def test_satisfy_inter(self): v_space = VectorSpace(QQ,4) sub = v_space.subspace([[1,-1,1,1],[2,-3,4,5]]) comp = orth_complement(v_space,sub) zero = v_space.subspace([v_space.zero()]) inter = sub.intersection(comp) self.assertEqual(zero,inter)
def homology(self,varient="complement",*args):
hom = {}
cc = self.chain_complex(varient,(-1,self.poly_ring.ngens()+1),*args)
#Some need wider return range
for i in range(self.poly_ring.ngens()+1):
vs_am = VectorSpace(QQ,len(cc[i]))
if len(cc[i])==0:
hom[i] = []
continue
if len(cc[i-1])!=0:
d_im = []
for b in cc[i-1]:
d_b = self.differential(b,varient,*args)
d_im.append(lift_to_basis(d_b,cc[i]))
img = vs_am.subspace(d_im)
else:
img = vs_am.subspace([vs_am.zero()])
if len(cc[i+1])!=0:
d_ker = []
for b in cc[i]:
d_b = self.differential(b,varient,*args)
d_ker.append(lift_to_basis(d_b,cc[i+1]))
ker = (matrix(QQ,d_ker)).left_kernel()
else:
ker = vs_am
quo = ker.quotient(img)
hom[i] = []
for b in quo.basis():
vec = quo.lift(b)
part_sum = LogarithmicDifferentialForm.make_zero(i,self)
for c,f in zip(vec,cc[i]):
part_sum = part_sum + c*f
hom[i].append(part_sum)
return hom
def _complex_relative(self,n,*args):
if len(args)==2:
complex = []
for i in range(args[0],args[1]):
complex.append(self._complex_relative(n,i))
return complex
if n<0 or n>self.poly_ring.ngens():
return []
if n==0:
hom_basis = self._p_graded_module(n).homogeneous_part_basis(self.degree+args[0])
return [LogarithmicDifferentialForm(n,b,self) for b in hom_basis]
base = self._p_graded_module(n).homogeneous_part_basis(self.degree+args[0])
if len(base)==0:
return []
vs_base = VectorSpace(QQ,len(base))
df_base = [LogarithmicDifferentialForm(n,b,self) for b in base]
pre_base = self._p_graded_module(n-1).homogeneous_part_basis(self.degree+args[0])
if len(pre_base)==0:
return df_base
dh = [self.divisor.derivative(g) for g in self.poly_ring.gens()]
dh = LogarithmicDifferentialForm(1,dh,self)
rel_gens = []
for b in pre_base:
b_form = LogarithmicDifferentialForm(n-1,b,self)
w = dh.wedge(b_form)
rel_gens.append(lift_to_basis([w],df_base))
rel = vs_base.subspace(rel_gens)
comp = orth_complement(vs_base,rel)
#Lift
rel_complex = []
for vec in comp.basis():
rel_complex.append(_weighted_sum(vec,df_base,self))
return rel_complex
def _differential_relative(self,form,*args):
n = form.degree
deg = self._p_graded_module(n).total_degree(form.vec)
deg -= self.degree
der = form.derivative()
full = self._p_graded_module(n+1).homogeneous_part_basis(self.degree+deg)
full_forms = [LogarithmicDifferentialForm(n+1,b,self) for b in full]
full_space = VectorSpace(QQ,len(full))
target_comp = self._complex_relative(n+1,deg)
comp_vecs = []
for b in target_comp:
comp_vecs.append(lift_to_basis([b],full_forms))
comp_vecs = full_space.subspace(comp_vecs)
lift_full = lift_to_basis([der],full_forms)
lift_prog = comp_vecs.basis_matrix()*vector(lift_full)
return [_weighted_sum(lift_prog,target_comp,self)]
def reduced_charges(M):
"""
Given a snappy manifold M, we find all reduced charges so that:
(1) no loop in the triangulation passes an odd number of pi's.
(2) no tetrahedron has three pi's and
"""
out = sol_and_kernel(M)
x, A = out
nt = M.num_tetrahedra()
dim = 3 * nt
V = VectorSpace(ZZ2, dim)
AA = V.subspace(A) # the reduced kernel
xx = V(x) # the reduced solution
charges = [xx + sum(B) for B in powerset(AA.basis())]
charges = [c for c in charges if not has_pi_triple(c)
] # reject if there are three pi's in any tet.
return charges
def subfield_from_elements(self,
alpha,
name=None,
polred=True,
threshold=None):
r"""
Return the subfield generated by the elements ``alpha``.
