def test_flattenings_from_tetrahedra_shapes_of_manifold():
old_precision = pari.set_real_precision(100)
# real parts need to be equal
# imaginary parts need to be equal up to pi^2/6
p = pari('Pi * Pi / 6')
def is_close(cvol1, cvol2, epsilon):
diff = cvol1 - cvol2
return diff.real().abs() < epsilon and ((diff.imag() % p) < epsilon or
(-diff.imag() % p) < epsilon)
from snappy import OrientableCuspedCensus
for M in (list(OrientableCuspedCensus()[0:10]) +
list(OrientableCuspedCensus()[10000:10010])):
flattening = Flattenings.from_tetrahedra_shapes_of_manifold(M)
flattening.check_against_manifold(M, epsilon=1e-80)
if not is_close(
flattening.complex_volume(),
M.complex_volume(), # returns only double precision
epsilon=1e-13):
raise Exception("Wrong volume")
# test high precision
M = ManifoldGetter("5_2")
flattening = Flattenings.from_tetrahedra_shapes_of_manifold(M)
flattening.check_against_manifold(M, epsilon=1e-80)
if not is_close(
flattening.complex_volume(),
pari(
'2.828122088330783162763898809276634942770981317300649477043520327258802548322471630936947017929999108 - 3.024128376509301659719951221694600993984450242270735312503300643508917708286193746506469158300472966*I'
),
epsilon=1e-80):
raise Exception("Wrong volume")
pari.set_real_precision(old_precision)
def main(verbose=False, doctest=True):
print("Testing in sage:", _within_sage)
print("Testing in regina:", test_regina)
if doctest:
print("Running doctests...")
run_doctests(verbose)
print()
if test_regina:
print("Testing that regina agrees with snappy obstruction classes")
test_num_obstruction_class_match()
if not test_regina:
print("Testing Flattenings.from_tetrahedra_shapes_of_manifold...")
test_flattenings_from_tetrahedra_shapes_of_manifold()
compute_solutions = False
if '--compute' in sys.argv:
compute_solutions = True
if test_regina and not compute_solutions:
print("regina testing requires --compute")
sys.exit(1)
old_precision = pari.set_real_precision(100)
print("Testing induced representation...")
test_induced_representation()
print("Testing induced SL(4,C) representation...")
test_induced_sl4_representation()
print("Running manifold tests for generalized obstruction class...")
testGeneralizedObstructionClass(compute_solutions)
if not test_regina:
print("Testing RUR for m052__sl3_c0.rur")
testMapleLikeRur()
print("Testing numerical solution retrieval method...")
testNumericalSolutions()
print("Testing geometricRep...")
testGeometricRep(compute_solutions)
if _within_sage:
print("Testing in sage command line...")
testSageCommandLine()
print("Running manifold tests...")
