33.19 IsSemiEchelonBasis

IsSemiEchelonBasis( B )

returns true if B is a semi-echelonized basis (see SemiEchelonBasis), and false otherwise. If B is semi-echelonized, and this was not yet stored before, after the call the operations record of B will be SemiEchelonBasisRowSpaceOps.

    gap> v:= GF(2)^2; v.name:= "v";;
    RowSpace( GF(2), [ [ Z(2)^0, 0*Z(2) ], [ 0*Z(2), Z(2)^0 ] ] )
    gap> b1:= Basis( v, [ [ 0, 1 ], [ 1, 0 ] ] * Z(2) );
    Basis( v, [ [ 0*Z(2), Z(2)^0 ], [ Z(2)^0, 0*Z(2) ] ] )
    gap> IsSemiEchelonBasis( b1 );
    true
    gap> b1;
    SemiEchelonBasis( v, [ [ 0*Z(2), Z(2)^0 ], [ Z(2)^0, 0*Z(2) ] ] )
    gap> b2:= Basis( v, [ [ 0, 1 ], [ 1, 1 ] ] * Z(2) );
    Basis( v, [ [ 0*Z(2), Z(2)^0 ], [ Z(2)^0, Z(2)^0 ] ] )
    gap> IsSemiEchelonBasis( b2 );
    false
    gap> b2;
    Basis( v, [ [ 0*Z(2), Z(2)^0 ], [ Z(2)^0, Z(2)^0 ] ] ) 

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