INPUT:
- ``alpha`` - list of elements in this number field
- ``name`` - a name for the generator of the new number field
- ``polred`` (boolean, default ``True``) - whether to optimize the generator of
the newly created field
- ``threshold`` (positive number, default ``None``) - threshold to be passed to
the ``do_polred`` function
EXAMPLES::
sage: from flatsurf.geometry.subfield import subfield_from_elements
sage: x = polygen(QQ)
sage: poly = x^4 - 4*x^2 + 1
sage: emb = AA.polynomial_root(poly, RIF(0.51, 0.52))
sage: K.<a> = NumberField(poly, embedding=emb)
sage: sqrt2 = -a^3 + 3*a
sage: sqrt3 = -a^2 + 2
sage: assert sqrt2 ** 2 == 2 and sqrt3 ** 2 == 3
sage: L, elts, phi = subfield_from_elements(K, [sqrt2, 1 - sqrt2/3])
sage: L
Number Field in a0 with defining polynomial x^2 - 2 with a0 = 1.414213562373095?
sage: elts
[a0, -1/3*a0 + 1]
sage: phi
Ring morphism:
From: Number Field in a0 with defining polynomial x^2 - 2 with a0 = 1.414213562373095?
To: Number Field in a with defining polynomial x^4 - 4*x^2 + 1 with a = 0.5176380902050415?
Defn: a0 |--> -a^3 + 3*a
sage: assert phi(elts[0]) == sqrt2
sage: assert phi(elts[1]) == 1 - sqrt2/3
sage: L, elts, phi = subfield_from_elements(K, [1, sqrt3])
sage: assert phi(elts[0]) == 1
sage: assert phi(elts[1]) == sqrt3
TESTS::
sage: from flatsurf.geometry.subfield import subfield_from_elements
sage: x = polygen(QQ)
sage: p = x^8 - 12*x^6 + 23*x^4 - 12*x^2 + 1
sage: K.<a> = NumberField(p)
sage: sqrt2 = 6/7*a^7 - 71/7*a^5 + 125/7*a^3 - 43/7*a
sage: sqrt3 = 3/7*a^6 - 32/7*a^4 + 24/7*a^2 + 10/7
sage: sqrt5 = 8/7*a^6 - 90/7*a^4 + 120/7*a^2 - 27/7
sage: assert sqrt2**2 == 2 and sqrt3**2 == 3 and sqrt5**2 == 5
sage: L, elts, phi = subfield_from_elements(K, [sqrt2, sqrt3], name='b')
sage: assert phi(elts[0]) == sqrt2
sage: assert phi(elts[1]) == sqrt3
sage: L, elts, phi = subfield_from_elements(K, [sqrt2, sqrt5], name='b')
sage: assert phi(elts[0]) == sqrt2
sage: assert phi(elts[1]) == sqrt5
sage: L, elts, phi = subfield_from_elements(K, [sqrt3, sqrt5], name='b')
sage: assert phi(elts[0]) == sqrt3
sage: assert phi(elts[1]) == sqrt5
sage: L, elts, phi = subfield_from_elements(K, [-149582/214245 + 21423/5581*sqrt2], name='b')
sage: assert L.polynomial() == x^2 - 2
sage: L, elts, phi = subfield_from_elements(K, [131490/777 - 1359/22*sqrt3], name='b')
sage: assert L.polynomial() == x^2 - 3
sage: L, elts, phi = subfield_from_elements(K, [12241829/177 - 321121/22459 * sqrt5], name='b')
sage: assert L.polynomial() == x^2 - x - 1
sage: from sage.rings.qqbar import number_field_elements_from_algebraics
sage: R.<x> = QQ[]
sage: p1 = x^3 - x - 1
sage: roots1 = p1.roots(QQbar, False)
sage: for _ in range(10):
....: p2 = R.random_element(degree=2)
....: while not p2.is_irreducible(): p2 = R.random_element(degree=2)
....: roots2 = p2.roots(QQbar, False)
....: K, (a1,b1,c1,a2,b2), phi = number_field_elements_from_algebraics(roots1 + roots2)
....: u1 = 1 - a1/17 + 3/7*a1**2
....: u2 = 2 + 33/35 * a1
....: L, (v1,v2), phi = subfield_from_elements(K, [u1, u2], threshold=100)
....: assert L.polynomial() == p1
....: assert phi(v1) == u1 and phi(v2) == u2
"""
V = VectorSpace(QQ, self.degree())
alpha = [self(a) for a in alpha]
# Rational case
if all(a.is_rational() for a in alpha):
return (QQ, [QQ(a) for a in alpha], self.coerce_map_from(QQ))
# Saturate with multiplication
vecs = [a.vector() for a in alpha]
U = V.subspace(vecs)
modified = True
while modified:
modified = False
d = U.dimension()
if d == self.degree():
return (self, alpha, Hom(self, self, Fields()).identity())
B = U.basis()
for i in range(d):
for j in range(i, d):
v = (self(B[i]) * self(B[j])).vector()
if v not in U:
U += V.subspace([v])
modified = True
# Strict subfield, find a generator
vgen = None
for b in U.basis():
if self(b).minpoly().degree() == d:
vgen = b
break
if vgen is None:
s = 1
while True:
vgen = U.random_element(proba=0.5, x=-s, y=s)
if self(vgen).minpoly().degree() == d:
break
s *= 2
