def alpha_alt_fn(data):
try:
alternating_group = AlternatingGroup(len(data))
data_perm = Permutation(alternating_group(data))
except TypeError:
raise TypeError(
"The data element given is not an element of the alternating group"
)
def alpha_alt(roots, p):
""" Computes invariant alpha in the 'ALT' case
"""
from sage.all import prod, Permutation
tmp = prod(roots[i] - roots[j] for i in range(len(roots))
for j in range(i))
try:
frob_perm = Permutation(
alternating_group(frobenius_permutation(roots, p)))
except TypeError:
raise TypeError(
"The Frobenius element does not generate an element of the alternating group"
)
sign = -(-1)**are_conjugate_in_alternating(frob_perm, data_perm)
return tmp * sign
return alpha_alt
def switch_rows(A, i, j):
r""" Switch the ith and the jth row of A.
"""
from sage.all import Permutation
assert i >= 0 and i < A.nrows(), "i = {}, j = {}".format(i, j)
assert j >= 0 and j < A.nrows(), "i = {}, j = {}".format(i, j)
if i != j:
A.permute_rows(Permutation([(i + 1, j + 1)]))
def cusp_sums_from_signature_to_standard_basis(cuspsums,signatures,level):
"""
Converts a list of cuspsums where each entry is a list of multiplicities with respect
to the input signature order. To a list of cuspsums where each entry is a list of multiplicities
with respect to the standard order of the cusps.
"""
P = Permutation([cusp_number_from_signature(s,level)+1 for s in signatures]).inverse()
return [permutation_action(P,s) for s in cuspsums]
def MatrixToPermutation(P):
n = P.dimensions()[1]
ei = lambda i: vector([int(i == j) for j in range(n)])
def ie(v):
for _ in range(n):
if v[_] == 1: return _
for i in range(n):
assert (ie(ei(i)) == i) # check
p = [ie(P * ei(i)) + 1 for i in range(n)] # need to shift up by one
return Permutation(p)
def factor_perm_repn(self, nfgg=None):
if 'artincoefs' in self._data:
return self._data['artincoefs']
try:
if nfgg is not None:
self._data["nfgg"] = nfgg
elif "nfgg" not in self._data:
from lmfdb.artin_representations.math_classes import NumberFieldGaloisGroup
nfgg = NumberFieldGaloisGroup(self._data['coeffs'])
self._data["nfgg"] = nfgg
else:
nfgg = self._data["nfgg"]
cc = nfgg.conjugacy_classes()
# cc is list, each has methods group, size, order, representative
ccreps = [x.representative() for x in cc]
ccns = [int(x.size()) for x in cc]
ccreps = [Permutation(x).cycle_string() for x in ccreps]
ccgen = '[' + ','.join(ccreps) + ']'
ar = nfgg.artin_representations() # list of artin reps from db
arfull = nfgg.artin_representations_full_characters(
) # list of artin reps from db
gap.set(
'fixed',
'function(a,b) if a*b=a then return 1; else return 0; fi; end;'
)
g = gap.Group(ccgen)
h = g.Stabilizer('1')
rc = g.RightCosets(h)
# Permutation character for our field
permchar = [gap.Sum(rc, 'j->fixed(j,' + x + ')') for x in ccreps]
charcoefs = [0 for x in arfull]
# list of lists (inner are giving char values
ar2 = [x[0] for x in arfull]
for j in range(len(ar)):
fieldchar = int(arfull[j][1])
zet = CyclotomicField(fieldchar).gen()
ar2[j] = [psum(zet, x) for x in ar2[j]]
for j in range(len(ar)):
charcoefs[j] = 0
for k in range(len(ccns)):
charcoefs[j] += int(permchar[k]) * ccns[k] * ar2[j][k]
charcoefs = [x / int(g.Size()) for x in charcoefs]
self._data['artincoefs'] = charcoefs
return charcoefs
except AttributeError:
return []
return []
def show():
r"""
This gets called when an adress of that kind gets loaded:
http://127.0.0.1:37777/Permutations/show?data=3.4.2.1
"""
assert request.method == "GET", "request.method is assumed to be GET"
data = str(request.args.get('data', ''))
try:
data = map(Integer, data.split('.'))
