def render_group_webpage(args):
data = {}
if 'label' in args:
label = clean_input(args['label'])
label = label.replace('t', 'T')
data = db.gps_transitive.lookup(label)
if data is None:
if re.match(r'^\d+T\d+$', label):
flash_error("Group %s was not found in the database.", label)
else:
flash_error("%s is not a valid label for a Galois group.",
label)
return redirect(url_for(".index"))
title = 'Galois group: ' + label
wgg = WebGaloisGroup.from_nt(data['n'], data['t'])
data['wgg'] = wgg
n = data['n']
t = data['t']
data['yesno'] = yesno
order = data['order']
data['orderfac'] = latex(ZZ(order).factor())
orderfac = latex(ZZ(order).factor())
data['ordermsg'] = "$%s=%s$" % (order, latex(orderfac))
if order == 1:
data['ordermsg'] = "$1$"
if ZZ(order).is_prime():
data['ordermsg'] = "$%s$ (is prime)" % order
pgroup = len(ZZ(order).prime_factors()) < 2
if wgg.num_conjclasses() < 50:
data['cclasses'] = wgg.conjclasses()
if ZZ(order) < ZZ(10000000) and wgg.num_conjclasses() < 21:
data['chartable'] = chartable(n, t)
data['gens'] = wgg.generator_string()
if n == 1 and t == 1:
data['gens'] = 'None needed'
data['num_cc'] = comma(wgg.num_conjclasses())
data['parity'] = "$%s$" % data['parity']
data['subinfo'] = subfield_display(n, data['subfields'])
data['resolve'] = resolve_display(data['quotients'])
if data['gapid'] == 0:
data['gapid'] = "not available"
else:
data['gapid'] = small_group_display_knowl(
int(data['order']), int(data['gapid']),
str([int(data['order']),
int(data['gapid'])]))
data['otherreps'] = wgg.otherrep_list()
ae = data['arith_equiv']
if ae > 0:
if ae > 1:
data[
'arith_equiv'] = r'A number field with this Galois group has %d <a knowl="nf.arithmetically_equivalent", title="arithmetically equivalent">arithmetically equivalent</a> fields.' % ae
else:
data[
'arith_equiv'] = r'A number field with this Galois group has exactly one <a knowl="nf.arithmetically_equivalent", title="arithmetically equivalent">arithmetically equivalent</a> field.'
elif ae > -1:
data[
'arith_equiv'] = r'A number field with this Galois group has no <a knowl="nf.arithmetically_equivalent", title="arithmetically equivalent">arithmetically equivalent</a> fields.'
else:
data[
'arith_equiv'] = r'Data on whether or not a number field with this Galois group has <a knowl="nf.arithmetically_equivalent", title="arithmetically equivalent">arithmetically equivalent</a> fields has not been computed.'
intreps = list(db.gps_gmodules.search({'n': n, 't': t}))
if len(intreps) > 0:
data['int_rep_classes'] = [str(z[0]) for z in intreps[0]['gens']]
for onerep in intreps:
onerep['gens'] = [
list_to_latex_matrix(z[1]) for z in onerep['gens']
]
data['int_reps'] = intreps
data['int_reps_complete'] = int_reps_are_complete(intreps)
dcq = data['moddecompuniq']
if dcq[0] == 0:
data['decompunique'] = 0
else:
data['decompunique'] = dcq[0]
data['isoms'] = [[mult2mult(z[0]),
mult2mult(z[1])] for z in dcq[1]]
data['isoms'] = [[
modules2string(n, t, z[0]),
modules2string(n, t, z[1])
] for z in data['isoms']]
#print dcq[1]
#print data['isoms']
friends = []
if db.nf_fields.exists({'galois_label': "%dT%d" % (n, t)}):
friends.append(
('Number fields with this Galois group',
url_for('number_fields.number_field_render_webpage') +
"?galois_group=%dT%d" % (n, t)))
prop2 = [
('Label', label),
('Degree', prop_int_pretty(data['n'])),
('Order', prop_int_pretty(order)),
('Cyclic', yesno(data['cyc'])),
('Abelian', yesno(data['ab'])),
('Solvable', yesno(data['solv'])),
('Primitive', yesno(data['prim'])),
('$p$-group', yesno(pgroup)),
]
pretty = group_display_short(n, t, emptyifnotpretty=True)
if len(pretty) > 0:
prop2.extend([('Group:', pretty)])
data['pretty_name'] = pretty
data['name'] = re.sub(r'_(\d+)', r'_{\1}', data['name'])
data['name'] = re.sub(r'\^(\d+)', r'^{\1}', data['name'])
data['nilpotency'] = '$%s$' % data['nilpotency']
if data['nilpotency'] == '$-1$':
data['nilpotency'] += ' (not nilpotent)'
bread = get_bread([(label, ' ')])
return render_template("gg-show-group.html",
credit=GG_credit,
title=title,
bread=bread,
info=data,
properties=prop2,
friends=friends,
KNOWL_ID="gg.%s" % label,
learnmore=learnmore_list())
def render_group_webpage(args):
data = None
info = {}
if 'label' in args:
label = clean_input(args['label'])
label = label.replace('t', 'T')
data = db.gps_transitive.lookup(label)
if data is None:
bread = get_bread([("Search Error", ' ')])
info['err'] = "Group " + label + " was not found in the database."