# Minimize the generator via PARI polred
gen = self(vgen)
p = gen.minpoly()
if polred:
if threshold:
fwd, back, q = do_polred(p, threshold)
else:
fwd, back, q = do_polred(p)
else:
q = p
fwd = back = self.polynomial_ring().gen()
new_gen = fwd(gen)
assert new_gen.minpoly() == q
K, hom = self.subfield(new_gen, name=name)
# need to express the elements in the basis 1, a, a^2, ..., a^(d-1)
M = matrix(QQ, [(new_gen**i).vector() for i in range(d)])
new_alpha = [K(M.solve_left(elt.vector())) for elt in alpha]
return (K, new_alpha, hom)
def run_tests(num_to_check=10, smaller_num_to_check = 10):
import taut
veering_isosigs = parse_data_file("Data/veering_census.txt")
print("testing is_taut")
for sig in random.sample(veering_isosigs, num_to_check):
tri, angle = taut.isosig_to_tri_angle(sig)
assert taut.is_taut(tri, angle), sig
print("testing isosig round trip")
for sig in random.sample(veering_isosigs, num_to_check):
tri, angle = taut.isosig_to_tri_angle(sig)
recovered_sig = taut.isosig_from_tri_angle(tri, angle)
assert sig == recovered_sig, sig
# we only test this round trip - the other round trip does not
# make sense because tri->isosig is many to one.
import transverse_taut
print("testing is_transverse_taut")
for sig in random.sample(veering_isosigs, num_to_check):
tri, angle = taut.isosig_to_tri_angle(sig)
assert transverse_taut.is_transverse_taut(tri, angle), sig
non_transverse_taut_isosigs = parse_data_file("Data/veering_non_transverse_taut_examples.txt")
print("testing not is_transverse_taut")
for sig in non_transverse_taut_isosigs:
tri, angle = taut.isosig_to_tri_angle(sig)
assert not transverse_taut.is_transverse_taut(tri, angle), sig
import veering
print("testing is_veering")
for sig in random.sample(veering_isosigs, num_to_check):
tri, angle = taut.isosig_to_tri_angle(sig)
assert veering.is_veering(tri, angle), sig
# tri, angle = taut.isosig_to_tri_angle("cPcbbbdxm_10")
# explore_mobius_surgery_graph(tri, angle, max_tetrahedra = 12)
# # tests to see that it makes only veering triangulations as it goes
import veering_dehn_surgery
print("testing veering_dehn_surgery")
for sig in random.sample(veering_isosigs, num_to_check):
tri, angle = taut.isosig_to_tri_angle(sig)
for face_num in veering_dehn_surgery.get_mobius_strip_indices(tri):
(tri_s, angle_s, face_num_s) = veering_dehn_surgery.veering_mobius_dehn_surgery(tri, angle, face_num)
assert veering.is_veering(tri_s, angle_s), sig
import veering_fan_excision
print("testing veering_fan_excision")
m003, _ = taut.isosig_to_tri_angle('cPcbbbdxm_10')
m004, _ = taut.isosig_to_tri_angle('cPcbbbiht_12')
for sig in random.sample(veering_isosigs, num_to_check):
tri, angle = taut.isosig_to_tri_angle(sig)
tet_types = veering.is_veering(tri, angle, return_type = "tet_types")
if tet_types.count("toggle") == 2:
excised_tri, _ = veering_fan_excision.excise_fans(tri, angle)
assert ( excised_tri.isIsomorphicTo(m003) != None or
excised_tri.isIsomorphicTo(m004) != None ), sig
import pachner
print("testing pachner with taut structure")
for sig in random.sample(veering_isosigs, num_to_check):
tri, angle = taut.isosig_to_tri_angle(sig)
face_num = random.randrange(tri.countTriangles())
result = pachner.twoThreeMove(tri, face_num, angle = angle, return_edge = True)
if result != False:
tri2, angle2, edge_num = result
tri3, angle3 = pachner.threeTwoMove(tri2, edge_num, angle = angle2)
assert taut.isosig_from_tri_angle(tri, angle) == taut.isosig_from_tri_angle(tri3, angle3), sig
import branched_surface
import regina
print("testing branched_surface and pachner with branched surface")
for sig in random.sample(veering_isosigs, num_to_check):
tri, angle = taut.isosig_to_tri_angle(sig)
tri_original = regina.Triangulation3(tri) #copy
branch = branched_surface.upper_branched_surface(tri, angle, return_lower = random.choice([True, False]))
### test branch isosig round trip
sig_with_branch = branched_surface.isosig_from_tri_angle_branch(tri, angle, branch)
