def testIdentityDiagram(self):
pmc_to_test = [splitPMC(1), splitPMC(2), linearPMC(2), antipodalPMC(2)]
pmc_to_test.append(PMC([(0, 2), (1, 6), (3, 5), (4, 7)]))
pmc_to_test += [splitPMC(3), antipodalPMC(4)]
genus_to_size = [2, 6, 20, 70]
for pmc in pmc_to_test:
diagram = getIdentityDiagram(pmc)
self.assertEqual(diagram.getPMCs(), [pmc.opp(), pmc])
expected_size = genus_to_size[pmc.genus - 1]
self.assertEqual(len(diagram.getHFGenerators()), expected_size)
self.assertEqual(len(diagram.getPeriodicDomains()), pmc.genus * 2)
def testAbsGrading(self):
def testOneAlgebra(alg, test_op = True):
abs_gr = AbsZ2Grading(alg)
for gen in alg.getGenerators():
# Test asserts in getAbsGrading
abs_gr.getAbsGrading(gen)
if not test_op:
return
# Test differential and multiplication
for a in alg.getGenerators():
for term in a.diff():
a_gr, da_gr = [abs_gr.getAbsGrading(gen) for gen in a, term]
assert (a_gr - 1) % 2 == da_gr
for a in alg.getGenerators():
for b in alg.getGenerators():
if a * b != 0:
a_gr, b_gr, ab_gr = [abs_gr.getAbsGrading(gen)
for gen in a, b, (a*b).getElt()]
assert (a_gr + b_gr) % 2 == ab_gr
for pmc in [splitPMC(1), splitPMC(2), linearPMC(2)]:
testOneAlgebra(pmc.getAlgebra())
for pmc in [antipodalPMC(2), splitPMC(3)]:
testOneAlgebra(pmc.getAlgebra(), test_op = False)
for (pmc, idem_size) in [(splitPMC(1), 1), (splitPMC(1), 2),
(splitPMC(2), 1), (splitPMC(2), 2)]:
testOneAlgebra(PreStrandAlgebra(F2, pmc, idem_size))
for (pmc, idem_size) in [(splitPMC(2), 3), (splitPMC(2), 4),
(splitPMC(3), 2)]:
testOneAlgebra(PreStrandAlgebra(F2, pmc, idem_size),
test_op = False)
def testGetIntervalOrdering(self):
tests = [(splitPMC(1), [0,1,2]),
(splitPMC(2), [4,5,6,3,0,1,2]),
(antipodalPMC(2), [2,5,0,3,6,1,4]),
(linearPMC(2), [4,0,1,3,5,6,2])]
for pmc, order in tests:
self.assertEqual(_getIntervalOrdering(pmc), order)
def testGeneralOverslideDown(self):
slides_to_test = [
Arcslide(splitPMC(1), 3, 2),
Arcslide(splitPMC(2), 3, 2),
Arcslide(splitPMC(2), 4, 3),
Arcslide(splitPMC(2), 7, 6),
Arcslide(linearPMC(2), 3, 2),
Arcslide(linearPMC(2), 5, 4),
Arcslide(linearPMC(2), 7, 6),
Arcslide(antipodalPMC(2), 5, 4),
Arcslide(antipodalPMC(2), 6, 5),
Arcslide(antipodalPMC(2), 7, 6),
]
for slide in slides_to_test:
print slide
dastr = ArcslideDA(slide).toSimpleDAStructure()
self.assertTrue(dastr.testDelta())
def testOverslideAgreesWithDD(self):
# This is not guaranteed (since there is choice involved in type DD for
# overslides, but appears to work
slides_to_test = [
# General overslides down
Arcslide(splitPMC(1), 3, 2),
Arcslide(splitPMC(2), 3, 2),
Arcslide(splitPMC(2), 4, 3),
Arcslide(splitPMC(2), 7, 6),
Arcslide(linearPMC(2), 3, 2),
Arcslide(linearPMC(2), 5, 4),
Arcslide(linearPMC(2), 7, 6),
Arcslide(antipodalPMC(2), 5, 4),
Arcslide(antipodalPMC(2), 6, 5),
Arcslide(antipodalPMC(2), 7, 6),
# General overslides up
Arcslide(splitPMC(1), 0, 1),
