def render_field_webpage(args):
data = None
info = {}
if 'label' in args:
label = clean_input(args['label'])
C = base.getDBConnection()
data = C.localfields.fields.find_one({'label': label})
if data is None:
bread = get_bread([("Search error", ' ')])
info['err'] = "Field " + label + " was not found in the database."
info['label'] = label
return search_input_error(info, bread)
title = 'Local Number Field:' + label
polynomial = coeff_to_poly(data['coeffs'])
p = data['p']
e = data['e']
f = data['f']
cc = data['c']
GG = data['gal']
gn = GG[0]
gt = GG[1]
prop2 = [
('Label', label),
('Base', '\(\Q_{%s}\)' % p),
('Degree', '\(%s\)' % data['n']),
('e', '\(%s\)' % e),
('f', '\(%s\)' % f),
('c', '\(%s\)' % cc),
('Galois group', group_display_short(gn, gt, C)),
]
Pt = PolynomialRing(QQ, 't')
Pyt = PolynomialRing(Pt, 'y')
eisenp = Pyt(str(data['eisen']))
unramp = Pyt(str(data['unram']))
# Look up the unram poly so we can link to it
unramdata = C.localfields.fields.find_one({'p': p, 'n': f, 'c': 0})
if len(unramdata) > 0:
unramfriend = "/LocalNumberField/%s" % unramdata['label']
else:
logger.fatal("Cannot find unramified field!")
unramfriend = ''
rfdata = C.localfields.fields.find_one({
'p': p,
'n': {
'$in': [1, 2]
},
'rf': data['rf']
})
if rfdata is None:
logger.fatal("Cannot find discriminant root field!")
rffriend = ''
else:
rffriend = "/LocalNumberField/%s" % rfdata['label']
info.update({
'polynomial': web_latex(polynomial),
'n': data['n'],
'p': data['p'],
'c': data['c'],
'e': data['e'],
'f': data['f'],
't': data['t'],
'u': data['u'],
'rf': printquad(data['rf'], p),
'hw': data['hw'],
'slopes': show_slopes(data['slopes']),
'gal': group_display_knowl(gn, gt, C),
'gt': gt,
'inertia': group_display_inertia(data['inertia'], C),
'unram': web_latex(unramp),
'eisen': web_latex(eisenp),
'gms': data['gms'],
'aut': data['aut'],
})
friends = [('Galois group', "/GaloisGroup/%dT%d" % (gn, gt))]
if unramfriend != '':
friends.append(('Unramified subfield', unramfriend))
if rffriend != '':
friends.append(('Discriminant root field', rffriend))
bread = get_bread([(label, ' ')])
learnmore = [('Completeness of the data',
url_for(".completeness_page")),
('Source of the data', url_for(".how_computed_page")),
('Local field labels', url_for(".labels_page"))]
return render_template("lf-show-field.html",
credit=LF_credit,
title=title,
bread=bread,
info=info,
properties2=prop2,
friends=friends,
learnmore=learnmore)
def render_field_webpage(args):
data = None
info = {}
if 'label' in args:
label = clean_input(args['label'])
data = lfdb().find_one({'label': label})
if data is None:
bread = get_bread([("Search error", ' ')])
info['err'] = "Field " + label + " was not found in the database."
info['label'] = label
return search_input_error(info, bread)
title = 'Local Number Field ' + label
polynomial = coeff_to_poly(string2list(data['coeffs']))
p = data['p']
e = data['e']
f = data['f']
cc = data['c']
GG = data['gal']
gn = GG[0]
gt = GG[1]
the_gal = WebGaloisGroup.from_nt(gn,gt)
isgal = ' Galois' if the_gal.order() == gn else ' not Galois'
abelian = ' and abelian' if the_gal.is_abelian() else ''
galphrase = 'This field is'+isgal+abelian+' over $\Q_{%d}$.'%p
autstring = r'\Gal' if the_gal.order() == gn else r'\Aut'
prop2 = [
('Label', label),
('Base', '\(\Q_{%s}\)' % p),
('Degree', '\(%s\)' % data['n']),
('e', '\(%s\)' % e),
('f', '\(%s\)' % f),
('c', '\(%s\)' % cc),
('Galois group', group_display_short(gn, gt, db())),
]
Pt = PolynomialRing(QQ, 't')
Pyt = PolynomialRing(Pt, 'y')
eisenp = Pyt(str(data['eisen']))
unramp = Pyt(str(data['unram']))
# Look up the unram poly so we can link to it
unramdata = lfdb().find_one({'p': p, 'n': f, 'c': 0})
if unramdata is not None:
unramfriend = "/LocalNumberField/%s" % unramdata['label']
else:
logger.fatal("Cannot find unramified field!")
