/*
Coxeter version 3.0 Copyright (C) 2009 Mike Hansen
See file main.cpp for full copyright notice
*/
#include "sage.h"
namespace sage {
void interval(List<CoxWord>& list, CoxGroup& W, const CoxWord& g, const CoxWord& h)
/*
Returns a list of the elements in the Bruhat interval between g and h.
Note that this assumes that g and h are in order.
*/
{
if (not W.inOrder(g,h)) {
return;
}
W.extendContext(h);
CoxNbr x = W.contextNumber(g);
CoxNbr y = W.contextNumber(h);
BitMap b(W.contextSize());
W.extractClosure(b,y);
BitMap::ReverseIterator b_rend = b.rend();
List<CoxNbr> res(0);
for (BitMap::ReverseIterator i = b.rbegin(); i != b_rend; ++i)
if (not W.inOrder(x,*i)) {
BitMap bi(W.contextSize());
W.extractClosure(bi,*i);
CoxNbr z = *i; // andnot will invalidate iterator
b.andnot(bi);
b.setBit(z); // otherwise the decrement will not be correct
} else
res.append(*i);
schubert::NFCompare nfc(W.schubert(),W.ordering());
Permutation a(res.size());
sortI(res,nfc,a);
list.setSize(0);
for (size_t j = 0; j < res.size(); ++j) {
CoxWord w(0);
W.schubert().append(w, res[a[j]]);
list.append(w);
}
return;
}
}