def jones_from_homfly():
'''Takes any knots with a homfly polynomial but lacking jones, and
computes the latter from the former.'''
knots = Knot.select().where(Knot.jones >> None)
output_knots = []
i = 0
for knot in knots:
if i % 100 == 0:
print(i, len(output_knots))
i += 1
if knot.jones is None and knot.homfly is not None:
homfly = knot.homfly
if 'Fail' not in homfly:
homfly = db2py_homfly(homfly)
jones = homfly_to_jones(homfly)
jones = py2db_jones(jones)
knot.jones = jones
output_knots.append(knot)
if i % 10000 == 0:
print('Saving changes')
with db.transaction():
for knot in output_knots:
knot.save()
output_knots = []
print('Saving changes')
with db.transaction():
for knot in output_knots:
knot.save()
def alexander_imags_from_alexander(min_crossings=None):
'''Takes any knots with an Alexander polynomial but lacking its values
at exp(2 pi I / 3) and exp(2 pi I / 4). It could also do the
determinant (some of the determinants in the knot atlas data are
wrong), but doesn't for now.
'''
knots = Knot.select().where(~(Knot.alexander >> None))
if min_crossings is not None:
knots = knots.where(Knot.min_crossings == min_crossings)
output_knots = []
for i, knot in enumerate(knots):
if i % 100 == 0:
print(i, len(output_knots))
if knot.alexander is not None:
array = json.loads(knot.alexander)
exp_2s = [(-1.)**i for i in range(len(array))]
alexander_imag_2 = int(n.round(n.abs(n.sum([
coefficient * exponential for coefficient, exponential
in zip(array, exp_2s)]))))
exp_3s = [n.exp(i*2*n.pi*1j/3.) for i in range(len(array))]
alexander_imag_3 = int(n.round(n.abs(n.sum([
coefficient * exponential for coefficient, exponential
in zip(array, exp_3s)]))))
exp_4s = [(1.j)**i for i in range(len(array))]
alexander_imag_4 = int(n.round(n.abs(n.sum([
coefficient * exponential for coefficient, exponential
in zip(array, exp_4s)]))))
knot.determinant = alexander_imag_2
knot.alexander_imag_3 = alexander_imag_3
knot.alexander_imag_4 = alexander_imag_4
output_knots.append(knot)
if i % 10000 == 0:
print('Saving changes')
with db.transaction():
for knot in output_knots:
knot.save()
output_knots = []
print('Saving changes')
with db.transaction():
for knot in output_knots:
knot.save()
output_knots = []
def alexander_at_roots_from_dt_code():
knots = Knot.select().where(Knot.alexander_imag_3 >> None)
output_knots = []
num_knots = knots.count()
for i, knot in enumerate(knots):
if i % 1 == 0:
print(i, '/', num_knots)
ks = knot.space_curve(verbose=False)
roots = ks.alexander_at_root((2, 3, 4))
knot.determinant = roots[0]
knot.alexander_imag_3 = roots[1]
knot.alexander_imag_4 = roots[2]
output_knots.append(knot)
print(knot, roots)
print('saving changes')
with db.transaction():
for knot in output_knots:
knot.save()
def vassiliev_2_invariants_from_space_curve(max_crossings=16):
knots = Knot.select().where(Knot.vassiliev_2 >> None).where(
Knot.min_crossings <= max_crossings)
print('Calculating Vassiliev 2 for {} knots'.format(knots.count()))
output_knots = []
num_knots = knots.count()
for i, knot in enumerate(knots):
if i % 1 == 0:
print(i, '/', num_knots)
assert knot.vassiliev_2 is None
ks = knot.space_curve(verbose=False)
v2 = ks.vassiliev_degree_2()
knot.vassiliev_2 = v2
output_knots.append(knot)
print(knot, v2)
print('saving changes')
with db.transaction():
for knot in output_knots:
knot.save()
output_knots = []
def planar_writhe_from_dt_code(max_crossings=12):
from pyknotid.catalogue import from_invariants
from pyknotid.representations import dtnotation as dt
knots = Knot.select().where(
Knot.min_crossings <= max_crossings).where(
Knot.planar_writhe >> None).where(
Knot.min_crossings > 0)
output_knots = []
i = 0
for knot in knots:
if i % 100 == 0:
print(i, len(output_knots))
i += 1
assert knot.planar_writhe is None
assert knot.min_crossings <= max_crossings
d = dt.DTNotation(knot.dt_code)
r = d.representation()
if r is None:
print('{} caused trouble, skipping'.format(knot))
continue
writhe = r.writhe()
if writhe < 0:
writhe *= -1
knot.planar_writhe = writhe
output_knots.append(knot)
if i % 10000 == 0:
print('Saving changes')
with db.transaction():
for knot in output_knots:
knot.save()
output_knots = []
print(knot, writhe)
print('Saving changes')
with db.transaction():
for knot in output_knots:
knot.save()
output_knots = []
def add_vassilievs_and_symmetry_from_rdf(filen):
'''Adds Vassiliev 2 and 3 from RDF files. This is only necessary for
pre-existing databases, these invariants are now added by
build.py.
