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LinKerBasis

find the kernel of a matrix

Syntax 
LinKerBasis(M: MAT): LIST of RINGELEM

Description
This function returns a list whose components are lists representing a basis for the kernel of M. Calling the function twice on the same input will not necessarily produce the same output, though in each case, a basis for the kernel is produced.

This function works only on matrices whose entries are in a field (from version CoCoA-5.0.3). The CoCoA-4 function returning a ZZ-basis for the kernel of M is not yet implemented.

Example 
/**/   M := mat([[1,2,3,4],[5,6,7,8],[9,10,11,12]]);
/**/   LinKerBasis(M);
[[-1, 2, -1, 0], [-2, 3, 0, -1]]

/**/  K := NewFractionField(NewPolyRing(QQ, "a,b"));
/**/  Use K;
/**/  M := mat([[1,2,3,a],[5,6,7,a*b]]);
/**/  LinKerBasis(M);
[[-1, 2, -1, 0], [(a*b -3*a)/2, (-a*b +5*a)/4, 0, -1]]

See Also