matkermod

Function: matkermod
Section: linear_algebra
C-Name: matkermod
Prototype: GGD&
Help: matkermod(x,d,&im): basis of the kernel of the matrix x modulo d.
Doc: gives a Howell basis (unique representation for submodules of~$(\Z/d\Z)^n$,
 cf. \kbd{matimagemod}) for the kernel of the matrix $x$ modulo $d$ as columns
 of a matrix. The matrix $x$ must have \typ{INT} entries, and $d$ can be an
 arbitrary positive integer. If $im$ is present, set it to a basis of the image
 of~$x$ (which is computed on the way).

 \bprog
 ? A = [1,2,3;5,1,4]
 %1 =
 [1 2 3]

 [5 1 4]

 ? K = matkermod(A,6)
 %2 =
 [2 1]

 [2 1]

 [0 3]

 ? (A*K)%6
 %3 =
 [0 0]

 [0 0]
 @eprog