def opposite_algebra(A_inf):
gen_by_name = AttrDict({})
for gen in A_inf.genset:
gen_by_name[gen.name + '*'] = Generator(gen.name + '*')
new_A_inf_actions = Bunch_of_arrows([])
for action in A_inf.a_inf_actions:
new_action = ()
for element in action:
new_action = new_action + (gen_by_name[element.name + '*'], )
new_A_inf_actions[new_action[:-1][::-1] + (new_action[-1], )] += 1
return simpler_A_inf_Algebra(gen_by_name, 'opposite of ' + A_inf.name,
new_A_inf_actions)
def rename_generators(A, list_of_tuples_to_rename):
new_generators = AttrDict({})
# for t in list_of_tuples_to_rename:
# new_generators[t[1]]=Generator(name=t[1], aux_info=A.gen_by_name[t[0]])
for gen in A.gen_by_name.values():
if gen.name in [t[0] for t in list_of_tuples_to_rename]:
t = next(t for t in list_of_tuples_to_rename if t[0] == gen.name)
new_generators[t[1]] = Generator(name=t[1],
aux_info=A.gen_by_name[t[0]])
else:
new_generators[gen.name] = Generator(name=gen.name, aux_info=gen)
new_A_inf_actions = Bunch_of_arrows({})
for action in A.a_inf_actions:
new_action = ()
for el in action:
new_action = new_action + (next(gen
for gen in new_generators.values()
if gen.aux_info == el), )
new_A_inf_actions[new_action] += 1
return simpler_A_inf_Algebra(new_generators, A.name + '_renamed',
new_A_inf_actions)
def u_i_rename_generators(A):
new_generators = AttrDict({})
i = 0
for gen in A.gen_by_name.values():
new_generators["u_" + str(i)] = Generator(name="u_" + str(i),
aux_info=gen)
i += 1
new_A_inf_actions = Bunch_of_arrows({})
for action in A.a_inf_actions:
new_action = ()
for el in action:
new_action = new_action + (next(gen
for gen in new_generators.values()
if gen.aux_info == el), )
new_A_inf_actions[new_action] += 1
return simpler_A_inf_Algebra(new_generators, A.name + '_renamed',
new_A_inf_actions)
def base_change_AA_from_fuk(Fuk, generators, left_dg_algebra,
right_dg_algebra):
def check_validity(x, action):
if action[:-1].count(x) == 1 and (action[-1] in generators):
index_of_x = action[:-1].index(x)
for el in action[:index_of_x]:
if not el.name in left_dg_algebra.gen_by_name.keys():
return False
for el in action[index_of_x + 1:-1]:
if not el.name in right_dg_algebra.gen_by_name.keys():
return False
return True
else:
return False
gen_by_name = AttrDict({})
for x in generators:
gen_by_name['' + x.name + ''] = Generator('' + x.name + '')
# gen_by_name[''+x.name+''].add_idems(x.idem.left, x.idem.right)
# adding idempotents
for action in [
act for act in Fuk.a_inf_actions if (len(act) == 3 and (
act[0].name in left_dg_algebra.idem_by_name.keys()) and (
x == act[1]) and (x == act[-1]))
]:
left_idem = left_dg_algebra.idem_by_name[action[0].name]
for action in [
act for act in Fuk.a_inf_actions if (len(act) == 3 and (
act[1].name in right_dg_algebra.idem_by_name.keys()) and (
x == act[0]) and (x == act[-1]))
]:
right_idem = right_dg_algebra.idem_by_name[action[1].name]
gen_by_name['' + x.name + ''].add_idems(left_idem, right_idem)
arrows = Bunch_of_arrows([])
for y in generators:
for action in Fuk.a_inf_actions:
if (len(action) == 3
and (action[0].name in left_dg_algebra.idem_by_name.keys())
and (y == action[1]) and (y == action[-1])):
continue
if (len(action) == 3 and
(action[1].name in right_dg_algebra.idem_by_name.keys())
and (y == action[0]) and (y == action[-1])):
continue
if check_validity(y, action):
index_of_y = action[:-1].index(y)
tuple_from_left = tuple([
(lambda z: left_dg_algebra.gen_by_name[z.name])(z)
for z in action[:index_of_y]
])
tuple_from_right = tuple([
(lambda z: right_dg_algebra.gen_by_name[z.name])(z)
for z in action[index_of_y + 1:-1]
])
arrows[(tuple_from_left, gen_by_name['' + y.name + ''],
tuple_from_right,
gen_by_name['' + action[-1].name + ''])] += 1
return AA_bimodule(gen_by_name,
arrows,
left_dg_algebra,
right_dg_algebra,
name='AA_from_Fuk',
to_check=True)
