addcoset.gd

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#W  addcoset.gd                 GAP library                     Thomas Breuer
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#Y  Copyright (C)  1996,  Lehrstuhl D für Mathematik,  RWTH Aachen,  Germany
#Y  (C) 1998 School Math and Comp. Sci., University of St Andrews, Scotland
#Y  Copyright (C) 2002 The GAP Group
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##  This file declares the operations for additive cosets.
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#C  IsAdditiveCoset( <D> )
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##  An additive coset is an external additive set whose additively acting
##  domain is an additive group.
##  The additive coset and its additively acting domain lie in the same
##  family.
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##  Note that additive cosets for non-commutative addition are not supported.
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DeclareCategory( "IsAdditiveCoset",
    IsExtASet and IsAssociativeAOpESum and IsTrivialAOpEZero );


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#O  AdditiveCoset( <A>, <a> )
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DeclareOperation( "AdditiveCoset", [ IsAdditiveGroup, IsAdditiveElement ] );


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#E