def type_da(etangle: ETangle) -> TypeDA:
components = [
type_da_in_left_grading(etangle, r)
for r in range(0,
len(etangle.left_points()) + 1)
]
return TypeDA.direct_sum(components)
def type_da_in_left_grading(etangle: ETangle, i: int) -> TypeDA:
out = TypeDA(etangle.ring, etangle.left_algebra, etangle.right_algebra,
etangle.left_scalar_action, etangle.right_scalar_action)
strands = [
ETangleStrands(etangle, left_strands, right_strands)
for left_strands, right_strands in enumerate_gens([
etangle.left_points(),
etangle.middle_points(),
etangle.right_points()
], i)
]
for x in strands:
out.add_generator(x.to_generator(out),
(x.to_strand_diagram().maslov(),
x.to_strand_diagram().twoalexander()))
for x in strands:
out.add_structure_map(x.to_generator(out), delta1_1(out, x))
for a in etangle.right_algebra.left_gens(list(
x.right_strands.values())):
out.add_structure_map(x.to_generator(out)**a, delta1_2(out, x, a))
return out
def valid_dictionaries(et: ETangle, ls: Dict, rs: Dict):
for key in ls.keys():
if key not in et.left_points():
return False
for val in rs.values():
if val not in et.right_points():
return False
return set(ls.values()).union(set(rs.keys())) == set(et.middle_points())