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hdiagramtest.py
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hdiagramtest.py
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"""Unit test for hdiagram.py"""
from hdiagram import *
from hdiagram import _Point, _Segment, _OrientedSegment, _Path, _Cell, \
_Domain, _OneChain
from arcslide import Arcslide
from cobordism import Cobordism
from cobordism import LEFT
from pmc import antipodalPMC, linearPMC, splitPMC
import unittest
class OrientedSegmentTest(unittest.TestCase):
def testOrientedSegment(self):
"""Testing functions in OrientedSegment."""
p1 = _Point(1)
p2 = _Point(2)
seg = _Segment(12, p1, p2)
segp = seg.oseg()
segn = segp.opp()
self.assertEqual(segp.start, p1)
self.assertEqual(segp.end, p2)
self.assertEqual(segn.start, p2)
self.assertEqual(segn.end, p1)
self.assertEqual(segp.toOneChain(), {seg : 1})
self.assertEqual(segn.toOneChain(), {seg : -1})
class PathTest(unittest.TestCase):
def setUp(self):
self.n = 10
self.pts = [_Point(i) for i in range(self.n)]
self.segs = [_Segment(i, self.pts[i], self.pts[(i+1)%self.n])
for i in range(self.n)]
self.osegs = [seg.oseg() for seg in self.segs]
self.osegsr = [seg.oseg().opp() for seg in self.segs]
self.loopseg = _Segment("loop", self.pts[0], self.pts[0])
self.oloopseg = self.loopseg.oseg()
# These should construct valid paths
self.path1 = _Path([], "empty")
self.path2 = _Path([self.oloopseg], "small_loop", True)
self.path3 = _Path(self.osegs[0:-1], "straight")
self.path4 = _Path(self.osegs, "loop", True)
self.path5 = _Path(self.osegs*2, "twoloops")
self.path6 = _Path(reversed(self.osegsr), "opploop", True)
def testPathValidity(self):
"""Testing the validity checks in Path."""
# Some FAIL tests
self.assertRaises(ValueError, _Path,
self.osegs[0:1] + self.osegs[2:])
self.assertRaises(ValueError, _Path,
self.osegs[0:-1], "notloop", True)
self.assertRaises(ValueError, _Path, self.osegsr)
def testOpp(self):
"""Testing the opp function in path."""
self.assertEqual(self.path1.opp("empty"), self.path1)
self.assertNotEqual(self.path2.opp("small_loop"), self.path2)
self.assertEqual(self.path4.opp("opploop"), self.path6)
def testToOneChain(self):
"""Testing toOneChain function in Path."""
self.assertEqual(list(self.path1.toOneChain().values()), [])
self.assertEqual(list(self.path5.toOneChain().values()), [2]*self.n)
self.assertEqual(list(self.path6.toOneChain().values()), [-1]*self.n)
class CellTest(unittest.TestCase):
def testCell(self):
"""Testing functions in Cell."""
pts = [_Point(i) for i in range(3)]
segs = [_Segment("0", pts[0], pts[1]),
_Segment("1", pts[1], pts[0]),
_Segment("2", pts[2], pts[2])]
cell1 = _Cell("c1", _Path([segs[0].oseg(), segs[1].oseg()],
iscycle = True))
cell2 = _Cell("c2", [_Path([segs[0].oseg(), segs[1].oseg()],
iscycle = True),
_Path([segs[2].oseg()], iscycle = True)])
self.assertEqual(cell1.toDomain(), {cell1 : 1})
self.assertEqual(cell1.bdOneChain(), {segs[0]:1, segs[1]:1})
self.assertEqual(cell2.bdOneChain(), {segs[0]:1, segs[1]:1, segs[2]:1})
class DomainTest(unittest.TestCase):
def testDiff(self):
"""Testing diff function in Domain."""
pts = [_Point(i) for i in range(4)]
segs = [_Segment("0", pts[0], pts[1]),
_Segment("1", pts[1], pts[2]),
_Segment("2", pts[2], pts[0]),
_Segment("3", pts[1], pts[3]),
_Segment("4", pts[3], pts[0])]
cell1 = _Cell("c1", _Path([seg.oseg() for seg in segs[0:3]],
iscycle = True))
cell2 = _Cell("c2", _Path([seg.oseg() for seg in segs[0:1]+segs[3:]],
iscycle = True).opp())
domain1 = cell1.toDomain() + cell2.toDomain()
self.assertEqual(domain1.diff(),
{segs[1]:1, segs[2]:1, segs[3]:-1, segs[4]:-1})
class DiagramBuildTest(unittest.TestCase):
def testDiagramFromCycleInfo(self):
"""Testing the function diagramFromCycleInfo."""
