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Fix CDATA usage #89

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54 changes: 18 additions & 36 deletions doc/algebra.xml
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Original file line number Diff line number Diff line change
Expand Up @@ -56,8 +56,7 @@ on an ideal <M>I</M> of <M>A</M>.
</Description>
</ManSection>

<Example>
<![CDATA[
<Example><![CDATA[
gap> A1 := GroupRing( GF(5), Group( (1,2,3,4,5,6) ) );;
gap> SetName( A1, "A1" );
gap> BA1 := BasisVectors( Basis( A1 ) );;
Expand All @@ -72,8 +71,7 @@ gap> m1 := RegularAlgebraMultiplier( A1, I1, v1 );
(Z(5)^0)*(1,2,3,4,5,6)+(Z(5)^0)*(1,4)(2,5)(3,6)+(Z(5)^0)*(1,6,5,4,3,2) ] ->
[ (Z(5)^0)*(1,2,3,4,5,6)+(Z(5)^0)*(1,4)(2,5)(3,6)+(Z(5)^0)*(1,6,5,4,3,2),
(Z(5)^0)*()+(Z(5)^0)*(1,3,5)(2,4,6)+(Z(5)^0)*(1,5,3)(2,6,4) ]
]]>
</Example>
]]></Example>

<ManSection>
<Oper Name="IsAlgebraMultiplier"
Expand All @@ -84,8 +82,7 @@ for all <M>a,b</M> in the basis for <M>A</M>.
</Description>
</ManSection>

<Example>
<![CDATA[
<Example><![CDATA[
gap> IsAlgebraMultiplier( m1 );
true
gap> id1 := One( A1 );;
Expand All @@ -97,8 +94,7 @@ gap> h1 := LeftModuleHomomorphismByImages( A1, A1, BA1, L1 );
(Z(5)^0)*() ]
gap> IsAlgebraMultiplier( h1 );
false
]]>
</Example>
]]></Example>

<ManSection>
<Oper Name="MultiplierAlgebraOfIdealBySubalgebra "
Expand All @@ -111,8 +107,7 @@ form an algebra with product <M>\mu_b \circ \mu_{b'} = \mu_{bb'}</M>.
</Description>
</ManSection>

<Example>
<![CDATA[
<Example><![CDATA[
gap> u1 := BA1[3];
(Z(5)^0)*(1,3,5)(2,4,6)
gap> S1 := Subalgebra( A3, [ u1 ] );;
Expand All @@ -123,8 +118,7 @@ gap> SetName( MS1, "MS1" );
gap> BMS1 := BasisVectors( Basis( MS1 ) );;
gap> BMS1[1];
<linear mapping by matrix, I1 -> I1>
]]>
</Example>
]]></Example>

<ManSection>
<Attr Name="MultiplierAlgebra"
Expand All @@ -137,16 +131,14 @@ This operation returns <C>MultiplierAlgebraOfIdealBySubalgebra(A,A,A);</C>.
</Description>
</ManSection>

<Example>
<![CDATA[
<Example><![CDATA[
gap> MA1 := MultiplierAlgebra( A1 );
<algebra of dimension 6 over GF(5)>
gap> BMA1 := BasisVectors( Basis( MA1 ) );;
gap> BMA1[3];
<linear mapping by matrix, <algebra-with-one of dimension
6 over GF(5)> -> <algebra-with-one of dimension 6 over GF(5)>>
]]>
</Example>
]]></Example>

<ManSection>
<Attr Name="MultiplierHomomorphism"
Expand All @@ -159,8 +151,7 @@ homomorphism from <M>B</M> to <M>M</M> mapping <M>b</M> to <M>\mu_b</M>.
</Description>
</ManSection>

