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james-d-mitchell committed Sep 19, 2023
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204 changes: 102 additions & 102 deletions doc/attr.xml
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116 changes: 58 additions & 58 deletions doc/attrinv.xml
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Original file line number Diff line number Diff line change
Expand Up @@ -63,33 +63,33 @@ gap> S := InverseMonoid([
> PartialPerm([1, 2, 3], [2, 4, 1]),
> PartialPerm([1, 3, 4], [3, 4, 1])]);;
gap> CharacterTableOfInverseSemigroup(S);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 3, 1, 1, 1, 0, 0, 0, 0 ],
[ 3, 1, E(3), E(3)^2, 0, 0, 0, 0 ],
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 3, 1, 1, 1, 0, 0, 0, 0 ],
[ 3, 1, E(3), E(3)^2, 0, 0, 0, 0 ],
[ 3, 1, E(3)^2, E(3), 0, 0, 0, 0 ], [ 6, 3, 0, 0, 1, -1, 0, 0 ],
[ 6, 3, 0, 0, 1, 1, 0, 0 ], [ 4, 3, 0, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 4 ]>,
<identity partial perm on [ 1, 3, 4 ]>, (1,3,4), (1,4,3),
<identity partial perm on [ 1, 3 ]>, (1,3),
[ 6, 3, 0, 0, 1, 1, 0, 0 ], [ 4, 3, 0, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 4 ]>,
<identity partial perm on [ 1, 3, 4 ]>, (1,3,4), (1,4,3),
<identity partial perm on [ 1, 3 ]>, (1,3),
<identity partial perm on [ 3 ]>, <empty partial perm> ] ]
gap> S := SymmetricInverseMonoid(4);;
gap> CharacterTableOfInverseSemigroup(S);
[ [ [ 1, -1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, -1, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, -2, 1, 0, 0, 1, -1, 1, 0, 0, 0, 0 ],
[ 8, 0, -1, 0, 0, 2, 0, -1, 0, 0, 0, 0 ],
[ 4, 2, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0 ],
[ 6, 0, 0, -2, 0, 3, -1, 0, 1, -1, 0, 0 ],
[ 6, 2, 0, 2, 0, 3, 1, 0, 1, 1, 0, 0 ],
[ 4, 2, 1, 0, 0, 3, 1, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 4 ]>, (1)(2)(3,4),
(1)(2,3,4), (1,2)(3,4), (1,2,3,4),
<identity partial perm on [ 1, 2, 3 ]>, (1)(2,3), (1,2,3),
<identity partial perm on [ 2, 3 ]>, (2,3),
[ [ [ 1, -1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, -1, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, -2, 1, 0, 0, 1, -1, 1, 0, 0, 0, 0 ],
[ 8, 0, -1, 0, 0, 2, 0, -1, 0, 0, 0, 0 ],
[ 4, 2, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0 ],
[ 6, 0, 0, -2, 0, 3, -1, 0, 1, -1, 0, 0 ],
[ 6, 2, 0, 2, 0, 3, 1, 0, 1, 1, 0, 0 ],
[ 4, 2, 1, 0, 0, 3, 1, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 4 ]>, (1)(2)(3,4),
(1)(2,3,4), (1,2)(3,4), (1,2,3,4),
<identity partial perm on [ 1, 2, 3 ]>, (1)(2,3), (1,2,3),
<identity partial perm on [ 2, 3 ]>, (2,3),
<identity partial perm on [ 1 ]>, <empty partial perm> ] ]]]></Example>
</Description>
</ManSection>
Expand All @@ -113,17 +113,17 @@ gap> S := InverseMonoid(
gap> MultiplicativeZero(S);