info['label'] = label
return search_input_error(info, bread)
data['label_raw'] = label.lower()
title = 'Galois Group: ' + label
wgg = WebGaloisGroup.from_data(data)
n = data['n']
t = data['t']
data['yesno'] = yesno
order = data['order']
data['orderfac'] = latex(ZZ(order).factor())
orderfac = latex(ZZ(order).factor())
data['ordermsg'] = "$%s=%s$" % (order, latex(orderfac))
if order == 1:
data['ordermsg'] = "$1$"
if ZZ(order).is_prime():
data['ordermsg'] = "$%s$ (is prime)" % order
pgroup = len(ZZ(order).prime_factors()) < 2
if n == 1:
G = gap.SmallGroup(n, t)
else:
G = gap.TransitiveGroup(n, t)
if ZZ(order) < ZZ('10000000'):
ctable = chartable(n, t)
else:
ctable = 'Group too large'
data['gens'] = generators(n, t)
if n == 1 and t == 1:
data['gens'] = 'None needed'
data['chartable'] = ctable
data['parity'] = "$%s$" % data['parity']
data['cclasses'] = conjclasses(G, n)
data['subinfo'] = subfield_display(n, data['subs'])
data['resolve'] = resolve_display(data['resolve'])
if data['gapid'] == 0:
data['gapid'] = "Data not available"
else:
data['gapid'] = small_group_display_knowl(int(data['order']),
int(data['gapid']),
str([int(data['order']), int(data['gapid'])]))
data['otherreps'] = wgg.otherrep_list()
ae = wgg.arith_equivalent()
if ae>0:
if ae>1:
data['arith_equiv'] = r'A number field with this Galois group has %d <a knowl="nf.arithmetically_equivalent", title="arithmetically equivalent">arithmetically equivalent</a> fields.'% ae
else:
data['arith_equiv'] = r'A number field with this Galois group has exactly one <a knowl="nf.arithmetically_equivalent", title="arithmetically equivalent">arithmetically equivalent</a> field.'
else:
data['arith_equiv'] = r'A number field with this Galois group has no <a knowl="nf.arithmetically_equivalent", title="arithmetically equivalent">arithmetically equivalent</a> fields.'
if len(data['otherreps']) == 0:
data['otherreps']="There is no other low degree representation."
intreps = list(db.gps_gmodules.search({'n': n, 't': t}))
if len(intreps) > 0:
data['int_rep_classes'] = [str(z[0]) for z in intreps[0]['gens']]
for onerep in intreps:
onerep['gens']=[list_to_latex_matrix(z[1]) for z in onerep['gens']]
data['int_reps'] = intreps
data['int_reps_complete'] = int_reps_are_complete(intreps)
dcq = data['moddecompuniq']
if dcq[0] == 0:
data['decompunique'] = 0
else:
data['decompunique'] = dcq[0]
data['isoms'] = [[mult2mult(z[0]), mult2mult(z[1])] for z in dcq[1]]
data['isoms'] = [[modules2string(n,t,z[0]), modules2string(n,t,z[1])] for z in data['isoms']]
#print dcq[1]
#print data['isoms']
friends = []
if db.nf_fields.exists({'degree': n, 'galt': t}):
friends.append(('Number fields with this Galois group', url_for('number_fields.number_field_render_webpage')+"?galois_group=%dT%d" % (n, t) ))
prop2 = [('Label', label),
('Order', '\(%s\)' % order),
('n', '\(%s\)' % data['n']),
('Cyclic', yesno(data['cyc'])),
('Abelian', yesno(data['ab'])),
('Solvable', yesno(data['solv'])),
('Primitive', yesno(data['prim'])),
('$p$-group', yesno(pgroup)),
]
pretty = group_display_pretty(n,t)
if len(pretty)>0:
prop2.extend([('Group:', pretty)])
info['pretty_name'] = pretty
data['name'] = re.sub(r'_(\d+)',r'_{\1}',data['name'])
data['name'] = re.sub(r'\^(\d+)',r'^{\1}',data['name'])
info.update(data)
bread = get_bread([(label, ' ')])
return render_template("gg-show-group.html", credit=GG_credit, title=title, bread=bread, info=info, properties2=prop2, friends=friends, KNOWL_ID="gg.%s"%info['label_raw'], learnmore=learnmore_list())