### Test for a non-hyperbolic manifold
cvols = [ # Expected Complex volumes
pari('0')
]
test__3_1__2 = (
ManifoldGetter("3_1"), # Manifold
2, # N = 2
cvols, # expected complex volumes
False) # No non-zero dimensional components
### Test for 4_1, amphichiral, expect zero CS
cvols = [ # Expected Complex volumes
2 * vol_tet
]
test__4_1__2 = (
ManifoldGetter("4_1"), # Manifold
2, # N = 2
cvols, # expected complex volumes
False) # expect non-zero dimensional components
### N = 3
cvols = [ # Expected Complex volumes
pari(0), 2 * 4 * vol_tet
]
test__4_1__3 = (
ManifoldGetter("4_1"), # Manifold
3, # N = 3
cvols, # expected complex volumes
False) # expect non-zero dimensional components
### N = 4
cvols = [ # Expected Complex volumes
2 * 10 * vol_tet,
pari(
'8.355502146379565994303773768814775354386025704336131822255670190659042090899812770381061831431114740 - 0.7836375483069721973241186952472609466029570462055317453592429525294418326815666413123016980810744089*I'
),
pari(
'7.327724753417752120436828119459072886193194994253377074131984956974104158210038155834852103408920850'
),
pari(
'4.260549384199988638895626360783795200167603461491438308495654794999595513880915593832371886868625127 + 0.1361281655780504266700965891301086052404492485996004213292764928775628027210816440355745847599247091*I'
),
pari(
'3.276320849776062968038680855240250653840691843746753028019901828179320044237305241434903501877259688 + 0.03882948511714102091208888807575164800651790439786747350853616215556190252003379560451275222880494392*I'
),
pari(
'3.230859569867059515989136707781810556962637199799080875515780771251800351524537196576706995730457048'
)
]
# amphicheiral, so complex volumes should appear in pairs
cvols = cvols + [cvol.conj() for cvol in cvols]
test__4_1__4 = (
ManifoldGetter("4_1"), # Manifold
4, # N = 2
cvols, # expected complex volumes
True) # expect non-zero dimensional components
### Test for 5_2, expect non-trivial CS
### Number field has one real embedding with non-trival CS
### And one pair of complex embeddings with non-trivial CS
cvols = [ # Expected Complex volumes
pari(
'+ 1.113454552473924010022656943451126420312050780921075311799926598907813005362784871512051614741669817*I'
),
pari(
'2.828122088330783162763898809276634942770981317300649477043520327258802548322471630936947017929999108 - 3.024128376509301659719951221694600993984450242270735312503300643508917708286193746506469158300472966*I'
)
]
test__5_2__2 = (
ManifoldGetter("5_2"), # Manifold
2, # N = 2
cvols, # expected complex volumes
False) # expect no non-zero dimensional components
### m015 which is isometric to 5_2
### This example is also appearing on the website
cvols = [ # Expected Complex volumes
pari(
'+ 0.4033353624187061319128390413376061001062613536896471642214173008084760853375773296525240139108027276*I'
),
pari(
'- 0.4809839906489832693266177261335698864086465799360940660069682924787703897584631354526802428925968492*I'
),
pari(
'+ 0.6579736267392905745889660666584100756875799604827193750942232917480029881612803495334515602479034826*I'
),
pari(
'- 0.6579736267392905745889660666584100756875799604827193750942232917480029881612803495334515602479034826*I'
),
pari(
'6.332666642499251344664115407516762513592210378740462564820401485540596854320653136703448734707430999 + 0.6207993522147601522797880626542095445563442737585756367570704642807656925328117720905524433544779886*I'
),
pari(
'11.31248835332313265105559523710653977108392526920259790817408130903521019328988652374778807171999643 - 0.5819750380996215835728987202562276514051516606353521858642949684456185403223688691904743288635809278*I'
)
]
test__m015__3 = (
ManifoldGetter("m015"), # Manifold
3, # N = 3
cvols, # expected volumes
False) # expect no non-zero dimensional components
### Test for m135
### Ptolemy Variety has one non-zero dimensional component
cvols = [ # Expected Complex volumes