p = Permutation(data)
except (TypeError, ValueError):
logger.info("Impossible to create a permutation from input.")
flash_error("Ooops, impossible to create a permutation from given input!")
return flask.redirect(url_for(".index"))
return render_template("permutations.html", permutation=p,
rankbread=get_bread())
def are_conjugate_in_alternating(rho, sigma):
""" Tests whether rho and sigma are conjugate in the corresponding alternating group.
Does not assume rho and sigma are the same length.
"""
# This seems 10x faster than calling corresponding IsConjugate on corresponding gap objects.
# Only used in the ALT case
rho_cycle_type = rho.cycle_type()
sigma_cycle_type = sigma.cycle_type()
if sum(rho_cycle_type) != sum(sigma_cycle_type):
return False
if rho_cycle_type != sigma_cycle_type:
return False
# Conjugacy classes in A_n are the same as in S_n, except when all the cycles are of odd and different lengths
# In that case, S_n conjugacy classes split up in 2 A_n conjugacy classes
if len(set(sigma_cycle_type)) != len(sigma_cycle_type):
return True
for x in sigma_cycle_type:
if x % 2 == 0:
return True
# Now we know we only have odd length cycles, all different
rho_augmented_cycles = sorted([(len(x), x) for x in rho.cycle_tuples()])
sigma_augmented_cycles = sorted([(len(x), x)
for x in sigma.cycle_tuples()])
# Because sort bases itself first on the first argument of the tuple, the
# cycles match up with their lengths
tmp = [0 for i in range(sum(rho_cycle_type))]
for i in range(len(rho_augmented_cycles)):
rho_tuple = rho_augmented_cycles[i][1]
sigma_tuple = sigma_augmented_cycles[i][1]
for j in range(len(rho_tuple)):
tmp[rho_tuple[j] - 1] = sigma_tuple[j]
from sage.all import Permutation
sig = Permutation(tmp).signature()
if sig == -1:
return False
else:
return True
def matching_permutation(a, b):
r"""Determines if a is an "approximate" permuation of b.
(Copied from Abelfunctions.)
"""
N = len(a)
if N != len(b):
raise ValueError, "Lists must be of same length."
perm = [-1] * N
eps = 0.5 * min([abs(a[i] - a[j]) for i in range(N) for j in range(i)])
for i in xrange(N):
for j in xrange(N):
dist = abs(a[i] - b[j])
if dist < eps:
perm[j] = i + 1
break
# an element is not accounted for if the numerical distance is too large
if -1 in perm:
raise ValueError, "Could not compute matching permutation " \
"between %s and %s." %(a,b)
return Permutation(perm)
def render_passport(args):
info = {}
if 'passport_label' in args:
label = clean_input(args['passport_label'])
C = base.getDBConnection()
dataz = C.curve_automorphisms.passports.find({'passport_label': label})
if dataz.count() is 0:
bread = get_bread([("Search error", url_for('.search'))])
flash_error(
"No refined passport with label %s was found in the database.",
label)
return redirect(url_for(".index"))
data = dataz[0]
g = data['genus']
GG = ast.literal_eval(data['group'])
gn = GG[0]
gt = GG[1]
gp_string = str(gn) + '.' + str(gt)
pretty_group = sg_pretty(gp_string)
if gp_string == pretty_group:
spname = False
else:
spname = True
numb = dataz.count()
try:
numgenvecs = request.args['numgenvecs']
numgenvecs = int(numgenvecs)
except:
numgenvecs = 20
info['numgenvecs'] = numgenvecs
title = 'One refined passport of genus ' + str(
g) + ' with automorphism group $' + pretty_group + '$'
smallgroup = "[" + str(gn) + "," + str(gt) + "]"
prop2 = [
('Genus', '\(%d\)' % g), ('Small Group', '\(%s\)' % pretty_group),
('Signature',
'\(%s\)' % sign_display(ast.literal_eval(data['signature']))),
('Generating Vectors', '\(%d\)' % numb)
]
info.update({
'genus': data['genus'],
'cc': cc_display(data['con']),
