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Merged
cdwensley merged 1 commit into from
Mar 16, 2026
Merged

doc: fix CDATA sections #89

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6 changes: 2 additions & 4 deletions doc/download.xml
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Original file line number Diff line number Diff line change
Expand Up @@ -82,8 +82,7 @@ The following components are supported.
</Item>
</List>
<P/>
<Example>
<![CDATA[
<Example><![CDATA[
gap> url:= "https://www.gap-system.org/index.html";;
gap> res1:= Download( url );;
gap> res1.success;
Expand All @@ -95,8 +94,7 @@ gap> res2.success;
false
gap> IsBound( res2.error ) and IsString( res2.error );
true
]]>
</Example>
]]></Example>
</Description>
</ManSection>

Expand Down
78 changes: 26 additions & 52 deletions doc/groups.xml
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Expand Up @@ -27,16 +27,14 @@ It provides a method for <C>Comm</C> when the argument is a list
<P/>
</Description>
</ManSection>
<Example>
<![CDATA[
<Example><![CDATA[
gap> Comm( [ (1,2), (2,3) ] );
(1,2,3)
gap> Comm( [(1,2),(2,3),(3,4),(4,5),(5,6)] );
(1,5,6)
gap> Comm(Comm(Comm(Comm((1,2),(2,3)),(3,4)),(4,5)),(5,6)); ## the same
(1,5,6)
]]>
</Example>
]]></Example>

<ManSection>
<Oper Name="IsCommuting"
Expand All @@ -48,16 +46,14 @@ It tests whether two elements in a group commute.
<P/>
</Description>
</ManSection>
<Example>
<![CDATA[
<Example><![CDATA[
gap> D12 := DihedralGroup( 12 );
<pc group of size 12 with 3 generators>
gap> SetName( D12, "D12" );
gap> a := D12.1;; b := D12.2;;
gap> IsCommuting( a, b );
false
]]>
</Example>
]]></Example>

<ManSection>
<Oper Name="ListOfPowers"
Expand All @@ -70,8 +66,7 @@ The operation <C>ListOfPowers(g,exp)</C> returns the list
<P/>
</Description>
</ManSection>
<Example>
<![CDATA[
<Example><![CDATA[
gap> ListOfPowers( 2, 20 );
[ 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384,
32768, 65536, 131072, 262144, 524288, 1048576 ]
Expand All @@ -80,8 +75,7 @@ gap> ListOfPowers( (1,2,3)(4,5), 12 );
(1,2,3)(4,5), (1,3,2), (4,5), (1,2,3), (1,3,2)(4,5), () ]
gap> ListOfPowers( D12.2, 6 );
[ f2, f3, f2*f3, f3^2, f2*f3^2, <identity> of ... ]
]]>
</Example>
]]></Example>

<ManSection>
<Oper Name="GeneratorsAndInverses"
Expand All @@ -94,14 +88,12 @@ followed by the inverses of these generators.
<P/>
</Description>
</ManSection>
<Example>
<![CDATA[
<Example><![CDATA[
gap> GeneratorsAndInverses( D12 );
[ f1, f2, f3, f1, f2*f3^2, f3^2 ]
gap> GeneratorsAndInverses( SymmetricGroup(5) );
[ (1,2,3,4,5), (1,2), (1,5,4,3,2), (1,2) ]
]]>
</Example>
]]></Example>


<ManSection>
Expand All @@ -121,8 +113,7 @@ group are described here:
<P/>
</Description>
</ManSection>
<Example>
<![CDATA[
<Example><![CDATA[
gap> UpperFittingSeries( D12 ); LowerFittingSeries( D12 );
[ Group([ ]), Group([ f3, f2*f3 ]), Group([ f1, f3, f2*f3 ]) ]
[ D12, Group([ f3 ]), Group([ ]) ]
Expand All @@ -141,8 +132,7 @@ gap> List( last, StructureDescription );
[ "S4", "A4", "C2 x C2", "1" ]
gap> FittingLength( S4);
3
]]>
</Example>
]]></Example>

</Section>

Expand Down Expand Up @@ -177,8 +167,7 @@ and, if necessary, converting back again to left cosets.
<P/>
</Description>
</ManSection>
<Example>
<![CDATA[
<Example><![CDATA[
gap> a4 := Group( (1,2,3), (2,3,4) );; SetName( a4, "a4" );
gap> k4 := Group( (1,2)(3,4), (1,3)(2,4) );; SetName( k4, "k4" );
gap> rc := RightCosets( a4, k4 );
Expand All @@ -199,8 +188,7 @@ gap> (1,2,3)*lc[2] = lc[3];
true
gap> lc[2]^(1,3,2) = lc[3];
true
]]>
</Example>
]]></Example>

