/usr/include/polymake/group/quotiented_representation.h is in libpolymake-dev-common 3.2r2-3.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 | /* Copyright (c) 1997-2018
Ewgenij Gawrilow, Michael Joswig (Technische Universitaet Berlin, Germany)
http://www.polymake.org
This program is free software; you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by the
Free Software Foundation; either version 2, or (at your option) any
later version: http://www.gnu.org/licenses/gpl.txt.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
--------------------------------------------------------------------------------
*/
#ifndef __GROUP_QUOTIENTED_REPRESENTATIONS_H
#define __GROUP_QUOTIENTED_REPRESENTATIONS_H
#include "polymake/group/representations.h"
#include "polymake/Bitset.h"
namespace polymake { namespace group {
typedef Bitset SetType;
namespace {
class QuotientedInducedAction
: public InducedAction<SetType> {
protected:
PermlibGroup G;
void set_entry(SparseMatrix<Rational>& rep, const SetType& image, int col_index) const {
++rep(index_of.at(G.lex_min_representative(image)), col_index);
}
public:
QuotientedInducedAction(int degree,
const Array<SetType>& domain,
const hash_map<SetType, int>& index_of,
const Array<Array<int> >& generators)
: InducedAction<SetType>(degree, domain, index_of)
, G(generators)
{}
};
// template<typename InducedAction, typename RowType>
// SparseMatrix<Rational> isotypic_projector_impl(const RowType& character,
// const InducedAction& induced_action,
// int degree,
// const Array<Set<Array<int> > >& conjugacy_classes,
// int order)
// {
// SparseMatrix<Rational> isotypic_projector(degree, degree);
// for (int i=0; i<conjugacy_classes.size(); ++i) {
// for (Entire<Set<Array<int> > >::const_iterator cit = entire(conjugacy_classes[i]); !cit.at_end(); ++cit) {
// isotypic_projector +=
// character[i] // FIXME: conjugate here, once complex character tables are implemented
// * induced_action.rep(*cit);
// }
// }
// // chi(G.identity())/G.order() * sum([chi(g).conjugate() * rep.rho(g) for g in G])
// return isotypic_projector * character[0] / order;
// }
// template<typename SparseMatrixType, typename InducedAction>
// IncidenceMatrix<> isotypic_supports_impl(const SparseMatrixType& S,
// const Matrix<Rational>& character_table,
// const InducedAction& IA,
// const Array<Set<Array<int> > >& conjugacy_classes,
// int order,
// int degree)
// {
// const int n_irreps = character_table.rows();
// IncidenceMatrix<> supp(n_irreps, S.rows());
// for (int i=0; i<n_irreps; ++i) {
// const SparseMatrix<Rational> proj = isotypic_projector_impl(character_table[i], IA, degree, conjugacy_classes, order);
// int j(0);
// for (typename Entire<Rows<SparseMatrixType> >::const_iterator rit = entire(rows(S)); !rit.at_end(); ++rit, ++j) {
// for (typename Entire<typename SparseMatrixType::row_type>::const_iterator e = entire(*rit); !e.at_end(); ++e) {
// if (proj.col(e.index()) != zero_vector<Rational>(degree)) {
// supp(i,j) = 1;
// break; // it's only necessary to prove support once
// }
// }
// }
// }
// return supp;
// }
} // end anonymous namespace
} }
#endif // __GROUP_QUOTIENTED_REPRESENTATIONS_H
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// mode:C++
// c-basic-offset:3
// indent-tabs-mode:nil
// End:
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