def __init__(self):
parity = ParityBox(name="parity",
label="Parity",
knowl="gg.parity",
width=50,
short_width=170)
cyc = YesNoBox(name="cyc",
label="Cyclic",
knowl="group.cyclic",
width=50,
short_width=170)
solv = YesNoBox(name="solv",
label="Solvable",
knowl="group.solvable",
width=50,
short_width=170)
prim = YesNoBox(name="prim",
label="Primitive",
knowl="gg.primitive",
width=50,
short_width=170)
n = TextBox(name="n",
label="Degree",
knowl="gg.degree",
example="6",
example_span="6 or 4,6 or 2..5 or 4,6..8")
t = TextBox(name="t",
label="$T$-number",
knowl="gg.tnumber",
example="3",
example_span="3 or 4,6 or 2..5 or 4,6..8")
order = TextBox(name="order",
label="Order",
knowl="group.order",
example="6",
example_span="6 or 4,6 or 2..35 or 4,6..80")
gal = TextBoxNoEg(
name="gal",
label="Group",
knowl="group",
example="[8,3]",
example_span=
"list of %s, e.g. [8,3] or [16,7], group names from the %s, e.g. C5 or S12, and %s, e.g., 7T2 or 11T5"
% (display_knowl("group.small_group_label", "GAP id's"),
display_knowl("nf.galois_group.name", "list of group labels"),
display_knowl("gg.label", "transitive group labels")))
nilpotency = TextBox(name="nilpotency",
label="Nilpotency class",
knowl="group.nilpotent",
example="1..100",
example_span="-1, or 1..3")
count = TextBox(name="count", label="Results to display", example=50)
self.bool_array = [[parity, cyc, solv, prim]]
self.browse_array = [[n], [t], [order], [gal], [nilpotency], [count]]
self.refine_array = [[parity, cyc, solv, prim],
[n, t, order, gal, nilpotency]]
def summary(self):
return "The database currently contains %s %s of %s up to %s, lying in %s %s. The tables below show counts of Galois orbits." % (
comma(self.nchars),
display_knowl("character.dirichlet", "Dirichlet characters"),
display_knowl("character.dirichlet.modulus",
"modulus"), comma(self.maxmod), comma(self.norbits),
display_knowl("character.dirichlet.galois_orbit", "Galois orbits"))
def short_summary(self):
return r'The database currently contains {nreps} Galois conjugacy classes of {repknowl}, for a total of {nfields} {nfknowl}. Here are some <a href="{url}">further statistics</a>.'.format(
nreps=comma(self.nreps),
repknowl=display_knowl("artin", "Artin representations"),
nfields=comma(self.nfields),
nfknowl=display_knowl("artin.number_field", "number fields"),
url=url_for(".statistics"))
def ratpts_table(pts,pts_v):
def sorted_points(pts):
return sorted(pts,key=lambda P:(max([abs(x) for x in P]),sum([abs(x) for x in P])))
if len(pts) > 1:
# always put points at infinity first, regardless of height
pts = sorted_points([P for P in pts if P[2] == 0]) + sorted_points([P for P in pts if P[2] != 0])
kid = 'g2c.all_rational_points' if pts_v else 'g2c.known_rational_points'
if len(pts) == 0:
if pts_v:
return 'This curve has no %s.' % display_knowl(kid, 'rational points')
else:
return 'No %s for this curve.' % display_knowl(kid, 'rational points are known')
spts = [point_string(P) for P in pts]
caption = 'All points' if pts_v else 'Known points'
tabcols = 6
if len(pts) <= tabcols+1:
return r'%s: \(%s\)' % (display_knowl(kid,caption),r',\, '.join(spts))
ptstab = ['<table class="ntdata">', '<thead>', '<tr>', th_wrap(kid, caption)]
ptstab.extend(['<th></th>' for i in range(tabcols-1)])
ptstab.extend(['</tr>', '</thead>', '<tbody>'])
for i in range(0,len(pts),6):
ptstab.append('<tr>')
ptstab.extend([td_wrapc(P) for P in spts[i:i+6]])
if i+6 > len(pts):
ptstab.extend(['<td></td>' for i in range(i+6-len(pts))]) # pad last line
ptstab.append('</tr>')
ptstab.extend(['</tbody>', '</table>'])
return '\n'.join(ptstab)
def ratpts_table(pts, pts_v):
if len(pts) > 1:
pts = sorted(pts,
key=lambda P:
(max([abs(x) for x in P]), sum([abs(x) for x in P])))
kid = 'g2c.all_rational_points' if pts_v else 'g2c.known_rational_points'
if len(pts) == 0:
if pts_v:
return '<p>This curve has no %s.</p>' % display_knowl(
kid, 'rational points')
else:
return '<p>No %s for this curve.</p>' % display_knowl(
kid, 'rational points are known')
strpts = ['(' + ' : '.join(map(str, P)) + ')' for P in pts]
caption = 'Points' if pts_v else 'Known points'
tabcols = 6
if len(pts) <= tabcols + 1:
return r'<p>%s: \(%s\)</p>' % (display_knowl(
kid, caption), r',\, '.join(strpts))