unramfriend = ''
rfdata = lfdb().find_one({'p': p, 'n': {'$in': [1, 2]}, 'rf': data['rf']})
if rfdata is None:
logger.fatal("Cannot find discriminant root field!")
rffriend = ''
else:
rffriend = "/LocalNumberField/%s" % rfdata['label']
gsm = data['gsm']
if gsm == '0':
gsm = 'Not computed'
elif gsm == '-1':
gsm = 'Does not exist'
else:
gsm = web_latex(coeff_to_poly(string2list(gsm)))
info.update({
'polynomial': web_latex(polynomial),
'n': data['n'],
'p': p,
'c': data['c'],
'e': data['e'],
'f': data['f'],
't': data['t'],
'u': data['u'],
'rf': printquad(data['rf'], p),
'hw': data['hw'],
'slopes': show_slopes(data['slopes']),
'gal': group_display_knowl(gn, gt, db()),
'gt': gt,
'inertia': group_display_inertia(data['inertia'], db()),
'unram': web_latex(unramp),
'eisen': web_latex(eisenp),
'gms': data['gms'],
'gsm': gsm,
'galphrase': galphrase,
'autstring': autstring,
'subfields': format_subfields(data['subfields'],p),
'aut': data['aut'],
})
friends = [('Galois group', "/GaloisGroup/%dT%d" % (gn, gt))]
if unramfriend != '':
friends.append(('Unramified subfield', unramfriend))
if rffriend != '':
friends.append(('Discriminant root field', rffriend))
bread = get_bread([(label, ' ')])
learnmore = [('Completeness of the data', url_for(".completeness_page")),
('Source of the data', url_for(".how_computed_page")),
('Local field labels', url_for(".labels_page"))]
return render_template("lf-show-field.html", credit=LF_credit, title=title, bread=bread, info=info, properties2=prop2, friends=friends, learnmore=learnmore)
def render_field_webpage(args):
data = None
info = {}
if 'label' in args:
label = clean_input(args['label'])
data = db.lf_fields.lookup(label)
if data is None:
if re.match(r'^\d+\.\d+\.\d+\.\d+$', label):
flash_error("Field %s was not found in the database.", label)
else:
flash_error("%s is not a valid label for a $p$-adic field.",
label)
return redirect(url_for(".index"))
title = '$p$-adic field ' + prettyname(data)
titletag = 'p-adic field ' + prettyname(data)
polynomial = coeff_to_poly(data['coeffs'])
p = data['p']
Qp = r'\Q_{%d}' % p
e = data['e']
f = data['f']
cc = data['c']
gt = int(data['galois_label'].split('T')[1])
gn = data['n']
the_gal = WebGaloisGroup.from_nt(gn, gt)
isgal = ' Galois' if the_gal.order() == gn else ' not Galois'
abelian = ' and abelian' if the_gal.is_abelian() else ''
galphrase = 'This field is' + isgal + abelian + r' over $\Q_{%d}.$' % p
autstring = r'\Gal' if the_gal.order() == gn else r'\Aut'
prop2 = [
('Label', label),
('Base', r'\(%s\)' % Qp),
('Degree', r'\(%s\)' % data['n']),
('e', r'\(%s\)' % e),
('f', r'\(%s\)' % f),
('c', r'\(%s\)' % cc),
('Galois group', group_pretty_and_nTj(gn, gt)),
]
# Look up the unram poly so we can link to it
unramlabel = db.lf_fields.lucky({'p': p, 'n': f, 'c': 0}, projection=0)
if unramlabel is None:
logger.fatal("Cannot find unramified field!")