tri2, angle2, branch2 = branched_surface.isosig_to_tri_angle_branch(sig_with_branch)
assert (branch == branch2) and (angle == angle2), sig
branch_original = branch[:] #copy
face_num = random.randrange(tri.countTriangles())
out = pachner.twoThreeMove(tri, face_num, branch = branch, return_edge = True)
if out != False:
tri, possible_branches, edge_num = out
tri, branch = pachner.threeTwoMove(tri, edge_num, branch = possible_branches[0])
all_isoms = tri.findAllIsomorphisms(tri_original)
all_branches = [branched_surface.apply_isom_to_branched_surface(branch, isom) for isom in all_isoms]
assert branch_original in all_branches, sig
import flow_cycles
import drill
print("testing taut and branched drill + semiflows on drillings")
for sig in random.sample(veering_isosigs, smaller_num_to_check):
tri, angle = taut.isosig_to_tri_angle(sig)
branch = branched_surface.upper_branched_surface(tri, angle) ### also checks for veering and transverse taut
found_loops = flow_cycles.find_flow_cycles(tri, branch)
for loop in random.sample(found_loops, min(len(found_loops), 5)): ## drill along at most 5 loops
tri, angle = taut.isosig_to_tri_angle(sig)
branch = branched_surface.upper_branched_surface(tri, angle)
tri_loop = flow_cycles.flow_cycle_to_triangle_loop(tri, branch, loop)
if tri_loop != False:
if not flow_cycles.tri_loop_is_boundary_parallel(tri_loop, tri):
drill.drill(tri, tri_loop, angle = angle, branch = branch, sig = sig)
assert branched_surface.has_non_sing_semiflow(tri, branch), sig
print("all basic tests passed")
try:
import snappy
import snappy_util
snappy_working = True
except:
print("failed to import from snappy?")
snappy_working = False
if snappy_working:
print("testing algebraic intersection")
census = snappy.OrientableCuspedCensus() # not a set or list, so can't use random.sample
for i in range(10):
M = random.choice(census)
n = M.num_cusps()
peripheral_curves = M.gluing_equations()[-2*n:]
for i in range(2*n):
for j in range(i, 2*n):
alg_int = snappy_util.algebraic_intersection(peripheral_curves[i], peripheral_curves[j])
if i % 2 == 0 and j == i + 1:
assert alg_int == 1, M.name()
else:
assert alg_int == 0, M.name()
if snappy_working:
import veering_drill_midsurface_bdy
print("testing veering drilling and filling")
for sig in random.sample(veering_isosigs[:3000], num_to_check):
T, per = veering_drill_midsurface_bdy.drill_midsurface_bdy(sig)
M = snappy.Manifold(T.snapPea())
M.set_peripheral_curves("shortest")
L = snappy_util.get_slopes_from_peripherals(M, per)
M.dehn_fill(L)
N = snappy.Manifold(sig.split("_")[0])
assert M.is_isometric_to(N), sig
if snappy_working:
print("all tests depending on snappy passed")
# try:
# from hashlib import md5
# from os import remove
# import pyx
# from boundary_triangulation import draw_triangulation_boundary_from_veering_isosig
# pyx_working = True
# except:
# print("failed to import from pyx?")
# pyx_working = False
# ladders_style_sigs = {
# "cPcbbbiht_12": "f34c1fdf65db9d02994752814803ae01",
# "gLLAQbecdfffhhnkqnc_120012": "091c85b4f4877276bfd8a955b769b496",
# "kLALPPzkcbbegfhgijjhhrwaaxnxxn_1221100101": "a0f15a8454f715f492c74ce1073a13a4",
# }
# geometric_style_sigs = {
# "cPcbbbiht_12": "1e74d0b68160c4922e85a5adb20a0f1d",
# "gLLAQbecdfffhhnkqnc_120012": "856a1fce74eb64f519bcda083303bd8f",
# "kLALPPzkcbbegfhgijjhhrwaaxnxxn_1221100101": "33bd23b34c5d977a103fa50ffe63120a",
# }
# args = {
# "draw_boundary_triangulation":True,
# "draw_triangles_near_poles": False,
# "ct_depth":-1,
# "ct_epsilon":0.03,
# "global_drawing_scale": 4,
# "delta": 0.2,
# "ladder_width": 10.0,
# "ladder_height": 20.0,
# "draw_labels": True,
# }
# shapes_data = read_from_pickle("Data/veering_shapes_up_to_ten_tetrahedra.pkl")
# if pyx_working:
# for sig in ladders_style_sigs:
# print("testing boundary triangulation pictures, ladder style", sig)
# args["tet_shapes"] = shapes_data[sig]
# args["style"] = "ladders"
# file_name = draw_triangulation_boundary_from_veering_isosig(sig, args = args)
# f = open(file_name, "rb")
# file_hash = md5(f.read())
# assert file_hash.hexdigest() == ladders_style_sigs[sig]
# f.close()
# remove(file_name)
# if pyx_working:
# for sig in geometric_style_sigs:
# print("testing boundary triangulation pictures, ladder style", sig)
# args["tet_shapes"] = shapes_data[sig]
# args["style"] = "geometric"
# file_name = draw_triangulation_boundary_from_veering_isosig(sig, args = args)
# f = open(file_name, "rb")
# file_hash = md5(f.read())
# assert file_hash.hexdigest() == geometric_style_sigs[sig]
# f.close()
# remove(file_name)
# if pyx_working:
# print("all tests depending on pyx passed")
veering_polys = {
"cPcbbbiht_12": [-4, -1, 1, 4],
"eLMkbcddddedde_2100": [-2, -2, -2, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 2, 2],
"gLLAQbecdfffhhnkqnc_120012": [-1, -1, -1, -1, 1, 1, 1, 1],
"gLLPQcdfefefuoaaauo_022110": [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1],
}
# veering_polys = { ### old
# "cPcbbbiht_12": "a^3 - 4*a^2 + 4*a - 1",
# "eLMkbcddddedde_2100": "a^6*b - a^6 - 2*a^5*b - a^4*b^2 + a^5 + 2*a^4*b + a^3*b^2 - 2*a^3*b + a^3 + 2*a^2*b + a*b^2 - a^2 - 2*a*b - b^2 + b",
# "gLLAQbecdfffhhnkqnc_120012": "a^7 + a^6 + a^5 + a^4 - a^3 - a^2 - a - 1",
# "gLLPQcdfefefuoaaauo_022110": "a^12*b^3 - a^11*b^2 - a^10*b^3 - a^10*b^2 - a^7*b^3 - a^7*b^2 - a^6*b^3 + a^7*b + a^5*b^2 - a^6 - a^5*b - a^5 - a^2*b - a^2 - a*b + 1",
# }
taut_polys = {
"cPcbbbiht_12": [-3, 1, 1],
"eLMkbcddddedde_2100": [-1, -1, -1, 1, 1],
"iLLAwQcccedfghhhlnhcqeesr_12001122": [],
}
# taut_polys = { ### old
# "cPcbbbiht_12": "a^2 - 3*a + 1",
# "eLMkbcddddedde_2100": "a^2*b - a^2 - a*b - b^2 + b",
# "iLLAwQcccedfghhhlnhcqeesr_12001122": "0",
# }
torus_bundles = [
"cPcbbbiht_12",
"eLMkbcdddhhqqa_1220",
"gLMzQbcdefffhhqqqdl_122002",
]
measured = [
"gLLAQbecdfffhhnkqnc_120012",
"iLLALQcccedhgghhlnxkxrkaa_12001112",
"iLLAwQcccedfghhhlnhcqeesr_12001122",
]
empties = [
"fLAMcaccdeejsnaxk_20010",
"gLALQbcbeeffhhwsras_211220",
"hLALAkbcbeefgghhwsraqj_2112202",
]
try:
from sage.rings.integer_ring import ZZ
sage_working = True
except:
print("failed to import from sage?")
sage_working = False
if sage_working:
import taut_polytope
print("testing is_layered")
for sig in veering_isosigs[:17]:
assert taut_polytope.is_layered(sig), sig
for sig in veering_isosigs[17:21]:
assert not taut_polytope.is_layered(sig), sig
if sage_working:
import fibered
print("testing is_fibered")
mflds = parse_data_file("Data/mflds_which_fiber.txt")
mflds = [line.split("\t")[0:2] for line in mflds]
for (name, kind) in random.sample(mflds, num_to_check):
assert fibered.is_fibered(name) == (kind == "fibered"), name
if sage_working:
import veering_polynomial
import taut_polynomial
print("testing veering poly")
for sig in veering_polys:
p = veering_polynomial.veering_polynomial(sig)
assert check_polynomial_coefficients(p, veering_polys[sig]), sig
### Nov 2021: sage 9.4 changed how smith normal form works, which changed our polynomials
### to equivalent but not equal polynomials. To avoid this kind of change breaking things
### in the future, we changed to comparing the list of coefficients.
# assert p.__repr__() == veering_polys[sig]
print("testing taut poly")
for sig in taut_polys:
p = taut_polynomial.taut_polynomial_via_tree(sig)
assert check_polynomial_coefficients(p, taut_polys[sig]), sig
# assert p.__repr__() == taut_polys[sig]
print("testing divide")
for sig in random.sample(veering_isosigs[:3000], num_to_check):
p = veering_polynomial.veering_polynomial(sig)
q = taut_polynomial.taut_polynomial_via_tree(sig)
if q == 0:
assert p == 0, sig
else:
assert q.divides(p), sig
if sage_working:
print("testing alex")
for sig in random.sample(veering_isosigs[:3000], num_to_check):
snap_sig = sig.split("_")[0]
M = snappy.Manifold(snap_sig)
if M.homology().betti_number() == 1:
assert taut_polynomial.taut_polynomial_via_tree(sig, mode = "alexander") == M.alexander_polynomial(), sig
if sage_working:
