def hasDifferential(gen_from, gen_to):
"""Determine whether there is a differential between two generators
of the large chain complex.
"""
left_from, right_from = gen_from
left_to, right_to = gen_to
mult_left_from, mult_left_to = \
left_from.multiplicity, left_to.multiplicity
diff = [a-b for a, b in zip(mult_left_from, mult_left_to)]
if all([n == 0 for n in diff]):
if left_from == left_to and right_to in right_from.diff():
return True
if right_from == right_to and left_from in left_to.diff():
return True
elif all([n == 0 or n == 1 for n in diff]):
pos_one = [i for i in range(len(diff)) if diff[i] == 1]
start, end = pos_one[0], pos_one[-1]+1
if pos_one == range(start, end):
st_move = Strands(self.pmc, [(start, end)])
if not st_move.rightCompatible(left_to.getLeftIdem()):
return False
left_move = StrandDiagram(
self.pmc_alg, None, st_move, left_to.getLeftIdem())
if not st_move.rightCompatible(right_from.getLeftIdem()):
return False
right_move = StrandDiagram(
self.pmc_alg, None, st_move, right_from.getLeftIdem())
return left_move * left_to == 1*left_from and \
right_move * right_from == 1*right_to
else:
return False
def _StrandsFromChords(self, chord1, chord2):
"""Create strand objects from lists of chords. Points in chord2 are
reversed (refer to the opposite pmc).
"""
chord1 = [(self.to_s[p], self.to_s[q]) for p, q in chord1]
chord_small = Strands(self.small_pmc, chord1)
chord2 = [(p, q) for p, q in chord2]
chord_large = Strands(self.large_pmc, chord2)
if self.side == LEFT:
return (chord_large, chord_small.opp())
else:
return (chord_small, chord_large.opp())