<empty partial perm>
gap> Set(PrimitiveIdempotents(S));
[ <identity partial perm on [ 1 ]>, <identity partial perm on [ 2 ]>,
[ <identity partial perm on [ 1 ]>, <identity partial perm on [ 2 ]>,
<identity partial perm on [ 3 ]>, <identity partial perm on [ 4 ]> ]
gap> S := DualSymmetricInverseMonoid(4);
<inverse block bijection monoid of degree 4 with 3 generators>
gap> Set(PrimitiveIdempotents(S));
[ <block bijection: [ 1, 2, 3, -1, -2, -3 ], [ 4, -4 ]>,
<block bijection: [ 1, 2, 4, -1, -2, -4 ], [ 3, -3 ]>,
<block bijection: [ 1, 2, -1, -2 ], [ 3, 4, -3, -4 ]>,
<block bijection: [ 1, 3, 4, -1, -3, -4 ], [ 2, -2 ]>,
<block bijection: [ 1, 3, -1, -3 ], [ 2, 4, -2, -4 ]>,
<block bijection: [ 1, 4, -1, -4 ], [ 2, 3, -2, -3 ]>,
[ <block bijection: [ 1, 2, 3, -1, -2, -3 ], [ 4, -4 ]>,
<block bijection: [ 1, 2, 4, -1, -2, -4 ], [ 3, -3 ]>,
<block bijection: [ 1, 2, -1, -2 ], [ 3, 4, -3, -4 ]>,
<block bijection: [ 1, 3, 4, -1, -3, -4 ], [ 2, -2 ]>,
<block bijection: [ 1, 3, -1, -3 ], [ 2, 4, -2, -4 ]>,
<block bijection: [ 1, 4, -1, -4 ], [ 2, 3, -2, -3 ]>,
<block bijection: [ 1, -1 ], [ 2, 3, 4, -2, -3, -4 ]> ]]]></Example>
</Description>
</ManSection>
Expand Down Expand Up @@ -174,7 +174,7 @@ gap> B := InverseSemigroup([
<inverse block bijection semigroup of degree 7 with 4 generators>
gap> x := Bipartition([
> [1, 2, 3, 5, 6, 7, -2, -3, -4, -5, -6, -7], [4, -1]]);
<block bijection: [ 1, 2, 3, 5, 6, 7, -2, -3, -4, -5, -6, -7 ],
<block bijection: [ 1, 2, 3, 5, 6, 7, -2, -3, -4, -5, -6, -7 ],
[ 4, -1 ]>
gap> IsJoinIrreducible(B, x);
true
Expand All @@ -198,7 +198,7 @@ false]]></Example>
contains all elements of <A>S</A> which are greater than or equal to any
element of <A>T</A>, with respect to the natural partial order.
See <Ref Func = "NaturalLeqPartialPerm" BookName="ref"/>.<P/>

Note that <A>T</A> can be a subset of <A>S</A> or a subsemigroup of <A>S</A>.
</Description>
</ManSection>
Expand Down Expand Up @@ -251,8 +251,8 @@ gap> T := InverseSemigroup([
> PartialPerm([0, 2])]);
<inverse partial perm semigroup of rank 4 with 3 generators>
gap> JoinIrreducibleDClasses(T);
[ <Green's D-class: <identity partial perm on [ 1, 2, 3, 4 ]>>,
<Green's D-class: <identity partial perm on [ 1 ]>>,
[ <Green's D-class: <identity partial perm on [ 1, 2, 3, 4 ]>>,
<Green's D-class: <identity partial perm on [ 1 ]>>,
<Green's D-class: <identity partial perm on [ 2 ]>> ]
gap> D := DualSymmetricInverseSemigroup(3);
<inverse block bijection monoid of degree 3 with 3 generators>
Expand Down Expand Up @@ -285,9 +285,9 @@ gap> S := SymmetricInverseSemigroup(4);
gap> T := [PartialPerm([1, 0, 3, 0])];
[ <identity partial perm on [ 1, 3 ]> ]
gap> U := MajorantClosure(S, T);
[ <identity partial perm on [ 1, 3 ]>,
<identity partial perm on [ 1, 2, 3 ]>, [2,4](1)(3), [4,2](1)(3),