# would be nice to automate this - need to fetch the angle
# structure say via z_charge.py...
print("testing is_torus_bundle")
for sig in torus_bundles:
assert taut_polytope.is_torus_bundle(sig), sig
if sage_working:
# ditto
print("testing is_layered")
for sig in torus_bundles:
assert taut_polytope.is_layered(sig), sig
print("testing measured")
for sig in measured:
assert taut_polytope.LMN_tri_angle(sig) == "M", sig
print("testing empty")
for sig in empties:
assert taut_polytope.LMN_tri_angle(sig) == "N", sig
if sage_working: # warning - this takes random amounts of time!
print("testing hom dim")
for sig in random.sample(veering_isosigs[:3000], 3): # magic number
# dimension = zero if and only if nothing is carried.
assert (taut_polytope.taut_cone_homological_dim(sig) == 0) == (taut_polytope.LMN_tri_angle(sig) == "N"), sig
if sage_working:
boundary_cycles = {
("eLMkbcddddedde_2100",(2,5,5,1,3,4,7,1)): "((-7, -7, 0, 0, 4, -3, 7, 0), (7, 7, 0, 0, -4, 3, -7, 0))",
("iLLLQPcbeegefhhhhhhahahha_01110221",(0,1,0,0,0,1,0,0,0,0,0,0,1,0,1,0)): "((0, 0, -1, 1, 1, 0, 1, 1, -1, 0, 0, 0, 0, 1, 0, 1), (0, 0, 1, -1, -1, 0, -1, -1, 1, 0, 0, 0, 0, -1, 0, -1))",
("ivvPQQcfhghgfghfaaaaaaaaa_01122000",(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)): "((1, 1, 2, 0, -1, 2, 1, -3, 0, -1, 0, -2, -1, 0, 3, -2), (1, 1, 0, 2, -1, 0, -3, 1, 2, -1, -2, 0, 3, -2, -1, 0), (-2, 0, -3, 1, 2, -1, 0, 2, -1, 0, 3, 1, -2, 1, 0, -1), (0, -2, 1, -3, 0, -1, 2, 0, -1, 2, -1, 1, 0, 1, -2, 3))",
}
taut_polys_with_cycles = {
("eLMkbcddddedde_2100", ((7, 7, 0, 0, -4, 3, -7, 0),)): [-1, -1, -1, 1, 1],
("iLLLQPcbeegefhhhhhhahahha_01110221", ((0, 0, 1, -1, -1, 0, -1, -1, 1, 0, 0, 0, 0, -1, 0, -1),)): [1, 1, 2],
("ivvPQQcfhghgfghfaaaaaaaaa_01122000", ((1, 1, 2, 0, -1, 2, 1, -3, 0, -1, 0, -2, -1, 0, 3, -2), (1, 1, 0, 2, -1, 0, -3, 1, 2, -1, -2, 0, 3, -2, -1, 0))): [-4, -1, -1, 1, 1],
}
# taut_polys_with_cycles = {
# ("eLMkbcddddedde_2100", ((7, 7, 0, 0, -4, 3, -7, 0),)): "a^14 - a^8 - a^7 - a^6 + 1",
# ("iLLLQPcbeegefhhhhhhahahha_01110221", ((0, 0, 1, -1, -1, 0, -1, -1, 1, 0, 0, 0, 0, -1, 0, -1),)): "a^2 + 2*a + 1",
# ("ivvPQQcfhghgfghfaaaaaaaaa_01122000", ((1, 1, 2, 0, -1, 2, 1, -3, 0, -1, 0, -2, -1, 0, 3, -2), (1, 1, 0, 2, -1, 0, -3, 1, 2, -1, -2, 0, 3, -2, -1, 0))): "a*b^2 - a^2 - 4*a*b - b^2 + a",
# }
taut_polys_image = {
('eLMkbcddddedde_2100', ((7, 8, -1, 0, -4, 4, -8, 0),)):[-1, -1, -1, 1, 1],
('ivvPQQcfhghgfghfaaaaaaaaa_01122000', ((1, 1, 2, 0, -1, 2, 1, -3, 0, -1, 0, -2, -1, 0, 3, -2),)):[-2, -2, -1, -1, 1, 1],
('ivvPQQcfhghgfghfaaaaaaaaa_01122000', ((1, 1, 2, 0, -1, 2, 1, -3, 0, -1, 0, -2, -1, 0, 3, -2), (1, 1, 0, 2, -1, 0, -3, 1, 2, -1, -2, 0, 3, -2, -1, 0))):[-4, -1, -1, 1, 1]
}
