#############################################################################
##
#W congrees.
xml
#Y Copyright (C)
2015 Michael Young
##
## Licensing information can be found in the README file of this package.
##
#############################################################################
##
<#GAPDoc Label=
"SemigroupIdealOfReesCongruence">
<ManSection>
<Attr Name =
"SemigroupIdealOfReesCongruence" Arg =
"cong"/>
<Returns>A semigroup ideal.</Returns>
<Description>
If <A>cong</A> is a rees congruence (see <Ref Prop =
"IsReesCongruence"
BookName =
"ref"/>) then this attribute returns the two-sided ideal that was
used to define it, i.e.~the ideal of elements in the only non-trivial
congruence class of <A>cong</A>.
<Example><![
CDATA[
gap> S := Semigroup([
> Transformation([
2,
3,
4,
3,
1,
1]),
> Transformation([
6,
4,
4,
4,
6,
1])]);;
gap> I := SemigroupIdeal(S,
> Transformation([
4,
4,
4,
4,
4,
2]),
> Transformation([
3,
3,
3,
3,
3,
2]));;
gap> cong := ReesCongruenceOfSemigroupIdeal(I);;
gap> SemigroupIdealOfReesCongruence(cong);
<non-regular transformation semigroup ideal of degree
6 with
2 generators>]]></Example>
</Description>
</ManSection>
<#/GAPDoc>
<#GAPDoc Label=
"IsReesCongruenceClass">
<ManSection>
<Filt Name =
"IsReesCongruenceClass" Arg =
"obj" Type =
"category"/>
<Returns><K>true</K> or <K>false</K>.</Returns>
<Description>
This category describes a congruence class of a Rees congruence. A
congruence class of a Rees congruence either contains all the elements of
an ideal, or is a singleton (see <Ref Prop =
"IsReesCongruence"
BookName =
"ref"/>).<P/>
An object of this
type may be used in the same way as any other congruence
class object.
<Example><![
CDATA[
gap> S := Semigroup(
> Transformation([
2,
3,
4,
3,
1,
1]),
> Transformation([
6,
4,
4,
4,
6,
1]));;
gap> I := SemigroupIdeal(S,
> Transformation([
4,
4,
4,
4,
4,
2]),
> Transformation([
3,
3,
3,
3,
3,
2]));;
gap> cong := ReesCongruenceOfSemigroupIdeal(I);;
gap> classes := EquivalenceClasses(cong);;
gap> IsReesCongruenceClass(classes[
1]);
true]]></Example>
</Description>
</ManSection>
<#/GAPDoc>