unramfriend = ''
else:
unramfriend = "/LocalNumberField/%s" % unramlabel
unramdata = db.lf_fields.lookup(unramlabel)
Px = PolynomialRing(QQ, 'x')
Pt = PolynomialRing(QQ, 't')
Ptx = PolynomialRing(Pt, 'x')
if data['f'] == 1:
unramp = r'$%s$' % Qp
eisenp = Ptx(str(data['eisen']).replace('y', 'x'))
eisenp = web_latex(eisenp)
else:
unramp = data['unram'].replace('t', 'x')
unramp = web_latex(Px(str(unramp)))
unramp = prettyname(
unramdata
) + ' $\\cong ' + Qp + '(t)$ where $t$ is a root of ' + unramp
eisenp = Ptx(str(data['eisen']).replace('y', 'x'))
eisenp = '$' + web_latex(eisenp, False) + '\\in' + Qp + '(t)[x]$'
rflabel = db.lf_fields.lucky(
{
'p': p,
'n': {
'$in': [1, 2]
},
'rf': data['rf']
}, projection=0)
if rflabel is None:
logger.fatal("Cannot find discriminant root field!")
rffriend = ''
else:
rffriend = "/LocalNumberField/%s" % rflabel
gsm = data['gsm']
if gsm == [0]:
gsm = 'Not computed'
elif gsm == [-1]:
gsm = 'Does not exist'
else:
gsm = lf_formatfield(','.join([str(b) for b in gsm]))
info.update({
'polynomial':
web_latex(polynomial),
'n':
data['n'],
'p':
p,
'c':
data['c'],
'e':
data['e'],
'f':
data['f'],
't':
data['t'],
'u':
data['u'],
'rf':
lf_display_knowl(rflabel, name=printquad(data['rf'], p)),
'base':
lf_display_knowl(str(p) + '.1.0.1', name='$%s$' % Qp),
'hw':
data['hw'],
'slopes':
show_slopes(data['slopes']),
'gal':
group_pretty_and_nTj(gn, gt, True),
'gt':
gt,
'inertia':
group_display_inertia(data['inertia']),
'unram':
unramp,
'eisen':
eisenp,
'gms':
data['gms'],
'gsm':
gsm,
'galphrase':
galphrase,
'autstring':
autstring,
'subfields':
format_subfields(data['subfields'], p),
'aut':
data['aut'],
})
friends = [('Galois group', "/GaloisGroup/%dT%d" % (gn, gt))]
if unramfriend != '':
friends.append(('Unramified subfield', unramfriend))
if rffriend != '':
friends.append(('Discriminant root field', rffriend))
bread = get_bread([(label, ' ')])
return render_template(
"lf-show-field.html",
credit=LF_credit,
title=title,
titletag=titletag,
bread=bread,
info=info,
properties=prop2,
friends=friends,
learnmore=learnmore_list(),
KNOWL_ID="lf.%s" % label,
)
def render_field_webpage(args):
data = None
info = {}
if 'label' in args:
label = clean_input(args['label'])
C = base.getDBConnection()
data = C.localfields.fields.find_one({'label': label})
if data is None:
bread = get_bread([("Search error", url_for('.search'))])
info['err'] = "Field " + label + " was not found in the database."
info['label'] = label
return search_input_error(info, bread)
title = 'Local Number Field:' + label
polynomial = coeff_to_poly(data['coeffs'])
p = data['p']
e = data['e']
f = data['f']
cc = data['c']
GG = data['gal']
gn = GG[0]
gt = GG[1]
prop2 = [
('Base', '\(\Q_{%s}\)' % p),
('Degree', '\(%s\)' % data['n']),
('e', '\(%s\)' % e),
('f', '\(%s\)' % f),
('c', '\(%s\)' % cc),
('Galois group', group_display_short(gn, gt, C)),
]
Pt = PolynomialRing(QQ, 't')
Pyt = PolynomialRing(Pt, 'y')
eisenp = Pyt(str(data['eisen']))
unramp = Pyt(str(data['unram']))
# Look up the unram poly so we can link to it
unramdata = C.localfields.fields.find_one({'p': p, 'n': f, 'c': 0})
if len(unramdata) > 0:
unramfriend = "/LocalNumberField/%s" % unramdata['label']
else:
logger.fatal("Cannot find unramified field!")
