9.10 Coefficients

Coefficients( V, v )

Coefficients computes the coefficients that have to be used to write v as a linear combination in the base of V.

To make sure that this function produces the correct result, v has to be an element of V. If v does not lie in V the result is unpredictable.

The result of Coefficients is returned as a list of elements of the field over which the vector space V is written. Of course, the length of this list equals the dimension of V.

    gap> f := GF( 3^4 );
    GF(3^4)
    gap> f.base;
    [ Z(3)^0, Z(3^4), Z(3^4)^2, Z(3^4)^3 ]
    gap> V := VectorSpace( f.base, GF( 3 ) );
    VectorSpace( [ Z(3)^0, Z(3^4), Z(3^4)^2, Z(3^4)^3 ], GF(3) )
    gap> Dimension( V );
    4
    gap> Coefficients( V, f.root ^ 16 );
    [ Z(3), Z(3)^0, Z(3), 0*Z(3) ] 

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