<identity partial perm on [ 1, 3, 4 ]>,
[ <identity partial perm on [ 1, 3 ]>,
<identity partial perm on [ 1, 2, 3 ]>, [2,4](1)(3), [4,2](1)(3),
<identity partial perm on [ 1, 3, 4 ]>,
<identity partial perm on [ 1, 2, 3, 4 ]>, (1)(2,4)(3) ]
gap> B := InverseSemigroup([
> Bipartition([[1, -2], [2, -1], [3, -3], [4, 5, -4, -5]]),
Expand All @@ -297,14 +297,14 @@ gap> T := [Bipartition([[1, -2], [2, 3, 5, -1, -3, -5], [4, -4]]),
gap> IsMajorantlyClosed(B, T);
false
gap> MajorantClosure(B, T);
[ <block bijection: [ 1, -2 ], [ 2, 3, 5, -1, -3, -5 ], [ 4, -4 ]>,
<block bijection: [ 1, -4 ], [ 2, 3, 5, -1, -3, -5 ], [ 4, -2 ]>,
[ <block bijection: [ 1, -2 ], [ 2, 3, 5, -1, -3, -5 ], [ 4, -4 ]>,
<block bijection: [ 1, -4 ], [ 2, 3, 5, -1, -3, -5 ], [ 4, -2 ]>,
<block bijection: [ 1, -2 ], [ 2, 5, -1, -5 ], [ 3, -3 ], [ 4, -4 ]>
, <block bijection: [ 1, -2 ], [ 2, -1 ], [ 3, 5, -3, -5 ],
[ 4, -4 ]>,
, <block bijection: [ 1, -2 ], [ 2, -1 ], [ 3, 5, -3, -5 ],
[ 4, -4 ]>,
<block bijection: [ 1, -4 ], [ 2, 5, -3, -5 ], [ 3, -1 ], [ 4, -2 ]>
, <block bijection: [ 1, -4 ], [ 2, -3 ], [ 3, 5, -1, -5 ],
[ 4, -2 ]>, <block bijection: [ 1, -4 ], [ 2, -3 ], [ 3, -1 ],
, <block bijection: [ 1, -4 ], [ 2, -3 ], [ 3, 5, -1, -5 ],
[ 4, -2 ]>, <block bijection: [ 1, -4 ], [ 2, -3 ], [ 3, -1 ],
[ 4, -2 ], [ 5, -5 ]> ]
gap> IsMajorantlyClosed(B, last);
true
Expand Down Expand Up @@ -368,11 +368,11 @@ gap> T := InverseSemigroup(MajorantClosure(S, [PartialPerm([1])]));
gap> IsMajorantlyClosed(S, T);
true
gap> RC := RightCosetsOfInverseSemigroup(S, T);
[ [ <identity partial perm on [ 1 ]>,
<identity partial perm on [ 1, 2 ]>, [2,3](1), [3,2](1),
<identity partial perm on [ 1, 3 ]>,
<identity partial perm on [ 1, 2, 3 ]>, (1)(2,3) ],
[ [1,3], [2,1,3], [1,3](2), (1,3), [1,3,2], (1,3,2), (1,3)(2) ],
[ [ <identity partial perm on [ 1 ]>,
<identity partial perm on [ 1, 2 ]>, [2,3](1), [3,2](1),
<identity partial perm on [ 1, 3 ]>,
<identity partial perm on [ 1, 2, 3 ]>, (1)(2,3) ],
[ [1,3], [2,1,3], [1,3](2), (1,3), [1,3,2], (1,3,2), (1,3)(2) ],
[ [1,2], (1,2), [1,2,3], [3,1,2], [1,2](3), (1,2)(3), (1,2,3) ] ]]]></Example>
<#/GAPDoc>

Expand Down Expand Up @@ -401,7 +401,7 @@ gap> S := SymmetricInverseSemigroup(3);
gap> H := GroupHClass(DClass(S, PartialPerm([1, 2, 3])));
<Green's H-class: <identity partial perm on [ 1, 2, 3 ]>>
gap> Elements(H);
[ <identity partial perm on [ 1, 2, 3 ]>, (1)(2,3), (1,2)(3),
[ <identity partial perm on [ 1, 2, 3 ]>, (1)(2,3), (1,2)(3),
(1,2,3), (1,3,2), (1,3)(2) ]
gap> SameMinorantsSubgroup(H);
[ <identity partial perm on [ 1, 2, 3 ]> ]
Expand All @@ -410,8 +410,8 @@ gap> T := InverseSemigroup(
> PartialPerm([1], [1]), PartialPerm([2], [2]));
<inverse partial perm semigroup of rank 4 with 3 generators>
gap> Elements(T);