<Example>
<![CDATA[
<Example><![CDATA[
gap> hom1 := MultiplierHomomorphism( MA1 );;
gap> ImageElm( hom1, BA1[2] );
Basis( A1, [ (Z(5)^0)*(), (Z(5)^0)*(1,2,3,4,5,6), (Z(5)^0)*(1,3,5)(2\
Expand All @@ -169,8 +160,7 @@ Basis( A1, [ (Z(5)^0)*(), (Z(5)^0)*(1,2,3,4,5,6), (Z(5)^0)*(1,3,5)(2\
] ) -> [ (Z(5)^0)*(1,2,3,4,5,6), (Z(5)^0)*(1,3,5)(2,4,6),
(Z(5)^0)*(1,4)(2,5)(3,6), (Z(5)^0)*(1,5,3)(2,6,4), (Z(5)^0)*(1,6,5,4,3,2),
(Z(5)^0)*() ]
]]>
</Example>
]]></Example>

</Section>

Expand Down Expand Up @@ -242,8 +232,7 @@ as shown in <Ref Oper="AlgebraActionByHomomorphism"/>
</Description>
</ManSection>

<Example>
<![CDATA[
<Example><![CDATA[
gap> A1 := GroupRing( GF(5), Group( (1,2,3,4,5,6) ) );;
gap> BA1 := BasisVectors( Basis( A1 ) );;
gap> v := BA1[1] + BA1[3] + BA1[5];
Expand All @@ -253,8 +242,7 @@ gap> act1 := AlgebraActionByMultipliers( A1, I1, A1 );;
gap> act12 := Image( act1, BA1[2] );;
gap> Image( act12, v );
(Z(5)^0)*(1,2,3,4,5,6)+(Z(5)^0)*(1,4)(2,5)(3,6)+(Z(5)^0)*(1,6,5,4,3,2)
]]>
</Example>
]]></Example>

<ManSection>
<Oper Name="AlgebraActionBySurjection"
Expand Down Expand Up @@ -282,8 +270,7 @@ and the quotient <M>Q_2</M> has basis <M>\{[m_2],[m_2^2]\}</M>.
</Description>
</ManSection>

<Example>
<![CDATA[
<Example><![CDATA[
gap> theta1 := NaturalHomomorphismByIdeal( A1, I1 );
<linear mapping by matrix, <algebra-with-one of dimension
6 over GF(5)> -> <algebra of dimension 4 over GF(5)>>
Expand Down Expand Up @@ -321,8 +308,7 @@ gap> [ Image(b1,m2)=m2^2, Image(b1,m2^2)=m2^3, Image(b1,m2^3)=Zero(A2) ];
[ true, true, true ]
gap> [ Image(b2,m2)=m2^3, b2=b1^2 ];
[true, true ]
]]>
</Example>
]]></Example>


<#Include Label="AlgebraActionByHomomorphism">
Expand Down Expand Up @@ -393,8 +379,7 @@ Continuing the example above,
</Description>
</ManSection>

<Example>
<![CDATA[
<Example><![CDATA[
gap> P1 := SemidirectProductOfAlgebras( A1, act1, I1 );
<algebra of dimension 8 over GF(5)>
gap> Embedding( P1, 1 );
Expand All @@ -419,8 +404,7 @@ gap> Embedding( P2, 2 );
[ [ 0, 0, 1, 4 ], [ 0, 0, 0, 1 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ] ],
[ [ 0, 0, 0, 1 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ] ] ] ->
[ v.3, v.4, v.5 ]
]]>
</Example>
]]></Example>

<ManSection>
<Attr Name="SemidirectProductOfAlgebrasInfo"
Expand Down Expand Up @@ -453,8 +437,7 @@ small algebras.
</Description>
</ManSection>

<Example>
<![CDATA[
<Example><![CDATA[
gap> A2c6 := GroupRing( GF(2), Group( (1,2,3,4,5,6) ) );;
gap> R2c3 := GroupRing( GF(2), Group( (7,8,9) ) );;
gap> homAR := AllAlgebraHomomorphisms( A2c6, R2c3 );;
Expand Down Expand Up @@ -496,8 +479,7 @@ gap> List( bijAA, h -> MappingGeneratorsImages(h) );
gap> ideAA := AllIdempotentAlgebraHomomorphisms( A2c6, A2c6 );;
gap> Length( ideAA );
14
]]>
</Example>
]]></Example>