pari(
'3.66386237670887606021841405972953644309659749712668853706599247848705207910501907791742605170446042499429769047678479831614359521330343623772637894992 + 4.93480220054467930941724549993807556765684970362039531320667468811002241120960262150088670185927611591201295688701157203888617406101502336380530883900*I'
)
]
test__m135__2 = (
ManifoldGetter("m135"), # Manifold
2, # N = 2
cvols, # expected volumes
True) # expect a non-zero dimensional component
### Test for s000
### Number field has one real embedding with non-trival CS
### And two complex embeddings with non-trivial CS
cvols = [ # Expected Complex volumes
pari(
'3.296902414326637335562593088559162089146991699269941951875989849869324250860299302482577730785960256 + 0.4908671850777469648812718224097607532197026477625119178645010117072332396428578681905186509136879130*I'
),
pari(
'2.270424126345803402614201085375714538056567876339790536089272218685353247084791707534069624462050547 - 0.4107712000441024931074403997367404299427214514732528671142771778838924102954454212055598588991237349*I'
),
pari(
'0.8061270618942289713279174295562193428686541442399728535727328789432842090598108984711933183445551654 - 0.08009598503364447177383142267302032327698119628925905075022383382334082934741244698495879201456417902*I'
)
]
test__s000__2 = (
ManifoldGetter("s000"), # Manifold
2, # N = 2
cvols, # expected complex volumes
False) # expect non-zero dimensional components
### Test for v0000
### This also tests the case of having more than one (here two)
### cusps
cvols = [ # Expected Complex volumes
pari(
'3.377597408231442496961257171798882829176020069714519460350380851901055794392493960110119513942153791 + 0.3441889979504813554136570264352067044809511501367282461849580661783699588789118851518262199077361427*I'
),
pari(
'1.380586178282342062845519278761524817753278777803238623999221385504661588501960339341800843520223671 + 0.06704451876157525370444676522629959282378632516497136324893149116413190872188833330658100524720353406*I'
)
]
test__v0000__2 = (
ManifoldGetter("v0000"), # Manifold
2, # N = 2
cvols, # expected complex volumes
False) # expect non-zero dimensional components
### Test for t00000
### This also tests the case of having more than one (here two)
### cusps
cvols = [ # Expected Complex volumes
pari(
'1.801231981344929412976326011175173926741195258454700704383597306674496002389749200442131507334117933 - 0.5490336239273931479260463113980794374780078424892352183284248305887346671477869107359071072271699046*I'
),
pari(
'3.434540885902563701250335473165274495380101665474171663779718033441916041515556280543077990039279103 - 0.2258335622748003900958464044389939976977579115267501160859900439335840118881246299028850924706341411*I'
),
pari(
'2.781430316400743786576311128801205534982324055570742403430395886754122643539081915302290955978507418 - 0.1135489194824466736456241002458946823709871812077727407261274931826622024508518397031626436088171650*I'
),
pari(
'0.6223401945262803853426860070209275705147832620602921139947907237662088851273537136119288228151713940 + 0.06594907226052699343130923275995552293727798462035885627276325301997714628516294342514039299674185799*I'
)
]
test__t00000__2 = (
ManifoldGetter("t00000"), # Manifold
2, # N = 2
cvols, # expected complex volumes
False) # expect non-zero dimensional components
### Check a big link
### Also an example from the website
magma_file_name = os.path.join(
testing_files_directory, 'DT_mcbbiceaibjklmdfgh__sl2_c0.magma_out.bz2')
magma_file = bz2.BZ2File(magma_file_name, 'r').read().decode('ascii')
M = get_manifold(magma_file)
cvols = [ # Expected complex volumes
pari(
'+ 0.7322614121694386973039290771667413108310290182470824825342304051284154933661673470336385959164416421*I'
),
pari(
