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Update docs for operators on transformations & pperms
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This switches those docs to use ManSections, which results in
a nicer index.
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@fingolfin
fingolfin committed Jun 27, 2020
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131 changes: 76 additions & 55 deletions doc/ref/pperm.xml
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Expand Up @@ -1115,83 +1115,104 @@ gap> AsPartialPerm(f, [ 2 .. 4 ] );

<Section Label="sect:OperatorsPartialPerms">
<Heading>Operators and operations for partial permutations</Heading>
<List>
<Mark><C><A>f</A> ^ -1</C></Mark>
<Item>

<ManSection>
<Meth Name="Inverse" Arg="f" Label="for a partial permutation"/>
<Description>
returns the inverse of the partial permutation <A>f</A>.
</Item>
</Description>
</ManSection>

<Mark><C><A>i</A> ^ <A>f</A></C></Mark>
<Item>
<ManSection>
<Meth Name="\^" Arg="i, f" Label="for a positive integer and a partial permutation"/>
<Description>
returns the image of the positive integer <A>i</A> under the
partial permutation <A>f</A> if it is defined and <C>0</C> if it is not.
</Item>
<Mark><C><A>i</A> / <A>f</A></C></Mark>
<Item>
</Description>
</ManSection>

<ManSection>
<Meth Name="\/" Arg="i, f" Label="for a positive integer and a partial permutation"/>
<Description>
returns the preimage of the positive integer <A>i</A> under the
partial permutation <A>f</A> if it is defined and <C>0</C> if it is not.
Note that the inverse of <A>f</A> is not calculated to find the
preimage of <A>i</A>.
</Item>

<Mark><C><A>f</A> ^ <A>g</A></C></Mark>
<Item>
returns <C><A>g</A>^-1*<A>f</A>*<A>g</A></C> when
<A>f</A> is a partial permutation and <A>g</A> is a permutation or partial
permutation; see <Ref Oper="\^"/>. This operation requires
essentially the same number of steps as multiplying partial permutations,
which is around one third as many as inverting and multiplying twice.
</Item>

<Mark><C><A>f</A> * <A>g</A></C></Mark>
<Item>
returns the composition of <A>f</A> and <A>g</A> when <A>f</A> and
<A>g</A> are partial permutations or permutations. The product of a
permutation and a partial permutation is returned as a partial
permutation.
</Item>

<Mark><C><A>f</A> / <A>g</A></C></Mark>
<Item>
</Description>
</ManSection>

<ManSection>
<Meth Name="\^" Arg="f, g" Label="for a partial permutation and a permutation or partial permutation"/>
<Description>
<C><A>f</A> ^ <A>g</A></C>
returns <C><A>g</A>^-1*<A>f</A>*<A>g</A></C> when
<A>f</A> is a partial permutation and <A>g</A> is a permutation or partial
permutation; see <Ref Oper="\^"/>. This operation requires
essentially the same number of steps as multiplying partial permutations,
which is around one third as many as inverting and multiplying twice.
</Description>
</ManSection>

<ManSection>
<Meth Name="\*" Arg="f, g" Label="for permutations and partial permutations"/>
<Description>
<C><A>f</A> * <A>g</A></C>
returns the composition of <A>f</A> and <A>g</A> when <A>f</A> and
<A>g</A> are partial permutations or permutations. The product of a
permutation and a partial permutation is returned as a partial
permutation.
</Description>
</ManSection>

<ManSection>
<Meth Name="\/" Arg="f, g" Label="for a partial permutation and permutation or partial permutation"/>
<Description>
<C><A>f</A> / <A>g</A></C>
returns <C><A>f</A>*<A>g</A>^-1</C> when <A>f</A> is a partial
permutation and
<A>g</A> is a permutation or partial permutation.
This operation requires essentially the same number of steps
<A>g</A> is a permutation or partial permutation.
This operation requires essentially the same number of steps
as multiplying partial permutations, which is
approximately half that required to first invert <A>g</A> and then take
the product with <A>f</A>.
</Item>

<Mark><C>LQUO(<A>g</A>, <A>f</A>)</C></Mark>
<Item>
<Index Key="LQUO" Subkey="for a permutation or partial permutation
and partial permutation"><C>LQUO</C></Index>
the product with <A>f</A>.
</Description>
</ManSection>

<ManSection>
<Meth Name="LeftQuotient" Arg="g, f" Label="for a permutation or partial permutation
and a partial permutation"/>
<Description>
returns <C><A>g</A>^-1*<A>f</A></C>
when <A>f</A> is a partial permutation and
<A>g</A> is a permutation or partial permutation.
This operation requires essentially the same number of steps
<A>g</A> is a permutation or partial permutation.
This operation requires essentially the same number of steps
as multiplying partial permutations, which is
approximately half that required to first invert <A>g</A> and then take
the product with <A>f</A>.
</Item>

<Mark><C><A>f</A> &lt; <A>g</A></C></Mark>
<Item>
the product with <A>f</A>.
</Description>
</ManSection>

<ManSection>
<Meth Name="\&lt;" Arg="f, g" Label="for partial permutations"/>
<Description>
<C><A>f</A> &lt; <A>g</A></C>
returns <K>true</K> if the image of <A>f</A> on the range from 1 to the
degree of <A>f</A>
degree of <A>f</A>
is lexicographically less than the corresponding image for <A>g</A>
and <K>false</K> if it is not. See <Ref Func="NaturalLeqPartialPerm"/>
and <Ref Func="ShortLexLeqPartialPerm"/> for additional orders for
partial permutations.
</Item>

