/usr/share/gap/lib/mgmideal.gd is in gap-libs 4r7p5-2.
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#W mgmideal.gd GAP library Andrew Solomon
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#Y Copyright (C) 1997, 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 contains the declaration of operations for magma ideals.
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## Left Magma Ideals
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#P IsLeftMagmaIdeal( <D> )
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## A *left magma ideal* is a submagma (see~"Magmas") which is closed under
## left multiplication by elements of its parent magma.
##
DeclareSynonym("IsLeftMagmaIdeal", IsMagma and IsLeftActedOnBySuperset);
## As a sub magma, a left magma ideal has a Parent (the enclosing magma)
## and as LeftActedOnBySuperset it has a LeftActingDomain.
## We must ensure that these two are the same object when the
## left magma ideal is created.
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#F LeftMagmaIdeal(<D>, <gens> )
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## `LeftMagmaIdeal' returns the magma containing the elements in the
## homogeneous list <gens> and closed under left multiplication by elements
## of the magma <D> in which it embeds.
##
## This has to put in the parent and left acting set. Although it is a
## submagma, we can't call the generic submagma creation since that
## requires *magma* generators.
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DeclareGlobalFunction( "LeftMagmaIdeal" );
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#O AsLeftMagmaIdeal( <D>, <C> )
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## Let <D> be a domain and <C> a collection.
## If <C> is a subset of <D>
## `AsLeftMagmaIdeal' returns the LeftMagmaIdeal with generators <C>,
## and with parent <D>.
## Otherwise `fail' is returned.
## Probably more desirable would be to regard <C> as the set of
## elements of <D>.
##
DeclareOperation( "AsLeftMagmaIdeal", [ IsDomain, IsCollection ] );
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#A GeneratorsOfLeftMagmaIdeal( <I> )
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## These are left ideal generators, not magma generators.
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DeclareSynonymAttr( "GeneratorsOfLeftMagmaIdeal", GeneratorsOfExtLSet );
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#O LeftMagmaIdealByGenerators(<D>, <gens> )
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## is the underlying operation of `LeftMagmaIdeal'
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DeclareOperation( "LeftMagmaIdealByGenerators", [IsMagma, IsCollection ] );
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## Right Magma Ideals
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#P IsRightMagmaIdeal( <D> )
##
## A *right magma ideal* is a submagma (see~"Magmas") which is closed under
## right multiplication by elements of its parent magma.
##
DeclareSynonym("IsRightMagmaIdeal", IsMagma and IsRightActedOnBySuperset);
## As a sub magma, a right magma ideal has a Parent (the enclosing magma)
## and as RightActedOnBySuperset it has a RightActingDomain.
## We must ensure that these two are the same object when the
## right magma ideal is created.
##
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#F RightMagmaIdeal(<D>, <gens> ) . . . . . . . . . .
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## `RightMagmaIdeal' returns the magma containing the elements in the
## homogeneous list <gens> and closed under right multiplication by elements
## of the parent magma <D> in which it embeds.
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DeclareGlobalFunction( "RightMagmaIdeal" );
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#O AsRightMagmaIdeal( <D>, <C> )
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## Let <D> be a domain and <C> a collection.
## If <C> is a subset of <D> that forms a RightMagmaIdeal then
## `AsRightMagmaIdeal' returns this RightMagmaIdeal, with parent <D>.
## Otherwise `fail' is returned.
##
DeclareOperation( "AsRightMagmaIdeal", [ IsDomain, IsCollection ] );
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#A GeneratorsOfRightMagmaIdeal( <I> )
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## These are right ideal generators, not magma generators.
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DeclareSynonymAttr( "GeneratorsOfRightMagmaIdeal", GeneratorsOfExtRSet );
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#O RightMagmaIdealByGenerators(<D>, <gens> )
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## is the underlying operation of `RightMagmaIdeal'
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DeclareOperation( "RightMagmaIdealByGenerators", [IsMagma, IsCollection ] );
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## Two Sided Magma Ideals
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#P IsMagmaIdeal( <D> )
##
## A *magma ideal* is a submagma (see~"Magmas") which is closed under
## left and right multiplication by elements of its parent magma.
##
DeclareSynonym("IsMagmaIdeal", IsLeftMagmaIdeal and IsRightMagmaIdeal);
## As a sub magma, a magma ideal has a Parent (the enclosing magma)
## and as LeftActedOnBySuperset it has a LeftActingDomain,
## and as RightActedOnBySuperset it has a RightActingDomain.
## We must ensure that these three are the same object when the
## magma ideal is created.
##
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#F MagmaIdeal(<D>, <gens> )
##
## `MagmaIdeal' returns the magma containing the elements in the homogeneous
## list <gens> and closed under left and right multiplication by elements
## of the parent magma <D> in which it emeds.
##
##
DeclareGlobalFunction( "MagmaIdeal" );
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#O AsMagmaIdeal( <D>, <C> )
##
## Let <D> be a domain and <C> a collection.
## If <C> is a subset of <D> that forms a MagmaIdeal then
## `AsMagmaIdeal' returns this MagmaIdeal, with parent <D>.
## Otherwise `fail' is returned.
##
DeclareOperation( "AsMagmaIdeal", [ IsDomain, IsCollection ] );
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#A GeneratorsOfMagmaIdeal( <I> )
##
## These are ideal generators, not magma generators.
##
DeclareAttribute( "GeneratorsOfMagmaIdeal", IsMagmaIdeal );
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#O MagmaIdealByGenerators( <D>, <gens> )
##
## is the underlying operation of `MagmaIdeal'
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DeclareOperation( "MagmaIdealByGenerators", [IsMagma, IsCollection ] );
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#E
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