def projective_group(self):
gapid = self._data['Proj_GAP']
smallg = None
if gapid[0]:
smallg = db.gps_small.lookup('%s.%s' % (gapid[0], gapid[1]))
if smallg:
return small_group_display_knowl(gapid[0], gapid[1])
ntj = self._data['Proj_nTj']
if ntj[1]:
return group_display_knowl(ntj[0], ntj[1])
if smallg:
return 'Group with GAP id [%s, %s]' % (gapid[0], gapid[1])
return 'data not computed'
def getgroup(m1, ell):
pind = {2: 0, 3: 1, 5: 2, 7: 3, 11: 4, 13: 5}
if not m1[3][2]:
return [m1[2], m1[0]]
myA = m1[3][0]
myB = m1[3][1]
if not myA and not myB: # myA = myB = []
return [small_group_display_knowl(1, 1), 1]
mono = db.hgm_families.lucky({'A': myA, 'B': myB}, projection="mono")
if mono is None:
return ['??', 1]
newthing = mono[pind[ell]]
newthing = dogapthing(newthing[1])
return [newthing[2], newthing[0]]
def getgroup(m1, ell):
pind = {2: 0, 3: 1, 5: 2, 7: 3, 11: 4, 13: 5}
if len(m1[3][2]) == 0:
return [m1[2], m1[0]]
myA = list2string(m1[3][0])
myB = list2string(m1[3][1])
if len(myA) == 0 and len(myB) == 0:
return [small_group_display_knowl(1, 1), 1]
mono = db.hgm_families.lucky({'A': myA, 'B': myB}, projection="mono")
if mono is None:
return ['??', 1]
newthing = mono[pind[ell]]
newthing = dogapthing(newthing[1])
return [newthing[2], newthing[0]]
def getgroup(m1,ell):
pind = {2: 0,3:1,5:2,7:3,11:4,13:5}
if len(m1[3][2])==0:
return [m1[2], m1[0]]
myA = list2string(m1[3][0])
myB = list2string(m1[3][1])
if len(myA)==0 and len(myB)==0:
return [small_group_display_knowl(1,1), 1]
mono = db.hgm_families.lucky({'A': myA, 'B': myB}, projection="mono")
if mono is None:
return ['??', 1]
newthing = mono[pind[ell]]
newthing = dogapthing(newthing[1])
return [newthing[2], newthing[0]]
def dogapthing(m1):
mnew = str(m1[2])
mnew = mnew.replace(' ', '')
if GAP_ID_RE.match(mnew):
mnew = mnew[1:-1]
two = mnew.split(',')
two = [int(j) for j in two]
try:
m1[2] = small_group_display_knowl(two[0], two[1])
except TypeError:
m1[2] = 'Gap[%d,%d]' % (two[0], two[1])
else:
# Fix multiple backslashes
m1[2] = re.sub(r'\\+', r'\\', m1[2])
m1[2] = '$%s$' % m1[2]
return m1
def dogapthing(m1):
mnew = str(m1[2])
mnew = mnew.replace(' ','')
if GAP_ID_RE.match(mnew):
mnew = mnew[1:-1]
two = mnew.split(',')
two = [int(j) for j in two]
try:
m1[2] = small_group_display_knowl(two[0],two[1])
except TypeError:
m1[2] = 'Gap[%d,%d]' % (two[0],two[1])
else:
# Fix multiple backslashes
m1[2] = re.sub(r'\\+', r'\\', m1[2])
m1[2] = '$%s$'% m1[2]
return m1
def render_hgm_family_webpage(label):
data = None
info = {}
data = db.hgm_families.lookup(label)
if data is None:
abort(
404, "Hypergeometric motive family " + label +
" was not found in the database.")
