Changeset f620218 in git

Timestamp:

Jun 10, 2005, 7:04:59 PM (18 years ago)

Author:

Viktor Levandovskyy <levandov@…>

Branches:

(u'spielwiese', '8d54773d6c9e2f1d2593a28bc68b7eeab54ed529')

Children:

19fc57bf1d64049e9869d7a195dc56f156f8e197

Parents:

cd6ff4925c1335a6a1617eccfabad9197484c383

Message:

*levandov: unipotency added to findAuto


git-svn-id: file:///usr/local/Singular/svn/trunk@8351 2c84dea3-7e68-4137-9b89-c4e89433aadc

File:

• Singular/LIB/involut.lib (modified) (4 diffs)

Singular/LIB/involut.lib

@@ -1 @@
-version="$Id: involut.lib,v 1.7 2005-06-07 10:24:45 Singular Exp $";
+version="$Id: involut.lib,v 1.8 2005-06-10 17:04:59 levandov Exp $";
 category="Noncommutative";
 info="
@@ -673 +673 @@
 }
 /////////////////////////////////////////////////////////////////////
-proc findAuto()
-"USAGE: findAuto();
+proc findAuto(int n)
+"USAGE: findAuto(n); n an integer
 RETURN: a ring together with a list of pairs L, where
 @*        L[i][1]  =  Groebner Basis of an i-th associated prime,
 @*        L[i][2]  =  matrix, defining a linear map, with entries, reduced with respect to L[i][1]
-PURPOSE: computes the ideal of linear automorphisms of the basering
-NOTE: for convenience, the full ideal of relations @code{idJ}
+PURPOSE: computes the ideal of linear automorphisms of the basering, given by a matrix, n-th power of which gives identity (i.e. unipotent matrix)
+NOTE: if n=0, a matrix, defining an automorphism is not assumed to be unipotent. For convenience, the full ideal of relations @code{idJ}
 and the initial matrix with indeterminates @code{matD} are exported in the output ring
 SEE ALSO: findInvo
 EXAMPLE: example findAuto; shows examples
 "{
+  if ((n<0 ) || (n==1))
+  {
+    "The index of unipotency is too small.";
+    return(0);
+  }
   def @B    = basering; //save the name of basering
   int NVars = nvars(@B); //number of variables in basering
@@ -763 +768 @@
   execute("matrix @@D"+snv+snv+"="+s+";"); // matrix with entries=new variables
 
-  J = J, ideal( @@D*@@D-matrix( freemodule(NVars) ) ); // add the condition that homomorphism to square is just identity
+  if (n>=2)
+  {
+    J = J, ideal( @@D*@@D-matrix( freemodule(NVars) ) ); // add the condition that homomorphism to square is just identity
+  }
   J       = simplify(J,2); // without extra zeros
   list mL = minAssGTZ(J); // components not in GB
@@ -792 +800 @@
  def a = makeWeyl(1);
  setring a; // this algebra is a first Weyl algebra
- def X = findAuto();
+ def X = findAuto(2);
  setring X; // ring with new variables - unknown coefficients
  // look at matrices, defining linear automorphisms: