def length_rational_fraction(self, var='b'):
r"""
Return the generating series for the number of lengths with the given boundaries
"""
from sage.symbolic.ring import SR
F = SR.one()
for dart in range(self._total_darts):
if not self._active_darts[dart]:
continue
i = self._dart_to_edge_index[dart]
j1, j2 = self._edge_cycles[i]
if j1 == dart:
continue
else:
assert j2 == dart
f1 = self._dart_to_face_index[j1]
f2 = self._dart_to_face_index[j2]
b1 = SR.var('%s%d' %(var, f1))
b2 = SR.var('%s%d' %(var, f2))
F *= b1*b2 / (1 - b1*b2)
return F
def length_rational_fraction(self, var='b'):
r"""
Return the generating series for the number of lengths with the given boundaries
"""
from sage.symbolic.ring import SR
F = SR.one()
for dart in range(self._total_darts):
if not self._active_darts[dart]:
continue
i = self._dart_to_edge_index[dart]
j1, j2 = self._edge_cycles[i]
if j1 == dart:
continue
else:
assert j2 == dart
f1 = self._dart_to_face_index[j1]
f2 = self._dart_to_face_index[j2]
b1 = SR.var('%s%d' %(var, f1))
b2 = SR.var('%s%d' %(var, f2))
F *= b1*b2 / (1 - b1*b2)
return F