<Subsection Label="subsec-inverse">
<Heading>Inverse</Heading>
Expand All @@ -209,14 +197,12 @@ and conversely.
This is an abuse of the attribute <C>Inverse</C>, since the standard
requirement, that <M>x*x^{-1}</M> is an identity, does not hold.
<P/>
<Example>
<![CDATA[
<Example><![CDATA[
gap> Inverse( rc[3] ) = lc[3];
true
gap> Inverse( lc[2] ) = rc[2];
true
]]>
</Example>
]]></Example>
</Subsection>

</Section>
Expand All @@ -239,8 +225,7 @@ Note that anything may happen if the resulting map is not a homomorphism!
<P/>
</Description>
</ManSection>
<Example>
<![CDATA[
<Example><![CDATA[
gap> G := Group( (1,2,3), (3,4,5), (5,6,7), (7,8,9) );;
gap> phi := EpimorphismByGenerators( FreeGroup("a","b","c","d"), G );
[ a, b, c, d ] -> [ (1,2,3), (3,4,5), (5,6,7), (7,8,9) ]
Expand All @@ -259,8 +244,7 @@ gap> Image( epi, (1,2,3) );
()
gap> Image( epi, (1,3,2) );
(8,9)
]]>
</Example>
]]></Example>


<ManSection>
Expand Down Expand Up @@ -294,8 +278,7 @@ see <Ref Oper="Embedding" BookName="ref"/>.
<P/>
</Description>
</ManSection>
<Example>
<![CDATA[
<Example><![CDATA[
gap> s4 := Group( (1,2),(2,3),(3,4) );;
gap> s3 := Group( (5,6),(6,7) );;
gap> c3 := Subgroup( s3, [ (5,6,7) ] );;
Expand All @@ -320,8 +303,7 @@ gap> a := ImageElm( Embedding( dp, 1 ), (1,4,3) );;
gap> b := ImageElm( Embedding( dp, 2 ), (5,7,6) );;
gap> a*b in Pfi;
true
]]>
</Example>
]]></Example>


<ManSection>
Expand Down Expand Up @@ -420,8 +402,7 @@ The first of these is the zero map, the second is the identity.
<P/>
</Description>
</ManSection>
<Example>
<![CDATA[
<Example><![CDATA[
gap> gens := [ (1,2,3,4), (1,2)(3,4) ];;
gap> d8 := Group( gens );;
gap> SetName( d8, "d8" );
Expand All @@ -448,20 +429,17 @@ gap> IdempotentEndomorphisms( d8 );
[ (1,2,3,4), (1,2)(3,4) ] -> [ (), (1,4)(2,3) ],
[ (1,2,3,4), (1,2)(3,4) ] -> [ (1,4)(2,3), (1,4)(2,3) ],
[ (1,2,3,4), (1,2)(3,4) ] -> [ (1,2,3,4), (1,2)(3,4) ] ]
]]>
</Example>
]]></Example>

The quaternion group <C>q8</C> is an example of a group with a tail:
there is only one subgroup in the lattice which covers the identity subgroup.
The only idempotent isomorphisms of such groups are the identity mapping
and the zero mapping because the only pairs <M>N,R</M> are the whole group and the identity subgroup.
<Example>
<![CDATA[
<Example><![CDATA[
gap> q8 := QuaternionGroup( 8 );;
gap> IdempotentEndomorphisms( q8 );
[ [ x, y ] -> [ <identity> of ..., <identity> of ... ], [ x, y ] -> [ x, y ] ]
]]>
</Example>
]]></Example>

<ManSection>
<Oper Name="DirectProductOfFunctions"
Expand All @@ -473,8 +451,7 @@ this operation return the product homomorphism
<P/>
</Description>
</ManSection>
<Example>
<![CDATA[
<Example><![CDATA[
gap> c4 := Group( (1,2,3,4) );;
gap> c2 := Group( (5,6) );;
gap> f1 := GroupHomomorphismByImages( c4, c2, [(1,2,3,4)], [(5,6)] );;
Expand All @@ -489,8 +466,7 @@ gap> f := DirectProductOfFunctions( c4c3, c2c6, f1, f2 );
[ (1,2,3,4), (5,6,7) ] -> [ (1,2), (3,5,7)(4,6,8) ]
gap> ImageElm( f, (1,4,3,2)(5,7,6) );
(1,2)(3,7,5)(4,8,6)
]]>
</Example>
]]></Example>