'''
from rdflib import URIRef, Graph
from pyknotid.catalogue.build import get_rdf_object
rdfv2 = URIRef('invariant:V_2')
rdfv3 = URIRef('invariant:V_3')
rdfsymmetry = URIRef('invariant:Symmetry_Type')
g = Graph()
g.parse(filen, format='nt')
subjects = list(set(g.subjects(None, None)))
output_knots = []
for subject in subjects:
identifier = str(subject.toPython().split(':')[1])
knots = Knot.select().where(Knot.identifier == identifier)
first = knots.first()
if first is not None:
v2 = get_rdf_object(g, subject, rdfv2)
if v2 is not None:
v2 = int(v2)
v3 = get_rdf_object(g, subject, rdfv3)
if v3 is not None:
v3 = int(v3)
symmetry = get_rdf_object(g, subject, rdfsymmetry)
if symmetry is not None:
symmetry = symmetry.lower()
first.vassiliev_2 = v2
first.vassiliev_3 = v3
first.symmetry = symmetry
output_knots.append(first)
print('Added {}; {}, {}, {}'.format(identifier, v2, v3, symmetry))
else:
print('Failed to find {} in db'.format(identifier))
print('Attempting to save')
with db.transaction():
for knot in output_knots:
knot.save()
def add_two_bridgeness():
'''Adds two-bridge information to any knots where the information is
available in knotinfo's database.
'''
data = []
with open('/home/asandy/knotcatalogue/raw_data/knotinfo_data_complete.csv','r') as fileh:
reader = csv.reader(fileh, delimiter=',', quotechar='"')
for row in reader:
entries = []
for column in row:
entries.append(column)
data.append(entries)
output_knots = []
for row in data[2:]:
name = row[0]
twobridgenotation = row[24]
if twobridgenotation == '':
twobridgenotation = None
crossings, number = name.split('_')
number = int(number)
if int(crossings[:2]) >= 11:
realname = 'K{}{}'.format(crossings, number)
else:
crossings = int(crossings)
realname = '{}_{}'.format(crossings, number)
knots = list(Knot.select().where(Knot.identifier==realname))
if len(knots) != 1:
print('Failed to find {} in db'.format(realname))
else:
knot = knots[0]
knot.two_bridge = twobridgenotation
output_knots.append(knot)
print('Attempting to save')
with db.transaction():
for knot in output_knots:
knot.save()
def add_composite_knots():
from pyknotid.catalogue.identify import get_knot, from_invariants
k3_1 = get_knot('3_1')
k4_1 = get_knot('4_1')
k5_1 = get_knot('5_1')
k5_2 = get_knot('5_2')
prime_knots = Knot.select().where(
Knot.composite == False).where(
Knot.min_crossings < 8).where(
Knot.min_crossings >= 3)
new_knots = []
for k1 in (k3_1, k4_1, k5_1, k5_2):
for k2 in Knot.select().where(Knot.composite == False).where(Knot.min_crossings <= (11 - k1.min_crossings)).where(Knot.min_crossings > k1.min_crossings):
if k1.identifier != k2.identifier:
identifier = '{}#{}'.format(k1.identifier, k2.identifier)
else:
identifier = '{}^2'.format(k1.identifier)
if Knot.select().where(Knot.identifier == identifier).count() != 0:
print('{} already in db!'.format(identifier))
continue
composite = Knot(
identifier=identifier,
min_crossings=k1.min_crossings + k2.min_crossings,
determinant=k1.determinant * k2.determinant,
alexander_imag_3=k1.alexander_imag_3 * k2.alexander_imag_3,
alexander_imag_4=k1.alexander_imag_4 * k2.alexander_imag_4,
hyperbolic_volume='Not hyperbolic',
vassiliev_2=k1.vassiliev_2 + k2.vassiliev_2,
composite=True,
)
print(composite)
composite.pretty_print()
new_knots.append(composite)
with db.transaction():
for knot in new_knots:
knot.save()
new_knots = []
k3_1_2 = get_knot('3_1^2')
for k1 in (k3_1_2, ):
for k2 in prime_knots:
if k2.identifier == '3_1':
identifier = '3_1^3'
else:
identifier = '3_1^2#{}'.format(k2.identifier)
if Knot.select().where(Knot.identifier == identifier).count() != 0:
print('{} already in db!'.format(identifier))
continue
composite = Knot(
identifier=identifier,
min_crossings=k1.min_crossings + k2.min_crossings,
determinant=k1.determinant * k2.determinant,
alexander_imag_3=k1.alexander_imag_3 * k2.alexander_imag_3,
alexander_imag_4=k1.alexander_imag_4 * k2.alexander_imag_4,
hyperbolic_volume='Not hyperbolic',
vassiliev_2=k1.vassiliev_2 + k2.vassiliev_2,
composite=True,
)
print(composite)
composite.pretty_print()
new_knots.append(composite)
with db.transaction():
for knot in new_knots:
knot.save()
if Knot.select().where(Knot.identifier == '4_1^2').count() == 0:
k4_1_2 = Knot(identifier='4_1^2',
min_crossings=8,
determinant=25,
alexander_imag_3=16,
alexander_imag_4=9,
hyperbolic_volume='Not hyperbolic',
vassiliev_2=-2,
composite=True,
)
with db.transaction():
k4_1_2.save()