'+ 0.6559698855197901194421542799077526971594537987318704612418448259078988296037785866985260815280619566*I'
),
pari(
'+ 0.2247361398283578756297647616373802721002644994163825408181485469244129408530290519698535075998585820*I'
),
pari(
'- 0.2027422644881176424634704044404281277501368039784045126270573672316679046996639567741375438621581585*I'
),
pari(
'- 0.5165804080147074827389022895582362309867052040022748905555220755792330887283843134684241943604049933*I'
),
pari(
'- 0.6947370811282851128538476965898593866158843479399924653138487625940910866865914821776342801425993440*I'
),
pari(
'0.5540930202692745891960825388466975825977590423995169588735760161940190344506116205300980253997539517 + 0.4068295289298811130481298436200768517194764143946539028521976313233755795250413907401491036923026977*I'
),
pari(
'1.107573735539315638081527574351339252286206152514359620788778723352858972530297840033883810630372795 - 0.5969698437345460065934215233692845699554045087887375026603956452869723823599605032061849791769108861*I'
),
pari(
'2.930037687027569312623189945781681052278144410906236798293622026086427321638842320557907595726492995 + 0.3289208659101980133472847400704889056725461985759517831954390384444124055329869355087545294359968288*I'
),
pari(
'3.125178220789358723184584053682215536632004045535766511323850625359539915401419555941250425818672532 - 0.3045460696329709194663539414577718771554887499547088593863438059068830455709928110292357447645590516*I'
),
pari(
'4.421889017241566419690868074785716366646707154662264036268588279252613543336245268108457201245088608 + 0.6139898590804745843458673335891956572719167936270349811550161917334120397060146434004694625036091183*I'
),
pari(
'5.114841460302400721438106628468470523914735245629326811523719108779649554034504844499930511307337652 - 0.05922105399342951023220969900445652084832276940306885833938997476066822991673855494231393721309130829*I'
),
pari(
'6.222431566185758097679258799420253341029081314309961806975091338751806200485840320374430035873760649 - 0.4263260019368806638768168211894976779995931712761356294379973306148491137274105197747275282097587014*I'
),
pari(
'9.266495487232495996324305783134684559241087943387258046228284813849170601366096263130956023317432143 + 0.03172800820055749085258729263585301130211316529809616828980203075096987437740390637996179595789268661*I'
),
pari(
'11.33736073062520808632824769184286601589152410942391317127856679767752551409389094871647937428783709 - 0.5767482750608833159526763068340021498631801513808564565980389960163842898485087439099502988183940450*I'
),
pari(
'12.48005937399413830153052941177305767103579608241815594942757035041902652992672347868089986739774396 + 0.4828891402943609873677952178777231024869262986704386628808130740557195704279966401921665132533128189*I'
)
]
test__morwen_link__2 = (
M, # Manifold
2, # N = 2
cvols, # expected complex volumes
False) # expect no non-zero dimensional components
test_cases = [
test__3_1__2, test__4_1__2, test__5_2__2, test__m135__2, test__s000__2,
test__v0000__2, test__t00000__2, test__morwen_link__2, test__4_1__3,
test__m015__3, test__4_1__4
]
pari.set_real_precision(old_precision)
for manifold, N, cvols, expect_non_zero_dim in test_cases:
print("Checking for", manifold.name(), "N = %d" % N)
testComputeSolutionsForManifold(
manifold,
N,
compute_solutions=compute_solutions,
baseline_cvolumes=cvols,
expect_non_zero_dimensional=expect_non_zero_dim)
def testMapleLikeRur():
M = ManifoldGetter("m052")
p = M.ptolemy_variety(3, 0)
sols = parse_solutions(
bz2.BZ2File(
os.path.join(testing_files_rur_directory,
p.filename_base() + '.rur.bz2'),
'r').read().decode('ascii'))
assert len(sols) == 4
assert [sol.dimension for sol in sols] == [0, 0, 0, 1]
sols.check_against_manifold()
cross_ratios = sols.cross_ratios()
cross_ratios.check_against_manifold()
assert sols.number_field()[0:3] == [
