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