def identityDD(pmc, idem_size = None):
"""Returns the identity type DD structure for a given PMC."""
if idem_size is None:
idem_size = pmc.genus
n = pmc.n
pmcopp = pmc.opp()
alg1 = pmc.getAlgebra(idem_size = idem_size)
alg2 = pmcopp.getAlgebra(idem_size = 2*pmc.genus - idem_size)
ddstr = SimpleDDStructure(F2, alg1, alg2)
idems = pmc.getIdempotents(idem_size)
idem_pairs = [(idem, idem.opp().comp()) for idem in idems]
chord_pairs = [(Strands(pmc, [(i, j)]), Strands(pmcopp, [(n-1-j, n-1-i)]))
for i in range(n) for j in range(i+1, n)]
ddstr = DDStrFromChords(alg1, alg2, idem_pairs, chord_pairs)
# Any generator can serve as base_gen
for gen in ddstr.getGenerators():
base_gen = gen
break
ddstr.registerHDiagram(getIdentityDiagram(pmc), base_gen)
return ddstr
def identityDA(pmc):
"""Returns the identity type DA structure for a given PMC."""
alg = pmc.getAlgebra()
dastr = SimpleDAStructure(F2, alg, alg)
idems = pmc.getIdempotents()
idem_to_gen_map = {}
for i in range(len(idems)):
cur_gen = SimpleDAGenerator(dastr, idems[i], idems[i], i)
idem_to_gen_map[idems[i]] = cur_gen
dastr.addGenerator(cur_gen)
alg_gen = alg.getGenerators()
for gen in alg_gen:
if not gen.isIdempotent():
gen_from = idem_to_gen_map[gen.getLeftIdem()]
gen_to = idem_to_gen_map[gen.getRightIdem()]
dastr.addDelta(gen_from, gen_to, gen, (gen,), 1)
# Now add grading. Any generator can serve as base_gen
for gen in dastr.getGenerators():
base_gen = gen
break
dastr.registerHDiagram(getIdentityDiagram(pmc), base_gen)
return dastr