Arcslide(splitPMC(2), 0, 1),
Arcslide(splitPMC(2), 3, 4),
Arcslide(splitPMC(2), 4, 5),
Arcslide(linearPMC(2), 0, 1),
Arcslide(linearPMC(2), 2, 3),
Arcslide(linearPMC(2), 4, 5),
Arcslide(antipodalPMC(2), 0, 1),
Arcslide(antipodalPMC(2), 1, 2),
Arcslide(antipodalPMC(2), 2, 3),
]
for slide in slides_to_test:
dastr = ArcslideDA(slide)
ddstr = dastr.tensorDD(identityDD(slide.end_pmc))
ori_ddstr = slide.getDDStructure()
self.assertTrue(ddstr.compareDDStructures(ori_ddstr))
def testGeneralUnderslideDown(self):
slides_to_test = [
Arcslide(antipodalPMC(2), 1, 0),
Arcslide(antipodalPMC(2), 2, 1),
Arcslide(antipodalPMC(2), 3, 2),
Arcslide(antipodalPMC(2), 4, 3),
Arcslide(PMC([(0, 3), (1, 6), (2, 4), (5, 7)]), 1, 0),
Arcslide(PMC([(0, 5), (1, 3), (2, 6), (4, 7)]), 1, 0),
Arcslide(PMC([(0, 3), (1, 5), (2, 7), (4, 6)]), 1, 0),
Arcslide(PMC([(0, 2), (1, 4), (3, 6), (5, 7)]), 2, 1),
Arcslide(PMC([(0, 2), (1, 4), (3, 6), (5, 7)]), 4, 3),
Arcslide(PMC([(0, 3), (1, 6), (2, 4), (5, 7)]), 2, 1),
Arcslide(PMC([(0, 2), (1, 6), (3, 5), (4, 7)]), 2, 1),
Arcslide(PMC([(0, 3), (1, 5), (2, 7), (4, 6)]), 2, 1),
Arcslide(PMC([(0, 2), (1, 6), (3, 5), (4, 7)]), 5, 4),
Arcslide(PMC([(0, 3), (1, 5), (2, 7), (4, 6)]), 3, 2),
Arcslide(PMC([(0, 5), (1, 3), (2, 6), (4, 7)]), 5, 4),
]
for slide in slides_to_test:
print slide
dastr = ArcslideDA(slide).toSimpleDAStructure()
self.assertTrue(dastr.testDelta())
def testUnderslideAgreesWithDD(self):
slides_to_test = [
# Short underslides down
Arcslide(splitPMC(1), 1, 0),
Arcslide(linearPMC(2), 6, 5),
Arcslide(PMC([(0, 2), (1, 6), (3, 5), (4, 7)]), 1, 0),
# General underslides down
Arcslide(antipodalPMC(2), 1, 0),
Arcslide(PMC([(0, 2), (1, 4), (3, 6), (5, 7)]), 4, 3),
# Short underslides up
Arcslide(splitPMC(1), 1, 2),
Arcslide(linearPMC(2), 1, 2),
Arcslide(PMC([(0, 2), (1, 6), (3, 5), (4, 7)]), 4, 5),
# General underslides up
Arcslide(antipodalPMC(2), 6, 7),
Arcslide(PMC([(0, 3), (1, 6), (2, 4), (5, 7)]), 2, 3),
]
for slide in slides_to_test:
dastr = ArcslideDA(slide)
ddstr = dastr.tensorDD(identityDD(slide.end_pmc))
ori_ddstr = slide.getDDStructure()
self.assertTrue(ddstr.compareDDStructures(ori_ddstr))
def testPrintLocalDAStructure(self):
slide, pmc_map1, pmc_map2 = (
# Uncomment one of the following lines
# Arcslide(splitPMC(2), 2, 1), None, None, # short, down
# Arcslide(splitPMC(2), 2, 3), None, None, # short, up
# Arcslide(antipodalPMC(2), 2, 1), [0,1,2,3,4,6,7], [0,1,3,4,5,6,7],
Arcslide(antipodalPMC(2), 4, 5), [0,1,3,4,5,6,7], [0,1,2,3,4,6,7],
)
local_dastr = ArcslideDA(slide).getLocalDAStructure()
f = open("latex_output.txt", "w")
f.write(beginDoc())
f.write(showDAStructure(local_dastr, pmc_map1, pmc_map2))
f.write(endDoc())
f.close()
def testCreateRowSystem(self):
sign = SignLinAlg(StrandAlgebra(F2, antipodalPMC(2), idem_size = 2,
mult_one = True))
sign.createRowSystem()