unramfriend = ''
rfdata = C.localfields.fields.find_one({'p': p, 'n': {'$in': [1, 2]}, 'rf': data['rf']})
if rfdata is None:
logger.fatal("Cannot find discriminant root field!")
rffriend = ''
else:
rffriend = "/LocalNumberField/%s" % rfdata['label']
info.update({
'polynomial': web_latex(polynomial),
'n': data['n'],
'p': data['p'],
'c': data['c'],
'e': data['e'],
'f': data['f'],
't': data['t'],
'u': data['u'],
'rf': printquad(data['rf'], p),
'hw': data['hw'],
'slopes': show_slopes(data['slopes']),
'gal': group_display_knowl(gn, gt, C),
'gt': gt,
'inertia': group_display_inertia(data['inertia'], C),
'unram': web_latex(unramp),
'eisen': web_latex(eisenp),
'gms': data['gms'],
'aut': data['aut'],
})
friends = [('Galois group', "/GaloisGroup/%dT%d" % (gn, gt))]
if unramfriend != '':
friends.append(('Unramified subfield', unramfriend))
if rffriend != '':
friends.append(('Discriminant root field', rffriend))
bread = get_bread([(label, ' ')])
learnmore = [('Completeness of the data', url_for(".completeness_page")),
('Source of the data', url_for(".how_computed_page")),
('Local field labels', url_for(".labels_page"))]
return render_template("lf-show-field.html", credit=LF_credit, title=title, bread=bread, info=info, properties2=prop2, friends=friends, learnmore=learnmore)
def render_field_webpage(args):
data = None
info = {}
if 'label' in args:
label = clean_input(args['label'])
data = lfdb().find_one({'label': label})
if data is None:
bread = get_bread([("Search error", ' ')])
info['err'] = "Field " + label + " was not found in the database."
info['label'] = label
return search_input_error(info, bread)
title = 'Local Number Field ' + label
polynomial = coeff_to_poly(string2list(data['coeffs']))
p = data['p']
e = data['e']
f = data['f']
cc = data['c']
GG = data['gal']
gn = GG[0]
gt = GG[1]
the_gal = WebGaloisGroup.from_nt(gn,gt)
isgal = ' Galois' if the_gal.order() == gn else ' not Galois'
abelian = ' and abelian' if the_gal.is_abelian() else ''
galphrase = 'This field is'+isgal+abelian+' over $\Q_{%d}$.'%p
autstring = r'\Gal' if the_gal.order() == gn else r'\Aut'
prop2 = [
('Label', label),
('Base', '\(\Q_{%s}\)' % p),
('Degree', '\(%s\)' % data['n']),
('e', '\(%s\)' % e),
('f', '\(%s\)' % f),
('c', '\(%s\)' % cc),
('Galois group', group_display_short(gn, gt, db())),
]
Pt = PolynomialRing(QQ, 't')
Pyt = PolynomialRing(Pt, 'y')
eisenp = Pyt(str(data['eisen']))
unramp = Pyt(str(data['unram']))
# Look up the unram poly so we can link to it
unramdata = lfdb().find_one({'p': p, 'n': f, 'c': 0})
if unramdata is not None:
unramfriend = "/LocalNumberField/%s" % unramdata['label']
else:
logger.fatal("Cannot find unramified field!")
unramfriend = ''
rfdata = lfdb().find_one({'p': p, 'n': {'$in': [1, 2]}, 'rf': data['rf']})
if rfdata is None:
logger.fatal("Cannot find discriminant root field!")
