def restrictToMultA(self, start, end):
"""Restrict actions to those with multiplicity in the interval
(start, end). Here start and end specify points on the PMC. For example,
start, end = 0, pmc.n-1 will not change the action. Returns the new type
DA structure without changing the original structure.
"""
translate_dict = dict()
dastr = SimpleDAStructure(F2, self.algebra1, self.algebra2,
self.side1, self.side2)
for gen in self.generators:
translate_dict[gen] = SimpleDAGenerator(
dastr, gen.idem1, gen.idem2, gen.name)
dastr.addGenerator(translate_dict[gen])
mult_len = self.algebra1.pmc.n - 1
for (gen_from, coeffs_a), target in self.da_action.items():
total_mult = sumColumns([coeff.multiplicity for coeff in coeffs_a],
mult_len)
if all([total_mult[i] <= 0
for i in range(0, start) + range(end, mult_len)]):
for (coeff_d, gen_to), ring_coeff in target.items():
dastr.addDelta(translate_dict[gen_from],
translate_dict[gen_to],
coeff_d, coeffs_a, ring_coeff)
return dastr
def toStrWithMultA(self, mult_a):
"""Print all arrows with the given multiplicities on the D side."""
result = "Type DA Structure.\n"
for (gen_from, coeffs_a), target in self.da_action.items():
total_mult = sumColumns([coeff.multiplicity for coeff in coeffs_a],
len(mult_a))
if mult_a == total_mult:
result += "m(%s; %s) = %s\n" % (gen_from, coeffs_a, target)
return result
def compare_arrow(arrow1, arrow2):
gen_from1, coeffs_a1, coeff_d1, gen_to1 = arrow1
gen_from2, coeffs_a2, coeff_d2, gen_to2 = arrow2
def compare_mult(mult1, mult2):
if sum(mult1) != sum(mult2):
return sum(mult1) - sum(mult2)
mult1, mult2 = list(reversed(mult1)), list(reversed(mult2))
if mult1 < mult2:
return -1
if mult1 > mult2:
return 1
return 0
mult_d1, mult_d2 = coeff_d1.multiplicity, coeff_d2.multiplicity
if compare_mult(mult_d1, mult_d2) != 0:
return compare_mult(mult_d1, mult_d2)
if len(coeff_d1.strands) != len(coeff_d2.strands):
return len(coeff_d1.strands) - len(coeff_d2.strands)
mult_a1 = sumColumns([coeff.multiplicity for coeff in coeffs_a1], n1-1)
mult_a2 = sumColumns([coeff.multiplicity for coeff in coeffs_a2], n2-1)
return compare_mult(mult_a1, mult_a2)