def groups_per_genus(genus):
group_stats = db.hgcwa_passports.stats.get_oldstat('bygenus/' + genus +
'/group')
# Redirect to 404 if statistic is not found
if not group_stats:
return abort(
404,
'Group statistics for curves of genus %s not found in database.' %
genus)
# Groups are stored in sorted order
groups = group_stats['counts']
# Create isomorphism classes
iso_classes = []
for group in groups:
iso_classes.append(sg_pretty(re.sub(hgcwa_group, r'\1.\2', group[0])))
info = {'genus': genus, 'groups': groups, 'iso_classes': iso_classes}
title = ('Families of Higher Genus Curves with Automorphisms: Genus ' +
genus + ' Group Statistics')
bread = get_bread([('Statistics', url_for('.statistics')),
('Groups per Genus', url_for('.statistics')),
(str(genus), ' ')])
return render_template("hgcwa-stats-groups-per-genus.html",
info=info,
credit=credit,
title=title,
learnmore=learnmore_list(),
bread=bread)
def groups_per_genus(genus):
group_stats = db_hgcwa_stats().find_one(
{'_id': 'bygenus/' + genus + '/group'})
# Redirect to 404 if statistic is not found
if not group_stats:
return abort(
404,
'Group statistics for curves of genus %s not found in database.' %
genus)
# Groups are stored in sorted order
groups = group_stats['counts']
# Create isomorphism classes
hgcwa_group = re.compile(r'\[(\d+),(\d+)\]')
iso_classes = []
for group in groups:
iso_classes.append(sg_pretty(re.sub(hgcwa_group, r'\1.\2', group[0])))
info = {'genus': genus, 'groups': groups, 'iso_classes': iso_classes}
title = 'Families of Higher Genus Curves with Automorphisms: genus ' + genus + ' group statistics'
bread = get_bread([('statistics', url_for('.statistics')),
('Groups per Genus', url_for('.statistics')),
(str(genus), ' ')])
return render_template("hgcwa-stats-groups-per-genus.html",
info=info,
credit=credit,
title=title,
bread=bread)
def groups_per_genus(genus):
group_stats = db_hgcwa_stats().find_one({'_id':'bygenus/' + genus + '/group'})
# Redirect to 404 if statistic is not found
if not group_stats:
return abort(404, 'Group statistics for curves of genus %s not found in database.' % genus)
# Groups are stored in sorted order
groups = group_stats['counts']
# Create isomorphism classes
hgcwa_group = re.compile(r'\[(\d+),(\d+)\]')
iso_classes = []
for group in groups:
iso_classes.append(sg_pretty(re.sub(hgcwa_group, r'\1.\2', group[0])))
info = {
'genus' : genus,
'groups': groups,
'iso_classes' : iso_classes
}
title = 'Families of Higher Genus Curves with Automorphisms: Genus ' + genus + ' Group Statistics'
bread = get_bread([('Statistics', url_for('.statistics')), ('Groups per Genus', url_for('.statistics')), (str(genus), ' ')])
return render_template("hgcwa-stats-groups-per-genus.html", info=info, credit=credit, title=title, bread=bread)
def topological_action(fam, cc):
br_g, br_gp, br_sign = split_family_label(fam)
cc_list = cc_to_list(cc)
representative = fam + '.' + cc[2:]
#Get the equivalence class
topo_class = list(db.hgcwa_passports.search({'label': fam, 'topological': cc_list}))
GG = ast.literal_eval(topo_class[0]['group'])
gn = GG[0]
gt = GG[1]
gp_string = str(gn) + '.' + str(gt)
pretty_group = sg_pretty(gp_string)
bread_sign = label_to_breadcrumbs(br_sign)
bread_gp = label_to_breadcrumbs(br_gp)
bread = get_bread(
[(br_g, '../?genus=' + br_g),
('$%s$' % pretty_group, '../?genus=%s&group=%s' % (br_g, bread_gp)),
(bread_sign, '../' + fam),
('Topological Orbit for %s, %s' % (cc_list[0], cc_list[1]), ' ')
]
)
title = 'One Orbit Under Topological Action'
downloads = [('Download Magma code', url_for(".hgcwa_code_download", label=representative, download_type='rep_magma')),
('Download Gap code', url_for(".hgcwa_code_download", label=representative, download_type='rep_gap'))]
Lbraid = {}
for element in topo_class:
if str(element['braid']) in Lbraid:
Lbraid[str(element['braid'])].append(
(element['passport_label'],
element['total_label'],
' '))
