65.130 VerticalConversionFieldMat

VerticalConversionFieldMat( M, F )

VerticalConversionFieldMat returns the matrix M with its elements converted from a field <F>=GF(q^m), q prime, to a field GF(q). Each element is replaced by its representation over the latter field, placed vertically in the matrix.

If M is a k by n matrix, the result is a k*m by n matrix, since each element of GF(q^m) can be represented in GF(q) using m elements.

    gap> M := Z(9)*[[1,2],[2,1]];; PrintArray(M);
    [ [    Z(3^2),  Z(3^2)^5 ],
      [  Z(3^2)^5,    Z(3^2) ] ]
    gap> DefaultField( Flat(M) );
    GF(3^2)
    gap> VCFM := VerticalConversionFieldMat( M, GF(9) );; PrintArray(VCFM);
    [ [  0*Z(3),  0*Z(3) ],
      [  Z(3)^0,    Z(3) ],
      [  0*Z(3),  0*Z(3) ],
      [    Z(3),  Z(3)^0 ] ]
    gap> DefaultField( Flat(VCFM) );
    GF(3) 

A similar function is HorizontalConversionFieldMat (see HorizontalConversionFieldMat).

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