rffriend = ''
else:
rffriend = "/LocalNumberField/%s" % rfdata['label']
gsm = data['gsm']
if gsm == '0':
gsm = 'Not computed'
elif gsm == '-1':
gsm = 'Does not exist'
else:
gsm = web_latex(coeff_to_poly(string2list(gsm)))
info.update({
'polynomial': web_latex(polynomial),
'n': data['n'],
'p': p,
'c': data['c'],
'e': data['e'],
'f': data['f'],
't': data['t'],
'u': data['u'],
'rf': printquad(data['rf'], p),
'hw': data['hw'],
'slopes': show_slopes(data['slopes']),
'gal': group_display_knowl(gn, gt, db()),
'gt': gt,
'inertia': group_display_inertia(data['inertia'], db()),
'unram': web_latex(unramp),
'eisen': web_latex(eisenp),
'gms': data['gms'],
'gsm': gsm,
'galphrase': galphrase,
'autstring': autstring,
'subfields': format_subfields(data['subfields'],p),
'aut': data['aut'],
})
friends = [('Galois group', "/GaloisGroup/%dT%d" % (gn, gt))]
if unramfriend != '':
friends.append(('Unramified subfield', unramfriend))
if rffriend != '':
friends.append(('Discriminant root field', rffriend))
bread = get_bread([(label, ' ')])
learnmore = [('Completeness of the data', url_for(".completeness_page")),
('Source of the data', url_for(".how_computed_page")),
('Local field labels', url_for(".labels_page"))]
return render_template("lf-show-field.html", credit=LF_credit, title=title, bread=bread, info=info, properties2=prop2, friends=friends, learnmore=learnmore)
def render_field_webpage(args):
data = None
info = {}
if 'label' in args:
label = clean_input(args['label'])
data = db.lf_fields.lookup(label)
if data is None:
if re.match(r'^\d+\.\d+\.\d+\.\d+$', label):
flash_error("Field <span style='color:black'>%s</span> was not found in the database.", label)
else:
flash_error("<span style='color:black'>%s</span> is not a valid label for a local number field.", label)
return redirect(url_for(".index"))
title = 'Local Number Field ' + prettyname(data)
polynomial = coeff_to_poly(data['coeffs'])
p = data['p']
Qp = r'\Q_{%d}' % p
e = data['e']
f = data['f']
cc = data['c']
gt = data['gal']
gn = data['n']
the_gal = WebGaloisGroup.from_nt(gn,gt)
isgal = ' Galois' if the_gal.order() == gn else ' not Galois'
abelian = ' and abelian' if the_gal.is_abelian() else ''
galphrase = 'This field is'+isgal+abelian+' over $\Q_{%d}$.'%p
autstring = r'\Gal' if the_gal.order() == gn else r'\Aut'
prop2 = [
('Label', label),
('Base', '\(%s\)' % Qp),
('Degree', '\(%s\)' % data['n']),
('e', '\(%s\)' % e),
('f', '\(%s\)' % f),
('c', '\(%s\)' % cc),
('Galois group', group_pretty_and_nTj(gn, gt)),
]
# Look up the unram poly so we can link to it
unramlabel = db.lf_fields.lucky({'p': p, 'n': f, 'c': 0}, projection=0)
if unramlabel is None:
logger.fatal("Cannot find unramified field!")
unramfriend = ''
else:
unramfriend = "/LocalNumberField/%s" % unramlabel
unramdata = db.lf_fields.lookup(unramlabel)
Px = PolynomialRing(QQ, 'x')
Pxt=PolynomialRing(Px,'t')
Pt = PolynomialRing(QQ, 't')
Ptx = PolynomialRing(Pt, 'x')
if data['f'] == 1:
unramp = r'$%s$' % Qp
# Eliminate t from the eisenstein polynomial
eisenp = Pxt(str(data['eisen']).replace('y','x'))
eisenp = Pt(str(data['unram'])).resultant(eisenp)
eisenp = web_latex(eisenp)
else:
unramp = data['unram'].replace('t','x')
unramp = web_latex(Px(str(unramp)))
unramp = prettyname(unramdata)+' $\\cong '+Qp+'(t)$ where $t$ is a root of '+unramp
eisenp = Ptx(str(data['eisen']).replace('y','x'))
eisenp = '$'+web_latex(eisenp, False)+'\\in'+Qp+'(t)[x]$'
rflabel = db.lf_fields.lucky({'p': p, 'n': {'$in': [1, 2]}, 'rf': data['rf']}, projection=0)
if rflabel is None:
logger.fatal("Cannot find discriminant root field!")