'sign': sign_display(ast.literal_eval(data['signature'])),
'group': pretty_group,
'gpid': smallgroup,
'numb': numb,
'disp_numb': min(numb, numgenvecs)
})
if spname:
info.update({'specialname': True})
Ldata = []
HypColumn = False
Lfriends = []
for i in range(0, min(numgenvecs, numb)):
dat = dataz[i]
x1 = dat['total_label']
if 'full_auto' in dat:
x2 = 'No'
if dat['full_label'] not in Lfriends:
Lfriends.append(dat['full_label'])
else:
x2 = 'Yes'
if 'hyperelliptic' in dat:
x3 = tfTOyn(dat['hyperelliptic'])
HypColumn = True
else:
x3 = ' '
x4 = []
for perm in dat['gen_vectors']:
cycperm = Permutation(perm).cycle_string()
x4.append(sep.join(split_perm(cycperm)))
Ldata.append([x1, x2, x3, x4])
info.update({'genvects': Ldata, 'HypColumn': HypColumn})
info.update({'passport_cc': cc_display(ast.literal_eval(data['con']))})
if 'eqn' in data:
info.update({'eqns': data['eqn']})
if 'ndim' in data:
info.update({'Ndim': data['ndim']})
other_data = False
if 'hyperelliptic' in data:
info.update({'ishyp': tfTOyn(data['hyperelliptic'])})
other_data = True
if 'hyp_involution' in data:
inv = Permutation(data['hyp_involution']).cycle_string()
info.update({'hypinv': sep.join(split_perm(inv))})
if 'cyclic_trigonal' in data:
info.update({'iscyctrig': tfTOyn(data['cyclic_trigonal'])})
other_data = True
if 'jacobian_decomp' in data:
jcLatex, corrChar = decjac_format(data['jacobian_decomp'])
info.update({'corrChar': corrChar, 'jacobian_decomp': jcLatex})
if 'cinv' in data:
cinv = Permutation(data['cinv']).cycle_string()
info.update({'cinv': sep.join(split_perm(cinv))})
info.update({'other_data': other_data})
if 'full_auto' in data:
full_G = ast.literal_eval(data['full_auto'])
full_gn = full_G[0]
full_gt = full_G[1]
full_gp_string = str(full_gn) + '.' + str(full_gt)
full_pretty_group = sg_pretty(full_gp_string)
info.update({
'fullauto': full_pretty_group,
'signH': sign_display(ast.literal_eval(data['signH'])),
'higgenlabel': data['full_label']
})
urlstrng, br_g, br_gp, br_sign, refined_p = split_passport_label(label)
if Lfriends:
for Lf in Lfriends:
friends = [("Full automorphism " + Lf, Lf),
("Family containing this refined passport ",
urlstrng)]
else:
friends = [("Family containing this refined passport", urlstrng)]
bread_sign = label_to_breadcrumbs(br_sign)
bread_gp = label_to_breadcrumbs(br_gp)
bread = get_bread([(br_g, './?genus=' + br_g),
('$' + pretty_group + '$',
'./?genus=' + br_g + '&group=' + bread_gp),
(bread_sign, urlstrng), (data['cc'][0], ' ')])
learnmore = [('Completeness of the data',
url_for(".completeness_page")),
('Source of the data', url_for(".how_computed_page")),
('Labeling convention', url_for(".labels_page"))]
downloads = [('Download Magma code',
url_for(".hgcwa_code_download",
label=label,
download_type='magma')),
('Download Gap code',
url_for(".hgcwa_code_download",
label=label,
download_type='gap'))]
return render_template("hgcwa-show-passport.html",
title=title,
bread=bread,
info=info,
properties2=prop2,
friends=friends,
learnmore=learnmore,
downloads=downloads,
credit=credit)
def MatrixToPermutation(P):
return Permutation([list(v).index(1)+1 for v in P.columns()])
def perm_display(L):
return [Permutation(ell).cycle_string() for ell in L]
def render_family(args):
info = {}
if 'label' in args:
label = clean_input(args['label'])
C = base.getDBConnection()
dataz = C.curve_automorphisms.passports.find({'label': label}).sort('cc.0', pymongo.ASCENDING)
if dataz.count() is 0:
flash_error( "No family with label %s was found in the database.", label)
return redirect(url_for(".index"))
data=dataz[0]
g = data['genus']
