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## <#GAPDoc Label="Saturate">
## <Subsection Label="Saturate">
## <Heading>Saturate</Heading>
## <Example><![CDATA[
## gap> R := HomalgFieldOfRationalsInDefaultCAS( ) * "x,y,z";;
## gap> S := GradedRing( R );;
## gap> m := GradedLeftSubmodule( "x,y,z", S );
## <A graded torsion-free (left) ideal given by 3 generators>
## gap> I := Intersect( m^3, GradedLeftSubmodule( "x", S ) );
## <A graded torsion-free (left) ideal given by 6 generators>
## gap> NrRelations( I );
## 8
## gap> Im := SubobjectQuotient( I, m );
## <A graded torsion-free rank 1 (left) ideal given by 3 generators>
## gap> I_m := Saturate( I, m );
## <A graded principal (left) ideal of rank 1 on a free generator>
## gap> Is := Saturate( I );
## <A graded principal (left) ideal of rank 1 on a free generator>
## gap> Assert( 0, Is = I_m );
## ]]></Example>
## </Subsection>
## <#/GAPDoc>
LoadPackage( "GradedModules", false );
R := HomalgFieldOfRationalsInDefaultCAS( ) * "x,y,z";
S := GradedRing( R );
m := GradedLeftSubmodule( "x,y,z", S );
I := Intersect( m^3, GradedLeftSubmodule( "x", S ) );
NrRelations( I );
Im := SubobjectQuotient( I, m );
I_m := Saturate( I, m );
Is := Saturate( I );
Assert( 0, Is = I_m );
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