[ <empty partial perm>, <identity partial perm on [ 1 ]>,
<identity partial perm on [ 2 ]>,
[ <empty partial perm>, <identity partial perm on [ 1 ]>,
<identity partial perm on [ 2 ]>,
<identity partial perm on [ 1, 2, 3, 4 ]>, (1)(2)(3,4) ]
gap> x := GroupHClass(DClass(T, PartialPerm([1, 2, 3, 4])));
<Green's H-class: <identity partial perm on [ 1, 2, 3, 4 ]>>
Expand Down Expand Up @@ -443,7 +443,7 @@ gap> AsSet(SameMinorantsSubgroup(x));
gap> S := InverseSemigroup(PartialPerm([2, 1, 4, 3, 6, 5, 8, 7]));
<partial perm group of rank 8 with 1 generator>
gap> Elements(S);
[ <identity partial perm on [ 1, 2, 3, 4, 5, 6, 7, 8 ]>,
[ <identity partial perm on [ 1, 2, 3, 4, 5, 6, 7, 8 ]>,
(1,2)(3,4)(5,6)(7,8) ]
gap> iso := SmallerDegreePartialPermRepresentation(S);;
gap> Source(iso) = S;
Expand All @@ -454,11 +454,11 @@ gap> Elements(R);
[ <identity partial perm on [ 1, 2 ]>, (1,2) ]
gap> S := DualSymmetricInverseMonoid(5);;
gap> T := Range(IsomorphismPartialPermSemigroup(S));
<inverse partial perm monoid of size 6721, rank 6721 with 3
<inverse partial perm monoid of size 6721, rank 6721 with 3
generators>
gap> SmallerDegreePartialPermRepresentation(T);
<inverse partial perm monoid of size 6721, rank 6721 with 3
generators> -> <inverse partial perm monoid of rank 30 with 3
<inverse partial perm monoid of size 6721, rank 6721 with 3
generators> -> <inverse partial perm monoid of rank 30 with 3
generators>]]></Example>
<#/GAPDoc>

Expand Down Expand Up @@ -493,7 +493,7 @@ gap> S := SymmetricInverseSemigroup(2);
gap> Size(S);
7
gap> iso := VagnerPrestonRepresentation(S);
<symmetric inverse monoid of degree 2> ->
<symmetric inverse monoid of degree 2> ->
<inverse partial perm monoid of rank 7 with 2 generators>
gap> RespectsMultiplication(iso);
true
Expand All @@ -508,7 +508,7 @@ gap> V := InverseSemigroup(
gap> IsInverseSemigroup(V);
true
gap> VagnerPrestonRepresentation(V);
<inverse bipartition semigroup of size 394, degree 5 with 3
generators> -> <inverse partial perm semigroup of rank 394 with 5
<inverse bipartition semigroup of size 394, degree 5 with 3
generators> -> <inverse partial perm semigroup of rank 394 with 5
generators>]]></Example>
<#/GAPDoc>
46 changes: 23 additions & 23 deletions doc/bipart.xml
View file
Original file line number Diff line number Diff line change
Expand Up @@ -89,7 +89,7 @@ gap> NrBlocks(blocks);
3
gap> x := Bipartition([
> [1, 5], [2, 4, -2, -4], [3, 6, -1, -5, -6], [-3]]);
<bipartition: [ 1, 5 ], [ 2, 4, -2, -4 ], [ 3, 6, -1, -5, -6 ],
<bipartition: [ 1, 5 ], [ 2, 4, -2, -4 ], [ 3, 6, -1, -5, -6 ],
[ -3 ]>
gap> NrBlocks(x);
4]]></Example>
Expand Down Expand Up @@ -146,9 +146,9 @@ gap> NrRightBlocks(x);
transverse block of <A>x</A>, where <C>n</C> is the degree of <A>x</A>
(see <Ref Attr="DegreeOfBipartition"/>).