pari('3*x^5 - 3*x^4 + 7*x^3 - 11*x^2 + 6*x - 1'),
pari('x^5 - 3*x^4 + x^3 + x^2 + 2*x - 1'),
pari(
'29987478321*x^50 + 79088110854*x^49 + 146016538609*x^48 + 168029123283*x^47 + 195292402206*x^46 + 249251168329*x^45 + 342446347782*x^44 + 342999865332*x^43 + 169423424001*x^42 - 273623428749*x^41 - 913797131672*x^40 - 1673817412888*x^39 - 2346916788229*x^38 - 2864053668977*x^37 - 3089416575581*x^36 - 3067233025932*x^35 - 2754270808082*x^34 - 2290714735763*x^33 - 1691408820544*x^32 - 1128722560267*x^31 - 616892765351*x^30 - 264545491200*x^29 - 28918206196*x^28 + 65364520067*x^27 + 95427288700*x^26 + 68490651548*x^25 + 40427041992*x^24 + 8765319150*x^23 - 5368633716*x^22 - 14060382008*x^21 - 12638294169*x^20 - 10728252922*x^19 - 6615567685*x^18 - 4275928015*x^17 - 2168416333*x^16 - 1279131210*x^15 - 627103252*x^14 - 403508975*x^13 - 222568645*x^12 - 147840406*x^11 - 81185759*x^10 - 46353128*x^9 - 21481295*x^8 - 9738710*x^7 - 3418080*x^6 - 1145883*x^5 - 254870*x^4 - 44273*x^3 - 565*x^2 + 2925*x + 487'
)
]
sols[0].multiply_terms_in_RUR().check_against_manifold()
sols[0].multiply_and_simplify_terms_in_RUR().check_against_manifold()
sol_pur = sols[0].to_PUR()
sol_pur.check_against_manifold()
cross_ratios[0].multiply_terms_in_RUR().check_against_manifold()
cross_ratios[0].multiply_and_simplify_terms_in_RUR(
).check_against_manifold()
cross_ratio_pur = cross_ratios[0].to_PUR()
old_precision = pari.set_real_precision(60)
sols.numerical().check_against_manifold(epsilon=1e-50)
sols.numerical().cross_ratios().check_against_manifold(epsilon=1e-50)
cross_ratios.numerical().check_against_manifold(epsilon=1e-50)
sol_pur.numerical().check_against_manifold(epsilon=1e-50)
cross_ratio_pur.numerical().check_against_manifold(epsilon=1e-50)
expected_cvols = [
pari('-0.78247122081308825152609555186377860994691907952043*I'),
pari('-0.72702516069067618470921136741414357709195254197557*I'),
pari('-0.68391161907531103571619313072177855528960855942240*I'),
pari('-0.56931748709124386099667356226108260894423337722116*I'),
pari('-0.51896820855866930434990357344936169357239176536016*I'),
pari('-0.51572066892431201326839038002795162651553325964817*I'),
pari('-0.43203716183360487568405407399314603426109522825732*I'),
pari('-0.36010613661069069469455670342059458401551240819467*I'),
pari('-0.30859303742385031407330927444373574273739067157054*I'),
pari('-0.026277944917886842767978680898127354858352285383691*I'),
pari('0.0248303748672046904847696634069363554930433748091423*I'),
pari('0.099321499468818761939078653627745421972173499236569*I'),
pari('0.10014328074298669302370298811922885078531513167037*I'),
pari('0.26650486587884614841887735378855648561147071193673*I'),
pari('0.28149146457238928303062789829916587391163953396165*I'),
pari('0.31647148942727816629296211895022802382665885673450*I'),
pari('0.43039483620012844786769013182478937263427654168349*I'),
pari('0.69353686619303521491910998831602468798059163569136*I'),
pari(
'0.54467996179900207437301145027949601489757288486931 - 0.63094967104322016076042058145264363658770535751782*I'
),
pari(
'2.01433658377684250427882647709079550884158567943161 - 0.49992935281631459421725377501106345869263727223108*I'
),
pari(
'2.5032821968844998826603550693091792509880846739036 - 0.26075155111137757913541371074811175755130345738250*I'
),
pari(
'2.9278315480495821855974883510454022661942898386197 + 0.19505171376983273645226251276721729342140990274561*I'
),
pari(
'3.3588310807753976907039310005151876035685073404636 - 0.59541514146929793136574297969820009572263815053647*I'
),
pari(
'3.5588560966663108341691237279801529977950803397723 - 0.65837426652607617086885854703688633418948363301344*I'
),
pari(
'4.3805052030906555151826572095707468309691641904106 - 0.53144574794454652850763996164828079301339638663719*I'
),
pari(
