245 lines
9.3 KiB
C++
245 lines
9.3 KiB
C++
/*
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LA: linear algebra C++ interface library
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Copyright (C) 2021 Jiri Pittner <jiri.pittner@jh-inst.cas.cz> or <jiri@pittnerovi.com>
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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#ifndef _PERMUTATION_H
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#define _PERMUTATION_H
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#include "la_traits.h"
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#include "vec.h"
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#include "polynomial.h"
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typedef unsigned long long PERM_RANK_TYPE;
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//permutations are always numbered from 1; offset is employed when applied to vectors and matrices
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namespace LA {
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//forward declaration
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template <typename T> class CyclePerm;
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template <typename T> class Partition;
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template <typename T> class CompressedPartition;
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template <typename T> class YoungTableaux;
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template <typename T>
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class NRPerm : public NRVec_from1<T> {
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public:
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//basic constructors
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NRPerm(): NRVec_from1<T>() {};
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template<int SIZE> explicit NRPerm(const T (&a)[SIZE]) : NRVec_from1<T>(a) {};
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NRPerm(const int n) : NRVec_from1<T>(n) {};
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NRPerm(const NRVec_from1<T> &rhs): NRVec_from1<T>(rhs) {};
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NRPerm(const T *a, const int n): NRVec_from1<T>(a, n) {};
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explicit NRPerm(const CyclePerm<T> &rhs, const int n=0);
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//specific operations
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void identity();
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bool is_valid() const; //is it really a permutation
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bool is_identity() const;
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NRPerm inverse() const;
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NRPerm reverse() const; //backward order
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NRPerm operator*(const NRPerm q) const; //q is rhs and applied first, this applied second
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NRPerm conjugate_by(const NRPerm q) const; //q^-1 p q
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int parity() const;
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void randomize(void); //uniformly random by Fisher-Yates shuffle
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bool next(); //generate next permutation in lex order
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PERM_RANK_TYPE generate_all(void (*callback)(const NRPerm<T>&), int parity_select=0); //Algorithm from Knuth's vol.4, efficient but not in lex order!
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PERM_RANK_TYPE generate_all2(void (*callback)(const NRPerm<T>&)); //recursive method, also not lexicographic
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PERM_RANK_TYPE generate_all_lex(void (*callback)(const NRPerm<T>&)); //generate in lex order using next()
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PERM_RANK_TYPE rank() const; //counted from 0 to n!-1
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NRVec_from1<T> inversions(const int type, PERM_RANK_TYPE *prank=NULL) const; //inversion tables
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explicit NRPerm(const int type, const NRVec_from1<T> &inversions); //compute permutation from inversions
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explicit NRPerm(const int n, const PERM_RANK_TYPE rank); //compute permutation from its rank
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};
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extern PERM_RANK_TYPE factorial(const int n);
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extern PERM_RANK_TYPE binom(int n, int k);
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extern PERM_RANK_TYPE longpow(PERM_RANK_TYPE x, int i);
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//permutations represented in the cycle format
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template <typename T>
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class CyclePerm : public NRVec_from1<NRVec_from1<T> > {
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public:
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CyclePerm() : NRVec_from1<NRVec_from1<T> >() {};
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template<int SIZE> explicit CyclePerm(const NRVec_from1<T> (&a)[SIZE]) : NRVec_from1<NRVec_from1<T> >(a) {};
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//NOTE - how to do it so that direct nested brace initializer would work?
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explicit CyclePerm(const NRPerm<T> &rhs);
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bool is_valid() const; //is it really a permutation
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bool is_identity() const; //no cycles of length > 1
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void identity() {this->resize(0);};
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CyclePerm inverse() const; //reverse all cycles
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int parity() const; //negative if having odd number of even-length cycles
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T max() const {T m=0; for(int i=1; i<=this->size(); ++i) {T mm= (*this)[i].max(); if(mm>m) m=mm;} return m;}
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CompressedPartition<T> cycles(const T n) const;
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void readfrom(const std::string &line);
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CyclePerm operator*(const CyclePerm q) const; //q is rhs and applied first, this applied second
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PERM_RANK_TYPE order() const; //lcm of cycle lengths
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};
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template <typename T>
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T gcd(T big, T small)
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{
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if(big==0)
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{
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if(small==0) laerror("bad arguments in gcd");
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return small;
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}
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if(small==0) return big;
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if(small==1||big==1) return 1;
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T help;
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if(small>big) {help=big; big=small; small=help;}
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do {
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help=small;
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small= big%small;
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big=help;
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}
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while(small != 0);
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return big;
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}
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template <typename T>
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inline T lcm(T a, T b)
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{
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return (a/gcd(a,b))*b;
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}
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template <typename T>
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std::istream & operator>>(std::istream &s, CyclePerm<T> &x);
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template <typename T>
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std::ostream & operator<<(std::ostream &s, const CyclePerm<T> &x);
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//compressed partitions stored as #of 1s, #of 2s, etc.
