=================================================================== RCS file: /home/cvs/OpenXM/src/k097/lib/minimal/minimal.k,v retrieving revision 1.27 retrieving revision 1.35 diff -u -p -r1.27 -r1.35 --- OpenXM/src/k097/lib/minimal/minimal.k 2000/08/16 22:38:52 1.27 +++ OpenXM/src/k097/lib/minimal/minimal.k 2007/07/03 22:05:46 1.35 @@ -1,4 +1,4 @@ -/* $OpenXM: OpenXM/src/k097/lib/minimal/minimal.k,v 1.26 2000/08/10 02:59:08 takayama Exp $ */ +/* $OpenXM: OpenXM/src/k097/lib/minimal/minimal.k,v 1.34 2001/01/05 11:14:28 takayama Exp $ */ #define DEBUG 1 Sordinary = false; /* If you run this program on openxm version 1.1.2 (FreeBSD), @@ -44,18 +44,12 @@ def Sprint2(s) { */ +/* We cannot use load command in the if statement. */ +load("lib/minimal/cohom.k"); +Load_sm1(["k0-tower.sm1","lib/minimal/k0-tower.sm1"],"k0-tower.sm1.loaded"); +Load_sm1(["new.sm1","lib/minimal/new.sm1"],"new.sm1.loaded"); +sm1(" oxNoX "); -load("cohom.k"); -def load_tower() { - if (Boundp("k0-tower.sm1.loaded")) { - }else{ - sm1(" [(parse) (k0-tower.sm1) pushfile ] extension "); - sm1(" [(parse) (new.sm1) pushfile ] extension "); - sm1(" /k0-tower.sm1.loaded 1 def "); - } - sm1(" oxNoX "); -} -load_tower(); SonAutoReduce = true; def Factor(f) { sm1(f, " fctr /FunctionValue set"); @@ -145,6 +139,35 @@ def Max(v) { HelpAdd(["Max", ["Max(v) returns the maximal element in v."]]); +def Kernel(f,v) { + local ans; + /* v : string or ring */ + if (Length(Arglist) < 2) { + sm1(" [f] syz /ans set "); + }else{ + sm1(" [f v] syz /ans set "); + } + return(ans); +} +def Syz(f) { + sm1(" [f] syz /FunctionValue set "); +} +HelpAdd(["Kernel", +["Kernel(f) returns the syzygy of f.", + "Return value [b, c]: b is a set of generators of the syzygies of f", + " : c=[gb, backward transformation, syzygy without", + " dehomogenization", + "Example: Weyl(\"x,y\",[[\"x\",-1,\"Dx\",1]]); ", + " s=Kernel([x*Dx+1,Dx^2+x^5]); s[0]:"]]); +/* cf. sm1_syz in cohom.k */ +def Gb(f) { + sm1(" [f] gb /FunctionValue set "); +} +HelpAdd(["Gb", +["Gb(f) returns the Groebner basis of f.", + "cf. Kernel, Weyl."]]); + + /* End of standard functions that should be moved to standard libraries. */ def test0() { local f; @@ -165,7 +188,6 @@ def test1() { } - def Sweyl(v,w) { /* extern WeightOfSweyl ; */ local ww,i,n; @@ -224,9 +246,9 @@ def StoTower() { } def SsetTower(tower) { -sm1(" [(AvoidTheSameRing)] pushEnv - [ [(AvoidTheSameRing) 0] system_variable - [(gbListTower) tower (list) dc] system_variable +sm1(" [(AvoidTheSameRing)] pushEnv \ + [ [(AvoidTheSameRing) 0] system_variable \ + [(gbListTower) tower (list) dc] system_variable \ ] pop popEnv "); /* sm1("(hoge) message show_ring "); */ } @@ -336,13 +358,13 @@ def NewPolynomialVector(size) { } def SturnOffHomogenization() { - sm1(" - [(Homogenize)] system_variable 1 eq - { Sverbose { - (Warning: Homogenization and ReduceLowerTerms options are automatically turned off.) message } { } ifelse - [(Homogenize) 0] system_variable - [(ReduceLowerTerms) 0] system_variable - } { } ifelse + sm1(" \ + [(Homogenize)] system_variable 1 eq \ + { Sverbose { \ + (Warning: Homogenization and ReduceLowerTerms options are automatically turned off.) message } { } ifelse \ + [(Homogenize) 0] system_variable \ + [(ReduceLowerTerms) 0] system_variable \ + } { } ifelse \ "); } /* NOTE!!! Be careful these changes of global environmental variables. @@ -350,13 +372,13 @@ def SturnOffHomogenization() { after computation and interruption. August 15, 2000. */ def SturnOnHomogenization() { - sm1(" - [(Homogenize)] system_variable 0 eq - { Sverbose { - (Warning: Homogenization and ReduceLowerTerms options are automatically turned ON.) message } { } ifelse - [(Homogenize) 1] system_variable - [(ReduceLowerTerms) 1] system_variable - } { } ifelse + sm1(" \ + [(Homogenize)] system_variable 0 eq \ + { Sverbose { \ + (Warning: Homogenization and ReduceLowerTerms options are automatically turned ON.) message } { } ifelse \ + [(Homogenize) 1] system_variable \ + [(ReduceLowerTerms) 1] system_variable \ + } { } ifelse \ "); } @@ -1006,7 +1028,7 @@ def Sminimal(g,opt) { redundantTable = r[1]; reducer = r[2]; bettiTable = SbettiTable(redundantTable); - Sprintln2("Betti numbers are ------"); + Sprintln2("BettiTable ------"); if (Sverbose || Sverbose2) {sm1_pmat(bettiTable);} minRes = SnewArrayOfFormat(freeRes); seq = 0; @@ -1070,9 +1092,9 @@ def Sminimal(g,opt) { Println("0: minimal resolution, 3: Schreyer resolution "); Println("------------ Resolution Summary --------------"); Print("Betti numbers : "); - Println(Map(ansSminimal[0],"Length")); + Println(Join([Length(ansSminimal[0,0,0])],Map(ansSminimal[0],"Length"))); Print("Betti numbers of the Schreyer frame: "); - Println(Map(ansSminimal[3],"Length")); + Println(Join([Length(ansSminimal[3,0,0])],Map(ansSminimal[3],"Length"))); Println("-----------------------------------------------"); sm1(" restoreEnvAfterResolution "); @@ -1454,23 +1476,10 @@ HelpAdd(["IsSameIdeal_h", "cf. ReParse" ]]); -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" -]]); +/* + Output of S* functions may cause a trouble because it uses Schreyer orders. + In this case, use ReParse(). +*/ def ScheckIfSchreyer(s) { local ss; @@ -1509,10 +1518,10 @@ HelpAdd(["SgetShift", def SgetShifts(resmat,w) { local i,n,ans,m0; n = Length(resmat); - ans = NewArray(n); + ans = NewArray(n+1); m0 = NewArray(Length(resmat[0,0])); ans[0] = m0; - for (i=0; i