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regular representation of permutations implemented

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Jiri Pittner
2024-01-18 23:45:42 +01:00
parent 2cb5258cd0
commit 13c23fb85d
4 changed files with 103 additions and 8 deletions
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69
permutation.cc
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@@ -22,6 +22,7 @@
#include <string.h>
#include <list>
#include "qsort.h"
#include "bitvector.h"
namespace LA {
@@ -320,6 +321,8 @@ return ret;
}
template <typename T, typename R>
bool PermutationAlgebra<T,R>::operator==(PermutationAlgebra<T,R> &rhs)
{
@@ -426,6 +429,23 @@ if(callback) (*callback)(*this);
return np;
}
template <typename T>
PermutationAlgebra<T,T> NRPerm<T>::list_all_lex()
{
PERM_RANK_TYPE number = factorial(this->size());
PermutationAlgebra<T,T> ret(number);
PERM_RANK_TYPE np=0;
this->identity();
do{
ret[np].perm = *this; ret[np].perm.copyonwrite();
ret[np].weight=0;
++np;
}while(this->next());
return ret;
}
template <typename T>
static T _n2;
@@ -765,6 +785,7 @@ for(int i=0; i<this->size(); ++i)
return res;
}
template <typename T, typename R>
PermutationAlgebra<T,R> PermutationAlgebra<T,R>::operator*(const PermutationAlgebra<T,R> &rhs) const
{
@@ -777,6 +798,7 @@ res.simplify();
return res;
}
template <typename T, typename R>
PermutationAlgebra<T,R> PermutationAlgebra<T,R>::operator+(const PermutationAlgebra<T,R> &rhs) const
{
@@ -974,11 +996,12 @@ return r;
template <typename T>
CompressedPartition<T> CyclePerm<T>::cycles(const T n) const
CompressedPartition<T> CyclePerm<T>::cycles(T n) const
{
#ifdef DEBUG
if(!this->is_valid()) laerror("operation with an invalid cycleperm");
#endif
if(n==0) n=max();
CompressedPartition<T> r(n); r.clear();
T ncycles=this->size();
for(T i=1; i<=ncycles; ++i)
@@ -2040,6 +2063,48 @@ return r;
}
template<typename T>
NRMat<PERM_RANK_TYPE> Multable(T n)
{
NRPerm<T> p(n);
PermutationAlgebra<T,T> all = p.list_all_lex();
NRMat<PERM_RANK_TYPE> r(all.size(),all.size());
for(PERM_RANK_TYPE i=0; i<all.size(); ++i) r[0][i] = r[i][0]=i; //identity
for(PERM_RANK_TYPE i=1; i<all.size(); ++i)
for(PERM_RANK_TYPE j=1; j<all.size(); ++j)
{
NRPerm<T> tmp = all[i].perm * all[j].perm;
r(i,j) = tmp.rank();
}
//consistency checks
#ifdef DEBUG
bitvector occ(all.size());
for(PERM_RANK_TYPE i=0; i<all.size(); ++i)
{
occ.clear();
for(PERM_RANK_TYPE j=0; j<all.size(); ++j) {if(occ[r(i,j)]) laerror("inconsistency in Multable"); occ.set(r(i,j));}
occ.clear();
for(PERM_RANK_TYPE j=0; j<all.size(); ++j) {if(occ[r(j,i)]) laerror("inconsistency in Multable"); occ.set(r(j,i));}
}
#endif
return r;
}
template<typename T, typename R>
NRMat<R> RegularRepresentation(const PermutationAlgebra<T,R> &a, const NRMat<PERM_RANK_TYPE> &mtable)
{
NRMat<R> r(mtable.nrows(),mtable.ncols());
r.clear();
for(int i=0; i<a.size(); ++i)
{
PERM_RANK_TYPE rx=a[i].perm.rank();
for(PERM_RANK_TYPE j=0; j<mtable.nrows();++j) r(mtable(rx,j),j) += a[i].weight;
}
return r;
}
template<typename T>
PermutationAlgebra<T,T> general_antisymmetrizer(const NRVec<NRVec_from1<T> > &groups, int restriction_type, bool inverted)
{
@@ -2072,6 +2137,7 @@ template class Partition<T>; \
template class YoungTableaux<T>; \
template class Sn_characters<T>; \
template class CycleIndex<T>; \
template NRMat<PERM_RANK_TYPE> Multable(T n); \
template PermutationAlgebra<T,T> general_antisymmetrizer(const NRVec<NRVec_from1<T> > &groups, int, bool); \
template std::istream & operator>>(std::istream &s, CyclePerm<T> &x); \
template std::ostream & operator<<(std::ostream &s, const CyclePerm<T> &x); \
@@ -2086,6 +2152,7 @@ template class WeightPermutation<T,R>; \
template class PermutationAlgebra<T,R>; \
template std::istream & operator>>(std::istream &s, WeightPermutation<T,R> &x); \
template std::ostream & operator<<(std::ostream &s, const WeightPermutation<T,R> &x); \
template NRMat<R> RegularRepresentation(const PermutationAlgebra<T,R> &a, const NRMat<PERM_RANK_TYPE> &mtable); \
INSTANTIZE(int)