# taut_polys_image = {
# ('eLMkbcddddedde_2100', ((7, 8, -1, 0, -4, 4, -8, 0),)):"a^16 - a^9 - a^8 - a^7 + 1",
# ('ivvPQQcfhghgfghfaaaaaaaaa_01122000', ((1, 1, 2, 0, -1, 2, 1, -3, 0, -1, 0, -2, -1, 0, 3, -2),)):"a*b^2*c - 2*a*b*c - b^2*c - a^2 - 2*a*b + a",
# ('ivvPQQcfhghgfghfaaaaaaaaa_01122000', ((1, 1, 2, 0, -1, 2, 1, -3, 0, -1, 0, -2, -1, 0, 3, -2), (1, 1, 0, 2, -1, 0, -3, 1, 2, -1, -2, 0, 3, -2, -1, 0))):"a*b^2 - a^2 - 4*a*b - b^2 + a"
# }
alex_polys_with_cycles = {
("eLMkbcddddedde_2100",((7, 7, 0, 0, -4, 3, -7, 0),)): [-2, -1, -1, -1, 1, 1, 1, 2],
("iLLLQPcbeegefhhhhhhahahha_01110221", ((0, 0, 1, -1, -1, 0, -1, -1, 1, 0, 0, 0, 0, -1, 0, -1),)): [-3, -1, 1, 3],
("ivvPQQcfhghgfghfaaaaaaaaa_01122000", ((1, 1, 2, 0, -1, 2, 1, -3, 0, -1, 0, -2, -1, 0, 3, -2), (1, 1, 0, 2, -1, 0, -3, 1, 2, -1, -2, 0, 3, -2, -1, 0))): [-1, -1, 1, 1],
}
# alex_polys_with_cycles = {
# ("eLMkbcddddedde_2100",((7, 7, 0, 0, -4, 3, -7, 0),)): "a^15 - a^14 + a^9 - 2*a^8 + 2*a^7 - a^6 + a - 1",
# ("iLLLQPcbeegefhhhhhhahahha_01110221", ((0, 0, 1, -1, -1, 0, -1, -1, 1, 0, 0, 0, 0, -1, 0, -1),)): "3*a^3 - a^2 + a - 3",
# ("ivvPQQcfhghgfghfaaaaaaaaa_01122000", ((1, 1, 2, 0, -1, 2, 1, -3, 0, -1, 0, -2, -1, 0, 3, -2), (1, 1, 0, 2, -1, 0, -3, 1, 2, -1, -2, 0, 3, -2, -1, 0))): "a*b^2 - a^2 - b^2 + a",
# }
if sage_working:
import taut_carried
print("testing boundary cycles")
for sig, surface in boundary_cycles:
surface_list = list(surface)
cycles = taut_carried.boundary_cycles_from_surface(sig, surface_list)
cycles = tuple(tuple(cycle) for cycle in cycles)
assert cycles.__repr__() == boundary_cycles[(sig, surface)], sig
if sage_working:
print("testing taut with cycles")
for sig, cycles in taut_polys_with_cycles:
cycles_in = [list(cycle) for cycle in cycles]
p = taut_polynomial.taut_polynomial_via_tree(sig, cycles_in)
assert check_polynomial_coefficients(p, taut_polys_with_cycles[(sig, cycles)]), sig
# assert p.__repr__() == taut_polys_with_cycles[(sig, cycles)]
if sage_working:
print("testing taut with images")
for sig, cycles in taut_polys_image:
cycles_in = [list(cycle) for cycle in cycles]
p = taut_polynomial.taut_polynomial_image(sig, cycles_in)
assert check_polynomial_coefficients(p, taut_polys_image[(sig, cycles)]), sig
# assert p.__repr__() == taut_polys_image[(sig, cycles)]
if sage_working:
print("testing alex with cycles")
for sig, cycles in alex_polys_with_cycles:
cycles_in = [list(cycle) for cycle in cycles]
p = taut_polynomial.taut_polynomial_via_tree(sig, cycles_in, mode = "alexander")
assert check_polynomial_coefficients(p, alex_polys_with_cycles[(sig, cycles)]), sig
# assert p.__repr__() == alex_polys_with_cycles[(sig, cycles)]
if sage_working:
import edge_orientability
import taut_euler_class
print("testing euler and edge orientability")
for sig in random.sample(veering_isosigs[:3000], 3):
# Theorem: If (tri, angle) is edge orientable then e = 0.
assert not ( edge_orientability.is_edge_orientable(sig) and
(taut_euler_class.order_of_euler_class_wrapper(sig) == 2) ), sig
if sage_working:
