def d_mixed_case_1(module: Module, x: ETangleStrands, b1: int,
b2: int) -> Module.TensorElement:
c = x.etangle.ring.one()
powers = x.to_strand_diagram().figure_8_case_1b(b1, b2)
if powers is None:
return module.zero()
for orange, power in powers.items():
c *= x.etangle.strand_index_to_variable(orange)**power
x_out = ETangleStrands(x.etangle, x.left_strands,
swap_values(x.right_strands, b1, b2))
return c * x_out.to_generator(module)
def d_mixed_case_4(module: Module, x: ETangleStrands, b1: int,
b2: int) -> Module.TensorElement:
c = x.etangle.ring.one()
powers = x.to_strand_diagram().figure_8_case_4b(b1, b2)
if powers is None:
return module.zero()
for orange, power in powers.items():
c *= x.etangle.strand_index_to_variable(orange)**power
a1 = x.left_y_pos(b1)
a2 = x.right_y_pos(b2)
new_left_strands = dict(x.left_strands)
new_left_strands[a1] = b2
new_right_strands = dict(x.right_strands)
del new_right_strands[b2]
new_right_strands[b1] = a2
x_out = ETangleStrands(x.etangle, new_left_strands, new_right_strands)
return c * x_out.to_generator(module)
