def delta_ell_case_2(module: Module, x: ETangleStrands, a1: int,
a2: int) -> Module.TensorElement:
c1 = module.left_algebra.ring.one()
c2 = x.etangle.ring.one()
powers = x.idempotent_and_left_strands().figure_8_case_2a(a1, a2)
if powers is None:
return module.zero()
for orange, power in powers.items():
if x.etangle.strand_index_to_left_sign(orange) == 1:
c1 *= x.etangle.left_algebra_strand_index_to_variable(
orange)**power
else:
c2 *= x.etangle.strand_index_to_variable(orange)**power
elt = x.left_idempotent()
y = ETangleStrands(x.etangle, swap_values(x.left_strands, a1, a2),
x.right_strands)
return (c1 * elt)**(c2 * y.to_generator(module))
def delta1_2(module: TypeDA, x: ETangleStrands,
a: AMinus.Generator) -> Module.TensorElement:
return x.left_idempotent().to_element()**m2(module, x, a)
def delta1_1(module: TypeDA, x: ETangleStrands) -> Module.TensorElement:
return x.left_idempotent().to_element() ** (d_plus(module, x) + d_minus(module, x) + d_mixed(module, x)) \
+ delta_ell(module, x)