def make_galmap_object(self, galmap):
from lmfdb.belyi.main import url_for_belyi_passport_label
# all information about the map goes in the data dictionary
# most of the data from the database gets polished/formatted before we put it in the data dictionary
data = self.data = {}
# the stuff that does not need to be polished
for elt in ('label', 'plabel', 'triples_cyc', 'orbit_size', 'g', 'abc',
'deg'):
data[elt] = galmap[elt]
nt = galmap['group'].split('T')
data['group'] = group_display_knowl(int(nt[0]), int(nt[1]),
getDBConnection())
data['geomtype'] = geomtypelet_to_geomtypename_dict[galmap['geomtype']]
data['lambdas'] = [str(c)[1:-1] for c in galmap['lambdas']]
data['isQQ'] = False
data['in_LMFDB'] = False
F = belyi_base_field(galmap)
if F._data == None:
fld_coeffs = galmap['base_field']
pol = PolynomialRing(QQ, 'x')(fld_coeffs)
data['base_field'] = latex(pol)
else:
data['in_LMFDB'] = True
if F.poly().degree() == 1:
data['isQQ'] = True
F.latex_poly = web_latex(F.poly())
data['base_field'] = F
crv_str = galmap['curve']
if crv_str == 'PP1':
data['curve'] = '\mathbb{P}^1'
else:
data['curve'] = make_curve_latex(crv_str)
# change pairs of floats to complex numbers
embeds = galmap['embeddings']
embed_strs = []
for el in embeds:
if el[1] < 0:
el_str = str(el[0]) + str(el[1]) + "\sqrt{-1}"
else:
el_str = str(el[0]) + "+" + str(el[1]) + "\sqrt{-1}"
embed_strs.append(el_str)
data['map'] = make_map_latex(galmap['map'])
data['embeddings_and_triples'] = []
if data['isQQ']:
for i in range(0, len(data['triples_cyc'])):
triple_cyc = data['triples_cyc'][i]
data['embeddings_and_triples'].append([
"\\text{not applicable (over $\mathbb{Q}$)}",
triple_cyc[0], triple_cyc[1], triple_cyc[2]
])
else:
for i in range(0, len(data['triples_cyc'])):
triple_cyc = data['triples_cyc'][i]
data['embeddings_and_triples'].append([
embed_strs[i], triple_cyc[0], triple_cyc[1], triple_cyc[2]
])
data['lambdas'] = [str(c)[1:-1] for c in galmap['lambdas']]
# Properties
properties = [
('Label', galmap['label']),
('Group', str(galmap['group'])),
('Orders', str(galmap['abc'])),
('Genus', str(galmap['g'])),
('Size', str(galmap['orbit_size'])),
]
self.properties = properties
# Friends
self.friends = [('Passport',
url_for_belyi_passport_label(galmap['plabel']))]
# Breadcrumbs
groupstr, abcstr, sigma0, sigma1, sigmaoo, gstr, letnum = data[
'label'].split("-")
lambdasstr = '%s-%s-%s' % (sigma0, sigma1, sigmaoo)
lambdasgstr = lambdasstr + "-" + gstr
self.bread = [
('Belyi Maps', url_for(".index")),
(groupstr, url_for(".by_url_belyi_search_group", group=groupstr)),
(abcstr,
url_for(".by_url_belyi_search_group_triple",
group=groupstr,
abc=abcstr)),
(lambdasgstr,
url_for(".by_url_belyi_passport_label",
group=groupstr,
abc=abcstr,
sigma0=sigma0,
sigma1=sigma1,
sigmaoo=sigmaoo,
g=gstr)),
(letnum,
url_for(".by_url_belyi_galmap_label",
group=groupstr,
abc=abcstr,
sigma0=sigma0,
sigma1=sigma1,
sigmaoo=sigmaoo,
g=gstr,
letnum=letnum)),
]
# Title
self.title = "Belyi map " + data['label']
# Code snippets (only for curves)
self.code = {}
return
def make_galmap_object(self, galmap):
from lmfdb.belyi.main import url_for_belyi_passport_label
# all information about the map goes in the data dictionary
# most of the data from the database gets polished/formatted before we put it in the data dictionary
data = self.data = {}
# the stuff that does not need to be polished
for elt in ("label", "plabel", "triples_cyc", "orbit_size", "g", "abc",
"deg"):
data[elt] = galmap[elt]
nt = galmap["group"].split("T")
data["group"] = group_display_knowl(int(nt[0]), int(nt[1]))
data["geomtype"] = geomtypelet_to_geomtypename_dict[galmap["geomtype"]]
data["lambdas"] = [str(c)[1:-1] for c in galmap["lambdas"]]
data["isQQ"] = False
data["in_LMFDB"] = False
F = belyi_base_field(galmap)
if F._data is None:
fld_coeffs = galmap["base_field"]
pol = PolynomialRing(QQ, "x")(fld_coeffs)
data["base_field"] = latex(pol)
else:
data["in_LMFDB"] = True
if F.poly().degree() == 1:
data["isQQ"] = True
F.latex_poly = web_latex(F.poly())
data["base_field"] = F
crv_str = galmap["curve"]
if crv_str == "PP1":
data["curve"] = r"\mathbb{P}^1"
else:
data["curve"] = make_curve_latex(crv_str)
# change pairs of floats to complex numbers
embeds = galmap["embeddings"]
embed_strs = []
for el in embeds:
if el[1] < 0:
el_str = str(el[0]) + str(el[1]) + r"\sqrt{-1}"
else:
el_str = str(el[0]) + "+" + str(el[1]) + r"\sqrt{-1}"
embed_strs.append(el_str)
data["map"] = make_map_latex(galmap["map"])
data["embeddings_and_triples"] = []
if data["isQQ"]:
for i in range(0, len(data["triples_cyc"])):
triple_cyc = data["triples_cyc"][i]
data["embeddings_and_triples"].append([
r"\text{not applicable (over $\mathbb{Q}$)}",
triple_cyc[0],
triple_cyc[1],
triple_cyc[2],
])
else:
for i in range(0, len(data["triples_cyc"])):
triple_cyc = data["triples_cyc"][i]
data["embeddings_and_triples"].append([
embed_strs[i], triple_cyc[0], triple_cyc[1], triple_cyc[2]
])
data["lambdas"] = [str(c)[1:-1] for c in galmap["lambdas"]]
# Properties
properties = [
("Label", galmap["label"]),
("Group", str(galmap["group"])),
("Orders", str(galmap["abc"])),
("Genus", str(galmap["g"])),
("Size", str(galmap["orbit_size"])),
]
self.properties = properties
# Friends
self.friends = [("Passport",
url_for_belyi_passport_label(galmap["plabel"]))]
# Downloads
if galmap["g"] <= 2:
self.downloads = [
(
"Code to Magma",
url_for(".belyi_galmap_magma_download",
label=data["label"]),
),
(
"Code to SageMath",
url_for(".belyi_galmap_sage_download",
label=data["label"]),
),
(
"All data to text",
url_for(".belyi_galmap_text_download",
label=data["label"]),
),
]
else:
self.downloads = []
# Breadcrumbs
groupstr, abcstr, sigma0, sigma1, sigmaoo, gstr, letnum = data[
"label"].split("-")
lambdasstr = "%s-%s-%s" % (sigma0, sigma1, sigmaoo)
lambdasgstr = lambdasstr + "-" + gstr
self.bread = [
("Belyi Maps", url_for(".index")),
(groupstr, url_for(".by_url_belyi_search_group", group=groupstr)),
(
abcstr,
url_for(".by_url_belyi_search_group_triple",
group=groupstr,
abc=abcstr),
),
(
lambdasgstr,
url_for(
".by_url_belyi_passport_label",
group=groupstr,
abc=abcstr,
sigma0=sigma0,
sigma1=sigma1,
sigmaoo=sigmaoo,
g=gstr,
),
),
(
letnum,
url_for(
".by_url_belyi_galmap_label",
group=groupstr,
abc=abcstr,
sigma0=sigma0,
sigma1=sigma1,
sigmaoo=sigmaoo,
g=gstr,
letnum=letnum,
),
),
]
# Title
self.title = "Belyi map " + data["label"]
# Code snippets (only for curves)
self.code = {}
return
def make_passport_object(self, passport):
from lmfdb.belyi.main import url_for_belyi_galmap_label, url_for_belyi_passport_label
# all information about the map goes in the data dictionary
# most of the data from the database gets polished/formatted before we put it in the data dictionary
data = self.data = {}
for elt in ("plabel", "abc", "num_orbits", "g", "abc", "deg",
"maxdegbf", "is_primitive", "primitivization"):
data[elt] = passport[elt]
data["group"] = transitive_group_display_knowl(passport["group"])
data["geomtype"] = geomtypelet_to_geomtypename_dict[
passport["geomtype"]]
data["lambdas"] = [str(c)[1:-1] for c in passport["lambdas"]]
data["pass_size"] = passport["pass_size"]
data["primitivization_url"] = url_for_belyi_passport_label(
data['primitivization'])
# Permutation triples
galmaps_for_plabel = db.belyi_galmaps_fixed.search(
{"plabel": passport["plabel"]}) # , sort = ['label_index'])
galmapdata = []
for galmap in galmaps_for_plabel:
# wrap number field nonsense
F = belyi_base_field(galmap)
# inLMFDB = False
field = {}
if F._data is None:
field["in_LMFDB"] = False
fld_coeffs = galmap["base_field"]
pol = PolynomialRing(QQ, "x")(fld_coeffs)
field["base_field"] = latex(pol)
field["isQQ"] = False
else:
field["in_LMFDB"] = True
if F.poly().degree() == 1:
field["isQQ"] = True
F.latex_poly = web_latex(F.poly(var="t"))
field["base_field"] = F
galmapdatum = [
galmap["label"].split("-")[-1],
url_for_belyi_galmap_label(galmap["label"]),
galmap["orbit_size"],
field,
galmap["triples_cyc"][0][0],
galmap["triples_cyc"][0][1],
galmap["triples_cyc"][0][2],
]
galmapdata.append(galmapdatum)
data["galmapdata"] = galmapdata
# Properties
properties = [
("Label", passport["plabel"]),
("Group", str(passport["group"])),
("Orders", str(passport["abc"])),
("Genus", str(passport["g"])),
("Size", str(passport["pass_size"])),
("Galois orbits", str(passport["num_orbits"])),
]
self.properties = properties
# Friends
self.friends = []
# Breadcrumbs
label_spl = data["plabel"].split("-")
groupstr = label_spl[0]
gstr = str(data['g'])
sigmas = label_spl[1]
sigma0, sigma1, sigmaoo = sigmas.split("_")
abcstr = str(data['abc']).replace(' ', '')
# does lambdasstr need to be updated?
lambdasstr = "%s-%s-%s" % (sigma0, sigma1, sigmaoo)
lambdasgstr = lambdasstr + "-" + gstr
self.bread = [
("Belyi Maps", url_for(".index")),
(groupstr, url_for(".by_url_belyi_search_group", group=groupstr)),
(
abcstr,
url_for(".by_url_belyi_search_group_triple",
group=groupstr,
abc=abcstr),
),
(
lambdasgstr,
url_for(
".by_url_belyi_passport_label",
group=groupstr,
abc=abcstr,
sigma0=sigma0,
sigma1=sigma1,
sigmaoo=sigmaoo,
g=gstr,
),
),
]
# Title
self.title = "Passport " + data["plabel"]
# Code snippets (only for curves)
self.code = {}
self.__dict__.update(data)
return
def make_galmap_object(self, galmap):
from lmfdb.belyi.main import url_for_belyi_passport_label
# all information about the map goes in the data dictionary
# most of the data from the database gets polished/formatted before we put it in the data dictionary
data = self.data = {}
# the stuff that does not need to be polished
for elt in ('label', 'plabel', 'triples_cyc', 'orbit_size', 'g', 'abc', 'deg'):
data[elt] = galmap[elt]
nt = galmap['group'].split('T')
data['group'] = group_display_knowl(int(nt[0]),int(nt[1]))
data['geomtype'] = geomtypelet_to_geomtypename_dict[galmap['geomtype']]
data['lambdas'] = [str(c)[1:-1] for c in galmap['lambdas']]
data['isQQ'] = False
data['in_LMFDB'] = False
F = belyi_base_field(galmap)
if F._data == None:
fld_coeffs = galmap['base_field']
pol = PolynomialRing(QQ, 'x')(fld_coeffs)
data['base_field'] = latex(pol)
else:
data['in_LMFDB'] = True
if F.poly().degree()==1:
data['isQQ'] = True
F.latex_poly = web_latex(F.poly())
data['base_field'] = F
crv_str = galmap['curve']
if crv_str=='PP1':
data['curve'] = '\mathbb{P}^1'
else:
data['curve'] = make_curve_latex(crv_str)