</Section>

Expand Down
36 changes: 12 additions & 24 deletions doc/cat1.xml
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Expand Up @@ -121,8 +121,7 @@ constructed in section <Ref Sect="algebra-homomorphism-lists"/>.
</Description>
</ManSection>

<Example>
<![CDATA[
<Example><![CDATA[
gap> t4 := homAR[8];
[ (Z(2)^0)*(1,6,5,4,3,2) ] -> [ (Z(2)^0)*(7,9,8) ]
gap> e4 := homRA[8];
Expand Down Expand Up @@ -157,8 +156,7 @@ Cat1-algebra [..=>..] :-
: kernel embedding maps generators of kernel to:
[ (Z(2)^0)*()+(Z(2)^0)*(1,4)(2,5)(3,6), (Z(2)^0)*(1,2,3,4,5,6)+(Z(2)^0)*
(1,5,3)(2,6,4), (Z(2)^0)*(1,3,5)(2,4,6)+(Z(2)^0)*(1,6,5,4,3,2) ]
]]>
</Example>
]]></Example>

<ManSection>
<Oper Name="Cat1AlgebraSelect"
Expand Down Expand Up @@ -200,8 +198,7 @@ Now, we give examples of the use of this function.
</Description>
</ManSection>

<Example>
<![CDATA[
<Example><![CDATA[
gap> C := Cat1AlgebraSelect( 11 );
|--------------------------------------------------------|
| 11 is invalid value for the Galois Field (GFnum) |
Expand Down Expand Up @@ -236,17 +233,15 @@ There are 4 cat1-structures for the group algebra GF(2)_c6.
Usage: Cat1Algebra( GFnum, gpsize, gpnum, num );
Algebra has generators [ (Z(2)^0)*(), (Z(2)^0)*(1,2,3)(4,5) ]
4
]]>
</Example>
]]></Example>

The algebra <C>GF(n)_gp</C> has a list of <M>n^{|gp|}</M> elements.
The <C>[2, 10]</C> in the second structure above
indicates that the tail map, and also the head map,
of the cat<M>^1</M>-algebra maps the two generators of <C>c6</C>
to the second and tenth elements of this algebra respectively.

<Example>
<![CDATA[
<Example><![CDATA[
gap> C0 := Cat1AlgebraSelect( 4, 6, 2, 2 );
[GF(2^2)_c6 -> Algebra( GF(2^2),
[ (Z(2)^0)*(), (Z(2)^0)*()+(Z(2)^0)*(1,3,5)(2,4,6)+(Z(2)^0)*(1,4)(2,5)(3,6)+(
Expand Down Expand Up @@ -279,8 +274,7 @@ Cat1-algebra [GF(2^2)_c6=>..] :-
: kernel embedding maps generators of kernel to:
[ (Z(2)^0)*()+(Z(2)^0)*(1,2,3,4,5,6)+(Z(2)^0)*(1,3,5)(2,4,6)+(Z(2)^0)*(1,4)
(2,5)(3,6)+(Z(2)^0)*(1,5,3)(2,6,4)+(Z(2)^0)*(1,6,5,4,3,2) ]
]]>
</Example>
]]></Example>

<ManSection>
<Oper Name="SubCat1Algebra"
Expand Down Expand Up @@ -320,8 +314,7 @@ subcat<M>^{1}</M>-algebras of a given cat<M>^{1}</M>-algebra.
</Description>
</ManSection>

<Example>
<![CDATA[
<Example><![CDATA[
gap> C6 := Cat1AlgebraSelect( 2, 6, 2, 4 );;
gap> A6 := Source( C6 );
GF(2)_c6
Expand Down Expand Up @@ -360,8 +353,7 @@ Cat1-algebra [..=>..] :-
[ <zero> of ..., (Z(2)^0)*()+(Z(2)^0)*(4,5) ]
gap> IsSubCat1Algebra( C6, SC6 );
true
]]>
</Example>
]]></Example>

