Changeset ffdeea5 in git


Ignore:
Timestamp:
Aug 22, 2008, 11:41:17 AM (15 years ago)
Author:
Hans Schönemann <hannes@…>
Branches:
(u'jengelh-datetime', 'ceac47cbc86fe4a15902392bdbb9bd2ae0ea02c6')(u'spielwiese', '0604212ebb110535022efecad887940825b97c3f')
Children:
16643ec1a43713e7a67aeabfd52c3a248a77bd58
Parents:
c6c86ba35db6c94b41b12ad8e5eb5b1bc0552952
Message:
*hannes: kernel->ker


git-svn-id: file:///usr/local/Singular/svn/trunk@11027 2c84dea3-7e68-4137-9b89-c4e89433aadc
File:
1 edited

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  • Singular/LIB/homolog.lib

    rc6c86b rffdeea5  
    11///////////////////////////////////////////////////////////////////////////////
    2 version="$Id: homolog.lib,v 1.24 2008-02-22 10:25:06 Singular Exp $";
     2version="$Id: homolog.lib,v 1.25 2008-08-22 09:41:17 Singular Exp $";
    33category="Commutative Algebra";
    44info="
    … …  
    2222 isLocallyFree(M,r);    test if coker(M) is locally free of constant rank r
    2323 isReg(I,M);            test if I is coker(M)-sequence, I ideal, M module
    24  kernel(A,M,N);         ker(M'--A->N')  M,N modules, A matrix
     24 ker(A,M,N);            ker(M'--A->N')  M,N modules, A matrix
    2525 kohom(A,k);            Hom(R^k,A),     A matrix over basering R
    2626 kontrahom(A,k);        Hom(A,R^k),     A matrix over basering R
    … …  
    11271127//////////////////////////////////////////////////////////////////////////////
    11281128
    1129 proc kernel (matrix A,module M,module N)
    1130 "USAGE:   kernel(A,M,N);
     1129proc ker (matrix A,module M,module N)
     1130"USAGE:   ker(A,M,N);
    11311131COMPUTE: Let M and N be submodules of R^m and R^n, presenting M'=R^m/M,
    11321132         N'=R^n/N (R=basering), and let A:R^m-->R^n be a matrix inducing a
    1133          map A':M'-->N'. Then kernel(A,M,N); computes a presentation K of
     1133         map A':M'-->N'. Then ker(A,M,N); computes a presentation K of
    11341134         ker(A') as in the commutative diagram:
    11351135@example
    … …  
    11441144@end example
    11451145RETURN:  module K, a presentation of ker(A':coker(M)->coker(N)).
    1146 EXAMPLE: example kernel; shows examples.
     1146EXAMPLE: example ker; shows examples.
    11471147"
    11481148{
    … …  
    11561156  module M=maxideal(1)*freemodule(2);
    11571157  matrix A[2][3]=2x,0,x,y,z2,y;
    1158   module K=kernel(A,M,N);
     1158  module K=ker(A,M,N);
    11591159  // dimension of kernel:
    11601160  dim(std(K));
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