working on permutation
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@ -163,12 +163,19 @@ return q.inverse()*((*this)*q);
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}
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//NOTE: for larger permutations it might be more efficient to use cycle decomposition but where exactly the breakeven is?
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//at the moment we do it the trivial way for small permutations and using sort for larger ones
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template <typename T>
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int NRPerm<T>::parity() const
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{
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if(!this->is_valid()) return 0;
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T n=this->size();
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if(n==1) return 1;
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if(n>=10) //???
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{
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NRPerm<T> tmp(*this);
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return (tmp.sort()&1) ? -1:1;
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}
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T count=0;
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for(T i=2;i<=n;i++) for(T j=1;j<i;j++) if((*this)[j]>(*this)[i]) count++;
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return (count&1)? -1:1;
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@ -313,6 +320,17 @@ return ret;
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}
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template <typename T, typename R>
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bool PermutationAlgebra<T,R>::operator==(PermutationAlgebra<T,R> &rhs)
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{
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simplify();
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rhs.simplify();
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if(size()!=rhs.size()) return false;
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for(int i=0; i<size(); ++i) if((*this)[i].weight!=rhs[i].weight || (*this)[i].perm!=rhs[i].perm) return false;
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return true;
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}
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//Algorithm L2 from Knuth's volume 4 for multiset permutations
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//input must be initialized with (repeated) numbers in any order
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@ -755,6 +773,7 @@ PermutationAlgebra<T,R> res(this->size()*rhs.size());
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for(int i=0; i<this->size(); ++i)
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for(int j=0; j<rhs.size(); ++j)
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res[i*rhs.size()+j] = (*this)[i]*rhs[j];
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res.simplify();
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return res;
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}
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@ -762,17 +781,12 @@ template <typename T, typename R>
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PermutationAlgebra<T,R> PermutationAlgebra<T,R>::operator+(const PermutationAlgebra<T,R> &rhs) const
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{
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if(this->size()>0 && rhs.size()>0 && (*this)[0].perm.size()!=rhs[0].perm.size()) laerror("permutation sizes do not match");
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return this->concat(rhs);
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PermutationAlgebra<T,R> res=this->concat(rhs);
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res.simplify();
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return res;
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}
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template <typename T, typename R>
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void PermutationAlgebra<T,R>::simplify()
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{
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copyonwrite();
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sort();
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//@@@@implement merging weights of identical permutations and resize like we did in qubithamiltonian with other stuff
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}
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@ -107,6 +107,9 @@ public:
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NRPerm<T> perm;
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int size() const {return perm.size();};
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bool is_zero() const {return weight==0;}
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bool is_scaledidentity() const {return perm.is_identity();}
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bool is_identity() const {return weight==1 && is_scaledidentity();}
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bool is_plaindata() const {return false;};
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WeightPermutation() : weight(0) {};
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WeightPermutation(const R w, const NRPerm<T> &p) : weight(w), perm(p) {};
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@ -116,7 +119,6 @@ public:
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WeightPermutation operator|(const WeightPermutation &rhs) const {return WeightPermutation(weight*rhs.weight,perm|rhs.perm);};
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WeightPermutation operator*(const WeightPermutation &rhs) const {return WeightPermutation(weight*rhs.weight,perm*rhs.perm);};
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WeightPermutation operator*(const R &x) const {return WeightPermutation(weight*x,perm); }
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//@@@operator+ and - yielding Permutationalgebra
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bool operator==(const WeightPermutation &rhs) const {return this->perm == rhs.perm;}; //NOTE for sorting, compares only the permutation not the weight!