<Example><![CDATA[
gap> x := Bipartition([[1, 2], [3, 4, 5, -5], [6, -6],
gap> x := Bipartition([[1, 2], [3, 4, 5, -5], [6, -6],
> [-1, -2, -3], [-4]]);
<bipartition: [ 1, 2 ], [ 3, 4, 5, -5 ], [ 6, -6 ], [ -1, -2, -3 ],
<bipartition: [ 1, 2 ], [ 3, 4, 5, -5 ], [ 6, -6 ], [ -1, -2, -3 ],
[ -4 ]>
gap> DomainOfBipartition(x);
[ 3, 4, 5, 6 ]]]></Example>
Expand All @@ -167,9 +167,9 @@ gap> DomainOfBipartition(x);
in a transverse block of <A>x</A>, where <C>n</C> is the degree of
<A>x</A> (see <Ref Attr="DegreeOfBipartition"/>).
<Example><![CDATA[
gap> x := Bipartition([[1, 2], [3, 4, 5, -5], [6, -6],
gap> x := Bipartition([[1, 2], [3, 4, 5, -5], [6, -6],
> [-1, -2, -3], [-4]]);
<bipartition: [ 1, 2 ], [ 3, 4, 5, -5 ], [ 6, -6 ], [ -1, -2, -3 ],
<bipartition: [ 1, 2 ], [ 3, 4, 5, -5 ], [ 6, -6 ], [ -1, -2, -3 ],
[ -4 ]>
gap> CodomainOfBipartition(x);
[ -5, -6 ]]]></Example>
Expand Down Expand Up @@ -507,15 +507,15 @@ Error, the argument (a bipartition) does not define a partial perm]]></Example>
gap> x := PartialPerm([1, 2, 3, 6, 7, 10], [9, 5, 6, 1, 7, 8]);
[2,5][3,6,1,9][10,8](7)
gap> AsBipartition(x, 11);
<bipartition: [ 1, -9 ], [ 2, -5 ], [ 3, -6 ], [ 4 ], [ 5 ],
[ 6, -1 ], [ 7, -7 ], [ 8 ], [ 9 ], [ 10, -8 ], [ 11 ], [ -2 ],
<bipartition: [ 1, -9 ], [ 2, -5 ], [ 3, -6 ], [ 4 ], [ 5 ],
[ 6, -1 ], [ 7, -7 ], [ 8 ], [ 9 ], [ 10, -8 ], [ 11 ], [ -2 ],
[ -3 ], [ -4 ], [ -10 ], [ -11 ]>
gap> AsBlockBijection(x, 10);
Error, the 2nd argument (a pos. int.) is less than or equal to the max\
imum of the degree and codegree of the 1st argument (a partial perm)
gap> AsBlockBijection(x, 11);
<block bijection: [ 1, -9 ], [ 2, -5 ], [ 3, -6 ],
[ 4, 5, 8, 9, 11, -2, -3, -4, -10, -11 ], [ 6, -1 ], [ 7, -7 ],
<block bijection: [ 1, -9 ], [ 2, -5 ], [ 3, -6 ],
[ 4, 5, 8, 9, 11, -2, -3, -4, -10, -11 ], [ 6, -1 ], [ 7, -7 ],
[ 10, -8 ]>
gap> x := Bipartition([[1, -3], [2], [3, -2], [-1]]);;
gap> IsPartialPermBipartition(x);
Expand Down Expand Up @@ -604,23 +604,23 @@ gap> x := Transformation([3, 5, 3, 4, 1, 2]);;
gap> AsBipartition(x, 5);
<bipartition: [ 1, 3, -3 ], [ 2, -5 ], [ 4, -4 ], [ 5, -1 ], [ -2 ]>
gap> AsBipartition(x);
<bipartition: [ 1, 3, -3 ], [ 2, -5 ], [ 4, -4 ], [ 5, -1 ],
<bipartition: [ 1, 3, -3 ], [ 2, -5 ], [ 4, -4 ], [ 5, -1 ],
[ 6, -2 ], [ -6 ]>
gap> AsBipartition(x, 10);
<bipartition: [ 1, 3, -3 ], [ 2, -5 ], [ 4, -4 ], [ 5, -1 ],