</Section>

Expand Down Expand Up @@ -429,8 +421,7 @@ These are the six main attributes of a cat<M>^{1}</M>-algebra morphism.
</Description>
</ManSection>

<Example>
<![CDATA[
<Example><![CDATA[
gap> C1 := Cat1AlgebraSelect( 2, 1, 1, 1 );
[GF(2)_triv -> GF(2)_triv]
gap> Display( C1 );
Expand Down Expand Up @@ -513,8 +504,7 @@ gap> IsInjective( m12 );
true
gap> IsBijective( m12 );
false
]]>
</Example>
]]></Example>

<ManSection>
<Oper Name="ImagesSource2DimensionalMapping"
Expand All @@ -526,8 +516,7 @@ this operation returns the image crossed module.
</Description>
</ManSection>

<Example>
<![CDATA[
<Example><![CDATA[
gap> im12 := ImagesSource2DimensionalMapping( m12 );;
gap> Display( im12 );
Cat1-algebra [..=>..] :-
Expand All @@ -542,8 +531,7 @@ Cat1-algebra [..=>..] :-
: range embedding maps range generators to:
[ (Z(2)^0)*() ]
: the kernel is trivial.
]]>
</Example>
]]></Example>

</Section>

Expand Down
12 changes: 4 additions & 8 deletions doc/convert.xml
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Expand Up @@ -69,8 +69,7 @@ As an example we use the crossed module <C>XAB</C> constructed in section
</Description>
</ManSection>

<Example>
<![CDATA[
<Example><![CDATA[
gap> Cn := Cat1AlgebraOfXModAlgebra( Xn );
[An |X Bn -> An]
gap> Display( Cn );
Expand Down Expand Up @@ -107,8 +106,7 @@ Cat1-algebra [An |X Bn => An] :-
[ 0*Z(5), 0*Z(5), 0*Z(5) ] ] ]
: range embedding maps range generators to: [ v.1, v.2 ]
: kernel has generators: [ v.4, v.5 ]
]]>
</Example>
]]></Example>

<#Include Label="Cat1AlgebraOfXModAlgebra">

Expand All @@ -125,8 +123,7 @@ constructed in section <Ref Sect="SubCat1Algebra"/>.
</Description>
</ManSection>

<Example>
<![CDATA[
<Example><![CDATA[
gap> X6 := XModAlgebraOfCat1Algebra( C6 );
[ <algebra of dimension 3 over GF(2)> -> <algebra of dimension 3 over GF(2)> ]
gap> Display( X6 );
Expand All @@ -138,8 +135,7 @@ Crossed module [..->..] :-
[ (Z(2)^0)*(), (Z(2)^0)*(1,2,3) ]
: Boundary homomorphism maps source generators to:
[ <zero> of ..., <zero> of ..., <zero> of ... ]
]]>
</Example>
]]></Example>

</Section>

Expand Down
18 changes: 6 additions & 12 deletions doc/intro.xml
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Expand Up @@ -55,11 +55,9 @@ There are aspects of commutative algebras for which no &GAP; functions yet exist
We have included here functions for all homomorphisms of algebras.
<P/>
The package is loaded with the command
<Example>
<![CDATA[
<Example><![CDATA[
gap> LoadPackage( "xmodalg" );
]]>
</Example>
]]></Example>
<P/>

The package may be obtained as a compressed <Code>.tar</Code> file
Expand All @@ -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( "xmodalg", "makedoc.g" );
]]>
</Example>
]]></Example>
<P/>

It is possible to check that the package has been installed correctly
by running the test files (this terminates the &GAP; session):
<P/>
<Example>
<![CDATA[
<Example><![CDATA[
gap> TestPackage( "xmodalg" );
Architecture: . . . . .
testing: . . . . .
. . .
#I No errors detected while testing
]]>
</Example>
]]></Example>

</Chapter>
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