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MT-resource-bot committed Oct 3, 2017
1 parent 7f4a1f7 commit 94a8eb8
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Showing 7 changed files with 564 additions and 505 deletions.
48 changes: 24 additions & 24 deletions doc/translat.xml
Original file line number Diff line number Diff line change
Expand Up @@ -47,7 +47,7 @@ gap> GeneratorsOfSemigroup(L);
canonical list of elements of the underlying semigroup,
LeftTranslation and RightTranslation return the corresponding translations.
<Example><![CDATA[
gap> S := RectangularBand(3,4);;
gap> S := RectangularBand(3, 4);;
gap> L := LeftTranslationsSemigroup(S);;
gap> s := AsList(S)[1];;
gap> f := function(x)
Expand All @@ -57,7 +57,7 @@ gap> map := MappingByFunction(S, S, f);;
gap> l := LeftTranslation(L, map);
<left translation on <regular transformation semigroup of size 12,
degree 8 with 4 generators>>
gap> s^l;
gap> s ^ l;
Transformation( [ 1, 2, 1, 1, 5, 5, 5, 5 ] )
]]></Example>
</Description>
Expand Down Expand Up @@ -103,10 +103,10 @@ gap> Size(H);
(<A>l, r</A>) of translations, belonging to the translational hull
<A>H</A>.
<Example> <![CDATA[
gap> G := SmallGroup(4,2);;
gap> G := SmallGroup(4, 2);;
gap> A := AsList(G);;
gap> mat := [ [A[1], 0],
> [A[2], A[2]] ];;
gap> mat := [[A[1], 0],
> [A[2], A[2]]];;
gap> S := ReesZeroMatrixSemigroup(G, mat);;
gap> L := LeftTranslationsSemigroup(S);;
gap> R := RightTranslationsSemigroup(S);;
Expand All @@ -133,7 +133,7 @@ gap> x := Bitranslation(H, l, r);
of <C>IsTranslationsSemigroupElement</C>,
which itself is a subcategory of <C>IsAssociativeElement</C>.
<Example> <![CDATA[
gap> S := RectangularBand(3,4);;
gap> S := RectangularBand(3, 4);;
gap> l := Representative(LeftTranslations(S));
<left translation on <simple transformation semigroup of size 12,
degree 8 with 4 generators>>
Expand All @@ -156,9 +156,9 @@ false
belong to <C>IsBitranslation</C>. This is a subcategory of
<Ref Filt="IsAssociativeElement" BookName="ref"/>.
<Example> <![CDATA[
gap> G := SmallGroup(4,2);;
gap> G := SmallGroup(4, 2);;
gap> A := AsList(G);;
gap> mat := [ [A[1], 0, A[1]],
gap> mat := [[A[1], 0, A[1]],
> [A[2], A[2], A[4]]];;
gap> S := ReesZeroMatrixSemigroup(G, mat);;
gap> L := LeftTranslations(S);;
Expand Down Expand Up @@ -186,7 +186,7 @@ false
<C>IsXTranslationsSemigroupElementCollection</C> and
<C>IsSemigroup</C>.
<Example><![CDATA[
gap> S := RectangularBand(3,4);;
gap> S := RectangularBand(3, 4);;
gap> L := LeftTranslations(S);;
gap> R := RightTranslations(S);;
gap> IsLeftTranslationsSemigroup(L);
Expand All @@ -207,7 +207,7 @@ false
<C>IsTranslationalHull</C> is a synonym for <C>IsSemigroup</C> and
<Ref Filt="IsBitranslationCollection"/>
<Example><![CDATA[
gap> S := RectangularBand(3,3);;
gap> S := RectangularBand(3, 3);;
gap> H := TranslationalHull(S);;
gap> L := LeftTranslationsSemigroup(S);;
gap> IsTranslationalHull(H);
Expand Down Expand Up @@ -249,7 +249,7 @@ true
<C>XTranslationsSemigroupOfFamily</C>(<A>fam</A>) returns the left or right
translations semigroup which contains the objects of family <A>fam</A>
<Example><![CDATA[
gap> S := RectangularBand(3,3);;
gap> S := RectangularBand(3, 3);;
gap> L := LeftTranslations(S);;
gap> l := Representative(L);;
gap> LeftTranslationsSemigroupOfFamily(FamilyObj(l)) = L;
Expand All @@ -269,7 +269,7 @@ true
<C>TranslationalHullOfFamily</C>(<A>fam</A>) returns the translational hull
which contains the objects of family <A>fam</A>
<Example><![CDATA[
gap> S := RectangularBand(3,3);;
gap> S := RectangularBand(3, 3);;
gap> H := TranslationalHull(S);;
gap> h := Representative(H);;
gap> TranslationalHullOfFamily(FamilyObj(h)) = H;
Expand All @@ -293,8 +293,8 @@ true
of <A>S</A>. These are the translations defined by right multiplication by
a fixed element of <A>S</A>.