<Mark><C><A>f</A> = <A>g</A></C></Mark>
<Item>
partial permutations.
</Description>
</ManSection>

<ManSection>
<Meth Name="\=" Arg="f, g" Label="for partial permutations"/>
<Description>
<C><A>f</A> = <A>g</A></C>
returns <K>true</K> if the partial permutation <A>f</A> equals the
partial permutation <A>g</A> and returns <K>false</K> if it does not.
</Item>
</List>
</Description>
</ManSection>

<!-- *************************************************************** -->

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93 changes: 46 additions & 47 deletions doc/ref/trans.xml
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Original file line number Diff line number Diff line change
Expand Up @@ -589,87 +589,86 @@ gap> PermutationOfImage( f );

<Section Label="sect:OperatorsTransformations">
<Heading>Operators for transformations</Heading>
<List>

<Mark><C><A>i</A> ^ <A>f</A></C></Mark>
<Item>
<Index Key="\^"
Subkey="for a positive integer and a transformation">
<C>\^</C>
</Index>
<ManSection>
<Meth Name="\^" Arg="i, f" Label="for a positive integer and a transformation"/>
<Description>
<C><A>i</A> ^ <A>f</A></C>
returns the image of the positive integer <A>i</A> under the
transformation <A>f</A>.
</Item>
</Description>
</ManSection>

<Mark><C><A>f</A> ^ <A>g</A></C></Mark>
<Item>
<Index Key="\^"
Subkey="for a transformation and a permutation">
<C>\^</C>
</Index>
<ManSection>
<Meth Name="\^" Arg="f, g" Label="for a transformation and a permutation"/>
<Description>
<C><A>f</A> ^ <A>g</A></C>
returns <C><A>g</A> ^ -1 * <A>f</A> * <A>g</A></C> when
<A>f</A> is a transformation and <A>g</A> is a permutation
<Ref Oper="\^"/>.
<Ref Oper="\^"/>.
This operation requires essentially the same number of steps as
multiplying a transformation by a permutation, which is
approximately one third of the number required to first invert
<A>g</A>, take the product with <A>f</A>, and then the product
with <A>g</A>.
</Item>
with <A>g</A>.
</Description>
</ManSection>

<Mark><C><A>f</A> * <A>g</A></C></Mark>
<Item>
<Index Key="\*" Subkey="for transformations"><C>\*</C></Index>
<ManSection>
<Meth Name="\*" Arg="f, g" Label="for transformations"/>
<Description>
<C><A>f</A> * <A>g</A></C>
returns the composition of <A>f</A> and <A>g</A> when <A>f</A> and
<A>g</A> are transformations or permutations. The product of a
permutation and a transformation is returned as a transformation.
</Item>
permutation and a transformation is returned as a transformation.
</Description>
</ManSection>

<Mark><C><A>f</A> / <A>g</A></C></Mark>
<Item>
<Index Key="\/"
Subkey="for a transformation and a permutation">
<C>\/</C>
</Index>
<ManSection>
<Meth Name="\/" Arg="f, g" Label="for a transformation and a permutation"/>
<Description>
<C><A>f</A> / <A>g</A></C>
returns <C><A>f</A> * <A>g</A> ^ -1</C> when <A>f</A> is a
transformation and <A>g</A> is a permutation. This operation
requires essentially the same number of steps as multiplying a
transformation by a permutation, which is approximately half the
number required to first invert <A>g</A> and then take the product
with <A>f</A>.
</Item>
with <A>f</A>.
</Description>
</ManSection>

<Mark><C>LQUO( <A>g</A>, <A>f</A> )</C></Mark>
<Item>
<Index Key="LQUO"
Subkey="for a permutation and transformation">
<C>LQUO</C>
</Index>
<ManSection>
<Meth Name="LeftQuotient" Arg="g, f" Label="for a permutation and transformation"/>
<Description>
returns <C><A>g</A> ^ -1 * <A>f</A></C> when <A>f</A> is a
transformation and <A>g</A> is a permutation. This operation uses
essentially the same number of steps as multiplying a
transformation by a permutation, which is approximately half the
number required to first invert <A>g</A> and then take the product
with <A>f</A>.
</Item>
with <A>f</A>.
</Description>
</ManSection>

<Mark><C><A>f</A> &lt; <A>g</A></C></Mark>
<Item>
<Index Key="\&lt;" Subkey="for transformations"><C>\&lt;</C></Index>
<ManSection>
<Meth Name="\&lt;" Arg="i, f" Label="for transformations"/>
<Description>
<Index Subkey="for transformations">smaller</Index>
<C><A>f</A> &lt; <A>g</A></C>
returns <K>true</K> if the image list of <A>f</A> is
lexicographically less than the image list of <A>g</A> and
<K>false</K> if it is not.
</Item>
</Description>
</ManSection>

<Mark><C><A>f</A> = <A>g</A></C></Mark>
<Item>
<Index Key="\=" Subkey="for transformations"><C>\=</C></Index>
<ManSection>
<Meth Name="\=" Arg="f, g" Label="for transformations"/>
<Description>
<Index Subkey="for transformations">equality</Index>
<C><A>f</A> = <A>g</A></C>
returns <K>true</K> if the transformation <A>f</A> equals the
transformation <A>g</A> and returns <K>false</K> if it does not.
</Item>
</List>
</Description>
</ManSection>

<!-- *************************************************************** -->

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