RealRepresentationRing Class Reference

#include <repring.H>

Inheritance diagram for RealRepresentationRing:

List of all members.

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Detailed Description

RealRepresentationRing class.

We see a real representation ring as the same as an ordinary one, except that reading from a .gaprep.real file is done slightly differently. A difference is that there are less real irreps than complex irreps, but we need to keep track of the correspondance between real and complex reps. See read_variables() below.

Definition at line 119 of file repring.H.

Public Member Functions
virtual long	read_variables (ifstream &thefile, Tuple< Polynomial< QQ > > &thevars)
	read information on the variables from .gaprep.real file
Public Attributes
map< string, string >	conjugates

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Member Function Documentation

long RealRepresentationRing::read_variables (  ifstream &  thefile, Tuple< Polynomial< QQ > > &  thevars )  [virtual]

read information on the variables from .gaprep.real file This is similar to RepresentationRing::read_variables(), but with the following differences. The .gaprep.real file contains first an integer, call it n. This is the number of complex representations. Each of these "corresponds" (in one of three different possible ways, see below) to a real representation, but two conjugate complex representations give the same real one. So there will be less than n-1 variables created. Then the file contains a sequence of n-1 pairs of integers. The first in the pair can be: 1, the schur index, the representation has real type (and its complexification gives the complex representation back). The next integer is the real dimension. 2, also the schur index, the representation has complex type (and its character has been obtained as twice the real part of the complex one). The next integer is the real dimension. 4, the schur index yet again, the representation has quaternion type (and its character has been obtained as twice the complex one). The next integer is the real dimension. 0, in which case this is the complex conjugate of a complex (index 2) representation which has already been mentioned. So there must NOT be any variable created here. However, we increase a counter so the variables created subsequently will be named after the corresponding complex representations. Also, in this case the next integer is the index of the conjugate representation. We store in 'conjugates' the correspondence. Returns: the number of variables created + 1, which is typically less than n. Reimplemented from RepresentationRing. Definition at line 305 of file repring.cpp. References AffineAlgebra< QQ >::new_variable(), and AffineAlgebra< QQ >::one().

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The documentation for this class was generated from the following files:

• include/repring.H
• src/repring.cpp

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