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##########################################################################
##
#W basic.gd QuaGroup Willem de Graaf
##
##
## Declares some global variables and operations to be used throughout.
##
#############################################################################
##
#V QGPrivateFunctions
##
##
BindGlobal( "QGPrivateFunctions", rec(indetNo:= 1000) );
#############################################################################
##
#C IsQuantumField( <F> )
##
## The category to which the field Q(q) belongs.
##
DeclareCategory( "IsQuantumField", IsField );
#############################################################################
##
#V _q
##
## This is the generator of `QuantumField'. The element `q' will be
## fixed once the package {\sf QuaGroup} is loaded. It is used
## in many places in the code.
##
BindGlobal( "_q", Indeterminate( Rationals, QGPrivateFunctions.indetNo ) );
SetName( _q, "q" );
###########################################################################
##
#F GaussNumber( <n>, <a> )
##
## is defined as $a^(n-1)+a^(n-3)+...+a^(-n+1)$.
##
DeclareOperation( "GaussNumber", [ IsInt, IsMultiplicativeElement ] );
############################################################################
##
#F GaussianFactorial( <n>, <a> )
##
## is defined as $[n][n-1]...[1]$, where $[k]$ is the Gauss number with
## respect to $k$, and <a>.
##
DeclareOperation( "GaussianFactorial", [ IsInt,
IsMultiplicativeElement ] );
##########################################################################
##
#F GaussianBinomial( <n>, <k>, <a> )
##
## is defined as $[n]!/[k]![n-k]!$, where $[r]!$ is the Gaussian factorial
## with respect to $r$ and <a>.
##
DeclareOperation( "GaussianBinomial", [ IsInt, IsInt,
IsMultiplicativeElement ] );
############################################################################
##
#A WeightsAndVectors( <V> )
##
## A list of two lists; the first of these is a list of the weights
## of <V>, the second a list of corresponding weight vectors. These
## are again grouped in lists: if the multiplicity of a weight is
## $\mu$, then there are $\mu$ weight vectors, forming a basis of
## the corresponding weight space.
##
DeclareAttribute( "WeightsAndVectors", IsAlgebraModule );
############################################################################
##
#A HighestWeightsAndVectors( <V> )
##
## Is analogous to `WeightsAndVetors'; only now only the highest
## weights are listed along with the corresponding highest-weight vectors.
##
DeclareAttribute( "HighestWeightsAndVectors", IsAlgebraModule );
[ Dauer der Verarbeitung: 0.14 Sekunden
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