33.15 SiftedVector

SiftedVector( B, v )

returns the residuum of the vector v with respect to the basis B of the vector space V. The exact meaning of this depends on the special properties of B.

But in general this residuum is obtained on subtracting appropriate multiples of basis vectors, and v is contained in V if and only if SiftedVector( B, v ) is the zero vector of V.

    gap> v:= GF(3)^2; v.name:= "v";;
    RowSpace( GF(3), [ [ Z(3)^0, 0*Z(3) ], [ 0*Z(3), Z(3)^0 ] ] )
    gap> s:= Subspace( v, [ [ 1, -1 ] *Z(3)^0 ] ); s.name:= "s";;
    Subspace( v, [ [ Z(3)^0, Z(3) ] ] )
    gap> b:= Basis(s);
    SemiEchelonBasis( s, [ [ Z(3)^0, Z(3) ] ] )
    gap> SiftedVector( b, [ Z(3), 0*Z(3) ] );
    [ 0*Z(3), Z(3) ] 

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