#
# file:         lin.gap
# purpose:      linear algebra-related GAP stuff
# created:      pasha jan 19 2005
# modified:     pasha feb 15 2005
# modification: cosmetics
#


# find a kernel of linear mapping f
Ker := function (f)
	local V, W, B, C, A, K, i;	

	V := Source(f);  # supposed to be linear spaces defined over the same field
	W := Range(f);
	B := Basis(V);
	C := Basis(W);

	# matrix of linear mapping
	A := NullMat (Dimension(V), Dimension(W), LeftActingDomain(V));
	
	for i in [1..Dimension(V)] do
		A[i] := Coefficients (C, Image (f, B[i]));
	od;

	return (SubspaceNC (V, List (NullspaceMat(A), x -> LinearCombination (B, x)), 
			"basis"));
end;


# end of lin.gap