GG = ast.literal_eval(data['group'])
gn = GG[0]
gt = GG[1]
gp_string=str(gn) + '.' + str(gt)
pretty_group=sg_pretty(gp_string)
if gp_string == pretty_group:
spname=False
else:
spname=True
title = 'Family of Genus ' + str(g) + ' Curves with Automorphism Group $' + pretty_group +'$'
smallgroup="[" + str(gn) + "," +str(gt) +"]"
prop2 = [
('Genus', '\(%d\)' % g),
('Group', '\(%s\)' % pretty_group),
('Signature', '\(%s\)' % sign_display(ast.literal_eval(data['signature'])))
]
info.update({'genus': data['genus'],
'sign': sign_display(ast.literal_eval(data['signature'])),
'group': pretty_group,
'g0':data['g0'],
'dim':data['dim'],
'r':data['r'],
'gpid': smallgroup
})
if spname:
info.update({'specialname': True})
Lcc=[]
Lall=[]
Ltopo_rep=[] #List of topological representatives
Lelements=[] #List of lists of equivalence classes
for dat in dataz:
if ast.literal_eval(dat['con']) not in Lcc:
urlstrng=dat['passport_label']
Lcc.append(ast.literal_eval(dat['con']))
Lall.append([cc_display(ast.literal_eval(dat['con'])),dat['passport_label'],
urlstrng])
#Topological equivalence
if 'topological' in dat:
if dat['topological'] == dat['cc']:
x1=[] #A list of permutations of generating vectors of topo_rep
for perm in dat['gen_vectors']:
x1.append(sep.join(split_perm(Permutation(perm).cycle_string())))
Ltopo_rep.append([dat['passport_label'], dat['total_label'], x1])
topo_class = C.curve_automorphisms.passports.find({'label': dat['label'], 'topological': dat['cc']}).sort('cc.0', pymongo.ASCENDING)
elements=[] #An equivalence class
for element in topo_class:
elements.append((element['passport_label'], element['total_label']))
Lelements.append(elements)
Ltopo_class = zip(Ltopo_rep, Lelements)
topo_length = len(Ltopo_rep)
#Add topological equivalence to info
info.update({'topological_rep': Ltopo_rep})
info.update({'topological_class': Ltopo_class})
info.update({'topological_num': topo_length})
info.update({'passport': Lall})
info.update({'passport_num': len(Lall)})
g2List = ['[2,1]','[4,2]','[8,3]','[10,2]','[12,4]','[24,8]','[48,29]']
if g == 2 and data['group'] in g2List:
g2url = "/Genus2Curve/Q/?geom_aut_grp_id=" + data['group']
friends = [("Genus 2 curves over $\Q$", g2url ) ]
else:
friends = [ ]
br_g, br_gp, br_sign = split_family_label(label)
bread_sign = label_to_breadcrumbs(br_sign)
bread_gp = label_to_breadcrumbs(br_gp)
bread = get_bread([(br_g, './?genus='+br_g),('$'+pretty_group+'$','./?genus='+br_g + '&group='+bread_gp), (bread_sign,' ')])
learnmore =[('Completeness of the data', url_for(".completeness_page")),
('Source of the data', url_for(".how_computed_page")),
('Labeling convention', url_for(".labels_page"))]
if topo_length == 0:
downloads = [('Download Magma code', url_for(".hgcwa_code_download", label=label, download_type='magma')),
('Download Gap code', url_for(".hgcwa_code_download", label=label, download_type='gap'))]
else:
downloads = [('Magma code', None),
(u'\u2003 All vectors', url_for(".hgcwa_code_download", label=label, download_type='magma')),
(u'\u2003 Up to topological equivalence', url_for(".hgcwa_code_download", label=label, download_type='topo_magma')),
('Gap code', None),
(u'\u2003 All vectors', url_for(".hgcwa_code_download", label=label, download_type='gap')),
(u'\u2003 Up to topological equivalence', url_for(".hgcwa_code_download", label=label, download_type='topo_gap'))]
return render_template("hgcwa-show-family.html",
title=title, bread=bread, info=info,
properties2=prop2, friends=friends,
learnmore=learnmore, downloads=downloads, credit=credit)
def switch_columns(A, i, j):
r""" Switch the ith and the jth column of A.
