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Diff for /OpenXM/src/k097/lib/minimal/minimal.k between version 1.12 and 1.14

version 1.12, 2000/05/24 15:24:54 version 1.14, 2000/06/09 08:04:54
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Line 1 
 /* $OpenXM: OpenXM/src/k097/lib/minimal/minimal.k,v 1.11 2000/05/19 11:16:51 takayama Exp $ */  /* $OpenXM: OpenXM/src/k097/lib/minimal/minimal.k,v 1.13 2000/06/08 08:37:53 takayama Exp $ */
 #define DEBUG 1  #define DEBUG 1
 /* #define ORDINARY 1 */  /* #define ORDINARY 1 */
 /* If you run this program on openxm version 1.1.2 (FreeBSD),  /* If you run this program on openxm version 1.1.2 (FreeBSD),
Line 6 
Line 6 
    ln -s /usr/bin/cpp /lib/cpp     ln -s /usr/bin/cpp /lib/cpp
 */  */
 #define OFFSET 0  #define OFFSET 0
 /* #define TOTAL_STRATEGY */  #define TOTAL_STRATEGY 1
 /* #define OFFSET 20*/  /* #define OFFSET 20*/
 /* Test sequences.  /* Test sequences.
    Use load["minimal.k"];;     Use load["minimal.k"];;
Line 132  sm1(" [(AvoidTheSameRing)] pushEnv 
Line 132  sm1(" [(AvoidTheSameRing)] pushEnv 
       [ [(AvoidTheSameRing) 0] system_variable        [ [(AvoidTheSameRing) 0] system_variable
         [(gbListTower) tower (list) dc] system_variable          [(gbListTower) tower (list) dc] system_variable
       ] pop popEnv ");        ] pop popEnv ");
         /* sm1("(hoge) message show_ring "); */
 }  }
   
 def SresolutionFrameWithTower(g,opt) {  def SresolutionFrameWithTower(g,opt) {
Line 291  def Sres0FrameWithSkelton(g) {
Line 292  def Sres0FrameWithSkelton(g) {
   
   
 def StotalDegree(f) {  def StotalDegree(f) {
   sm1(" [(grade) f] gbext (universalNumber) dc /FunctionValue set ");    local d0;
     sm1(" [(grade) f] gbext (universalNumber) dc /d0 set ");
     /* Print("degree of "); Print(f); Print(" is "); Println(d0); */
     return(d0);
 }  }
   
 /* Sord_w(x^2*Dx*Dy,[x,-1,Dx,1]); */  /* Sord_w(x^2*Dx*Dy,[x,-1,Dx,1]); */
Line 444  def SlaScala(g) {
Line 448  def SlaScala(g) {
   ww = WeightOfSweyl;    ww = WeightOfSweyl;
   Print("WeightOfSweyl="); Println(WeightOfSweyl);    Print("WeightOfSweyl="); Println(WeightOfSweyl);
   rf = SresolutionFrameWithTower(g);    rf = SresolutionFrameWithTower(g);
     Print("rf="); sm1_pmat(rf);
   redundant_seq = 1;   redundant_seq_ordinary = 1;    redundant_seq = 1;   redundant_seq_ordinary = 1;
   tower = rf[1];    tower = rf[1];
   reductionTable = SgenerateTable(tower);    reductionTable = SgenerateTable(tower);
Line 661  def MonomialPart(f) {
Line 666  def MonomialPart(f) {
   sm1(" [(lmonom) f] gbext /FunctionValue set ");    sm1(" [(lmonom) f] gbext /FunctionValue set ");
 }  }
   
   /* WARNING:
     When you use SwhereInTower, you have to change gbList
     as below. Ofcourse, you should restrore the gbList
     SsetTower(StowerOf(tower,level));
     pos = SwhereInTower(syzHead,tower[level]);
   */
 def SwhereInTower(f,tower) {  def SwhereInTower(f,tower) {
   local i,n,p,q;    local i,n,p,q;
   if (f == Poly("0")) return(-1);    if (f == Poly("0")) return(-1);
Line 697  def SpairAndReduction(skel,level,ii,freeRes,tower,ww) 
Line 708  def SpairAndReduction(skel,level,ii,freeRes,tower,ww) 
   