<bipartition: [ 1, 3, -3 ], [ 2, -5 ], [ 4, -4 ], [ 5, -1 ],
[ 6, -2 ], [ 7, -7 ], [ 8, -8 ], [ 9, -9 ], [ 10, -10 ], [ -6 ]>
gap> AsBipartition((1, 3)(2, 4));
<block bijection: [ 1, -3 ], [ 2, -4 ], [ 3, -1 ], [ 4, -2 ]>
gap> AsBipartition((1, 3)(2, 4), 10);
<block bijection: [ 1, -3 ], [ 2, -4 ], [ 3, -1 ], [ 4, -2 ],
<block bijection: [ 1, -3 ], [ 2, -4 ], [ 3, -1 ], [ 4, -2 ],
[ 5, -5 ], [ 6, -6 ], [ 7, -7 ], [ 8, -8 ], [ 9, -9 ], [ 10, -10 ]>
gap> x := PartialPerm([1, 2, 3, 4, 5, 6], [6, 7, 1, 4, 3, 2]);;
gap> AsBipartition(x, 11);
<bipartition: [ 1, -6 ], [ 2, -7 ], [ 3, -1 ], [ 4, -4 ], [ 5, -3 ],
[ 6, -2 ], [ 7 ], [ 8 ], [ 9 ], [ 10 ], [ 11 ], [ -5 ], [ -8 ],
<bipartition: [ 1, -6 ], [ 2, -7 ], [ 3, -1 ], [ 4, -4 ], [ 5, -3 ],
[ 6, -2 ], [ 7 ], [ 8 ], [ 9 ], [ 10 ], [ 11 ], [ -5 ], [ -8 ],
[ -9 ], [ -10 ], [ -11 ]>
gap> AsBipartition(x);
<bipartition: [ 1, -6 ], [ 2, -7 ], [ 3, -1 ], [ 4, -4 ], [ 5, -3 ],
<bipartition: [ 1, -6 ], [ 2, -7 ], [ 3, -1 ], [ 4, -4 ], [ 5, -3 ],
[ 6, -2 ], [ 7 ], [ -5 ]>
gap> AsBipartition(Transformation([1, 1, 2]), 1);
<block bijection: [ 1, -1 ]>
Expand All @@ -631,7 +631,7 @@ gap> AsBipartition(x, 0);
gap> AsBipartition(x, 2);
<bipartition: [ 1, 2, -2 ], [ -1 ]>
gap> AsBipartition(x, 8);
<bipartition: [ 1, 2, -2 ], [ 3 ], [ 4, 5, 6, -1 ], [ 7 ], [ 8 ],
<bipartition: [ 1, 2, -2 ], [ 3 ], [ 4, 5, 6, -1 ], [ 7 ], [ 8 ],
[ -3, -4, -5, -6 ], [ -7 ], [ -8 ]>
gap> x := PBR(
> [[-1, 1, 2, 3, 4], [-1, 1, 2, 3, 4],
Expand All @@ -644,7 +644,7 @@ gap> AsBipartition(x, 2);
gap> AsBipartition(x, 4);
<bipartition: [ 1, 2, 3, 4, -1 ], [ -2 ], [ -3 ], [ -4 ]>
gap> AsBipartition(x, 5);
<bipartition: [ 1, 2, 3, 4, -1 ], [ 5 ], [ -2 ], [ -3 ], [ -4 ],
<bipartition: [ 1, 2, 3, 4, -1 ], [ 5 ], [ -2 ], [ -3 ], [ -4 ],
[ -5 ]>
gap> AsBipartition(x, 0);
<empty bipartition>]]></Example>
Expand Down Expand Up @@ -790,7 +790,7 @@ gap> y := Bipartition([[1, 4, 6, 7, 8, 10], [2, 5, -3, -6, -7, -9],
gap> PermLeftQuoBipartition(x, y);
(1,2,3)
gap> Star(x) * y;
<bipartition: [ 1, 2, 8, -3, -6, -7, -9 ], [ 3, 6, 7, 9, -4, -5 ],
<bipartition: [ 1, 2, 8, -3, -6, -7, -9 ], [ 3, 6, 7, 9, -4, -5 ],
[ 4, 5, -1, -2, -8 ], [ 10 ], [ -10 ]>]]></Example>
</Description>
</ManSection>
Expand All @@ -804,7 +804,7 @@ gap> Star(x) * y;
Returns the identity bipartition with degree <A>n</A>.