# change pairs of floats to complex numbers
embeds = galmap['embeddings']
embed_strs = []
for el in embeds:
if el[1] < 0:
el_str = str(el[0]) + str(el[1]) + "\sqrt{-1}"
else:
el_str = str(el[0]) + "+" + str(el[1]) + "\sqrt{-1}"
embed_strs.append(el_str)
data['map'] = make_map_latex(galmap['map'])
data['embeddings_and_triples'] = []
if data['isQQ']:
for i in range(0,len(data['triples_cyc'])):
triple_cyc = data['triples_cyc'][i]
data['embeddings_and_triples'].append(["\\text{not applicable (over $\mathbb{Q}$)}", triple_cyc[0], triple_cyc[1], triple_cyc[2]])
else:
for i in range(0,len(data['triples_cyc'])):
triple_cyc = data['triples_cyc'][i]
data['embeddings_and_triples'].append([embed_strs[i], triple_cyc[0], triple_cyc[1], triple_cyc[2]])
data['lambdas'] = [str(c)[1:-1] for c in galmap['lambdas']]
# Properties
properties = [('Label', galmap['label']),
('Group', str(galmap['group'])),
('Orders', str(galmap['abc'])),
('Genus', str(galmap['g'])),
('Size', str(galmap['orbit_size'])),
]
self.properties = properties
# Friends
self.friends = [('Passport', url_for_belyi_passport_label(galmap['plabel']))]
# Breadcrumbs
groupstr, abcstr, sigma0, sigma1, sigmaoo, gstr, letnum = data['label'].split("-");
lambdasstr = '%s-%s-%s' % (sigma0, sigma1, sigmaoo);
lambdasgstr = lambdasstr + "-" + gstr;
self.bread = [
('Belyi Maps', url_for(".index")),
(groupstr,
url_for(".by_url_belyi_search_group",
group=groupstr
)
),
(abcstr,
url_for(".by_url_belyi_search_group_triple",
group=groupstr,
abc=abcstr
)
),
(lambdasgstr,
url_for(".by_url_belyi_passport_label",
group=groupstr,
abc=abcstr,
sigma0=sigma0,
sigma1=sigma1,
sigmaoo=sigmaoo,
g = gstr )
),
(letnum,
url_for(".by_url_belyi_galmap_label",
group=groupstr,
abc=abcstr,
sigma0=sigma0,
sigma1=sigma1,
sigmaoo=sigmaoo,
g = gstr,
letnum = letnum)
),
];
# Title
self.title = "Belyi map " + data['label']
# Code snippets (only for curves)
self.code = {}
return
def __init__(self, galmap, triple=None):
from lmfdb.belyi.main import url_for_belyi_passport_label, url_for_belyi_galmap_label
# all information about the map goes in the data dictionary
# most of the data from the database gets polished/formatted before we put it in the data dictionary
data = self.data = {}
# the stuff that does not need to be polished
for elt in ("label", "plabel", "triples_cyc", "orbit_size", "g", "abc",
"deg", "primitivization", "is_primitive"):
data[elt] = galmap[elt]
if triple:
data["label"] += '-' + (triple).replace(' ', '')
data["triple"] = triple
data["group"] = transitive_group_display_knowl(galmap["group"])
data["geomtype"] = geomtypelet_to_geomtypename_dict[galmap["geomtype"]]
data["lambdas"] = [str(c)[1:-1] for c in galmap["lambdas"]]
data["primitivization_url"] = url_for_belyi_galmap_label(
data['primitivization'])
data["isQQ"] = False
data["in_LMFDB"] = False
F = belyi_base_field(galmap)
if F._data is None:
fld_coeffs = galmap["base_field"]
pol = PolynomialRing(QQ, "t")(fld_coeffs)
data["base_field"] = latex(pol)
else:
data["in_LMFDB"] = True
if F.poly().degree() == 1:
data["isQQ"] = True
F.latex_poly = web_latex(F.poly(var="t"))
data["base_field"] = F
data['embeddings'] = galmap['embeddings']
# change pairs of floats to complex numbers
embed_strs = []
for el in galmap["embeddings"]:
if el[1] < 0:
el_str = str(el[0]) + str(el[1]) + r"\sqrt{-1}"
else:
el_str = str(el[0]) + "+" + str(el[1]) + r"\sqrt{-1}"
embed_strs.append(el_str)