   tower2 = StowerOf(tower,level-1);    tower2 = StowerOf(tower,level-1);
   SsetTower(tower2);    SsetTower(tower2);
     Println(["level=",level]);
     Println(["tower2=",tower2]);
   /** sm1(" show_ring ");   */    /** sm1(" show_ring ");   */
   
   gi = Stoes_vec(bases[i]);    gi = Stoes_vec(bases[i]);
Line 730  def SpairAndReduction(skel,level,ii,freeRes,tower,ww) 
Line 743  def SpairAndReduction(skel,level,ii,freeRes,tower,ww) 
   sj = sj*tmp[1]+t_syz[j];    sj = sj*tmp[1]+t_syz[j];
   t_syz[i] = si;    t_syz[i] = si;
   t_syz[j] = sj;    t_syz[j] = sj;
   
     SsetTower(StowerOf(tower,level));
   pos = SwhereInTower(syzHead,tower[level]);    pos = SwhereInTower(syzHead,tower[level]);
   
     SsetTower(StowerOf(tower,level-1));
   pos2 = SwhereInTower(tmp[0],tower[level-1]);    pos2 = SwhereInTower(tmp[0],tower[level-1]);
   ans = [tmp[0],t_syz,pos,pos2,vdeg,vdeg_reduced];    ans = [tmp[0],t_syz,pos,pos2,vdeg,vdeg_reduced];
   /* pos is the place to put syzygy at level. */    /* pos is the place to put syzygy at level. */
Line 843  def Sbases_to_vec(bases,size) {
Line 860  def Sbases_to_vec(bases,size) {
   return(newbases);    return(newbases);
 }  }
   
   HelpAdd(["Sminimal",
   ["It constructs the V-minimal free resolution by LaScala-Stillman's algorithm",
    "Example:  Sweyl(\"x,y\",[[\"x\",-1,\"y\",-1,\"Dx\",1,\"Dy\",1]]);",
    "          v=[[2*x*Dx + 3*y*Dy+6, 0],",
    "             [3*x^2*Dy + 2*y*Dx, 0],",
    "             [0,  x^2+y^2],",
    "             [0,  x*y]];",
    "         a=Sminimal(v);",
    "         Sweyl(\"x,y\",[[\"x\",-1,\"y\",-1,\"Dx\",1,\"Dy\",1]]);",
    "         b = ReParse(a[0]); sm1_pmat(b); ",
    "         IsExact_h(b,[x,y]):",
    "Note:  a[0] is the V-minimal resolution. a[3] is the Schreyer resolution."]]);
   
 def Sminimal(g) {  def Sminimal(g) {
   local r, freeRes, redundantTable, reducer, maxLevel,    local r, freeRes, redundantTable, reducer, maxLevel,
         minRes, seq, maxSeq, level, betti, q, bases, dr,          minRes, seq, maxSeq, level, betti, q, bases, dr,
         betti_levelplus, newbases, i, j,qq;          betti_levelplus, newbases, i, j,qq, tminRes;
   r = SlaScala(g);    r = SlaScala(g);
   /* Should I turn off the tower?? */    /* Should I turn off the tower?? */
   freeRes = r[0];    freeRes = r[0];
Line 904  def Sminimal(g) {
Line 934  def Sminimal(g) {
       }        }
     }      }
    }     }
    return([Stetris(minRes,redundantTable),     tminRes = Stetris(minRes,redundantTable);
      return([SpruneZeroRow(tminRes), tminRes,
           [ minRes, redundantTable, reducer,r[3],r[4]],r[0]]);            [ minRes, redundantTable, reducer,r[3],r[4]],r[0]]);
   /* r[4] is the redundantTable_ordinary */    /* r[4] is the redundantTable_ordinary */
   /* r[0] is the freeResolution */    /* r[0] is the freeResolution */
Line 1315  def SpairAndReduction2(skel,level,ii,freeRes,tower,ww,
Line 1346  def SpairAndReduction2(skel,level,ii,freeRes,tower,ww,
   
   tower2 = StowerOf(tower,level-1);    tower2 = StowerOf(tower,level-1);
   SsetTower(tower2);    SsetTower(tower2);
     Println(["level=",level]);
     Println(["tower2=",tower2]);
   /** sm1(" show_ring ");   */    /** sm1(" show_ring ");   */
   
   gi = Stoes_vec(bases[i]);    gi = Stoes_vec(bases[i]);
Line 1381  def SpairAndReduction2(skel,level,ii,freeRes,tower,ww,
Line 1414  def SpairAndReduction2(skel,level,ii,freeRes,tower,ww,
     }      }
   }    }
   
