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some more functions in polynomials and permutations

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This commit is contained in:
Jiri Pittner
2021-06-26 22:41:40 +02:00
parent 3cf56c3f36
commit 3288e51fba
5 changed files with 192 additions and 6 deletions
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77
permutation.cc
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@@ -471,6 +471,48 @@ return a[n];
}
#define MAXBINOM 100
#define ibidxmaxeven(n) ((n-2)*(n-2)/4)
#define ibidx(n,k) (k-2+(n&1?(n-3)*(n-3)/4:(n/2-1)*(n/2-2)))
PERM_RANK_TYPE binom(int n, int k)
{
PERM_RANK_TYPE p,value;
register int d;
static PERM_RANK_TYPE ibitab[ibidxmaxeven(MAXBINOM)]= /*only nontrivial are stored,
zero initialization by compiler assumed*/
{
6,
10,
15,20,
21,35,
28,56,70
};
if(k>n||k<0) return(0);
if(k>n/2) k=n-k;
if(k==0) return(1);
if(k==1) return(n);
int ind=0;
if(n<=MAXBINOM)
{
ind=ibidx(n,k);
if (ibitab[ind]) return ibitab[ind];
}
/* nonrecurent method used anyway */
d=n-k;
p=1;
for(;n>d;n--) p *= n;
value=p/factorial(k);
if(n<=MAXBINOM) ibitab[ind]=value;
return value;
}
#undef ibidx
#undef ibidxmaxeven
#undef MAXBINOM
////////////////////////////////////////////////////////
template <typename T>
@@ -1599,6 +1641,40 @@ for(int i=1; i<=c.chi.nrows(); ++i)
return s;
}
template <typename T>
bool CycleIndex<T>::is_valid() const
{
if(classes.size()!=classsizes.size()) return false;
T n=classes[1].sum();
for(int i=2; i<=classes.size(); ++i)
{
if(classes[i].sum()!=n) return false;
}
return true;
}
template <typename T>
Polynomial<T> CycleIndex<T>::substitute(const Polynomial<T> &p, PERM_RANK_TYPE *denom) const
{
Polynomial<T> r(0);
r[0]=(T)0;
*denom =0;
for(int i=1; i<=classes.size(); ++i)
{
Polynomial<T> term(0);
term[0]=(T)1;
for(int j=1; j<=classes[i].size(); ++j) if(classes[i][j]) term *= (p.powx(j)).pow((int)classes[i][j]);
r += term*classsizes[i];
*denom += classsizes[i];
}
return r;
}
/***************************************************************************//**
* forced instantization in the corresponding object file
******************************************************************************/
@@ -1610,6 +1686,7 @@ template class CompressedPartition<T>; \
template class Partition<T>; \
template class YoungTableaux<T>; \
template class Sn_characters<T>; \
template class CycleIndex<T>; \
template std::istream & operator>>(std::istream &s, CyclePerm<T> &x); \
template std::ostream & operator<<(std::ostream &s, const CyclePerm<T> &x); \
template std::ostream & operator<<(std::ostream &s, const CompressedPartition<T> &x); \