ptstab = [
'<table class="ntdata">', '<thead>', '<tr>',
th_wrap(kid, caption)
]
ptstab.extend(['<th></th>' for i in range(tabcols - 1)])
ptstab.extend(['</tr>', '</thead>', '<tbody>'])
for i in range(0, len(pts), 6):
ptstab.append('<tr>')
ptstab.extend([td_wrapc(P) for P in strpts[i:i + 6]])
if i + 6 > len(pts):
ptstab.extend(['<td></td>'
for i in range(i + 6 - len(pts))]) # pad last line
ptstab.append('</tr>')
ptstab.extend(['</tbody>', '</table>'])
return '\n'.join(ptstab)
def __init__(self):
dimension = TextBox(name="dimension",
label="Dimension",
knowl="artin.dimension",
example="2",
example_span="1, 2-4")
conductor = TextBox(name="conductor",
label="Conductor",
knowl="artin.conductor",
example="51,100-200")
group = TextBoxNoEg(
name="group",
label="Group",
knowl="artin.gg_quotient",
example="A5",
example_span=
"list of %s, e.g. [8,3] or [16,7], group names from the %s, e.g. C5 or S12, and %s, e.g., 7T2 or 11T5"
% (display_knowl("group.small_group_label", "GAP id's"),
display_knowl("nf.galois_group.name", "list of group labels"),
display_knowl("gg.label", "transitive group labels")))
parity = ParityBox(name="parity", label="Parity", knowl="artin.parity")
container = TextBox(name="container",
label="Smallest permutation container",
knowl="artin.permutation_container",
example="6T13",
example_span="6T13 or 7T6")
ram_quantifier = SubsetNoExcludeBox(name="ram_quantifier")
ramified = TextBoxWithSelect(name="ramified",
label="Ramified primes",
knowl="artin.ramified_primes",
example="2, 3",
select_box=ram_quantifier,
example_span="2, 3 (no range allowed)")
unramified = TextBox(name="unramified",
label="Unramified primes",
knowl="artin.unramified_primes",
example="5,7",
example_span="5, 7, 13 (no range allowed)")
root_number = TextBoxNoEg(name="root_number",
label="Root number",
knowl="artin.root_number",
example="1",
example_span="at the moment, one of 1 or -1")
fsind = TextBoxNoEg(
name="frobenius_schur_indicator",
label="Frobenius-Schur indicator",
knowl="artin.frobenius_schur_indicator",
example="1",
example_span=
"+1 for orthogonal, -1 for symplectic, 0 for non-real character")
count = CountBox()
self.browse_array = [[dimension], [conductor], [group], [parity],
[container], [ramified], [unramified],
[root_number], [fsind], [count]]
self.refine_array = [[
dimension, conductor, group, root_number, parity
], [container, ramified, unramified, fsind]]
def short_summary(self):
return 'The database currently contains %s %s of %s up to %s, lying in %s %s. Among these, L-functions are available for characters of modulus up to 2,800 (and some of higher modulus). Here are some <a href="%s">further statistics</a>.' % (
comma(self.nchars),
display_knowl("character.dirichlet", "Dirichlet characters"),
display_knowl("character.dirichlet.modulus",
"modulus"), comma(self.maxmod), comma(self.norbits),
display_knowl("character.dirichlet.galois_orbit",
"Galois orbits"), url_for(".statistics"))
def display_character(self):
if self.char_order == 1:
ord_deg = " (trivial)"
else:
ord_knowl = display_knowl('character.dirichlet.order', title='order')
deg_knowl = display_knowl('character.dirichlet.degree', title='degree')
ord_deg = r" (of %s \(%d\) and %s \(%d\))" % (ord_knowl, self.char_order, deg_knowl, self.char_degree)
return self.char_orbit_link + ord_deg
def summary(self):
return r"The database currently contains %s %s of weight 2 over %s imaginary quadratic fields. It also contains %s %s over %s imaginary quadratic fields (including all with class number one)." % (
comma(self.nforms),
display_knowl(
"mf.bianchi.bianchimodularforms",
"Bianchi modular forms"), self.nformfields, comma(self.ndims),
display_knowl("mf.bianchi.spaces",
"spaces of cusp forms"), self.ndimfields)
def display_character(self):
if self.char_order == 1:
ord_deg = " (trivial)"
else:
ord_knowl = display_knowl('character.dirichlet.order', title='order')
deg_knowl = display_knowl('character.dirichlet.degree', title='degree')
ord_deg = r" (of %s \(%d\) and %s \(%d\))" % (ord_knowl, self.char_order, deg_knowl, self.char_degree)
return self.char_orbit_link + ord_deg
def short_summary(self):
