def modules2string(n, t, modlist):
modlist = [[galois_module_knowl(n, t, z[0]), int(z[1])] for z in modlist]
ans = modlist[0][0]
modlist[0][1] -= 1
for j in range(len(modlist)):
while modlist[j][1] > 0:
ans += r' $\oplus$ ' + modlist[j][0]
modlist[j][1] -= 1
return ans
def modules2string(n, t, modlist):
modlist = [[galois_module_knowl(n, t, z[0]), int(z[1])] for z in modlist]
ans = modlist[0][0]
modlist[0][1] -= 1
for j in range(len(modlist)):
while modlist[j][1]>0:
ans += r' $\oplus$ '+modlist[j][0]
modlist[j][1] -= 1
return ans
def unit_galois_action_show(self):
ugm = self.unit_galois_action()
if ugm == []:
return ''
C = base.getDBConnection()
gmods = C.transitivegroups.Gmodules
n = self.degree()
t = self.galois_t()
ugm = [[galois_module_knowl(n, t, z[0], C), int(z[1])] for z in ugm]
#ugm = [do_mult(a) for a in ugm]
ans = ugm[0][0]
ugm[0][1] -= 1
for j in range(len(ugm)):
while ugm[j][1] > 0:
ans += r' $\oplus$ ' + ugm[j][0]
ugm[j][1] -= 1
return ans
def unit_galois_action_show(self):
ugm = self.unit_galois_action()
if ugm == []:
return ''
C = base.getDBConnection()
gmods = C.transitivegroups.Gmodules
n = self.degree()
t = self.galois_t()
ugm = [[galois_module_knowl(n, t, z[0], C), int(z[1])] for z in ugm]
#ugm = [do_mult(a) for a in ugm]
ans = ugm[0][0]
ugm[0][1] -= 1
for j in range(len(ugm)):
while ugm[j][1]>0:
ans += r' $\oplus$ '+ugm[j][0]
ugm[j][1] -= 1
return ans
def render_group_webpage(args):
data = None
info = {}
if 'label' in args:
label = clean_input(args['label'])
label = label.replace('t', 'T')
C = base.getDBConnection()
data = C.transitivegroups.groups.find_one({'label': label})
if data is None:
bread = get_bread([("Search error", url_for('.search'))])
info['err'] = "Group " + label + " was not found in the database."
info['label'] = label
return search_input_error(info, bread)
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('10000000000'):
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(C, n, data['subs'])
data['resolve'] = resolve_display(C, data['resolve'])
# if len(data['resolve']) == 0: data['resolve'] = 'None'
data['otherreps'] = wgg.otherrep_list()
query={'galois': bson.SON([('n', n), ('t', t)])}
C = base.getDBConnection()
intreps = C.transitivegroups.Gmodules.find({'n': n, 't': t})
# turn cursor into a list
intreps = [z for z in intreps]
data['int_reps'] = [galois_module_knowl(n, t, z['index'], C) for z in intreps]
data['int_reps_complete'] = int_reps_are_complete(intreps)
friends = []
one = C.numberfields.fields.find_one(query)
if one:
friends.append(('Number fields with this Galois group', url_for('number_fields.number_field_render_webpage')+"?galois_group=%dT%d" % (n, t) ))
prop2 = [
('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)),
('Name:', group_display_short(n, t, C)),
]
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)