=================================================================== RCS file: /home/cvs/OpenXM/src/k097/lib/minimal/minimal.k,v retrieving revision 1.5 retrieving revision 1.19 diff -u -p -r1.5 -r1.19 --- OpenXM/src/k097/lib/minimal/minimal.k 2000/05/05 08:13:49 1.5 +++ OpenXM/src/k097/lib/minimal/minimal.k 2000/07/31 01:21:41 1.19 @@ -1,10 +1,12 @@ -/* $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 1.18 2000/07/30 02:26:25 takayama Exp $ */ #define DEBUG 1 -/* #define ORDINARY 1 */ +Sordinary = false; /* 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 OFFSET 20*/ /* Test sequences. Use load["minimal.k"];; @@ -34,6 +36,7 @@ def load_tower() { sm1(" [(parse) (k0-tower.sm1) pushfile ] extension "); sm1(" /k0-tower.sm1.loaded 1 def "); } + sm1(" oxNoX "); } load_tower(); SonAutoReduce = true; @@ -46,6 +49,41 @@ def Reverse(f) { def Sgroebner(f) { sm1(" [f] groebner /FunctionValue set"); } + + +def Error(s) { + sm1(" s error "); +} + +def IsNull(s) { + if (Stag(s) == 0) return(true); + else return(false); +} + +def MonomialPart(f) { + sm1(" [(lmonom) f] gbext /FunctionValue set "); +} + +def Warning(s) { + Print("Warning: "); + Println(s); +} +def RingOf(f) { + local r; + if (IsPolynomial(f)) { + if (f != Poly("0")) { + sm1(f," (ring) dc /r set "); + }else{ + sm1(" [(CurrentRingp)] system_variable /r set "); + } + }else{ + Warning("RingOf(f): the argument f must be a polynomial. Return the current ring."); + sm1(" [(CurrentRingp)] system_variable /r set "); + } + return(r); +} + +/* End of standard functions that should be moved to standard libraries. */ def test0() { local f; Sweyl("x,y,z"); @@ -128,15 +166,36 @@ sm1(" [(AvoidTheSameRing)] pushEnv [ [(AvoidTheSameRing) 0] system_variable [(gbListTower) tower (list) dc] system_variable ] pop popEnv "); + /* sm1("(hoge) message show_ring "); */ } def SresolutionFrameWithTower(g,opt) { local gbTower, ans, ff, count, startingGB, opts, skelton,withSkel, autof, - gbasis; + gbasis, nohomog,i,n; + /* extern Sordinary */ + nohomog = false; + count = -1; Sordinary = false; /* default value for options. */ if (Length(Arglist) >= 2) { - if (IsInteger(opt)) count = opt; - }else{ - count = -1; + if (IsArray(opt)) { + n = Length(opt); + for (i=0; i SresolutionFrameWithTower */ + + ScheckIfSchreyer("Sminimal:0"); + r = SlaScala(g,opt); /* Should I turn off the tower?? */ + ScheckIfSchreyer("Sminimal:1"); freeRes = r[0]; redundantTable = r[1]; reducer = r[2]; @@ -889,10 +978,12 @@ def Sminimal(g) { } } } - return([Stetris(minRes,redundantTable), - [ minRes, redundantTable, reducer,r[3],r[4]],r[0]]); + tminRes = Stetris(minRes,redundantTable); + return([SpruneZeroRow(tminRes), tminRes, + [ minRes, redundantTable, reducer,r[3],r[4]],r[0],r[5]]); /* r[4] is the redundantTable_ordinary */ /* r[0] is the freeResolution */ + /* r[5] is the skelton */ } @@ -1024,209 +1115,270 @@ def Sannfs(f,v) { def Sannfs2(f) { local p,pp; p = Sannfs(f,"x,y"); -/* - 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]]); - pp = Map(p[0],"Spoly"); - return(Sminimal(pp)); + sm1(" p 0 get { [(x) (y) (Dx) (Dy)] laplace0 } map /p set "); + Sweyl("x,y",[["x",-1,"y",-1,"Dx",1,"Dy",1]]); + pp = Map(p,"Spoly"); + return(Sminimal(pp)); } +HelpAdd(["Sannfs2", +["Sannfs2(f) constructs the V-minimal free resolution for the weight (-1,1)", + "of the Laplace transform of the annihilating ideal of the polynomial f in x,y.", + "See also Sminimal, Sannfs3.", + "Example: a=Sannfs2(\"x^3-y^2\");", + " b=a[0]; sm1_pmat(b);", + " b[1]*b[0]:", + "Example: a=Sannfs2(\"x*y*(x-y)*(x+y)\");", + " b=a[0]; sm1_pmat(b);", + " b[1]*b[0]:" +]]); +/* Some samples. + The betti numbers of most examples are 2,1. (0-th and 1-th). + a=Sannfs2("x*y*(x+y-1)"); ==> The betti numbers are 3, 2. + a=Sannfs2("x^3-y^2-x"); + a=Sannfs2("x*y*(x-y)"); +*/ + + 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"); + pp = Map(p,"Spoly"); return(Sminimal(pp)); } -/* - The betti numbers of most examples are 2,1. (0-th and 1-th). - a=Sannfs2("x*y*(x+y-1)"); ==> The betti numbers are 3, 2. - a=Sannfs2("x^3-y^2-x"); : it causes an error. It should be fixed. - a=Sannfs2("x*y*(x-y)"); : it causes an error. It should be fixed. +HelpAdd(["Sannfs3", +["Sannfs3(f) constructs the V-minimal free resolution for the weight (-1,1)", + "of the Laplace transform of the annihilating ideal of the polynomial f in x,y,z.", + "See also Sminimal, Sannfs2.", + "Example: a=Sannfs3(\"x^3-y^2*z^2\");", + " b=a[0]; sm1_pmat(b);", + " b[1]*b[0]: b[2]*b[1]:"]]); -*/ +/* Sannfs2("x*y*(x-y)*(x+y)"); is a test problem */ +/* x y (x+y-1)(x-2), x^3-y^2, x^3 - y^2 z^2, + x y z (x+y+z-1) seems to be interesting, because the first syzygy + contains 1. +*/ -/* The below is under construction. */ -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; - /* extern WeightOfSweyl; */ - ww = WeightOfSweyl; - Print("WeghtOfSweyl="); Println(WeightOfSweyl); - rf = SresolutionFrameWithTower(g); - redundant_seq = 1; redundant_seq_ordinary = 1; - tower = rf[1]; - reductionTable = SgenerateTable(tower); - skel = rf[2]; - redundantTable = SnewArrayOfFormat(rf[1]); - redundantTable_ordinary = SnewArrayOfFormat(rf[1]); - reducer = SnewArrayOfFormat(rf[1]); - freeRes = SnewArrayOfFormat(rf[1]); - bettiTable = SsetBettiTable(rf[1],g); +def CopyArray(m) { + local ans,i,n; + if (IsArray(m)) { + n = Length(m); + ans = NewArray(n); + for (i=0; i f[5]) { - /* Zero in the gr-module */ - Print("v-degree of [org,remainder] = "); - Println([f[4],f[5]]); - Print("[level,i] = "); Println([level,i]); - redundantTable[level-1,place] = 0; - }else{ - redundantTable[level-1,place] = redundant_seq; - redundant_seq++; - } -#endif - redundantTable_ordinary[level-1,place] - =redundant_seq_ordinary; - redundant_seq_ordinary++; - bases[i] = SunitOfFormat(place,f[1])-f[1]; /* syzygy */ - /* redundantTable[level,i] = 0; - redundantTable_ordinary[level,i] = 0; */ - /* i must be equal to f[2], I think. Double check. */ +def IsZeroVector(m) { + local n,i; + n = Length(m); + for (i=0; i= 1 */ - } - } /* i loop */ - } /* level loop */ - n = Length(freeRes); - freeResV = SnewArrayOfFormat(freeRes); + minRes = CopyArray(res); + n = Length(minRes); for (i=0; i= 1 in SpairAndReduction."); - p = skel[level,ii]; - myindex = p[0]; - i = myindex[0]; j = myindex[1]; - bases = freeRes[level-1]; - Println(["p and bases ",p,bases]); - if (IsNull(bases[i]) || IsNull(bases[j])) { - Println([level,i,j,bases[i],bases[j]]); - Error("level, i, j : bases[i], bases[j] must not be NULL."); +def ToString_array(p) { + local ans; + if (IsArray(p)) { + ans = Map(p,"ToString_array"); + }else{ + ans = ToString(p); } + return(ans); +} - tower2 = StowerOf(tower,level-1); - SsetTower(tower2); - /** sm1(" show_ring "); */ +/* sm1_res_div([[x],[y]],[[x^2],[x*y],[y^2]],[x,y]): */ - gi = Stoes_vec(bases[i]); - gj = Stoes_vec(bases[j]); +def sm1_res_div(I,J,V) { + I = ToString_array(I); + J = ToString_array(J); + V = ToString_array(V); + sm1(" [[ I J] V ] res*div /FunctionValue set "); +} - ssp = Sspolynomial(gi,gj); - si = ssp[0,0]; - sj = ssp[0,1]; - syzHead = si*es^i; - /* This will be the head term, I think. But, double check. */ - Println([si*es^i,sj*es^j]); +/* It has not yet been working */ +def sm1_res_kernel_image(m,n,v) { + m = ToString_array(m); + n = ToString_array(n); + v = ToString_array(v); + sm1(" [m n v] res-kernel-image /FunctionValue set "); +} +def Skernel(m,v) { + m = ToString_array(m); + v = ToString_array(v); + sm1(" [ m v ] syz /FunctionValue set "); +} - Print("[gi, gj] = "); Println([gi,gj]); - sm1(" [(Homogenize)] system_variable message "); - Print("Reduce the element "); Println(si*gi+sj*gj); - Print("by "); Println(bases); - tmp = Sreduction(si*gi+sj*gj, bases); +def sm1_gb(f,v) { + f =ToString_array(f); + v = ToString_array(v); + sm1(" [f v] gb /FunctionValue set "); +} - Print("result is "); Println(tmp); - t_syz = tmp[2]; - si = si*tmp[1]+t_syz[i]; - sj = sj*tmp[1]+t_syz[j]; - t_syz[i] = si; - t_syz[j] = sj; - c2 = null; - /* tmp[0] must be zero */ - n = Length(t_syz); - for (i=0; i (homogenized Weyl algebra)", + "cf. ReParse" +]]); - pos = SwhereInTower(syzHead,tower[level]); - pos2 = SwhereInTower(tmp[0],tower[level-1]); - ans = [tmp[0],t_syz,pos,pos2,vdeg,vdeg_reduced,c2]; - /* pos is the place to put syzygy at level. */ - /* pos2 is the place to put a new GB at level-1. */ - Println(ans); - return(ans); -} +def ReParse(a) { + local c; + if (IsArray(a)) { + c = Map(a,"ReParse"); + }else{ + sm1(a," toString . /c set"); + } + return(c); +} +HelpAdd(["ReParse", +["Reparse(obj): obj", + "It parses the given object in the current ring.", + "Outputs from SlaScala, Sschreyer may cause a trouble in other functions,", + "because it uses the Schreyer order.", + "In this case, ReParse the outputs from these functions.", + "cf. IsExaxt_h" +]]); + +def ScheckIfSchreyer(s) { + local ss; + sm1(" (report) (grade) switch_function /ss set "); + if (ss != "module1v") { + Print("ScheckIfSchreyer: from "); Println(s); + Error("grade is not module1v"); + } + /* + sm1(" (report) (mmLarger) switch_function /ss set "); + if (ss != "tower") { + Print("ScheckIfSchreyer: from "); Println(s); + Error("mmLarger is not tower"); + } + */ + sm1(" [(Schreyer)] system_variable (universalNumber) dc /ss set "); + if (ss != 1) { + Print("ScheckIfSchreyer: from "); Println(s); + Error("Schreyer order is not set."); + } + /* More check will be necessary. */ + return(true); +} \ No newline at end of file