<ManSection>
<Oper Name="DirectProductOfAutomorphismGroups"
Expand All @@ -502,8 +478,7 @@ of automorphisms of <M>G_1 \times G_2</M>.
<P/>
</Description>
</ManSection>
<Example>
<![CDATA[
<Example><![CDATA[
gap> c9 := Group( (1,2,3,4,5,6,7,8,9) );;
gap> ac9 := AutomorphismGroup( c9 );;
gap> q8 := QuaternionGroup( IsPermGroup, 8 );;
Expand All @@ -520,8 +495,7 @@ gap> a := genA[1]*genA[5];
(10,11,12,13)(14,15,16,17) ]
gap> ImageElm( a, (1,9,8,7,6,5,4,3,2)(10,14,12,16)(11,17,13,15) );
(1,8,6,4,2,9,7,5,3)(10,16,12,14)(11,15,13,17)
]]>
</Example>
]]></Example>

</Section>

Expand Down
18 changes: 6 additions & 12 deletions doc/intro.xml
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Expand Up @@ -20,11 +20,9 @@ This package was first distributed as part of the &GAP; 4.8.2 distribution.
<P/>

The package is loaded with the command
<Example>
<![CDATA[
<Example><![CDATA[
gap> LoadPackage( "utils" );
]]>
</Example>
]]></Example>
<P/>
Functions have been transferred from the following packages:
<List>
Expand Down Expand Up @@ -75,24 +73,20 @@ can be found in the documentation folder.
The <Code>html</Code> versions, with or without &MathJax;,
may be rebuilt as follows:
<P/>
<Example>
<![CDATA[
<Example><![CDATA[
gap> ReadPackage( "utils", "makedoc.g" );
]]>
</Example>
]]></Example>
<P/>
It is possible to check that the package has been installed correctly
by running the test files (which terminates the &GAP; session):
<P/>
<Example>
<![CDATA[
<Example><![CDATA[
gap> ReadPackage( "utils", "tst/testall.g" );
Architecture: . . . . .
testing: . . . . .
. . .
#I No errors detected while testing
]]>
</Example>
]]></Example>
<P/>

Note that functions listed in this manual that are currently
Expand Down
24 changes: 8 additions & 16 deletions doc/iterator.xml
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Expand Up @@ -42,8 +42,7 @@ The operation <C>AllIsomorphisms</C> produces the list or isomorphisms.
<P/>
</Description>
</ManSection>
<Example>
<![CDATA[
<Example><![CDATA[
gap> G := SmallGroup( 6,1);;
gap> iter := AllIsomorphismsIterator( G, s3 );;
gap> NextIterator( iter );
Expand All @@ -57,8 +56,7 @@ gap> AllIsomorphisms( G, s3 );
gap> iter := AllIsomorphismsIterator( G, s3 );;
gap> for h in iter do Print( ImageElm( h, G.1 ) = (6,7), ", " ); od;
true, false, false, true, false, false,
]]>
</Example>
]]></Example>

<ManSection>
<Oper Name="AllSubgroupsIterator"
Expand All @@ -74,8 +72,7 @@ over the entries in these classes.
<P/>
</Description>
</ManSection>
<Example>
<![CDATA[
<Example><![CDATA[
gap> c3c3 := Group( (1,2,3), (4,5,6) );;
gap> iter := AllSubgroupsIterator( c3c3 );
<iterator>
Expand All @@ -86,8 +83,7 @@ Group( [ (1,2,3) ] )
Group( [ (1,2,3)(4,5,6) ] )
Group( [ (1,3,2)(4,5,6) ] )
Group( [ (4,5,6), (1,2,3) ] )
]]>
</Example>
]]></Example>

</Section>

Expand All @@ -109,8 +105,7 @@ of a first iterator and <M>y</M> is the output of a second iterator.
<P/>
</Description>
</ManSection>
<Example>
<![CDATA[
<Example><![CDATA[
gap> it1 := Iterator( [ 1, 2, 3 ] );;
gap> it2 := Iterator( [ 4, 5, 6 ] );;
gap> iter := CartesianIterator( it1, it2 );;
Expand All @@ -124,8 +119,7 @@ gap> while not IsDoneIterator(iter) do Print(NextIterator(iter),"\n"); od;
[ 3, 4 ]
[ 3, 5 ]
[ 3, 6 ]
]]>
</Example>
]]></Example>

<ManSection>
<Oper Name="UnorderedPairsIterator"
Expand All @@ -140,8 +134,7 @@ In the case <M>L = [1,2,3,\ldots]</M> the pairs are ordered as
<P/>
</Description>
</ManSection>
<Example>
<![CDATA[
<Example><![CDATA[
gap> L := [6,7,8,9];;
gap> iterL := IteratorList( L );;
gap> pairsL := UnorderedPairsIterator( iterL );;
Expand All @@ -164,8 +157,7 @@ gap> NextIterator( pairs4 );
[ 4, 4 ]
gap> IsDoneIterator( pairs4 );
true
]]>
</Example>
]]></Example>

</Section>

Expand Down
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