# We include the space so that we don't have duplicate conjugacy
# classes displayed
else:
Lbraid[str(element['braid'])] = [
(element['passport_label'],
element['total_label'],
cc_display(ast.literal_eval(element['con'])))]
# Sort braid ascending
key_for_sorted = sorted(ast.literal_eval(key) for key in Lbraid)
sorted_braid = [Lbraid[str(key)] for key in key_for_sorted]
info = {'topological_class': sorted_braid, 'representative': representative, 'braid_num': len(Lbraid)}
return render_template("hgcwa-topological-action.html", info=info, credit=credit, title=title, bread=bread, downloads=downloads)
def groups_per_genus(genus):
un_grps = db.hgcwa_unique_groups
# Redirect to 404 if statistic is not found
if not un_grps.count({'genus':genus}):
return abort(404, 'Group statistics for curves of genus %s not found in database.' % genus)
info = {}
gp_data = un_grps.search({'genus':genus},projection=['group','g0_is_gt0','g0_gt0_list','gen_vectors','topological','braid'],info=info)
# Make list groups_0 where each entry is a list [ group, gen_vectors, tops, braids
groups_0 = []
# Make list groups_gt0 where each entry is a list [group, gen_vectors]
groups_gt0 = []
complete_info = db.hgcwa_complete.lucky({'genus':genus})
show_top_braid = complete_info['top_braid_compute']
show_g0_gt0 = complete_info['g0_gt0_compute']
for dataz in gp_data:
group = dataz['group']
group_str = str(dataz['group'])
iso_class = sg_pretty("%s.%s" % tuple(group))
if dataz['g0_is_gt0']:
groups_gt0.append((iso_class, group_str, dataz['gen_vectors'], cc_display(dataz['g0_gt0_list'])))
elif not show_top_braid:
groups_0.append((iso_class, group_str, dataz['gen_vectors']))
else:
groups_0.append((iso_class, group_str, dataz['gen_vectors'], dataz['topological'], dataz['braid']))
info = {
'genus': genus,
'groups_0': groups_0,
'groups_gt0': groups_gt0,
'show_top_braid' : show_top_braid,
'show_g0_gt0' : show_g0_gt0,
'group_display' : group_display
}
title = 'Families of higher genus curves with automorphisms: Genus %s group statistics' % genus
bread = get_bread([('Statistics', url_for('.statistics')),
('Groups per genus', url_for('.statistics')),
(str(genus), ' ')])
return render_template("hgcwa-stats-groups-per-genus.html",
info=info,
credit=credit,
title=title,
learnmore=learnmore_list(),
bread=bread)
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 render_family(args):
info = {}
if 'label' in args:
label = clean_input(args['label'])
C = base.getDBConnection()
dataz = C.curve_automorphisms.passports.find({'label': label})
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 = []
i = 1
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
])
i = i + 1
info.update({'passport': 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"))]
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-family.html",
title=title,
bread=bread,
info=info,
properties2=prop2,
friends=friends,
learnmore=learnmore,
downloads=downloads,
credit=credit)
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 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 len(dataz) == 0:
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']
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 = 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 render_family(args):
info = {}
if 'label' in args:
label = clean_input(args['label'])
dataz = list(db.hgcwa_passports.search({'label':label}))
if len(dataz) == 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=[]
i=1
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])
i=i+1
info.update({'passport': 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"))]
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-family.html",
title=title, bread=bread, info=info,
properties2=prop2, friends=friends,
learnmore=learnmore, downloads=downloads, credit=credit)
def group_display(strg):
return sg_pretty(re.sub(hgcwa_group, r'\1.\2', strg))
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)