# Changeset ffdeea5 in git

Ignore:
Timestamp:
Aug 22, 2008, 11:41:17 AM (15 years ago)
Branches:
Children:
16643ec1a43713e7a67aeabfd52c3a248a77bd58
Parents:
Message:
```*hannes: kernel->ker

File:
1 edited

Unmodified
Removed
• ## Singular/LIB/homolog.lib

 rc6c86b /////////////////////////////////////////////////////////////////////////////// version="\$Id: homolog.lib,v 1.24 2008-02-22 10:25:06 Singular Exp \$"; version="\$Id: homolog.lib,v 1.25 2008-08-22 09:41:17 Singular Exp \$"; category="Commutative Algebra"; info=" isLocallyFree(M,r);    test if coker(M) is locally free of constant rank r isReg(I,M);            test if I is coker(M)-sequence, I ideal, M module kernel(A,M,N);         ker(M'--A->N')  M,N modules, A matrix ker(A,M,N);            ker(M'--A->N')  M,N modules, A matrix kohom(A,k);            Hom(R^k,A),     A matrix over basering R kontrahom(A,k);        Hom(A,R^k),     A matrix over basering R ////////////////////////////////////////////////////////////////////////////// proc kernel (matrix A,module M,module N) "USAGE:   kernel(A,M,N); proc ker (matrix A,module M,module N) "USAGE:   ker(A,M,N); COMPUTE: Let M and N be submodules of R^m and R^n, presenting M'=R^m/M, N'=R^n/N (R=basering), and let A:R^m-->R^n be a matrix inducing a map A':M'-->N'. Then kernel(A,M,N); computes a presentation K of map A':M'-->N'. Then ker(A,M,N); computes a presentation K of ker(A') as in the commutative diagram: @example @end example RETURN:  module K, a presentation of ker(A':coker(M)->coker(N)). EXAMPLE: example kernel; shows examples. EXAMPLE: example ker; shows examples. " { module M=maxideal(1)*freemodule(2); matrix A[2][3]=2x,0,x,y,z2,y; module K=kernel(A,M,N); module K=ker(A,M,N); // dimension of kernel: dim(std(K));
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