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bool operator>(const WeightPermutation &rhs) const {return this->perm > rhs.perm;};
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@ -135,9 +137,13 @@ public:
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static bool is_plaindata() {return false;};
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static void copyonwrite(WeightPermutation<T,R>& x) {x.perm.copyonwrite();};
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typedef typename LA_traits<R>::normtype normtype;
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typedef R coefficienttype;
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typedef NRPerm<T> elementtype;
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static inline bool smaller(const WeightPermutation<T,R>& x, const WeightPermutation<T,R>& y) {return x.perm<y.perm;};
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static inline bool bigger(const WeightPermutation<T,R>& x, const WeightPermutation<T,R>& y) {return x.perm>y.perm;};
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static R coefficient(const WeightPermutation<T,R>& x){return x.weight;};
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static R& coefficient(WeightPermutation<T,R>& x) {return x.weight;};
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static typename LA_traits<R>::normtype abscoefficient(const WeightPermutation<T,R>& x){return LA_traits<R>::abs2(x.weight);};
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};
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@ -168,7 +174,7 @@ public:
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PermutationAlgebra(const NRVec<WeightPermutation<T,R> > &x) : NRVec<WeightPermutation<T,R> >(x) {};
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int size() const {return NRVec<WeightPermutation<T,R> >::size();};
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void copyonwrite() {NRVec<WeightPermutation<T,R> >::copyonwrite();};
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void sort(int direction = 0, int from = 0, int to = -1, int *permut = NULL, bool stable=false) {NRVec<WeightPermutation<T,R> >::sort(direction,from, to,permut,stable);};
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int sort(int direction = 0, int from = 0, int to = -1, int *permut = NULL, bool stable=false) {return NRVec<WeightPermutation<T,R> >::sort(direction,from, to,permut,stable);};
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PermutationAlgebra operator&(const PermutationAlgebra &rhs) const;
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PermutationAlgebra operator|(const PermutationAlgebra &rhs) const;
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@ -176,10 +182,13 @@ public:
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PermutationAlgebra operator+(const PermutationAlgebra &rhs) const;
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PermutationAlgebra &operator*=(const R &x) {this->copyonwrite(); for(int i=1; i<=size(); ++i) (*this)[i].weight *= x; return *this;};
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PermutationAlgebra operator*(const R &x) const {PermutationAlgebra r(*this); return r*=x;};
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void simplify();
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void simplify(const typename LA_traits<R>::normtype thr=0) {NRVec_simplify(*this,thr);};
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bool operator==(PermutationAlgebra &rhs); //do NOT inherit from NRVec, as the underlying one ignores weights for the simplification; also we have to simplify before comparison
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bool is_zero() const {return size()==0;}; //assume it was simplified
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bool is_scaled_identity() const {return size()==1 && (*this)[0]. is_scaledidentity();}; //assume it was simplified
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bool is_identity() const {return size()==1 && (*this)[0]. is_identity();}; //assume it was simplified
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};
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//TODO@@@ also simplification after operation
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//TODO@@@ permutationalgebra for Kucharski style antisymmetrizers
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@ -343,6 +352,8 @@ 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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T irrepdim(T i) const {return chi(i,1);};
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T sumirrepdims() const {T s=0; for(T i=1; i<=chi.nrows(); ++i) s+=irrepdim(i); return s;};
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};
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template <typename T> class Polynomial; //forward declaration
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46
t.cc
46
t.cc
@ -90,28 +90,38 @@ cout<<p;
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static int unitary_n;
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static PERM_RANK_TYPE space_dim;
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static NRVec<PermutationAlgebra<int,int> > allyoung;
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static NRVec<int> allyoung_irrep;
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int current_irrep;
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int allyoung_index;
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void yprintme(const YoungTableaux<int>&y)
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{
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cout <<y;
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if(!y.is_standard()) laerror("internal error in young");
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cout << y.young_operator();
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allyoung[allyoung_index] = y.young_operator();
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cout <<"Young "<<allyoung_index<<" (irrep "<<current_irrep<<") = "<<allyoung[allyoung_index]<<endl;
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allyoung_irrep[allyoung_index]=current_irrep;
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allyoung_index++;
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}
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void pprintme(const Partition<int> &p)
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{
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CompressedPartition<int> pc(p);
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++current_irrep;
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cout<<'['<<pc<<"]\n";
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PERM_RANK_TYPE snd=p.Sn_irrep_dim();
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cout<<"Sn IR dim "<<snd<<endl;
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YoungTableaux<int> y(p);
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PERM_RANK_TYPE dim=y.generate_all_standard(yprintme);
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Partition<int> q=p.adjoint();
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PERM_RANK_TYPE snd=p.Sn_irrep_dim();
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cout<<"IR dim "<<snd<<endl;
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if(dim!=snd) laerror("inconsistency in standard tableaux generation");
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PERM_RANK_TYPE und=p.Un_irrep_dim(unitary_n);
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cout<<"U("<<unitary_n<<") ir dim "<<und<<endl;