"""
from sage.all import Permutation
if i != j:
A.permute_columns(Permutation([(i + 1, j + 1)]))
def render_passport(args):
info = {}
if 'passport_label' in args:
label = clean_input(args['passport_label'])
dataz = list(db.hgcwa_passports.search({'passport_label': label}))
if not dataz:
bread = get_bread([("Search Error", url_for('.index'))])
flash_error("No refined passport with label %s was found in the database.", label)
return redirect(url_for(".index"))
data=dataz[0]
g = data['genus']
g0=data['g0']
GG = ast.literal_eval(data['group'])
gn = GG[0]
gt = GG[1]
gp_string=str(gn) + '.' + str(gt)
pretty_group=sg_pretty(gp_string)
if gp_string == pretty_group:
spname=False
else:
spname=True
numb = len(dataz)
try:
numgenvecs = int(request.args['numgenvecs'])
numbraidreps = int(request.args['numbraidreps'])
except Exception:
numgenvecs = 20
numbraidreps = 20
info['numgenvecs']=numgenvecs
info['numbraidreps']=numbraidreps
title = 'One refined passport of genus ' + str(g) + ' with automorphism group $' + pretty_group +'$'
smallgroup="[" + str(gn) + "," +str(gt) +"]"
prop2 = [
('Label', label),
('Genus', r'\(%d\)' % g),
('Quotient genus', r'\(%d\)' % g0),
('Group', r'\(%s\)' % pretty_group),
('Signature', r'\(%s\)' % sign_display(ast.literal_eval(data['signature']))),
('Generating Vectors', r'\(%d\)' % numb)
]
info.update({'genus': data['genus'],
'cc': cc_display(data['con']),
'sign': sign_display(ast.literal_eval(data['signature'])),
'group': pretty_group,
'gpid': smallgroup,
'numb': numb,
'disp_numb': min(numb, numgenvecs),
'g0': data['g0']
})
if spname:
info.update({'specialname': True})
Ldata = []
HypColumn = False
Lfriends = []
Lbraid = []
for i in range(0, min(numgenvecs,numb)):
dat = dataz[i]
x1 = dat['total_label']
if 'full_auto' in dat:
x2 = 'no'
if dat['full_label'] not in Lfriends:
Lfriends.append(dat['full_label'])
else:
x2 = 'yes'
if 'hyperelliptic' in dat:
x3 = tfTOyn(dat['hyperelliptic'])
HypColumn = True
else:
x3 = ' '
x4 = []
if dat['g0'] == 0:
for perm in dat['gen_vectors']:
cycperm = Permutation(perm).cycle_string()
x4.append(sep.join(split_perm(cycperm)))
elif dat['g0'] > 0:
for perm in dat['gen_vectors']:
cycperm = Permutation(perm).cycle_string()
#if display_perm == '()':
if cycperm == '()':
x4.append('Id(G)')
else:
x4.append(sep.join(split_perm(cycperm)))
Ldata.append([x1, x2, x3, x4])
info.update({'genvects': Ldata, 'HypColumn': HypColumn})
info.update({'passport_cc': cc_display(ast.literal_eval(data['con']))})
#Generate braid representatives
if 'braid' in dataz[0]:
braid_data = [entry for entry in dataz if entry['braid'] == entry['cc']]
for dat in braid_data:
x5 = []
for perm in dat['gen_vectors']:
x5.append(sep.join(split_perm(Permutation(perm).cycle_string())))
Lbraid.append([dat['total_label'], x5])
braid_length = len(Lbraid)
#Add braid equivalence into info
info.update({'braid': Lbraid,
'braid_numb': braid_length,
'braid_disp_numb': min(braid_length, numbraidreps)})
if 'eqn' in data:
info.update({'eqns': data['eqn']})
if 'ndim' in data:
info.update({'Ndim': data['ndim']})