'5.2749826604398957699736902920967737019972675833349 + 0.72096167973012423863761073630614422902154219296456*I'
),
pari(
'5.5615522795375430947143486065492921841179004148132 - 0.28072986489486989042244876551205538542949560983728*I'
),
pari(
'8.0573463351073700171153059083631820353663427177264 - 0.35478334441703194039659993339822864555159918771765*I'
),
pari(
'13.232966218921677854715244009824382732164844146922 + 0.13989736389653471530824083989755826875684215156147*I'
)
]
expected_cvols = expected_cvols + [-a.conj() for a in expected_cvols]
cvols = sols.complex_volume_numerical().flatten(2) # Include witnesses
check_volumes(cvols, expected_cvols, epsilon=1e-40)
vols = sols.volume_numerical().flatten(2) # Include witnesses
check_volumes(vols,
expected_cvols,
check_real_part_only=True,
epsilon=1e-40)
pari.set_real_precision(old_precision)
def testSolutionsForManifold(M,
N,
solutions,
baseline_cvolumes=None,
expect_non_zero_dimensional=None,
against_geometric=True):
old_precision = pari.set_real_precision(100)
# check solutions exactly
found_non_zero_dimensional = False
numerical_solutions = []
numerical_cross_ratios = []
numerical_cross_ratios_alt = []
for solution in solutions:
if isinstance(solution, ptolemy.component.NonZeroDimensionalComponent):
# encountered non-zero dimensional component
found_non_zero_dimensional = True
else:
assert solution.N() == N
assert solution.num_tetrahedra() == M.num_tetrahedra()
# check exact solutions
solution.check_against_manifold(M)
# compute numerical solutions and cross ratios
for numerical_solution in solution.numerical():
numerical_solutions.append(numerical_solution)
numerical_cross_ratios.append(
numerical_solution.cross_ratios())
# check exact cross ratios
cross_ratios = solution.cross_ratios()
if not test_regina:
cross_ratios.check_against_manifold(M)
assert cross_ratios.N() == N
# compute numerical cross ratios alternatively
# (above we converted exact Ptolemy's to numerical and then
# converted to cross ratio, here we first compute cross ratios
# exactly and then convert to numerical)
numerical_cross_ratios_alt += cross_ratios.numerical()
# check we encountered non-zero dimensional component if that's
# expected
if not expect_non_zero_dimensional is None:
assert expect_non_zero_dimensional == found_non_zero_dimensional
# check the numerical solutions against the manifold
for s in numerical_solutions:
s.check_against_manifold(M, epsilon=1e-80)
# check that they make a flattening
if not test_regina:
s.flattenings_numerical().check_against_manifold(M, epsilon=1e-80)
if not test_regina:
for s in numerical_cross_ratios:
s.check_against_manifold(M, epsilon=1e-80)
for s in numerical_cross_ratios_alt:
s.check_against_manifold(M, epsilon=1e-80)
# compute complex volumes and volumes
complex_volumes = [
s.complex_volume_numerical() for s in numerical_solutions
]
volumes = [s.volume_numerical() for s in numerical_cross_ratios]
# there should be equally many
assert len(complex_volumes) == len(volumes)
# and real part of cvol should be equal to vol
for vol, cvol in zip(volumes, complex_volumes):
diff = vol - cvol.real()
assert diff.abs() < 1e-80
# volumes from cross ratios computed the different way
volumes_alt = [s.volume_numerical() for s in numerical_cross_ratios_alt]
# volumes should be equal
assert len(volumes) == len(volumes_alt)
volumes.sort(key=float)
volumes_alt.sort(key=float)
for vol1, vol2 in zip(volumes, volumes_alt):
assert (vol1 - vol2).abs() < 1e-80
if against_geometric and not test_regina:
if M.solution_type() == 'all tetrahedra positively oriented':
geom_vol = M.volume() * (N - 1) * N * (N + 1) / 6
assert True in [abs(geom_vol - vol) < 1e-11 for vol in volumes]
# check that complex volumes match baseline volumes
if not baseline_cvolumes is None:
check_volumes(complex_volumes, baseline_cvolumes)
pari.set_real_precision(old_precision)