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template <typename T>
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class CompressedPartition : public NRVec_from1<T> {
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public:
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CompressedPartition(): NRVec_from1<T>() {};
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template<int SIZE> explicit CompressedPartition(const T (&a)[SIZE]) : NRVec_from1<T>(a) {};
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CompressedPartition(const int n) : NRVec_from1<T>(n) {};
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T sum() const {T s=0; for(int i=1; i<=this->size(); ++i) s += i*(*this)[i]; return s;}
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T nparts() const {T s=0; for(int i=1; i<=this->size(); ++i) s += (*this)[i]; return s;}
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T nclasses() const {T s=0; for(int i=1; i<=this->size(); ++i) if((*this)[i]) ++s; return s;}
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bool is_valid() const {return this->size() == this->sum();}
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explicit CompressedPartition(const Partition<T> &rhs) : NRVec_from1<T>(rhs.size()) {this->clear(); for(int i=1; i<=rhs.size(); ++i) if(!rhs[i]) break; else (*this)[rhs[i]]++; }
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PERM_RANK_TYPE Sn_class_size() const;
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int parity() const; //of a permutation with given cycle lengths
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};
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template <typename T>
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std::ostream & operator<<(std::ostream &s, const CompressedPartition<T> &x);
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template <typename T>
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class Partition : public NRVec_from1<T> {
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public:
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Partition(): NRVec_from1<T>() {};
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template<int SIZE> explicit Partition(const T (&a)[SIZE]) : NRVec_from1<T>(a) {};
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Partition(const int n) : NRVec_from1<T>(n) {};
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T nparts() const {T s=0; for(int i=1; i<=this->size(); ++i) if((*this)[i]) ++s; return s;}
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bool is_valid() const {if(this->size() != this->sum()) return false; for(int i=2; i<=this->size(); ++i) if((*this)[i]>(*this)[i-1]) return false; return true; }
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explicit Partition(const CompressedPartition<T> &rhs) : NRVec_from1<T>(rhs.size()) {this->clear(); int ithru=0; for(int i=rhs.size(); i>=1; --i) for(int j=0; j<rhs[i]; ++j) (*this)[++ithru]=i; }
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explicit Partition(const YoungTableaux<T> &x); //extract a partition as a shape of Young tableaux
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Partition adjoint() const; //also called conjugate partition
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PERM_RANK_TYPE Sn_irrep_dim() const;
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PERM_RANK_TYPE Un_irrep_dim(const int n) const;
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PERM_RANK_TYPE generate_all(void (*callback)(const Partition<T>&), int nparts=0); //nparts <0 means at most to -nparts
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int parity() const; //of a permutation with given cycle lengths
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};
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template <typename T>
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extern T Sn_character(const Partition<T> &irrep, const Partition<T> &cclass);
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template <typename T>
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inline T Sn_character(const CompressedPartition<T> &irrep, const CompressedPartition<T> &cclass)
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{
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return Sn_character(Partition<T>(irrep),Partition<T>(cclass));
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}
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template <typename T>
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class YoungTableaux : public NRVec_from1<NRVec_from1<T> > {
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public:
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YoungTableaux() : NRVec_from1<NRVec_from1<T> >() {};
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explicit YoungTableaux(const Partition<T> &frame);
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template<int SIZE> explicit YoungTableaux(const NRVec_from1<T> (&a)[SIZE]) : NRVec_from1<NRVec_from1<T> >(a) {};
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//NOTE - how to do it so that direct nested brace initializer would work?
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bool is_valid() const; //check whether its shape forms a partition
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int nrows() const {return this->size();}
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int ncols() const {return (*this)[1].size();}
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bool is_standard() const; //is it filled in standard way (possibly with repeated numbers)
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T sum() const; //get back sum of the partition
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T max() const; //get back highest number filled in
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NRVec_from1<T> yamanouchi() const; //yamanouchi symbol
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T character_contribution(int ncyc=0) const; //contribution of filled tableaux to Sn character
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PERM_RANK_TYPE generate_all_standard(void (*callback)(const YoungTableaux<T>&));
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PERM_RANK_TYPE young_operator(void (*callback)(const NRPerm<T>&p, const T parity, const PERM_RANK_TYPE nterms)) const; //generate young operator for a standard tableaux
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};
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template <typename T>
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std::ostream & operator<<(std::ostream &s, const YoungTableaux<T> &x);
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extern PERM_RANK_TYPE partitions(int n, int k= -1); //enumerate partitions to k parts; k== -1 for total # of partitions
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//Sn character table
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template <typename T>
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class Sn_characters {
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public:
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T n;
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NRVec_from1<CompressedPartition<T> > classes;
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NRVec_from1<CompressedPartition<T> > irreps; //can be in different order than classes
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NRVec_from1<PERM_RANK_TYPE> classsizes;
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NRMat_from1<T> chi; //characters
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Sn_characters(const int n0); //compute the table
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bool is_valid() const; //check internal consistency
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};
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template <typename T> class Polynomial; //forward declaration
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template <typename T>
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class CycleIndex {
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public:
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NRVec_from1<CompressedPartition<T> > classes;
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NRVec_from1<PERM_RANK_TYPE> classsizes;
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CycleIndex(const Sn_characters<T> &rhs): classes(rhs.classes),classsizes(rhs.classsizes) {};
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bool is_valid() const; //check internal consistency
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Polynomial<T> substitute(const Polynomial<T> &p, PERM_RANK_TYPE *denom) const;
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};
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template <typename T>
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extern std::ostream & operator<<(std::ostream &s, const Sn_characters<T> &c);
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}//namespace
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#endif
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