def simplify(self, cancellation_constraint = None):
"""Simplify a type DD structure using cancellation lemma.
cancellation_constraint is a function from two generators to boolean,
stating whether they can be cancelled.
"""
# Simplification is best done in terms of coefficients
# Build dictionary of coefficients
arrows = dict()
for gen in self.generators:
arrows[gen] = dict()
bialgebra = TensorDGAlgebra((self.algebra1, self.algebra2))
for gen in self.generators:
for (AGen1, AGen2, MGen), coeff in self.delta_map[gen].items():
if MGen not in arrows[gen]:
arrows[gen][MGen] = E0
arrows[gen][MGen] += TensorGenerator(
(AGen1, AGen2), bialgebra) * coeff
arrows = simplifyComplex(
arrows, default_coeff = E0,
cancellation_constraint = cancellation_constraint)
# Now rebuild the type DD structure
self.generators = set()
self.delta_map = dict()
for x in arrows:
self.generators.add(x)
self.delta_map[x] = E0
for y, coeff in arrows[x].items():
for (a1, a2), ring_coeff in coeff.items():
target_gen = TensorGenerator((a1, a2, y), self.AAtensorM)
self.delta_map[x] += ring_coeff * target_gen
def simplify(self, cancellation_constraint = None):
"""Simplify a type D structure using cancellation lemma."""
# Simplification is best done in terms of coefficients
# Build dictionary of coefficients
arrows = dict()
for gen in self.generators:
arrows[gen] = dict()
for gen in self.generators:
for (AGen, MGen), coeff in self.delta_map[gen].items():
if MGen not in arrows[gen]:
arrows[gen][MGen] = E0
arrows[gen][MGen] += AGen * coeff
arrows = simplifyComplex(
arrows, E0,
cancellation_constraint = cancellation_constraint)
# Now rebuild the type D structure
self.generators = set()
self.delta_map = dict()
for x in arrows:
self.generators.add(x)
self.delta_map[x] = E0
for y, coeff in arrows[x].items():
self.delta_map[x] += coeff * y
# This is a good place to simplify gradings
if hasattr(self, "gr_set"):
new_gr_set = self.gr_set.simplifiedSet()
for gen in self.generators:
self.grading[gen] = self.gr_set.simplifiedElt(self.grading[gen])
self.gr_set = new_gr_set
def simplify(self, cancellation_constraint=None):
"""Simplify a type D structure using cancellation lemma."""
# Simplification is best done in terms of coefficients
# Build dictionary of coefficients
arrows = dict()
for gen in self.generators:
arrows[gen] = dict()
for gen in self.generators:
for (AGen, MGen), coeff in self.delta_map[gen].items():
if MGen not in arrows[gen]:
arrows[gen][MGen] = E0
arrows[gen][MGen] += AGen * coeff
arrows = simplifyComplex(
arrows, E0, cancellation_constraint=cancellation_constraint)
# Now rebuild the type D structure
self.generators = set()
self.delta_map = dict()
for x in arrows:
self.generators.add(x)
self.delta_map[x] = E0
for y, coeff in arrows[x].items():
self.delta_map[x] += coeff * y
# This is a good place to simplify gradings #CB and remove
if hasattr(self, "gr_set"):
new_gr_set = self.gr_set.simplifiedSet()
for gen in self.generators:
self.grading[gen] = self.gr_set.simplifiedElt(
self.grading[gen])
self.gr_set = new_gr_set