     SsetTower(StowerOf(tower,level));
   pos = SwhereInTower(syzHead,tower[level]);    pos = SwhereInTower(syzHead,tower[level]);
   
     SsetTower(StowerOf(tower,level-1));
   pos2 = SwhereInTower(tmp[0],tower[level-1]);    pos2 = SwhereInTower(tmp[0],tower[level-1]);
   ans = [tmp[0],t_syz,pos,pos2,vdeg,vdeg_reduced,c2];    ans = [tmp[0],t_syz,pos,pos2,vdeg,vdeg_reduced,c2];
   /* pos is the place to put syzygy at level. */    /* pos is the place to put syzygy at level. */
   /* pos2 is the place to put a new GB at level-1. */    /* pos2 is the place to put a new GB at level-1. */
   Println(ans);    Println(ans);
   Println("  ");    Println("--- end of SpairAndReduction2  ");
   return(ans);    return(ans);
 }  }
   
 HelpAdd(["Sminimal_v",  HelpAdd(["Sminimal_v",
 ["It constructs the V-minimal free resolution from the Schreyer resolution",  ["It constructs the V-minimal free resolution from the Schreyer resolution",
  "step by step.",   "step by step.",
    "This code still contains bugs. It sometimes outputs wrong answer.",
  "Example:   Sweyl(\"x,y\",[[\"x\",-1,\"y\",-1,\"Dx\",1,\"Dy\",1]]);",   "Example:   Sweyl(\"x,y\",[[\"x\",-1,\"y\",-1,\"Dx\",1,\"Dy\",1]]);",
  "          v=[[2*x*Dx + 3*y*Dy+6, 0],",   "          v=[[2*x*Dx + 3*y*Dy+6, 0],",
  "             [3*x^2*Dy + 2*y*Dx, 0],",   "             [3*x^2*Dy + 2*y*Dx, 0],",
Line 1404  HelpAdd(["Sminimal_v",
Line 1440  HelpAdd(["Sminimal_v",
  "         sm1_pmat(a[0]); b=a[0]; b[1]*b[0]:",   "         sm1_pmat(a[0]); b=a[0]; b[1]*b[0]:",
  "Note:  a[0] is the V-minimal resolution. a[3] is the Schreyer resolution."]]);   "Note:  a[0] is the V-minimal resolution. a[3] is the Schreyer resolution."]]);
   
   /* This code still contains bugs. It sometimes outputs wrong answer. */
   /* See test12() in minimal-test.k.  */
   /* There may be remaining 1, too */
 def Sminimal_v(g) {  def Sminimal_v(g) {
   local r, freeRes, redundantTable, reducer, maxLevel,    local r, freeRes, redundantTable, reducer, maxLevel,
         minRes, seq, maxSeq, level, betti, q, bases, dr,          minRes, seq, maxSeq, level, betti, q, bases, dr,
Line 1641  def sm1_gb(f,v) {
Line 1679  def sm1_gb(f,v) {
   sm1(" [f v] gb /FunctionValue set ");    sm1(" [f v] gb /FunctionValue set ");
 }  }
   
   
 def SisComplex(a) {  def SisComplex(a) {
   local n,i,j,k,b,p,q;    local n,i,j,k,b,p,q;
   n = Length(a);    n = Length(a);
Line 1660  def SisComplex(a) {
Line 1699  def SisComplex(a) {
     }      }
   }    }
   return(true);    return(true);
 }  
   
   }
   
   def IsExact_h(c,v) {
     local a;
     v = ToString_array(v);
     a = [c,v];
     sm1(a," isExact_h /FunctionValue set ");
   }
   HelpAdd(["IsExact_h",
   ["IsExact_h(complex,var): bool",
    "It checks the given complex is exact or not in D<h> (homogenized Weyl algebra)",
    "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"
   ]]);
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Removed from v.1.12  
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  Added in v.1.14
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