<Example><![CDATA[
gap> IdentityBipartition(10);
<block bijection: [ 1, -1 ], [ 2, -2 ], [ 3, -3 ], [ 4, -4 ],
<block bijection: [ 1, -1 ], [ 2, -2 ], [ 3, -3 ], [ 4, -4 ],
[ 5, -5 ], [ 6, -6 ], [ 7, -7 ], [ 8, -8 ], [ 9, -9 ], [ 10, -10 ]>]]></Example>
</Description>
</ManSection>
Expand All @@ -825,7 +825,7 @@ gap> IdentityBipartition(10);
<Example><![CDATA[
gap> x := Bipartition([[1, 2, 6, 7, -4, -5, -7], [3, 4, 5, -1, -3],
> [8, -9], [9, -2], [-6], [-8]]);
<bipartition: [ 1, 2, 6, 7, -4, -5, -7 ], [ 3, 4, 5, -1, -3 ],
<bipartition: [ 1, 2, 6, 7, -4, -5, -7 ], [ 3, 4, 5, -1, -3 ],
[ 8, -9 ], [ 9, -2 ], [ -6 ], [ -8 ]>
gap> RankOfBipartition(x);
4]]></Example>
Expand Down Expand Up @@ -919,7 +919,7 @@ gap> ExtRepOfObj(x);
gap> x := Bipartition([
> [1, 4, -1, -2, -6], [2, 3, 5, -4], [6, -3], [-5]]);;
gap> LeftOne(x);
<block bijection: [ 1, 4, -1, -4 ], [ 2, 3, 5, -2, -3, -5 ],
<block bijection: [ 1, 4, -1, -4 ], [ 2, 3, 5, -2, -3, -5 ],
[ 6, -6 ]>
gap> LeftBlocks(x);
<blocks: [ 1*, 4* ], [ 2*, 3*, 5* ], [ 6* ]>
Expand Down Expand Up @@ -977,10 +977,10 @@ true]]></Example>
external representation of <A>x</A>.
<Example><![CDATA[
gap> x := Bipartition([[1, -4], [2, 3, 4], [5], [-1], [-2, -3], [-5]]);
<bipartition: [ 1, -4 ], [ 2, 3, 4 ], [ 5 ], [ -1 ], [ -2, -3 ],
<bipartition: [ 1, -4 ], [ 2, 3, 4 ], [ 5 ], [ -1 ], [ -2, -3 ],
[ -5 ]>
gap> y := Star(x);
<bipartition: [ 1 ], [ 2, 3 ], [ 4, -1 ], [ 5 ], [ -2, -3, -4 ],
<bipartition: [ 1 ], [ 2, 3 ], [ 4, -1 ], [ 5 ], [ -2, -3, -4 ],
[ -5 ]>
gap> x * y * x = x;
true
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