|
# SPDX-License-Identifier: GPL-2.0-or-later
# Modules: A homalg based package for the Abelian category of finitely presented modules over computable rings
#
# Declarations
#
## Declarations of operations for exterior powers.
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" );
[ Dauer der Verarbeitung: 0.16 Sekunden
(vorverarbeitet)
]
|