<Example><![CDATA[
gap> S := Semigroup([Transformation([2,2,3,1]),
> Transformation([1,4,3,3])]);;
gap> S := Semigroup([Transformation([2, 2, 3, 1]),
> Transformation([1, 4, 3, 3])]);;
gap> L := InnerLeftTranslations(S);
<semigroup of left translations of <transformation semigroup of
degree 4 with 2 generators> with 2 generators>
Expand All @@ -321,8 +321,8 @@ true
right translations defined respectively by left multiplication
and right multiplication by the same fixed element of <A>S</A>.
<Example><![CDATA[
gap> S := Semigroup([Transformation([2,2,3,1]),
> Transformation([1,4,3,3])]);;
gap> S := Semigroup([Transformation([2, 2, 3, 1]),
> Transformation([1, 4, 3, 3])]);;
gap> InnerTranslationalHull(S);
<semigroups of translational hull elements over <transformation
semigroup of degree 4 with 2 generators>>
Expand All @@ -338,13 +338,13 @@ gap> InnerTranslationalHull(S);
<Returns> The left or right translation component of <A>x</A>.
</Returns>
<Description>
For a bitranslation <A>b</A> consisting of a linked pair <A>(l, r)</A>,i
For a bitranslation <A>b</A> consisting of a linked pair <A>(l, r)</A>,
<C>LeftPartOfBitranslation</C><A>b</A> returns the left translation
<A>l</A>, and <C>RightPartOfBitranslation</C><A>b</A> returns the
right translation <A>r</A>.
<Example><![CDATA[
gap> S := Semigroup([Transformation([4,2,3,3]),
> Transformation([2,2,3,1])]);
gap> S := Semigroup([Transformation([4, 2, 3, 3]),
> Transformation([2, 2, 3, 1])]);
<transformation semigroup of degree 4 with 2 generators>
gap> H := TranslationalHull(S);;
gap> h := AsList(H)[2];;
Expand Down Expand Up @@ -400,7 +400,7 @@ gap> S := ReesMatrixSemigroup(G, mat);;
gap> R := Range(RMSNormalization(S));;
gap> L := LeftTranslations(R);;
gap> RT := RightTranslations(R);;
gap> gpfunc := [G.1, G.2*G.1];
gap> gpfunc := [G.1, G.2 * G.1];
[ f1, f1*f2 ]
gap> t := IdentityTransformation;;
gap> l := LeftTranslationOfNormalRMS(L, gpfunc, t);
Expand Down Expand Up @@ -433,10 +433,10 @@ gap> G := UnderlyingSemigroup(R);
gap> L := LeftTranslations(R);;
gap> RT := RightTranslations(R);;
gap> H := TranslationalHull(R);;
gap> lgpfunc := [G.1*G.3*G.3, G.2];;
gap> rgpfunc := [G.1*G.3*G.3, G.3*G.3, G.2];;
gap> lt := Transformation([2,2]);;
gap> rt := Transformation([3,3,3]);;
gap> lgpfunc := [G.1 * G.3 * G.3, G.2];;
gap> rgpfunc := [G.1 * G.3 * G.3, G.3 * G.3, G.2];;
gap> lt := Transformation([2, 2]);;
gap> rt := Transformation([3, 3, 3]);;
gap> l := LeftTranslationOfNormalRMS(L, lgpfunc, lt);;
gap> r := RightTranslationOfNormalRMS(RT, rgpfunc, rt);;
gap> h := BitranslationOfNormalRMS(H, l, r);
Expand Down
4 changes: 2 additions & 2 deletions gap/attributes/rms-translat.gd
Original file line number Diff line number Diff line change
Expand Up @@ -11,10 +11,10 @@
DeclareCategory("IsTranslationOfNormalRMS",
IsTranslationsSemigroupElement);
DeclareCategory("IsLeftTranslationOfNormalRMS",
IsTranslationOfNormalRMS and
IsTranslationOfNormalRMS and
IsLeftTranslationsSemigroupElement);
DeclareCategory("IsRightTranslationOfNormalRMS",
IsTranslationOfNormalRMS and
IsTranslationOfNormalRMS and
IsRightTranslationsSemigroupElement);
DeclareCategory("IsBitranslationOfNormalRMS", IsBitranslation);

Expand Down
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