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cout<<"U("<<unitary_n<<") IR dim "<<und<<endl;
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space_dim += und*snd;
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CompressedPartition<int> qc(q);
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cout <<"("<<qc<<')';
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@ -2211,7 +2221,7 @@ int tot=p.generate_all_multi(printme0);
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cout <<"generated "<<tot<<endl;
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}
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if(1)
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if(0)
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{
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int n; cin >>n;
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NRPerm<int> p(n);
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@ -2230,14 +2240,36 @@ if(0)
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{
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int n;;
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cin >>n >>unitary_n;
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Sn_characters<int> Sn(n);
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cout <<Sn;
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if(!Sn.is_valid()) laerror("internal error in Sn character calculation");
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cout <<"allyoung.resize "<<Sn.sumirrepdims()<<endl;
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allyoung.resize(Sn.sumirrepdims());
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allyoung_irrep.resize(Sn.sumirrepdims());
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allyoung_index=0;
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Partition<int> p(n);
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space_dim=0;
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int tot=p.generate_all(pprintme,0);
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cout <<"partitions generated "<<tot<<endl;
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if(tot!=partitions(n)) laerror("internal error in partition generation or enumerations");
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if(space_dim!=longpow(unitary_n,n)) {cout<<space_dim<<" "<<ipow(unitary_n,n)<<endl;laerror("integer overflow or internal error in space dimensions");}
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for(int i=0; i<allyoung.size(); ++i)
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for(int j=0; j<allyoung.size(); ++j)
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{
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PermutationAlgebra<int,int> r=allyoung[i]*allyoung[j];
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//cout <<"Young "<<i<<" "<<allyoung[i]<<endl;
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//cout <<"Young "<<j<<" "<<allyoung[j]<<endl;
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cout <<"Product of Young "<<i<<" and "<<j<<" = "<<r<<"\n";
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if(i!=j && !r.is_zero()) cout <<"NONORTHOGONAL Young operators found "<<i<< " "<<j<<" (irreps "<<allyoung_irrep[i]<<" "<<allyoung_irrep[j]<<")\n";
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if(allyoung_irrep[i]!=allyoung_irrep[j] && !r.is_zero()) laerror("internal error in PermutationAlgebra");
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}
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}
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if(0)
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{
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int n;
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@ -3051,4 +3083,8 @@ if(!dif.is_zero()) laerror("error in gf 2^n sqrt");
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}
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if(1)
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{
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}
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}
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45
vec.h
45
vec.h
@ -1986,6 +1986,51 @@ for(typename std::list<T>::const_iterator i=l.begin(); i!=l.end(); ++i) (*this)[
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}
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//general simplification template for a NRVec of a class consisting from a coefficient and an element
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//the class T must have traits for sorting, normtype, elementtype, coefficienttype, coefficient, abscoefficient, and operator== which ignores the coefficient and uses just the element
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//it is not a member function to avoid the need of extra traits when this is not needed
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template<typename T>
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void NRVec_simplify(NRVec<T> &x, const typename LA_traits<T>::normtype thr=0, bool alwayskeepfirst=false)
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{
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if(x.size()==0) return;
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x.copyonwrite();
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//first sort to identify identical terms
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x.sort();
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//the following operations conserve the sorting, so no need to reset the issorted flag
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int newsize=1;
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//add factors of identical elements
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for(int next=1; next<x.size(); ++next)
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{
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if(x[next] == x[newsize-1])
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{
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LA_traits<T>::coefficient(x[newsize-1]) += LA_traits<T>::coefficient(x[next]);
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}
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else
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{
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if(next!=newsize) x[newsize] = x[next];
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++newsize;
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}
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}
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//now skip terms with zero coefficients
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int newsize2=0;
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for(int next=0; next<newsize; ++next)
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{
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if(next==0 && alwayskeepfirst || !(LA_traits<T>::coefficient(x[next])==0 || LA_traits<T>::abscoefficient(x[next]) <thr))
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{
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if(next!=newsize2) x[newsize2] = x[next];
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++newsize2;
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}
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}
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x.resize(newsize2,true);
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}
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}//namespace
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