other_data = False
if 'hyperelliptic' in data:
info.update({'ishyp': tfTOyn(data['hyperelliptic'])})
other_data = True
if 'hyp_involution' in data:
inv=Permutation(data['hyp_involution']).cycle_string()
info.update({'hypinv': sep.join(split_perm(inv))})
if 'cyclic_trigonal' in data:
info.update({'iscyctrig': tfTOyn(data['cyclic_trigonal'])})
other_data = True
if 'jacobian_decomp' in data:
jcLatex, corrChar = decjac_format(data['jacobian_decomp'])
info.update({'corrChar': corrChar, 'jacobian_decomp': jcLatex})
if 'cinv' in data:
cinv=Permutation(data['cinv']).cycle_string()
info.update({'cinv': sep.join(split_perm(cinv))})
info.update({'other_data': other_data})
if 'full_auto' in data:
full_G = ast.literal_eval(data['full_auto'])
full_gn = full_G[0]
full_gt = full_G[1]
full_gp_string = str(full_gn) + '.' + str(full_gt)
full_pretty_group = sg_pretty(full_gp_string)
info.update({'fullauto': full_pretty_group,
'signH': sign_display(ast.literal_eval(data['signH'])),
'higgenlabel': data['full_label']})
urlstrng, br_g, br_gp, br_sign, _ = split_passport_label(label)
if Lfriends:
friends = [("Full automorphism " + Lf, Lf) for Lf in Lfriends]
friends += [("Family containing this refined passport ", urlstrng)]
else:
friends = [("Family containing this refined passport", urlstrng)]
bread_sign = label_to_breadcrumbs(br_sign)
bread_gp = label_to_breadcrumbs(br_gp)
bread = get_bread([
(br_g, './?genus='+br_g),
('$'+pretty_group+'$', './?genus='+br_g + '&group='+bread_gp),
(bread_sign, urlstrng),
(data['cc'][0], ' ')])
if numb == 1 or braid_length == 0:
downloads = [('Code to Magma', url_for(".hgcwa_code_download", label=label, download_type='magma')),
('Code to Gap', url_for(".hgcwa_code_download", label=label, download_type='gap'))]
else:
downloads = [('Code to Magma', None),
(u'\u2003 All vectors', url_for(".hgcwa_code_download", label=label, download_type='magma')),
(u'\u2003 Up to braid equivalence', url_for(".hgcwa_code_download", label=label, download_type='braid_magma')),
('Code to Gap', None),
(u'\u2003 All vectors', url_for(".hgcwa_code_download", label=label, download_type='gap')),
(u'\u2003 Up to braid equivalence', url_for(".hgcwa_code_download", label=label, download_type='braid_gap'))]
downloads.append(('Underlying data', url_for(".hgcwa_data", label=label)))
return render_template("hgcwa-show-passport.html",
title=title, bread=bread, info=info,
properties=prop2, friends=friends,
learnmore=learnmore_list(), downloads=downloads,
KNOWL_ID="curve.highergenus.aut.%s" % label)
def render_family(args):
info = {}
if 'label' in args:
label = clean_input(args['label'])
dataz = list(db.hgcwa_passports.search({'label':label}))
if not dataz:
flash_error("No family with label %s was found in the database.", label)
return redirect(url_for(".index"))
data = dataz[0]
g = data['genus']
g0 = data['g0']
GG = ast.literal_eval(data['group'])
gn = GG[0]
gt = GG[1]
gp_string = str(gn) + '.' + str(gt)
pretty_group = sg_pretty(gp_string)
if gp_string == pretty_group:
spname = False
else:
spname = True
