def tensorAAandDD(self, dd_graph):
"""Returns the type DA structure formed by tensoring dd_graph with
self, with self placed at left and dd_graph placed at right.
"""
assert dd_graph.tensor_side == 1
assert dd_graph.algebra1 == self.pmc_alg
alg_opp = self.pmc_alg.opp()
# The generating set for the type DA structure and the dd_graph is the
# same.
result = SimpleDAStructure(F2, dd_graph.algebra2, alg_opp)
ddgen_to_dagen_map = {}
for ddgen in dd_graph.ddgen_node:
cur_gen = SimpleDAGenerator(
result, ddgen.idem2, ddgen.idem1.opp().comp(), str(ddgen))
ddgen_to_dagen_map[ddgen] = cur_gen
result.addGenerator(cur_gen)
univ_digraph = UniversalDiGraph(alg_opp)
for ddgen, d2_pos in dd_graph.ddgen_node.items():
d1_pos = univ_digraph.getInitialNode()
aa_pos = self.homology_node[ddgen.idem1.comp()]
pos = [(d1_pos, d2_pos, aa_pos)]
end_states = self._searchDoubleD(univ_digraph, dd_graph, pos)[0]
for d1_end, d2_end, aa_end in end_states:
gen_from = ddgen_to_dagen_map[ddgen]
gen_to = ddgen_to_dagen_map[d2_end.ddgen]
result.addDelta(gen_from, gen_to, d2_end.sd, tuple(d1_end), 1)
return result
def tensorDDandAA(self, dd_graph):
"""Returns the type DA structure formed by tensoring dd_graph with
self, with dd_graph placed at left and self placed at right.
"""
# Currently very slow, only really work in genus 1 case
assert dd_graph.tensor_side == 2
assert dd_graph.algebra2 == self.pmc_alg.opp()
alg = self.pmc_alg
# The generating set for the type DA structure and the dd_graph is the
# same.
result = SimpleDAStructure(F2, dd_graph.algebra1, alg)
ddgen_to_dagen_map = {}
for ddgen in dd_graph.ddgen_node:
cur_gen = SimpleDAGenerator(
result, ddgen.idem1, ddgen.idem2.opp().comp(), str(ddgen))
ddgen_to_dagen_map[ddgen] = cur_gen
result.addGenerator(cur_gen)
univ_digraph = UniversalDiGraph(alg)
for ddgen, d1_pos in dd_graph.ddgen_node.items():
d2_pos = univ_digraph.getInitialNode()
aa_pos = self.homology_node[ddgen.idem2.comp()]
pos = [(d1_pos, d2_pos, aa_pos)]
end_states = self._searchDoubleD(dd_graph, univ_digraph, pos)[0]
for d1_end, d2_end, aa_end in end_states:
gen_from = ddgen_to_dagen_map[ddgen]
gen_to = ddgen_to_dagen_map[d1_end.ddgen]
result.addDelta(gen_from, gen_to, d1_end.sd, tuple(d2_end), 1)
return result
def azDA(pmc,mult_one = True):
"The type DA module associated to the Auroux-Zarev piece. Input: the alpha pointed matched circle."
algebra = pmc.getAlgebra(mult_one = mult_one)
answer = SimpleDAStructure(F2, algebra, algebra)
#Compute the generators
for a in pmc.getStrandDiagrams(answer.algebra1):
gen = SimpleDAGenerator(answer, a.left_idem.comp(), a.right_idem, a)
answer.addGenerator(gen)
#Terms in the differential coming from the differential on the algebra:
for x in answer.generators:
dx = x.name.diff()
for y in dx.keys():
ygen = SimpleDAGenerator(answer, y.left_idem.comp(), y.right_idem, y)
answer.addDelta(x,ygen,x.idem1.toAlgElt(algebra),list(),dx[y])
#Terms coming from multiplying by algebra elements on the right
for x in answer.generators:
xa = x.name
could_multiply = algebra.getGeneratorsForIdem(left_idem = xa.right_idem)
for b in could_multiply:
if not b.isIdempotent():
xab = xa*b
for y in xab.keys():
ygen = SimpleDAGenerator(answer,y.left_idem.comp(), y.right_idem, y)
answer.addDelta(x,ygen,x.idem1.toAlgElt(algebra),[b,],xab[y])
#Terms coming from differential on CFDD(Id):
chord_pairs = chordPairs(pmc)
for (sigma, rho) in chord_pairs:
for x in algebra.getGeneratorsForIdem(left_idem = rho.right_idem):
xgen = SimpleDAGenerator(answer,x.left_idem.comp(), x.right_idem, x)
rhox = rho*x
for y in rhox.keys():
ygen = SimpleDAGenerator(answer, y.left_idem.comp(), y.right_idem, y)
answer.addDelta(xgen, ygen, sigma, list(),rhox[y])
return answer
