ExteriorAlgebra.gd

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##
##  ExteriorAlgebra.gd                                       Modules package
##
##  Copyright 2011, Florian Diebold, University of Kaiserslautern
##
##  Declarations of operations for exterior powers.
##
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DeclareAttribute( "ExteriorPowers",
        IsHomalgModule, "mutable" );

##  <#GAPDoc Label="ExteriorPower">
##  <ManSection>
##    <Oper Arg="k, M" Name="ExteriorPower"/>
##    <Returns>a &homalg; module</Returns>
##    <Description>
##      Construct the <A>k</A>-th exterior power of module <A>M</A>.
##    </Description>
##  </ManSection>
##  <#/GAPDoc>
DeclareOperation( "ExteriorPower",
        [ IsInt, IsHomalgModule ]);

DeclareOperation( "ExteriorPower",
        [ IsInt, IsHomalgMatrix ]);

DeclareOperation( "ExteriorPower",
        [ IsInt, IsHomalgMorphism ]);

DeclareOperation( "ExteriorPowerOfPresentationMorphism",
        [ IsInt, IsHomalgMorphism ]);

##  <#GAPDoc Label="IsExteriorPower">
##  <ManSection>
##    <Prop Arg="M" Name="IsExteriorPower"/>
##    <Returns><C>true</C> or <C>false</C></Returns>
##    <Description>
##      Marks a module as an exterior power of another module.
##    </Description>
##  </ManSection>
##  <#/GAPDoc>
##
DeclareProperty( "IsExteriorPower",
        IsHomalgModule );

##  <#GAPDoc Label="ExteriorPowerExponent">
##  <ManSection>
##    <Attr Arg="M" Name="ExteriorPowerExponent"/>
##    <Returns>an integer</Returns>
##    <Description>
##      The exponent of the exterior power.
##    </Description>
##  </ManSection>
##  <#/GAPDoc>
##
DeclareAttribute( "ExteriorPowerExponent",
        IsHomalgModule );

##  <#GAPDoc Label="ExteriorPowerBaseModule">
##  <ManSection>
##    <Attr Arg="M" Name="ExteriorPowerBaseModule"/>
##    <Returns>a homalg module</Returns>
##    <Description>
##      The module that <A>M</A> is an exterior power of.
##    </Description>
##  </ManSection>
##  <#/GAPDoc>
##
DeclareAttribute( "ExteriorPowerBaseModule",
        IsHomalgModule );


##  <#GAPDoc Label="IsExteriorPowerElement">
##  <ManSection>
##    <Prop Arg="x" Name="IsExteriorPowerElement"/>
##    <Returns><C>true</C> or <C>false</C></Returns>
##    <Description>
##      Checks if the element <A>x</A> is from an exterior power.
##    </Description>
##  </ManSection>
##  <#/GAPDoc>
##
DeclareProperty( "IsExteriorPowerElement",
        IsHomalgModuleElement );

DeclareGlobalFunction( "_Homalg_CombinationIndex" );
DeclareGlobalFunction( "_Homalg_IndexCombination" );

DeclareGlobalFunction( "_Homalg_FreeModuleElementFromList" );

DeclareOperation( "Wedge",
        [ IsHomalgModuleElement, IsHomalgModuleElement ] );
DeclareOperation( "ExteriorPowerElementDual",
        [ IsHomalgModuleElement ] );
DeclareOperation( "SingleValueOfExteriorPowerElement",
        [ IsHomalgModuleElement ] );


DeclareOperation( "KoszulCocomplex",
        [ IsList, IsHomalgModule ] );
DeclareAttribute( "GradeIdeal",
        IsHomalgModule );
DeclareOperation( "GradeIdealOnModule",
        [ IsHomalgModule, IsHomalgRingOrModule ] );
DeclareOperation( "GradeList",
        [ IsList, IsHomalgRingOrModule ] );
DeclareGlobalFunction( "Grade_UsingKoszulCocomplex" );


DeclareGlobalFunction( "WedgeMatrixBaseImages" );
DeclareGlobalFunction( "CayleyDeterminant_Step" );

DeclareAttribute( "CayleyDeterminant",
        IsHomalgComplex );

##  <#GAPDoc Label="Gcd_UsingCayleyDeterminant">
##  <ManSection>
##    <Func Arg="x, y[, ...]" Name="Gcd_UsingCayleyDeterminant"/>
##    <Returns>a ring element</Returns>
##    <Description>
##      Returns the greatest common divisor of the given ring elements,
##      calculated using the Cayley determinant.
##    </Description>
##  </ManSection>
##  <#/GAPDoc>
##
DeclareGlobalFunction( "Gcd_UsingCayleyDeterminant" );

DeclareOperation( "GcdOp",
        [ IsHomalgRingElement, IsHomalgRingElement ] );

DeclareGlobalFunction( "Lcm_UsingCayleyDeterminant" );