title = 'Hypergeometric Motive Family:' + label
A = data['A']
B = data['B']
hodge = data['famhodge']
mydet = data['det']
detexp = QQ(data['weight'] * data['degree'])
detexp = -detexp / 2
mydet = r'\Q(%s)\otimes\Q(\sqrt{' % str(detexp)
if int(data['det'][0]) != 1:
mydet += str(data['det'][0])
if len(data['det'][1]) > 0:
mydet += data['det'][1]
if int(data['det'][0]) == 1 and len(data['det'][1]) == 0:
mydet += '1'
mydet += '})'
bezoutmat = matrix(data['bezout'])
bezoutdet = bezoutmat.det()
bezoutmat = latex(bezoutmat)
snf = data['snf']
snf = list2Cnstring(snf)
typee = 'Orthogonal'
if (data['weight'] % 2) == 1 and (data['degree'] % 2) == 0:
typee = 'Symplectic'
ppart = [[2, [data['A2'], data['B2'], data['C2']]],
[3, [data['A3'], data['B3'], data['C3']]],
[5, [data['A5'], data['B5'], data['C5']]],
[7, [data['A7'], data['B7'], data['C7']]]]
prop2 = [('Degree', '\(%s\)' % data['degree']),
('Weight', '\(%s\)' % data['weight'])]
mono = [m for m in data['mono'] if m[1] != 0]
mono = [[
m[0],
dogapthing(m[1]),
getgroup(m[1], m[0]),
latex(ZZ(m[1][0]).factor())
] for m in mono]
mono = [[m[0], m[1], m[2][0],
splitint(m[1][0] / m[2][1], m[0]), m[3]] for m in mono]
info.update({
'A': A,
'B': B,
'degree': data['degree'],
'weight': data['weight'],
'hodge': hodge,
'det': mydet,
'snf': snf,
'bezoutmat': bezoutmat,
'bezoutdet': bezoutdet,
'mono': mono,
'imprim': data['imprim'],
'ppart': ppart,
'type': typee,
'junk': small_group_display_knowl(18, 2),
'showlist': showlist
})
friends = [('Motives in the family',
url_for('hypergm.index') + "?A=%s&B=%s" % (str(A), str(B)))]
# if unramfriend != '':
# friends.append(('Unramified subfield', unramfriend))
# if rffriend != '':
# friends.append(('Discriminant root field', rffriend))
info.update({
"plotcircle":
url_for(".hgm_family_circle_image",
AB="A" + ".".join(map(str, A)) + "_B" + ".".join(map(str, B)))
})
info.update({
"plotlinear":
url_for(".hgm_family_linear_image",
AB="A" + ".".join(map(str, A)) + "_B" + ".".join(map(str, B)))
})
info.update({
"plotconstant":
url_for(".hgm_family_constant_image",
AB="A" + ".".join(map(str, A)) + "_B" + ".".join(map(str, B)))
})
bread = get_bread([(label, ' ')])
return render_template("hgm-show-family.html",
credit=HGM_credit,
title=title,
bread=bread,
info=info,
properties2=prop2,
friends=friends,
learnmore=learnmore_list())
def compformatter(comp):
n, k = compdata(comp)
return small_group_display_knowl(n, k, cache=compcache())
def render_hgm_family_webpage(label):
data = None
info = {}
data = db.hgm_families.lookup(label)
if data is None:
abort(404, "Hypergeometric motive family " + label + " was not found in the database.")
title = 'Hypergeometric Motive Family:' + label
A = data['A']
B = data['B']
hodge = data['famhodge']
mydet = data['det']
detexp = QQ(data['weight']*data['degree'])
detexp = -detexp/2
mydet = r'\Q(%s)\otimes\Q(\sqrt{'%str(detexp)
if int(data['det'][0]) != 1:
mydet += str(data['det'][0])
if len(data['det'][1])>0:
mydet += data['det'][1]
if int(data['det'][0]) == 1 and len(data['det'][1])==0:
mydet += '1'
mydet += '})'
bezoutmat = matrix(data['bezout'])
bezoutdet = bezoutmat.det()
bezoutmat = latex(bezoutmat)
snf = data['snf']
snf = list2Cnstring(snf)
typee = 'Orthogonal'
if (data['weight'] % 2) == 1 and (data['degree'] % 2) == 0:
typee = 'Symplectic'
ppart = [[2, [data['A2'],data['B2'],data['C2']]],
[3, [data['A3'],data['B3'],data['C3']]],
[5, [data['A5'],data['B5'],data['C5']]],
[7, [data['A7'],data['B7'],data['C7']]]]
prop2 = [
('Degree', '\(%s\)' % data['degree']),
