=================================================================== RCS file: /home/cvs/OpenXM/src/k097/lib/minimal/minimal.k,v retrieving revision 1.5 retrieving revision 1.9 diff -u -p -r1.5 -r1.9 --- OpenXM/src/k097/lib/minimal/minimal.k 2000/05/05 08:13:49 1.5 +++ OpenXM/src/k097/lib/minimal/minimal.k 2000/05/06 13:41:12 1.9 @@ -1,10 +1,13 @@ -/* $OpenXM: OpenXM/src/k097/lib/minimal/minimal.k,v 1.4 2000/05/04 11:05:20 takayama Exp $ */ +/* $OpenXM: OpenXM/src/k097/lib/minimal/minimal.k,v 1.8 2000/05/06 10:45:43 takayama Exp $ */ #define DEBUG 1 /* #define ORDINARY 1 */ /* If you run this program on openxm version 1.1.2 (FreeBSD), make a symbolic link by the command ln -s /usr/bin/cpp /lib/cpp */ +#define OFFSET 0 +#define TOTAL_STRATEGY +/* #define OFFSET 20*/ /* Test sequences. Use load["minimal.k"];; @@ -34,6 +37,7 @@ def load_tower() { sm1(" [(parse) (k0-tower.sm1) pushfile ] extension "); sm1(" /k0-tower.sm1.loaded 1 def "); } + sm1(" oxNoX "); } load_tower(); SonAutoReduce = true; @@ -336,11 +340,21 @@ def test_SinitOfArray() { /* f is assumed to be a monomial with toes. */ def Sdegree(f,tower,level) { - local i; + local i,ww, wd; + /* extern WeightOfSweyl; */ + ww = WeightOfSweyl; f = Init(f); if (level <= 1) return(StotalDegree(f)); i = Degree(f,es); - return(StotalDegree(f)+Sdegree(tower[level-2,i],tower,level-1)); +#ifdef TOTAL_STRATEGY + return(StotalDegree(f)+Sdegree(tower[level-2,i],tower,level-1)); +#endif + /* Strategy must be compatible with ordering. */ + /* Weight vector must be non-negative, too. */ + /* See Sdegree, SgenerateTable, reductionTable. */ + wd = Sord_w(f,ww); + return(wd+Sdegree(tower[level-2,i],tower,level-1)); + } def SgenerateTable(tower) { @@ -351,7 +365,8 @@ def SgenerateTable(tower) { n = Length(tower[i]); ans_at_each_floor=NewArray(n); for (j=0; j<n; j++) { - ans_at_each_floor[j] = Sdegree(tower[i,j],tower,i+1)-(i+1); + ans_at_each_floor[j] = Sdegree(tower[i,j],tower,i+1)-(i+1) + + OFFSET; /* Println([i,j,ans_at_each_floor[j]]); */ } ans[i] = ans_at_each_floor; @@ -427,7 +442,7 @@ def SlaScala(g) { reductionTable_tmp; /* extern WeightOfSweyl; */ ww = WeightOfSweyl; - Print("WeghtOfSweyl="); Println(WeightOfSweyl); + Print("WeightOfSweyl="); Println(WeightOfSweyl); rf = SresolutionFrameWithTower(g); redundant_seq = 1; redundant_seq_ordinary = 1; tower = rf[1]; @@ -1024,10 +1039,26 @@ def Sannfs(f,v) { def Sannfs2(f) { local p,pp; p = Sannfs(f,"x,y"); + sm1(" p 0 get { [(x) (y) (Dx) (Dy)] laplace0 } map /p set "); /* Sweyl("x,y",[["x",1,"y",1,"Dx",1,"Dy",1,"h",1], ["x",-1,"y",-1,"Dx",1,"Dy",1]]); */ - Sweyl("x,y",[["x",-1,"y",-1,"Dx",1,"Dy",1]]); + /* Sweyl("x,y",[["x",1,"y",1,"Dx",1,"Dy",1,"h",1]]); */ + Sweyl("x,y",[["x",-1,"y",-1,"Dx",1,"Dy",1]]); + pp = Map(p,"Spoly"); + return(Sminimal_v(pp)); + /* return(Sminimal(pp)); */ +} + +/* Do not forget to turn on TOTAL_STRATEGY */ +def Sannfs2_laScala(f) { + local p,pp; + p = Sannfs(f,"x,y"); + /* Do not make laplace transform. + sm1(" p 0 get { [(x) (y) (Dx) (Dy)] laplace0 } map /p set "); + p = [p]; + */ + Sweyl("x,y",[["x",-1,"y",-1,"Dx",1,"Dy",1]]); pp = Map(p[0],"Spoly"); return(Sminimal(pp)); } @@ -1035,9 +1066,10 @@ def Sannfs2(f) { def Sannfs3(f) { local p,pp; p = Sannfs(f,"x,y,z"); + sm1(" p 0 get { [(x) (y) (z) (Dx) (Dy) (Dz)] laplace0 } map /p set "); Sweyl("x,y,z",[["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]]); - pp = Map(p[0],"Spoly"); - return(Sminimal(pp)); + pp = Map(p,"Spoly"); + return(Sminimal_v(pp)); } /* @@ -1050,13 +1082,13 @@ def Sannfs3(f) { -/* The below is under construction. */ +/* The below does not use LaScala-Stillman's algorithm. */ def Sschreyer(g) { local rf, tower, reductionTable, skel, redundantTable, bases, strategy, maxOfStrategy, height, level, n, i, freeRes,place, f, reducer,pos, redundant_seq,bettiTable,freeResV,ww, redundantTable_ordinary, redundant_seq_ordinary, - reductionTable_tmp,c2,ii,nn; + reductionTable_tmp,c2,ii,nn, m,ii, jj, reducerBase; /* extern WeightOfSweyl; */ ww = WeightOfSweyl; Print("WeghtOfSweyl="); Println(WeightOfSweyl); @@ -1121,19 +1153,49 @@ def Sschreyer(g) { /* i must be equal to f[2], I think. Double check. */ /* Correction Of Constant */ - c2 = f[6]; + /* Correction of syzygy */ + c2 = f[6]; /* or -f[6]? Double check. */ + Print("c2="); Println(c2); nn = Length(bases); for (ii=0; ii<nn;ii++) { - if (ii != place) { - bases[ii] = bases[ii]*c2; + if ((ii != i) && (! IsNull(bases[ii]))) { + m = Length(bases[ii]); + for (jj=0; jj<m; jj++) { + if (jj != place) { + bases[ii,jj] = bases[ii,jj]*c2; + } + } } } + Print("Old freeRes[level] = "); sm1_pmat(freeRes[level]); freeRes[level] = bases; - /* bases = freeRes[level-1]; - bases[place] = f[0]; - freeRes[level-1] = bases; It is already set. */ - reducer[level-1,place] = f[1]; + Print("New freeRes[level] = "); sm1_pmat(freeRes[level]); + + /* Update the freeRes[level-1] */ + Print("Old freeRes[level-1] = "); sm1_pmat(freeRes[level-1]); + bases = freeRes[level-1]; + bases[place] = f[0]; + freeRes[level-1] = bases; + Print("New freeRes[level-1] = "); sm1_pmat(freeRes[level-1]); + + reducer[level-1,place] = f[1]-SunitOfFormat(place,f[1]); + /* This reducer is different from that of SlaScala(). */ + + reducerBasis = reducer[level-1]; + nn = Length(reducerBasis); + for (ii=0; ii<nn;ii++) { + if ((ii != place) && (! IsNull(reducerBasis[ii]))) { + m = Length(reducerBasis[ii]); + for (jj=0; jj<m; jj++) { + if (jj != place) { + reducerBasis[ii,jj] = reducerBasis[ii,jj]*c2; + } + } + } + } + reducer[level-1] = reducerBasis; + }else{ /* redundantTable[level,i] = 0; */ bases = freeRes[level]; @@ -1143,6 +1205,33 @@ def Sschreyer(g) { } /* end of level >= 1 */ } } /* i loop */ + + /* Triangulate reducer */ + if (level >= 1) { + Println(" "); + Print("Triangulating reducer at level "); Println(level-1); + Println("freeRes[level]="); sm1_pmat(freeRes[level]); + reducerBase = reducer[level-1]; + Print("reducerBase="); Println(reducerBase); + Println("Compare freeRes[level] and reducerBase (put -1)"); + m = Length(reducerBase); + for (ii=m-1; ii>=0; ii--) { + if (!IsNull(reducerBase[ii])) { + for (jj=ii-1; jj>=0; jj--) { + if (!IsNull(reducerBase[jj])) { + if (!IsZero(reducerBase[jj,ii])) { + /* reducerBase[ii,ii] should be always constant. */ + reducerBase[jj] = reducerBase[ii,ii]*reducerBase[jj]-reducerBase[jj,ii]*reducerBase[ii]; + } + } + } + } + } + Println("New reducer"); + sm1_pmat(reducerBase); + reducer[level-1] = reducerBase; + } + } /* level loop */ n = Length(freeRes); freeResV = SnewArrayOfFormat(freeRes); @@ -1151,6 +1240,18 @@ def Sschreyer(g) { bases = Sbases_to_vec(bases,bettiTable[i]); freeResV[i] = bases; } + + /* Mark the non-redundant elements. */ + for (i=0; i<n; i++) { + m = Length(redundantTable[i]); + for (jj=0; jj<m; jj++) { + if (IsNull(redundantTable[i,jj])) { + redundantTable[i,jj] = 0; + } + } + } + + return([freeResV, redundantTable,reducer,bettiTable,redundantTable_ordinary]); } @@ -1158,7 +1259,7 @@ def SpairAndReduction2(skel,level,ii,freeRes,tower,ww, local i, j, myindex, p, bases, tower2, gi, gj, si, sj, tmp, t_syz, pos, ans, ssp, syzHead,pos2, vdeg,vdeg_reduced,n,c2; - Println("SpairAndReduction2:"); + Println("SpairAndReduction2 : -------------------------"); if (level < 1) Error("level should be >= 1 in SpairAndReduction."); p = skel[level,ii]; @@ -1193,6 +1294,11 @@ def SpairAndReduction2(skel,level,ii,freeRes,tower,ww, tmp = Sreduction(si*gi+sj*gj, bases); Print("result is "); Println(tmp); + if (!IsZero(tmp[0])) { + Print("Error: base = "); + Println(Map(bases,"Stoes_vec")); + Error("SpairAndReduction2: the remainder should be zero. See tmp. tower2. show_ring."); + } t_syz = tmp[2]; si = si*tmp[1]+t_syz[i]; sj = sj*tmp[1]+t_syz[j]; @@ -1203,15 +1309,18 @@ def SpairAndReduction2(skel,level,ii,freeRes,tower,ww, /* tmp[0] must be zero */ n = Length(t_syz); for (i=0; i<n; i++) { - if (IsConstant(t_syz[i])) { + if (IsConstant(t_syz[i])){ + if (!IsZero(t_syz[i])) { if (IsNull(redundantTable[level-1,i])) { /* i must equal to pos2 below. */ c2 = -t_syz[i]; - tmp[0] = freeRes[level-1,i]; + tmp[0] = c2*Stoes_vec(freeRes[level-1,i]); t_syz[i] = 0; + /* tmp[0] = t_syz . g */ /* break; does not work. Use */ i = n; } + } } } @@ -1228,5 +1337,72 @@ def SpairAndReduction2(skel,level,ii,freeRes,tower,ww, /* pos is the place to put syzygy at level. */ /* pos2 is the place to put a new GB at level-1. */ Println(ans); + Println(" "); return(ans); } + +def Sminimal_v(g) { + local r, freeRes, redundantTable, reducer, maxLevel, + minRes, seq, maxSeq, level, betti, q, bases, dr, + betti_levelplus, newbases, i, j,qq; + r = Sschreyer(g); + sm1_pmat(r); + Debug_Sminimal_v = r; + Println(" Return value of Schreyer(g) is set to Debug_Sminimal_v"); + /* Should I turn off the tower?? */ + freeRes = r[0]; + redundantTable = r[1]; + reducer = r[2]; + minRes = SnewArrayOfFormat(freeRes); + seq = 0; + maxSeq = SgetMaxSeq(redundantTable); + maxLevel = Length(freeRes); + for (level = 0; level < maxLevel; level++) { + minRes[level] = freeRes[level]; + } + for (level = 0; level < maxLevel; level++) { + betti = Length(freeRes[level]); + for (q = betti-1; q>=0; q--) { + if (redundantTable[level,q] > 0) { + Print("[seq,level,q]="); Println([seq,level,q]); + if (level < maxLevel-1) { + bases = freeRes[level+1]; + dr = reducer[level,q]; + /* dr[q] = -1; We do not need this in our reducer format. */ + /* dr[q] should be a non-zero constant. */ + newbases = SnewArrayOfFormat(bases); + betti_levelplus = Length(bases); + /* + bases[i,j] ---> bases[i,j]+bases[i,q]*dr[j] + */ + for (i=0; i<betti_levelplus; i++) { + newbases[i] = dr[q]*bases[i] - bases[i,q]*dr; + } + Println(["level, q =", level,q]); + Println("bases="); sm1_pmat(bases); + Println("dr="); sm1_pmat(dr); + Println("newbases="); sm1_pmat(newbases); + minRes[level+1] = newbases; + freeRes = minRes; +#ifdef DEBUG + for (qq=q; qq<betti; qq++) { + for (i=0; i<betti_levelplus; i++) { + if ((!IsZero(newbases[i,qq])) && (redundantTable[level,qq] >0)) { + Println(["[i,qq]=",[i,qq]," is not zero in newbases."]); + Print("redundantTable ="); sm1_pmat(redundantTable[level]); + Error("Stop in Sminimal for debugging."); + } + } + } +#endif + } + } + } + } + return([Stetris(minRes,redundantTable), + [ minRes, redundantTable, reducer,r[3],r[4]],r[0]]); + /* r[4] is the redundantTable_ordinary */ + /* r[0] is the freeResolution */ +} + +/* Sannfs2("x*y*(x-y)*(x+y)"); is a test problem */