Changeset f620218 in git
 Timestamp:
 Jun 10, 2005, 7:04:59 PM (19 years ago)
 Branches:
 (u'fiekerDuVal', '117eb8c30fc9e991c4decca4832b1d19036c4c65')(u'spielwiese', 'c7af8613769b29c741d6c338945669719f1fc4f8')
 Children:
 19fc57bf1d64049e9869d7a195dc56f156f8e197
 Parents:
 cd6ff4925c1335a6a1617eccfabad9197484c383
 File:

 1 edited
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Singular/LIB/involut.lib
rcd6ff49 rf620218 1 version="$Id: involut.lib,v 1. 7 20050607 10:24:45 SingularExp $";1 version="$Id: involut.lib,v 1.8 20050610 17:04:59 levandov Exp $"; 2 2 category="Noncommutative"; 3 3 info=" … … 673 673 } 674 674 ///////////////////////////////////////////////////////////////////// 675 proc findAuto( )676 "USAGE: findAuto( );675 proc findAuto(int n) 676 "USAGE: findAuto(n); n an integer 677 677 RETURN: a ring together with a list of pairs L, where 678 678 @* L[i][1] = Groebner Basis of an ith associated prime, 679 679 @* L[i][2] = matrix, defining a linear map, with entries, reduced with respect to L[i][1] 680 PURPOSE: computes the ideal of linear automorphisms of the basering 681 NOTE: for convenience, the full ideal of relations @code{idJ}680 PURPOSE: computes the ideal of linear automorphisms of the basering, given by a matrix, nth power of which gives identity (i.e. unipotent matrix) 681 NOTE: if n=0, a matrix, defining an automorphism is not assumed to be unipotent. For convenience, the full ideal of relations @code{idJ} 682 682 and the initial matrix with indeterminates @code{matD} are exported in the output ring 683 683 SEE ALSO: findInvo 684 684 EXAMPLE: example findAuto; shows examples 685 685 "{ 686 if ((n<0 )  (n==1)) 687 { 688 "The index of unipotency is too small."; 689 return(0); 690 } 686 691 def @B = basering; //save the name of basering 687 692 int NVars = nvars(@B); //number of variables in basering … … 763 768 execute("matrix @@D"+snv+snv+"="+s+";"); // matrix with entries=new variables 764 769 765 J = J, ideal( @@D*@@Dmatrix( freemodule(NVars) ) ); // add the condition that homomorphism to square is just identity 770 if (n>=2) 771 { 772 J = J, ideal( @@D*@@Dmatrix( freemodule(NVars) ) ); // add the condition that homomorphism to square is just identity 773 } 766 774 J = simplify(J,2); // without extra zeros 767 775 list mL = minAssGTZ(J); // components not in GB … … 792 800 def a = makeWeyl(1); 793 801 setring a; // this algebra is a first Weyl algebra 794 def X = findAuto( );802 def X = findAuto(2); 795 803 setring X; // ring with new variables  unknown coefficients 796 804 // look at matrices, defining linear automorphisms:
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