('Weight', '\(%s\)' % data['weight'])
]
mono = [m for m in data['mono'] if m[1] != 0]
mono = [[m[0], dogapthing(m[1]),
getgroup(m[1],m[0]),
latex(ZZ(m[1][0]).factor())] for m in mono]
mono = [[m[0], m[1], m[2][0], splitint(m[1][0]/m[2][1],m[0]), m[3]] for m in mono]
info.update({
'A': A,
'B': B,
'degree': data['degree'],
'weight': data['weight'],
'hodge': hodge,
'det': mydet,
'snf': snf,
'bezoutmat': bezoutmat,
'bezoutdet': bezoutdet,
'mono': mono,
'imprim': data['imprim'],
'ppart': ppart,
'type': typee,
'junk': small_group_display_knowl(18,2),
'showlist': showlist
})
friends = [('Motives in the family', url_for('hypergm.index')+"?A=%s&B=%s" % (str(A), str(B)))]
# if unramfriend != '':
# friends.append(('Unramified subfield', unramfriend))
# if rffriend != '':
# friends.append(('Discriminant root field', rffriend))
info.update({"plotcircle": url_for(".hgm_family_circle_image", AB = "A"+".".join(map(str,A))+"_B"+".".join(map(str,B)))})
info.update({"plotlinear": url_for(".hgm_family_linear_image", AB = "A"+".".join(map(str,A))+"_B"+".".join(map(str,B)))})
info.update({"plotconstant": url_for(".hgm_family_constant_image", AB = "A"+".".join(map(str,A))+"_B"+".".join(map(str,B)))})
bread = get_bread([(label, ' ')])
return render_template("hgm-show-family.html", credit=HGM_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'])
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 = url_for_label(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 = raw_typeset(eisenp, web_latex(eisenp))
else:
unramp = data['unram'].replace('t', 'x')
unramp = raw_typeset(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 = raw_typeset(str(eisenp),
web_latex(eisenp),
extra=r'$\ \in' + Qp + '(t)[x]$')
rflabel = db.lf_fields.lucky(
{
'p': p,
'n': {
'$in': [1, 2]
},
'rf': data['rf']
}, projection=0)
if rflabel is None:
logger.fatal("Cannot find discriminant root field!")
rffriend = ''
else:
rffriend = url_for_label(rflabel)
gsm = data['gsm']
if gsm == [0]:
gsm = 'Not computed'
elif gsm == [-1]:
gsm = 'Does not exist'
else:
gsm = lf_formatfield(','.join(str(b) for b in gsm))
if 'wild_gap' in data:
wild_inertia = small_group_display_knowl(data['wild_gap'][0],
data['wild_gap'][1])
else:
wild_inertia = 'data not computed'
info.update({
'polynomial':
raw_typeset(polynomial),
'n':
data['n'],
'p':
p,
'c':
data['c'],
'e':
data['e'],
'f':
data['f'],
't':
data['t'],
'u':
data['u'],
'rf':
lf_display_knowl(rflabel, name=printquad(data['rf'], p)),
'base':
lf_display_knowl(str(p) + '.1.0.1', name='$%s$' % Qp),
'hw':
data['hw'],
'slopes':
show_slopes(data['slopes']),
'gal':
group_pretty_and_nTj(gn, gt, True),
'gt':
gt,
'inertia':
group_display_inertia(data['inertia']),
'wild_inertia':
wild_inertia,
'unram':
unramp,
'eisen':
eisenp,
'gms':
data['gms'],
'gsm':
gsm,
'galphrase':
galphrase,
'autstring':
autstring,
'subfields':
format_subfields(data['subfields'], p),
'aut':
data['aut'],
})
friends = [('Galois group', "/GaloisGroup/%dT%d" % (gn, gt))]
if unramfriend != '':
friends.append(('Unramified subfield', unramfriend))
if rffriend != '':
friends.append(('Discriminant root field', rffriend))
if db.nf_fields.exists({'local_algs': {'$contains': label}}):
friends.append(
('Number fields with this completion',
url_for('number_fields.number_field_render_webpage') +
"?completions={}".format(label)))
bread = get_bread([(label, ' ')])
return render_template(
"lf-show-field.html",
title=title,
titletag=titletag,
bread=bread,
info=info,
properties=prop2,
friends=friends,
learnmore=learnmore_list(),
KNOWL_ID="lf.%s" % label,
)
