Coverage for local/lib/python2.7/site-packages/sage/combinat/subword_complex_c.pyx : 95%

cpdef int _flip_c(W, set positions, list extended_root_conf_indices, 

int i, side="both"): 

r""" 

Flip a facet. 

INPUT: 

- W -- a Coxeter group 

- positions -- the positions of the elements of the facet 

- extended_root_conf_indices -- also attached to the facet ? 

- i -- the position where to flip 

- side -- optional, can be 'positive', 'negative' or 'both' (default) 

OUTPUT: 

the new position j that has replaced i 

EXAMPLES:: 

sage: from sage.combinat.subword_complex_c import _flip_c 

sage: W = ReflectionGroup(['A',2]) # optional - gap3 

sage: w = W.from_reduced_word([1,2,1]) # optional - gap3 

sage: SC = SubwordComplex([1,2,1,2,1], w) # optional - gap3 

sage: F = SC([0, 1]) # optional - gap3 

sage: _flip_c(W, set([0,1]), F._extended_root_configuration_indices(), 1) # optional - gap3 

4 

sage: _flip_c(W, set([0,1]), F._extended_root_configuration_indices(), 0) # optional - gap3 

3 

sage: W = CoxeterGroup(['A',2]) 

sage: w = W.from_reduced_word([1,2,1]) 

sage: SC = SubwordComplex([1,2,1,2,1], w) 

sage: F = SC([0, 1]) 

sage: _flip_c(W, set([0,1]), F._extended_root_configuration_indices(), 1) 

4 

sage: _flip_c(W, set([0,1]), F._extended_root_configuration_indices(), 0) 

3 

""" 

cdef int r, nr_ref, r_minus, j, k 

cdef list R 

r = extended_root_conf_indices[i] 

nr_ref = W.number_of_reflections() 

r_minus = (r + nr_ref) % (2 * nr_ref) # get the negative root -r 

j = i 

for k in xrange(len(extended_root_conf_indices)): 

if extended_root_conf_indices[k] == r_minus and k not in positions and side != "positive": 

j = k 

break 

elif extended_root_conf_indices[k] == r and k not in positions and side != "negative": 

j = k 

break 

positions.remove(i) 

positions.add(j) 

R = list(W.reflections()) 

if j != i: 

t = R[min(r, r_minus)] 

for k in xrange(min(i, j) + 1, max(i, j) + 1): 

extended_root_conf_indices[k] = t.action_on_root_indices(extended_root_conf_indices[k],side="left") 

return j 

cpdef list _construct_facets_c(tuple Q, w, int n=-1, int pos=0, int l=-1): 

r""" 

Return the list of facets of the subword complex associated to the 

word `Q` and the element `w` in a Coxeter group `W`. 

EXAMPLES:: 

sage: from sage.combinat.subword_complex_c import _construct_facets_c 

sage: W = CoxeterGroup(['A',2]) 

sage: w = W.from_reduced_word([1,2]) 

sage: _construct_facets_c((2,1), w) 

[] 

sage: _construct_facets_c((2,1,2), w) 

[[0]] 

sage: _construct_facets_c((2,1,2,1), w) 

[[0, 3]] 

sage: w = W.from_reduced_word([1,2,1]) 

sage: _construct_facets_c((1,2,1,2,1), w) 

[[0, 1], [0, 4], [1, 2], [2, 3], [3, 4]] 

""" 

cdef int s 

cdef list X, Y 

if n == -1: 

n = len(Q) 

if l == -1: 

first = True 

l = w.length() 

else: 

first = False 

if l == 0: 

return [list(xrange(pos, n))] 

elif n < l + pos: 

return [] 

s = Q[pos] 

X = _construct_facets_c(Q, w, n=n, pos=pos + 1, l=l) 

for f in X: 

f.append(pos) 

if w.has_left_descent(s): 

Y = _construct_facets_c(Q, w.apply_simple_reflection_left(s), 

n=n, pos=pos + 1, l=l - 1) 

Y = X + Y 

else: 

Y = X 

if first: 

return sorted([sorted(x) for x in Y]) 

else: 

return Y