Changeset e2f3ad in git

Timestamp:

Aug 18, 2022, 1:44:44 PM (21 months ago)

Author:

Hans Schoenemann <hannes@…>

Branches:

(u'spielwiese', 'fe61d9c35bf7c61f2b6cbf1b56e25e2f08d536cc')

Children:

d0731c963230ccafabf460a89208f06831979612

Parents:

cd8a89918073438ccbaf9e823dda24cf8ab16709

Message:

add minimalGenerators to sagbi.lib

File:

• Singular/LIB/sagbi.lib (modified) (1 diff)

Singular/LIB/sagbi.lib

@@ -1255 +1255 @@
   setring DI; algDep;
 */
+
+proc minimalGenerators(ideal a, list #)
+"USAGE: minimalGenerators(id[,w]); id ideal, w: weight vector.
+RETURN: ideal (list of minimal generators of the subalgebra a)
+EXAMPLE: example minimalGenerators; shows an example"
+{
+  if(!homog(a))
+  {
+    ERROR("generators must be homogeneous");
+  }
+  ring br=basering;
+  intvec w;
+  if (size(#)==0) { w=1:nvars(basering); }
+  else            { w=#[1]; }
+  int elems=size(a);
+  int j; ideal ad; poly p; ideal sb; ideal mingen; ideal h;
+  for (int d=0;elems>0;d++)
+  {
+    ad=jet(jet(a,d,w),-d,-w); // degree d part of a
+    if (size(ad)>0)
+    {
+      "sagbi for deg ",d-1;sb;
+      "testing deg ",d;
+      "ad=",ad;
+      for(j=1;j<=ncols(ad);j++) // 2.1
+      {
+        if (ad[j]!=0)
+        {
+          p=sagbiReduce(ad[j],sb);
+          "reduced:",p;
+          if(p==0) { a[j]=0; "a[",j,"] not needed"; }
+          else
+          {"min gen",j," = ",p;
+            sb=sb,p;
+            mingen=mingen,p;
+          }
+          elems--;
+        }
+      }
+    }
+    h=relations_apply(sb,a); // 2.3
+    h=jet(jet(h,d+1,w),-d-1,w); // deg d+1 part
+    "rel. in deg ",d+1," =",h;
+    for(j=1;j<=ncols(h);j++) // 2.4
+    {
+      h[j]=sagbiReduce(h[j],sb);
+    }
+    sb=sb,h; // 2.5
+    sb=simplify(sb,2); // 2.6
+  }
+  "sb=",sb;
+  return(simplify(a,2));
+}
+example
+{
+  "EXAMPLE:";echo=2;
+  ring r= 0,(a0,a1,a2),dp;
+  ideal A=a0,a1*a2-a0*a1+a0*a2,a1^2-a2^2+a0*a1,a1^3-a0*a2^2;
+  A=A,A[1]*A[4]+A[2]*A[3];
+  minimalGenerators(A);
+}
+
+proc relations_apply(ideal s, ideal a)
+{
+  ideal ls=lead(s);
+  // new vars, #=ncols(s)
+  ring savering=basering;
+  ring d1=0,(y(1..ncols(a))),dp;
+  def e1=d1+savering;
+  setring e1;
+  ideal ls=imap(savering,ls);
+  poly m=1;
+  for(int i=1;i<=nvars(savering);i++)
+  { m=m*var(i+nvars(d1)); }
+  for(i=1;i<=ncols(ls);i++)
+  {
+    if (ls[i]!=0)
+    {
+      ls[i]=ls[i]-y(i);
+    }
+  }
+  ls=eliminate(ls,m); // eliminate original vars from ls
+  "orig rel:",ls;
+  // apply the relations
+  setring savering;
+  // image of map;
+  ideal im;
+  im[nvars(savering)]=0;
+  im=im,a;
+  // map:
+  map f=e1,im;
+  // apply relations
+  ideal rel=f(ls);
+  "Relations:",rel;
+  return(rel);
+}
+