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Clarify and correct documentation of CompositionMapping, add an example #3449

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May 18, 2019
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Clarify and correct documentation of CompositionMapping, add an example #3449

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22 changes: 19 additions & 3 deletions lib/mapping.gd
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Original file line number Diff line number Diff line change
Expand Up @@ -1204,11 +1204,13 @@ DeclareGlobalFunction("CompositionMapping2General");
## <Ref Func="CompositionMapping"/> allows one to compose arbitrarily many
## general mappings,
## and delegates each step to <Ref Oper="CompositionMapping2"/>.
## The result is a map that maps an element first under the last argument,
## then under the penultimate argument and so forth.
## <P/>
## Additionally, the properties <Ref Prop="IsInjective"/> and
## <Ref Prop="IsSingleValued"/> are maintained;
## if the source of the <M>i+1</M>-th general mapping is identical to
## the range of the <M>i</M>-th general mapping,
## <Ref Prop="IsSingleValued"/> are maintained.
## If the range of the <M>i+1</M>-th argument is identical to
## the range of the <M>i</M>-th argument,
## also <Ref Prop="IsTotal"/> and <Ref Prop="IsSurjective"/> are maintained.
## (So one should not call <Ref Oper="CompositionMapping2"/> directly
## if one wants to maintain these properties.)
Expand All @@ -1220,6 +1222,20 @@ DeclareGlobalFunction("CompositionMapping2General");
## decompose elements of the source of <A>map2</A> into generators) or as an
## (iterated) composition
## (see&nbsp;<Ref Filt="IsCompositionMappingRep"/>).
## <P/>
## <Example><![CDATA[
## gap> f := GroupHomomorphismByImages(CyclicGroup(IsPermGroup, 2),
## > CyclicGroup(IsPermGroup, 1));
## [ (1,2) ] -> [ () ]
## gap> g := GroupHomomorphismByImages(CyclicGroup(IsPermGroup, 6),
## > CyclicGroup(IsPermGroup, 2));
## [ (1,2,3,4,5,6) ] -> [ (1,2) ]
## gap> CompositionMapping(f, g);
## [ (1,2,3,4,5,6) ] -> [ () ]
## gap> CompositionMapping(g, f);
## [ (1,2) ] -> [ () ]
## ]]></Example>
## <P/>
## </Description>
## </ManSection>
## <#/GAPDoc>
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