title = 'Family of genus ' + str(g) + ' curves with automorphism group $' + pretty_group +'$'
smallgroup="[" + str(gn) + "," +str(gt) + "]"
prop2 = [
('Label', label),
('Genus', r'\(%d\)' % g),
('Quotient genus', r'\(%d\)' % g0),
('Group', r'\(%s\)' % pretty_group),
('Signature', r'\(%s\)' % sign_display(ast.literal_eval(data['signature'])))
]
info.update({'genus': data['genus'],
'sign': sign_display(ast.literal_eval(data['signature'])),
'group': pretty_group,
'g0': data['g0'],
'dim': data['dim'],
'r': data['r'],
'gpid': smallgroup,
'numb': len(dataz)
})
if spname:
info.update({'specialname': True})
Lcc=[]
Lall=[]
Ltopo_rep=[] #List of topological representatives
for dat in dataz:
if ast.literal_eval(dat['con']) not in Lcc:
urlstrng = dat['passport_label']
Lcc.append(ast.literal_eval(dat['con']))
Lall.append([cc_display(ast.literal_eval(dat['con'])),dat['passport_label'],
urlstrng,dat['cc']])
#Topological equivalence
if 'topological' in dat:
if dat['topological'] == dat['cc']:
x1 = [] #A list of permutations of generating vectors of topo_rep
for perm in dat['gen_vectors']:
x1.append(sep.join(split_perm(Permutation(perm).cycle_string())))
Ltopo_rep.append([dat['total_label'],
x1,
dat['label'],
'T.' + '.'.join(str(x) for x in dat['cc']),
dat['cc']]) #2nd to last element is used for webpage tag
#Add topological equivalence to info
info.update({'topological_rep': Ltopo_rep})
info.update({'topological_num': len(Ltopo_rep)})
info.update({'passport': Lall})
info.update({'passport_num': len(Lall)})
g2List = ['[2,1]', '[4,2]', '[8,3]', '[10,2]', '[12,4]', '[24,8]', '[48,29]']
if g == 2 and data['group'] in g2List:
g2url = "/Genus2Curve/Q/?geom_aut_grp_label=" + ".".join(data['group'][1:-1].split(','))
friends = [(r"Genus 2 curves over $\Q$", g2url)]
else:
friends = []
br_g, br_gp, br_sign = split_family_label(label)
bread_sign = label_to_breadcrumbs(br_sign)
bread_gp = label_to_breadcrumbs(br_gp)
bread = get_bread([(br_g, './?genus='+br_g),
('$'+pretty_group+'$',
'./?genus='+br_g + '&group='+bread_gp),
(bread_sign,' ')])
if len(Ltopo_rep) == 0 or len(dataz) == 1:
downloads = [('Code to Magma', url_for(".hgcwa_code_download", label=label, download_type='magma')),
('Code to Gap', url_for(".hgcwa_code_download", label=label, download_type='gap'))]
else:
downloads = [('Code to Magma', None),
(u'\u2003 All vectors', url_for(".hgcwa_code_download", label=label, download_type='magma')),
(u'\u2003 Up to topological equivalence', url_for(".hgcwa_code_download", label=label, download_type='topo_magma')),
('Code to Gap', None),
(u'\u2003 All vectors', url_for(".hgcwa_code_download", label=label, download_type='gap')),
(u'\u2003 Up to topological equivalence', url_for(".hgcwa_code_download", label=label, download_type='topo_gap'))]
downloads.append(('Underlying data', url_for(".hgcwa_data", label=label)))
return render_template("hgcwa-show-family.html",
title=title, bread=bread, info=info,
properties=prop2, friends=friends,
KNOWL_ID="curve.highergenus.aut.%s" % label,
learnmore=learnmore_list(), downloads=downloads)