# Theorem: If (tri, angle) is edge orientable then taut poly = alex poly.
# taut_polynomial.taut_polynomial_via_tree(sig, mode = "alexander") ==
# taut_polynomial.taut_polynomial_via_tree(sig, mode = "taut")
pass
if sage_working:
print("testing exotics")
for sig in random.sample(veering_isosigs[:3000], 3):
tri, angle = taut.isosig_to_tri_angle(sig)
T = veering.veering_triangulation(tri, angle)
is_eo = T.is_edge_orientable()
for angle in T.exotic_angles():
assert taut_polytope.taut_cone_homological_dim(tri, angle) == 0, sig
assert is_eo == transverse_taut.is_transverse_taut(tri, angle), sig
### test for drill_midsurface_bdy: drill then fill, check you get the same manifold
if sage_working:
from sage.combinat.words.word_generators import words
from sage.modules.free_module_integer import IntegerLattice
from sage.modules.free_module import VectorSpace
from sage.matrix.constructor import Matrix
import z_charge
import z2_taut
import regina
ZZ2 = ZZ.quotient(ZZ(2))
sig_starts = ["b+-LR", "b++LR"]
print("testing lattice for punc torus bundle")
for i in range(3):
for sig_start in sig_starts:
sig = sig_start + str(words.RandomWord(8, 2, "LR")) # 8 is a magic number
M = snappy.Manifold(sig)
tri = regina.Triangulation3(M)
t, A = z_charge.sol_and_kernel(M)
B = z_charge.leading_trailing_deformations(M)
C = z2_taut.cohomology_loops(tri)
AA = IntegerLattice(A)
BB = IntegerLattice(B)
assert AA == BB.saturation(), sig
dim = 3*M.num_tetrahedra()
V = VectorSpace(ZZ2, dim)
AA = V.subspace(A)
BB = V.subspace(B)
CM = Matrix(ZZ2, C)
CC = CM.right_kernel()
assert AA.intersection(CC) == BB , sig
## so l-t defms are the part of the kernel that doesn't flip over
if sage_working:
print("testing charges for punc torus bundle")
for i in range(3):
for sig_start in sig_starts:
sig = sig_start + str(words.RandomWord(8, 2, "LR")) # 8 is a magic number
M = snappy.Manifold(sig)
assert z_charge.can_deal_with_reduced_angles(M), sig
if sage_working:
import carried_surface
import mutation
print("testing building carried surfaces and mutations")
sigs_weights = [
['iLLLPQccdgefhhghqrqqssvof_02221000', (0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0)],
['jLLAvQQcedehihiihiinasmkutn_011220000', (2, 0, 1, 0, 0, 0, 1, 2, 0, 2, 0, 2, 1, 0, 0, 0, 1, 0)],
['jLLAvQQcedehihiihiinasmkutn_011220000', (0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0)],
['jLLLMPQcdgfhfhiiihshassspiq_122201101', (0, 0, 4, 0, 4, 1, 0, 2, 2, 0, 1, 0, 0, 4, 0, 4, 0, 0)]
]
strata = [
((1, 2), [2, 2]),
((2, 4), [5, 5, 1, 1]),
((0, 3), [2, 0, 0]),
((6, 1), [22])
]
orders_of_veering_symmetry_groups = [4, 2, 2, 2]
for i in range(len(sigs_weights)):
tri, angle = taut.isosig_to_tri_angle(sigs_weights[i][0])
weights = sigs_weights[i][1]
surface, edge_colours = carried_surface.build_surface(tri, angle, weights, return_edge_colours = True)
assert strata[i] == carried_surface.stratum_from_weights_surface(weights, surface)
veering_isoms = carried_surface.veering_symmetry_group(surface, edge_colours)
assert len(veering_isoms) == orders_of_veering_symmetry_groups[i]
isom = veering_isoms[1]
mutation.mutate(tri, angle, weights, isom, quiet = True)
if i == 0:
assert tri.isoSig() == 'ivLLQQccfhfeghghwadiwadrv'
#print('svof to wadrv passed')
elif i == 1:
assert tri.isoSig() == 'jvLLAQQdfghhfgiiijttmtltrcr'
#print('smkutn to tltrcr passed')
elif i == 2:
assert tri.isoSig() == 'jLLMvQQcedehhiiihiikiwnmtxk'
#print('smkutn to mtxk passed')
elif i == 3:
assert tri.isoSig() == 'jLLALMQcecdhggiiihqrwqwrafo'
#print('spiq to rafo passed')
if sage_working:
print("all tests depending on sage passed")
def test_satisfy_sum(self): v_space = VectorSpace(QQ,4) sub = v_space.subspace([[1,1,1,-1],[2,-3,41,5]]) comp = orth_complement(v_space,sub) self.assertEqual(v_space,sub+comp)
def test_comp(self): v_space = VectorSpace(QQ,4) sub = v_space.subspace([[1,1,1,1],[2,2,-3,-1]]) comp = orth_complement(v_space,sub) true_comp = v_space.subspace([[19,-17,3,-5],[1,-1,0,0]]) self.assertEqual(comp,true_comp)
def test_full(self): v_space = VectorSpace(QQ,4) zero = v_space.subspace([v_space.zero()]) comp = orth_complement(v_space,v_space) self.assertEqual(zero,comp)
