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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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12
permutation.h
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@@ -60,6 +60,7 @@ public:
void identity();
bool is_valid() const; //is it really a permutation
bool is_identity() const;
CompressedPartition<T> cycles() const {return CyclePerm<T>(*this).cycles(size());};
NRPerm inverse() const;
NRPerm reverse() const; //backward order
NRPerm operator&(const NRPerm &rhs) const; //concatenate the permutations this,rhs, renumbering rhs (not commutative)
@@ -72,6 +73,7 @@ public:
bool next(); //generate next permutation in lex order
PERM_RANK_TYPE generate_all(void (*callback)(const NRPerm<T>&), int parity_select=0); //Algorithm L from Knuth's vol.4, efficient but not in lex order!
PermutationAlgebra<T,T> list_all(int parity_select=0);
PermutationAlgebra<T,T> list_all_lex();
PERM_RANK_TYPE generate_all_multi(void (*callback)(const NRPerm<T>&)); //Algorithm L2 from Knuth's vol.4, for a multiset (repeated numbers, not really permutations)
PERM_RANK_TYPE generate_all2(void (*callback)(const NRPerm<T>&)); //recursive method, also not lexicographic
PERM_RANK_TYPE generate_all_lex(void (*callback)(const NRPerm<T>&)); //generate in lex order using next()
@@ -126,6 +128,7 @@ public:
bool operator<(const WeightPermutation &rhs) const {return this->perm < rhs.perm;};
bool operator>=(const WeightPermutation &rhs) const {return !(*this < rhs);};
bool operator<=(const WeightPermutation &rhs) const {return !(*this > rhs);};
WeightPermutation & operator=(const WeightPermutation &rhs) {weight=rhs.weight; perm=rhs.perm; return *this;};
};
@@ -145,6 +148,7 @@ public:
static R coefficient(const WeightPermutation<T,R>& x){return x.weight;};
static R& coefficient(WeightPermutation<T,R>& x) {return x.weight;};
static typename LA_traits<R>::normtype abscoefficient(const WeightPermutation<T,R>& x){return LA_traits<R>::abs2(x.weight);};
static void clear(WeightPermutation<T,R> *v, int nn) {for(int i=0; i<nn; ++i) {v[i].weight=0; v[i].perm.clear();}}
};
@@ -211,7 +215,7 @@ public:
CyclePerm inverse() const; //reverse all cycles
int parity() const; //negative if having odd number of even-length cycles
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;}
CompressedPartition<T> cycles(const T n) const;
CompressedPartition<T> cycles(T n = 0) const;
void readfrom(const std::string &line);
CyclePerm operator*(const CyclePerm &q) const; //q is rhs and applied first, this applied second
NRPerm<T> operator*(const NRPerm<T> &r) const;
@@ -390,6 +394,12 @@ else for(int i=1; i<=n; ++i) r[p[i]-1] = v[i-1];
return r;
}
template<typename T>
NRMat<PERM_RANK_TYPE> Multable(T n);
template<typename T, typename R>
NRMat<R> RegularRepresentation(const PermutationAlgebra<T,R> &a, const NRMat<PERM_RANK_TYPE> &mtable);
template<typename T>
PermutationAlgebra<T,T> general_antisymmetrizer(const NRVec<NRVec_from1<T> > &groups, int restriction_type=0, bool inverted=false);