def _find_values(self, commutators):
results_list = []
for c in commutators:
vector_multipliers = c.x.ms + c.y.ms + c.z.ms
vectors_sign = c.x.sign * c.y.sign * c.z.sign
commutator = Commutator(
Vector(c.x.value), Vector(c.y.value), Vector(c.z.value),
sign=c.sign*vectors_sign,
multipliers=c.multipliers+vector_multipliers
)
commutator = commutator.flip()
for v in self.get(commutator):
v.ms += commutator.multipliers
results_list.append(v)
return results_list
def _find_values(self, commutators):
results_list = []
for c in commutators:
vector_multipliers = c.x.ms + c.y.ms + c.z.ms
vectors_sign = c.x.sign * c.y.sign * c.z.sign
commutator = Commutator(Vector(c.x.value),
Vector(c.y.value),
Vector(c.z.value),
sign=c.sign * vectors_sign,
multipliers=c.multipliers +
vector_multipliers)
commutator = commutator.flip()
for v in self.get(commutator):
v.ms += commutator.multipliers
results_list.append(v)
return results_list
def init_basis_and_commutators():
global evens, odds, basis, commutators, odd_count, even_count
evens = tuple([Vector('e%d' % (i + 1)) for i in range(EVEN_COUNT)])
odds = tuple([Vector('f%d' % (i + 1)) for i in range(ODD_COUNT)])
basis = evens + odds
commutators = tuple(Commutator.get_commutators(basis))
for c in commutators:
multiplier_count = len(odds) if c.is_odd() else len(evens)
if c.is_zero():
values = []
elif c.is_odd():
multipliers = [
"m_%d" % (odd_count + i + 1) for i in range(multiplier_count)
]
odd_count += multiplier_count
values = [
Vector('f%d' % i, [m]) for i, m in enumerate(multipliers, 1)
]
else:
multipliers = [
"l_%d" % (even_count + i + 1) for i in range(multiplier_count)
]
even_count += multiplier_count
values = [
Vector('e%d' % i, [m]) for i, m in enumerate(multipliers, 1)
]
c.set_values_list(values)
commutator_map[c] = values
def get(self, commutator):
v1 = Vector(commutator.x.value)
v2 = Vector(commutator.y.value)
v3 = Vector(commutator.z.value)
invert = commutator.sign == -1
return [
v.copy(invert=invert)
for v in self.commutator_map[Commutator(v1, v2, v3)]
]
def init_basis_and_commutators():
global evens, odds, basis, commutators, odd_count, even_count
evens = tuple([Vector('e%d' % (i + 1)) for i in range(EVEN_COUNT)])
odds = tuple([Vector('f%d' % (i + 1)) for i in range(ODD_COUNT)])
basis = evens + odds
commutators = tuple(Commutator.get_commutators(basis))
for c in commutators:
multiplier_count = len(odds) if c.is_odd() else len(evens)
if c.is_zero():
values = []
elif c.is_odd():
multipliers = ["m_%d" % (odd_count + i+1) for i in range(multiplier_count)]
odd_count += multiplier_count
values = [Vector('f%d' % i, [m]) for i, m in enumerate(multipliers, 1)]
else:
multipliers = ["l_%d" % (even_count + i+1) for i in range(multiplier_count)]
even_count += multiplier_count
values = [Vector('e%d' % i, [m]) for i, m in enumerate(multipliers, 1)]
c.set_values_list(values)
commutator_map[c] = values
def calculate_identity_value(self, y1, y2, commutator):
"""
Returns right hand side of Jacobi identity of given vectors
[y1, y2, [x1, x2, x3]] =
[[y1, y2, x1], x2, x3] +
(-1)^{|x1|(|y1|+|y2|)} [x1, [y1, y2, x2], x3] +
(-1)^{(|x1|+|x2|)(|y1|+|y2|)} [x1, x2, [y1, y2, x3]]
"""
x1, x2, x3 = commutator.x, commutator.y, commutator.z
if any([v.ms for v in (x1, x2, x3, y1, y2)]):
raise ValueError("One of %s has multipliers" %
[x1, x2, x3, y1, y2])
elif commutator.sign != 1:
raise ValueError("Invalid commutator with negative sign: %s" %
commutator)
y_sign = abs(y1) + abs(y2)
middle_sign = (-1)**(abs(x1) * y_sign)
right_sign = (-1)**((abs(x1) + abs(x2)) * y_sign)
left_inner = Commutator(y1, y2, x1).flip()
middle_inner = Commutator(y1, y2, x2, sign=middle_sign).flip()
right_inner = Commutator(y1, y2, x3, sign=right_sign).flip()
# print("[{y1}, {y2}, [{x1}, {x2}, {x3}]] = [{li}, {x2}, {x3}] + [{x1}, {mi}, {x3}] + [{x1}, {x2}, {ri}]".format(
# x1=x1, x2=x2, x3=x3, y1=y1, y2=y2, li=left_inner, ri=right_inner, mi=middle_inner
# ))
left_commutators = [
Commutator(v, x2, x3) for v in self.get(left_inner)
]
middle_commutators = [
Commutator(x1, v, x3) for v in self.get(middle_inner)
]
right_commutators = [
Commutator(x1, x2, v) for v in self.get(right_inner)
]
vecs = self._find_values(left_commutators) +\
self._find_values(middle_commutators) +\
self._find_values(right_commutators)
# print(vecs)
return vecs
def calculate_value(self, y1, y2, commutator):
commutators = [Commutator(y1, y2, v) for v in self.get(commutator)]
return self._find_values(commutators)