Changeset 03f29c in git

Timestamp:

May 8, 2000, 11:42:58 AM (23 years ago)

Author:

Gerhard Pfister <pfister@…>

Branches:

(u'spielwiese', 'f6c3dc58b0df4bd712574325fe76d0626174ad97')

Children:

0ad3597762e2f64054f1324b098d198434537d9b

Parents:

ba9453910d26fdb676fa083bc02d866111ea5ece

Message:

Prozeduren equidimMax, equidimMaxEHV eingebaut


git-svn-id: file:///usr/local/Singular/svn/trunk@4292 2c84dea3-7e68-4137-9b89-c4e89433aadc

File:

• Singular/LIB/primdec.lib (modified) (6 diffs)

Singular/LIB/primdec.lib

@@ -1 @@
-// $Id: primdec.lib,v 1.55 2000-05-08 08:59:17 pfister Exp $
+// $Id: primdec.lib,v 1.56 2000-05-08 09:42:58 pfister Exp $
 ///////////////////////////////////////////////////////////////////////////////
 // primdec.lib                                                               //
@@ -11 +11 @@
 ///////////////////////////////////////////////////////////////////////////////
 
-version="$Id: primdec.lib,v 1.55 2000-05-08 08:59:17 pfister Exp $";
+version="$Id: primdec.lib,v 1.56 2000-05-08 09:42:58 pfister Exp $";
 info="
 LIBRARY: primdec.lib   PROCEDURES FOR PRIMARY DECOMPOSITION
@@ -28 +28 @@
   prepareAss(I);    list of radicals of the equidimensional components of I
   equidim(I);       equidimensional decomposition of I
+  equidimMax(I);    equidimensional locus of I
+  equidimMaxEHV(I); equidimensional locus of I (Algorithm of Eisenbud,
+                    Huneke and Vasconcelos)
 REMARK:
 These procedures are implemented to be used in characteristic 0.
@@ -1762 +1765 @@
 ///////////////////////////////////////////////////////////////////////////////
 proc equidim(ideal i)
-"USAGE:  equidimensiona(i); i ideal           
+"USAGE:  equidim(i); i ideal           
  RETURN:  list = list of equidimensional ideals a1,...,as such that
           i is the intersection of a1,...,as
- EXAMPLE: example equidimensional; shows an example
+ EXAMPLE: example equidim; shows an example
 "
 {
@@ -1875 +1878 @@
    ideal i=intersect(ideal(z),ideal(x,y),ideal(x2,z2),ideal(x5,y5,z5));
    equidim(i);
+}
+///////////////////////////////////////////////////////////////////////////////
+proc equidimMax(ideal i)
+"USAGE:  equidimMax(i); i ideal           
+ RETURN:  ideal = ideal of equidimensional locus
+ EXAMPLE: example equidimMax; shows an example
+"
+{
+  def  P = basering;
+  ideal eq;
+  intvec w;
+  int n;
+  int a=attrib(i,"isSB");
+  int homo=homog(i);
+   
+  if(((homo==1)||(a==1))&&(find(ordstr(basering),"l")==0)
+                                &&(find(ordstr(basering),"s")==0))
+  {
+     execute "ring gnir = ("+charstr(basering)+"),("+varstr(basering)+"),("
+                              +ordstr(basering)+");";
+     ideal i=imap(P,i);
+     ideal j=i;
+     if(a==1)
+     {
+       attrib(j,"isSB",1); 
+     }
+     else
+     {
+       j=groebner(i);
+     }
+  }
+  else
+  {
+     execute "ring gnir = ("+charstr(basering)+"),("+varstr(basering)+"),dp;";
+     ideal i=imap(P,i);
+     ideal j=groebner(i);
+  }
+  list indep;
+  ideal equ,equi;
+  if(homo==1)
+  {
+     for(n=1;n<=nvars(basering);n++)
+     {
+        w[n]=ord(var(n));
+     }
+     intvec hil=hilb(j,1,w);
+  }
+  if ((dim(j)==-1)||(size(j)==0)||(nvars(basering)==1)||(dim(j)==0))
+  {
+    setring P;
+    eq=i;
+    return(eq);
+  }
+
+  indep=maxIndependSet(j);
+  string va=string(maxideal(1));
+  execute "ring gnir1 = ("+charstr(basering)+"),("+indep[1][1]+"),("
+                              +indep[1][2]+");";
+  execute "map phi=gnir,"+va+";";
+  if(homo==1)
+  {
+     ideal j=std(phi(i),hil,w);
+  }
+  else
+  {
+     ideal j=groebner(phi(i));
+  }
+  string quotring=prepareQuotientring(nvars(basering)-indep[1][3]);
+  execute quotring;
+  ideal j=imap(gnir1,j);
+  kill gnir1;
+  j=clearSB(j);
+  ideal h;
+  for(n=1;n<=size(j);n++)
+  {
+     h[n]=leadcoef(j[n]);
+  }
+
+  setring gnir;
+  ideal h=imap(quring,h);
+  kill quring;
+
+  list l=minSat(j,h);
+  equ=l[1];
+  attrib(equ,"isSB",1);
+  
+  j=std(j,l[2]);
+
+  equi=equidimMax(j);
+  attrib(equi,"isSB",1);
+
+  if(dim(equ)==dim(equi))
+  {
+    equ=intersect(equ,equi);
+  }
+  setring P;
+  eq=imap(gnir,equ);
+  kill gnir;
+  return(eq);
+}
+example
+{ "EXAMPLE:"; echo = 2;
+   ring  r = 32003,(x,y,z),dp;
+   ideal i=intersect(ideal(z),ideal(x,y),ideal(x2,z2),ideal(x5,y5,z5));
+   equidimMax(i);
 }
 
@@ -4415 +4523 @@
    pr;
 }
+///////////////////////////////////////////////////////////////////////////////
+proc equidimMaxEHV(ideal i)
+"USAGE:  equidimMaxEHV(i); i ideal
+RETURN:  ideal = equidimensional componente of i
+NOTE:    uses algorithm of Eisenbud, Huneke and Vasconcelos
+EXAMPLE: example equidimMaxEHV; shows an example
+"
+{
+  ideal j=std(i);
+  int cod=nvars(basering)-dim(j);
+  int e;
+  ideal ann;
+  if(homog(i)==1)
+  {
+     list re=sres(i,0);                   //the resolution
+     re=minres(re);                       //minimized resolution
+  }
+  else
+  {
+    list re=mres(i,0);
+  }
+  ann=AnnExt_R(cod,re);
+  return(ann);
+}
+example
+{ "EXAMPLE:";  echo = 2;
+   ring  r = 32003,(x,y,z),dp;
+   ideal i=intersect(ideal(z),ideal(x,y),ideal(x2,z2),ideal(x5,y5,z5));
+   equidimMaxEHV(i);
+}
 
 proc testPrimary(list pr, ideal k)