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##  GaussDense.gd                Gauss package                Simon Goertzen
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##  Copyright 2007-2008 Lehrstuhl B für Mathematik, RWTH Aachen
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##  Declaration stuff for Gauss algorithms on dense (IsMatrix) matrices.
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DeclareOperation( "EchelonMatTransformationDestructive", #RREF over a ring, returns the same record as SemiEchelonMatTransformation but with ordered vectors
        [ IsMatrix ] );

DeclareAttribute( "EchelonMatTransformation",
        IsMatrix );

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DeclareOperation( "EchelonMatDestructive", #RREF over a ring, returns the same record as SemiEchelonMat but with ordered vectors
        [ IsMatrix ] );

DeclareAttribute( "EchelonMat",
        IsMatrix );

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DeclareOperation( "ReduceMat",
        [ IsMatrix, IsMatrix ] );

DeclareOperation( "ReduceMatWithEchelonMat", #Reduce the rows of a matrix with another matrix, which MUST be at least in REF.
        [ IsMatrix, IsMatrix ] );

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DeclareOperation( "ReduceMatTransformation",
        [ IsMatrix, IsMatrix ] );

DeclareOperation( "ReduceMatWithEchelonMatTransformation", #same as above, with transformation matrix.
        [ IsMatrix, IsMatrix ] );

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DeclareOperation( "KernelEchelonMatDestructive", #REF over a ring, returns a record with relations (list: certain columns of relations) as only entry
        [ IsMatrix, IsList ] );

DeclareGlobalFunction( "KernelMat" );