rffriend = ''
else:
rffriend = "/LocalNumberField/%s" % rflabel
gsm = data['gsm']
if gsm == [0]:
gsm = 'Not computed'
elif gsm == [-1]:
gsm = 'Does not exist'
else:
gsm = web_latex(coeff_to_poly(gsm))
info.update({
'polynomial': web_latex(polynomial),
'n': data['n'],
'p': p,
'c': data['c'],
'e': data['e'],
'f': data['f'],
't': data['t'],
'u': data['u'],
'rf': lf_display_knowl( rflabel, name=printquad(data['rf'], p)),
'base': lf_display_knowl(str(p)+'.1.0.1', name='$%s$'%Qp),
'hw': data['hw'],
'slopes': show_slopes(data['slopes']),
'gal': group_pretty_and_nTj(gn, gt, True),
'gt': gt,
'inertia': group_display_inertia(data['inertia']),
'unram': unramp,
'eisen': eisenp,
'gms': data['gms'],
'gsm': gsm,
'galphrase': galphrase,
'autstring': autstring,
'subfields': format_subfields(data['subfields'],p),
'aut': data['aut'],
})
friends = [('Galois group', "/GaloisGroup/%dT%d" % (gn, gt))]
if unramfriend != '':
friends.append(('Unramified subfield', unramfriend))
if rffriend != '':
friends.append(('Discriminant root field', rffriend))
bread = get_bread([(label, ' ')])
return render_template("lf-show-field.html", credit=LF_credit, title=title, bread=bread, info=info, properties2=prop2, friends=friends, learnmore=learnmore_list())
def render_field_webpage(args):
data = None
info = {}
if "label" in args:
label = clean_input(args["label"])
C = base.getDBConnection()
data = C.localfields.fields.find_one({"label": label})
if data is None:
bread = get_bread([("Search error", " ")])
info["err"] = "Field " + label + " was not found in the database."
info["label"] = label
return search_input_error(info, bread)
title = "Local Number Field " + label
polynomial = coeff_to_poly(data["coeffs"])
p = data["p"]
e = data["e"]
f = data["f"]
cc = data["c"]
GG = data["gal"]
gn = GG[0]
gt = GG[1]
prop2 = [
("Label", label),
("Base", "\(\Q_{%s}\)" % p),
("Degree", "\(%s\)" % data["n"]),
("e", "\(%s\)" % e),
("f", "\(%s\)" % f),
("c", "\(%s\)" % cc),
("Galois group", group_display_short(gn, gt, C)),
]
Pt = PolynomialRing(QQ, "t")
Pyt = PolynomialRing(Pt, "y")
eisenp = Pyt(str(data["eisen"]))
unramp = Pyt(str(data["unram"]))
# Look up the unram poly so we can link to it
unramdata = C.localfields.fields.find_one({"p": p, "n": f, "c": 0})
if len(unramdata) > 0:
unramfriend = "/LocalNumberField/%s" % unramdata["label"]
else:
logger.fatal("Cannot find unramified field!")
unramfriend = ""
rfdata = C.localfields.fields.find_one({"p": p, "n": {"$in": [1, 2]}, "rf": data["rf"]})
if rfdata is None:
logger.fatal("Cannot find discriminant root field!")
rffriend = ""
else:
rffriend = "/LocalNumberField/%s" % rfdata["label"]
info.update(
{
"polynomial": web_latex(polynomial),
"n": data["n"],
"p": data["p"],
"c": data["c"],
"e": data["e"],
"f": data["f"],
"t": data["t"],
"u": data["u"],
"rf": printquad(data["rf"], p),
"hw": data["hw"],
"slopes": show_slopes(data["slopes"]),
"gal": group_display_knowl(gn, gt, C),
"gt": gt,
"inertia": group_display_inertia(data["inertia"], C),
"unram": web_latex(unramp),
"eisen": web_latex(eisenp),
"gms": data["gms"],
"aut": data["aut"],
}
)
friends = [("Galois group", "/GaloisGroup/%dT%d" % (gn, gt))]
if unramfriend != "":
friends.append(("Unramified subfield", unramfriend))
if rffriend != "":
friends.append(("Discriminant root field", rffriend))
bread = get_bread([(label, " ")])
learnmore = [
("Completeness of the data", url_for(".completeness_page")),
("Source of the data", url_for(".how_computed_page")),
("Local field labels", url_for(".labels_page")),
]
return render_template(
"lf-show-field.html",
credit=LF_credit,
title=title,
bread=bread,
info=info,
properties2=prop2,
friends=friends,
learnmore=learnmore,
)