# A standard diagram for solid torus
diagram1 = diagramFromCycleInfo("Solid torus",
num_interior_point = 1, length_border = [4],
alpha_arcs = [[(0,0),0,(0,2)], [(0,1),(0,3)]],
beta_cycles = [[0]], crossing_orientation = [-1])
# A standard diagram for the identity cobordism
diagram2 = diagramFromCycleInfo("Identity cobordism",
num_interior_point = 4, length_border = [4,4],
alpha_arcs = [[(0,0),3,(0,2)], [(0,1),1,(0,3)],
[(1,0),0,(1,2)], [(1,1),2,(1,3)]],
beta_cycles = [[0,1],[2,3]], crossing_orientation = [1,-1,1,-1])
# A standard diagram for the anti-braid resolution
diagram3 = diagramFromCycleInfo("Antibraid resolution",
num_interior_point = 3, length_border = [4,4],
alpha_arcs = [[(0,0),2,(0,2)], [(0,1),(0,3)],
[(1,0),(1,2)], [(1,1),0,1,(1,3)]],
beta_cycles = [[0], [1,2]], crossing_orientation = [1,1,-1])
# Uncomment to see full printout of diagrams
# print repr(diagram1), repr(diagram2), repr(diagram3)
class CommonDiagramsTest(unittest.TestCase):
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 testArcslideDiagram(self):
slide_to_test = [Arcslide(splitPMC(2), 4, 3),
Arcslide(splitPMC(2), 2, 3)]
for slide in slide_to_test:
diagram = getArcslideDiagram(slide)
self.assertEqual(diagram.getPMCs(),
[slide.start_pmc.opp(), slide.end_pmc])
self.assertEqual(len(diagram.getHFGenerators()), 8)
periodic_domains = diagram.getPeriodicDomains()
self.assertEqual(len(periodic_domains), 4)
for domain in periodic_domains:
alpha_bd = diagram.restrictOneChain(domain.diff(), ALPHA)
self.assertEqual(diagram.restrictZeroChain(alpha_bd.diff()), 0)
def testHandlebodyDiagram(self):
diagram = getInfFrameDiagram(2)
self.assertEqual(diagram.getPMCs(), [splitPMC(2)])
self.assertEqual(len(diagram.getHFGenerators()), 1)
periodic_domains = diagram.getPeriodicDomains()
self.assertEqual(len(periodic_domains), 2)
for domain in periodic_domains:
alpha_bd = diagram.restrictOneChain(domain.diff(), ALPHA)
self.assertEqual(diagram.restrictZeroChain(alpha_bd.diff()), 0)
diagram2 = getPlatDiagram(2)
# Uncomment to see full printout of diagrams
# print repr(diagram), repr(diagram2)
def testAdmHandlebodyDiagram(self):
diagram = getZeroFrameAdmDiagram(2)
# Uncomment to see full printout of diagrams
# print repr(diagram)
def testSimpleCobordismDiagram(self):
diagram = getSimpleCobordismDiagram(splitPMC(1), 1)
# Uncomment to see full printout of diagrams
# print repr(diagram)
def testGetCobordismDiagramLeft(self):
for c_pair in [0, 2, 3]:
diagram = getCobordismDiagramLeft(Cobordism(2, c_pair, LEFT))
# Uncomment to see full printout of diagrams
# print repr(diagram)
def testConnectingDomain(self):
diagram = getIdentityDiagram(splitPMC(2))
gens = diagram.getHFGenerators()
for x in gens:
for y in gens:
domain = diagram.getConnectingDomain(x, y)
self.assertTrue(domain is not None)
# Alpha curves go from x to y
alpha_bd = diagram.restrictOneChain(domain.diff(), ALPHA)
self.assertEqual(diagram.restrictZeroChain(alpha_bd.diff()),
y.toZeroChain() - x.toZeroChain())
self.assertEqual(diagram.getMaslov(domain, x, y), 0)
gr = diagram.getBigGrading(domain, x, y)
self.assertEqual(gr[0] * gr[1].Ropp(), 0)
class ComputeGradingTest(unittest.TestCase):
def testDDBigGrading(self):
# Just check it will compute grading without raising errors.
# Correctness of grading is crossed checked with DD structures.
diagram = getIdentityDiagram(splitPMC(2))
base_gen = diagram.getHFGenerators()[0]
gr_set, gr_vals = diagram.computeDDGrading(base_gen)
if __name__ == "__main__":
unittest.main()