data["embeddings_and_triples"] = []
self.triple = None
self.embedding = None
for i in range(0, len(data["triples_cyc"])):
my_dict = {}
triple_str = ', '.join(data['triples_cyc'][i])
triple_link = triple_str.replace(' ', '')
if triple_link == triple:
self.triple = data['triples_cyc'][i]
self.embedding = CC(data['embeddings'][i])
my_dict['triple'] = triple_str
my_dict['triple_link'] = triple_link
if data["isQQ"]:
my_dict[
'embedding'] = r"\text{not applicable (over $\mathbb{Q}$)}"
else:
my_dict['embedding'] = embed_strs[i]
data['embeddings_and_triples'].append(my_dict)
crv_str = galmap["curve"]
if crv_str == "PP1":
data["curve"] = r"\mathbb{P}^1"
else:
data["curve"] = make_curve_latex(crv_str, nu=self.embedding)
data["map"] = make_map_latex(galmap["map"], nu=self.embedding)
data["lambdas"] = [str(c)[1:-1] for c in galmap["lambdas"]]
# Properties
self.plot = db.belyi_galmap_portraits.lucky({"label": galmap['label']},
projection="portrait")
plot_link = '<a href="{0}"><img src="{0}" width="200" height="200" style="background-color: white;"/></a>'.format(
self.plot)
properties = [("Label", galmap["label"])]
if triple:
properties += [("Triple", "$%s$" % triple)]
if self.plot:
properties += [(None, plot_link)]
properties += [
("Group", str(galmap["group"])),
("Orders", "$%s$" % (data["abc"])),
("Genus", prop_int_pretty(data["g"])),
("Size", prop_int_pretty(data["orbit_size"])),
]
self.properties = properties
# Friends
self.friends = [("Passport",
url_for_belyi_passport_label(galmap["plabel"]))]
if galmap['label'] != galmap['primitivization']:
self.friends.append(
("Primitivization",
url_for_belyi_galmap_label(galmap["primitivization"])))
self.friends.extend(names_and_urls(galmap['friends']))
#add curve link, if in LMFDB
if 'curve_label' in galmap.keys():
data['curve_label'] = galmap['curve_label']
for name, url in self.friends:
if "curve" in name.lower() and data['curve_label'] in name:
data["curve_url"] = url
# Downloads
if galmap["g"] <= 2:
data_label = data["label"]
if triple:
spl = data_label.split("-")
data_label = "-".join(spl[0:-1])
self.downloads = [
(
"Code to Magma",
url_for(".belyi_galmap_magma_download", label=data_label),
),
(
"Code to SageMath",
url_for(".belyi_galmap_sage_download", label=data_label),
),
(
"All data to text",
url_for(".belyi_galmap_text_download", label=data_label),
),
]
else:
self.downloads = []
# Breadcrumbs
label_spl = data["label"].split("-")
groupstr = label_spl[0]
letnum = label_spl[2]
gstr = str(data['g'])
sigmas = label_spl[1]
sigma0, sigma1, sigmaoo = sigmas.split("_")
abcstr = str(data['abc']).replace(' ', '')
# does lambdasstr need to be updated?
lambdasstr = "%s-%s-%s" % (sigma0, sigma1, sigmaoo)
lambdasgstr = lambdasstr + "-" + gstr
self.bread = [
("Belyi Maps", url_for(".index")),
(groupstr, url_for(".by_url_belyi_search_group", group=groupstr)),
(
abcstr,
url_for(".by_url_belyi_search_group_triple",
group=groupstr,
abc=abcstr),
),
(
lambdasgstr,
url_for(
".by_url_belyi_passport_label",
group=groupstr,
abc=abcstr,
sigma0=sigma0,
sigma1=sigma1,
sigmaoo=sigmaoo,
g=gstr,
),
),
(
letnum,
url_for(
".by_url_belyi_galmap_label",
group=groupstr,
abc=abcstr,
sigma0=sigma0,
sigma1=sigma1,
sigmaoo=sigmaoo,
g=gstr,
letnum=letnum,
),
),
]
# Title
if self.triple:
self.title = "Embedded Belyi map " + data["label"]
else:
self.title = "Belyi map orbit " + data["label"]
# Code snippets (only for curves)
self.code = {}
self.__dict__.update(data)
return