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D.11.2.5 leftKernel

Procedure from library control.lib (see control_lib).

Usage:
leftKernel(M); M a matrix

Return:
module

Purpose:
computes left kernel of matrix M (a module of all elements v such that vM=0)

Example:
 
LIB "control.lib";
ring r= 0,(x,y,z),dp;
matrix M[3][1] = x,y,z;
print(M);
==> x,
==> y,
==> z 
matrix L = leftKernel(M);
print(L);
==> 0, -z,y,
==> -y,x, 0,
==> -z,0, x 
// check:
print(L*M);
==> 0,
==> 0,
==> 0