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Document TensorProduct, ExteriorPower and SymmetricPower (they existed since at least GAP 4.4) #4339

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Aug 3, 2022
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Document TensorProduct, ExteriorPower and SymmetricPower (they existed since at least GAP 4.4) #4339

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11 changes: 11 additions & 0 deletions doc/ref/vspc.xml
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Original file line number Diff line number Diff line change
Expand Up @@ -183,6 +183,17 @@
<#Include Label="CheckForHandlingByNiceBasis">

</Section>


<Section Label="Tensor Products and Exterior and Symmetric Powers">
<Heading>Tensor Products and Exterior and Symmetric Powers</Heading>

<#Include Label="TensorProduct">
<#Include Label="ExteriorPower">
<#Include Label="SymmetricPower">

</Section>

</Chapter>


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34 changes: 34 additions & 0 deletions lib/algrep.gd
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Expand Up @@ -836,6 +836,7 @@ DeclareCategoryCollections( "IsTensorElement" );
#O TensorProduct( <list> )
#O TensorProduct( <V>, <W>, ... )
##
## <#GAPDoc Label="TensorProduct">
## <ManSection>
## <Oper Name="TensorProduct" Arg='list'
## Label="for a list of vector spaces"/>
Expand All @@ -862,8 +863,19 @@ DeclareCategoryCollections( "IsTensorElement" );
## This does not mean that all tensor products have the
## same zero element: zeros of different tensor products have different
## families.
## <Example><![CDATA[
## gap> V:=TensorProduct(Rationals^2, Rationals^3);
## <vector space over Rationals, with 6 generators>
## gap> Basis(V);
## Basis( <vector space over Rationals, with 6 generators>,
## [ 1*([ 0, 1 ]<x>[ 0, 0, 1 ]), 1*([ 0, 1 ]<x>[ 0, 1, 0 ]),
## 1*([ 0, 1 ]<x>[ 1, 0, 0 ]), 1*([ 1, 0 ]<x>[ 0, 0, 1 ]),
## 1*([ 1, 0 ]<x>[ 0, 1, 0 ]), 1*([ 1, 0 ]<x>[ 1, 0, 0 ]) ] )
## ]]></Example>
## See also <Ref Oper="KroneckerProduct"/>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareOperation( "TensorProductOp", [ IsList, IsVectorSpace ] );
DeclareGlobalFunction( "TensorProduct" );
Expand Down Expand Up @@ -926,6 +938,7 @@ DeclareCategoryCollections( "IsWedgeElement" );
##
#O ExteriorPower( <V>, <k> )
##
## <#GAPDoc Label="ExteriorPower">
## <ManSection>
## <Oper Name="ExteriorPower" Arg='V, k'/>
##
Expand All @@ -948,8 +961,17 @@ DeclareCategoryCollections( "IsWedgeElement" );
## This does not mean that all exterior powers have the
## same zero element: zeros of different exterior powers have different
## families.
## <Example><![CDATA[
## gap> V:=ExteriorPower(Rationals^3, 2);
## <vector space of dimension 3 over Rationals>
## gap> Basis(V);
## Basis( <vector space of dimension 3 over Rationals>, [
## 1*([ 0, 1, 0 ]/\[ 0, 0, 1 ]), 1*([ 1, 0, 0 ]/\[ 0, 0, 1 ]),
## 1*([ 1, 0, 0 ]/\[ 0, 1, 0 ]) ] )
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareOperation( "ExteriorPower", [ IsLeftModule, IsInt ] );

Expand Down Expand Up @@ -1004,14 +1026,26 @@ DeclareCategoryCollections( "IsSymmetricPowerElement" );
##
#O SymmetricPower( <V>, <k> )
##
## <#GAPDoc Label="SymmetricPower">
## <ManSection>
## <Oper Name="SymmetricPower" Arg='V, k'/>
##
## <Description>
## Here <A>V</A> must be a vector space. This function returns the <A>k</A>-th
## symmetric power of <A>V</A>.
## <Example><![CDATA[
## gap> V:=SymmetricPower(Rationals^3, 2);
## <vector space over Rationals, with 6 generators>
## gap> Basis(V);
## Basis( <vector space over Rationals, with 6 generators>,
## [ 1*([ 0, 0, 1 ].[ 0, 0, 1 ]), 1*([ 0, 1, 0 ].[ 0, 0, 1 ]),
## 1*([ 0, 1, 0 ].[ 0, 1, 0 ]), 1*([ 1, 0, 0 ].[ 0, 0, 1 ]),
## 1*([ 1, 0, 0 ].[ 0, 1, 0 ]), 1*([ 1, 0, 0 ].[ 1, 0, 0 ])
## ] )
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareOperation( "SymmetricPower", [ IsLeftModule, IsInt ] );

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