return r'The database currently contains all %s %s of %s 1 and %s up to 4, as well as all Sato-Tate groups of weight 0 and degree 1 with %s of order at most $10^{20}$. Here are some <a href="%s">further statistics</a>.' % (
display_knowl('st_group.rational', 'rational'),
display_knowl('st_group.definition', 'Sato-Tate groups'),
display_knowl('st_group.weight', 'weight'),
display_knowl('st_group.degree', 'degree'),
display_knowl('st_group.component_group',
'component group'), url_for('.statistics'))
def __init__(self):
ncurves = comma(db.g2c_curves.count())
nclasses = comma(db.lfunc_instances.count({'type':'G2Q'}))
max_D = comma(db.g2c_curves.max('abs_disc'))
g2c_knowl = display_knowl('g2c.g2curve', title='genus 2 curves')
disc_knowl = display_knowl('g2c.abs_discriminant', title = "absolute discriminant")
stats_url = url_for(".statistics")
self.short_summary = 'The database currently contains %s %s over $\Q$ of %s up to %s. Here are some <a href="%s">further statistics</a>.' % (ncurves, g2c_knowl, disc_knowl, max_D, stats_url)
self.summary = 'The database currently contains %s genus 2 curves in %s isogeny classes, with %s at most %s.' % (ncurves, nclasses, disc_knowl, max_D)
def show_special_labels(self):
raw = [x.split(".")[-1] for x in self.special_labels]
specials = []
for x in raw:
if (
x == "N" or x == "M"
): # labels for normal subgroups and maximal subgroups
continue
if x == "Z":
specials.append(display_knowl("group.center", "center"))
elif x == "D":
specials.append(
display_knowl("group.commutator_subgroup", "commutator subgroup")
)
elif x == "F":
specials.append(
display_knowl("group.fitting_subgroup", "Fitting subgroup")
)
elif x == "Phi":
specials.append(
display_knowl("group.frattini_subgroup", "Frattini subgroup")
)
elif x == "R":
specials.append(display_knowl("group.radical", "radical"))
elif x == "S":
specials.append(display_knowl("group.socle", "socle"))
else:
n = to_ordinal(int(x[1:]) + 1)
if x.startswith("U"):
specials.append(
"%s term in the %s"
% (
n,
display_knowl("group.upper_central_series", "upper central series"),
)
)
elif x.startswith("L"):
specials.append(
"%s term in the %s"
% (
n,
display_knowl("group.lower_central_series", "lower central series"),
)
)
elif x.startswith("D"):
specials.append(
"%s term in the %s"
% (n, display_knowl("group.derived_series", "derived series"))
)
# Don't show chief series since it's not canonical
if self.sylow:
specials.append(
display_knowl("group.sylow_subgroup", "%s-Sylow subgroup" % self.sylow)
)
return ", ".join(specials)
def short_summary(self):
return 'The database currently contains %s %s of %s up to %s, lying in %s %s. Among these, L-functions are available for characters of modulus up to 2,800 (and some of higher modulus). In addition, %s, Galois orbits and %s are available up to modulus $10^{20}$. Here are some <a href="%s">futher statistics</a>.' % (
comma(self.nchars),
display_knowl("character.dirichlet", "Dirichlet characters"),
display_knowl("character.dirichlet.modulus", "modulus"),
comma(self.maxmod),
comma(self.norbits),
display_knowl("character.dirichlet.galois_orbit", "Galois orbits"),
display_knowl("character.dirichlet.basic_properties", "basic properties"),
display_knowl("character.dirichlet.value_field", "field of values"),
url_for(".statistics"))
def summary(self):
return r"The database currently contains {nreps} Galois conjugacy classes of {repknowl}, for a total of {nfields} {nfknowl} with {ngroups} {gpknowl}. The largest {dimknowl} is ${mdim}$ and the largest {condknowl} is ${mcond} \approx {amcond}$.".format(
nreps=comma(self.nreps),
repknowl=display_knowl("artin", "Artin representations"),
nfields=comma(self.nfields),
nfknowl=display_knowl("artin.number_field", "number fields"),
ngroups=self.ngroups,
gpknowl=display_knowl("artin.gg_quotient", "Galois groups"),
dimknowl=display_knowl("artin.dimension", "dimension"),
mdim=self.maxdim,
condknowl=display_knowl("artin.conductor", "conductor"),
mcond=self.maxcond,
amcond=self.amaxcond)
def __init__(self):
nforms = comma(db.mf_newforms.count())
nspaces = comma(db.mf_newspaces.count())
ndim = comma(db.mf_hecke_cc.count())
weight_knowl = display_knowl('mf.elliptic.weight', title='weight')
level_knowl = display_knowl('mf.elliptic.level', title='level')
newform_knowl = display_knowl('mf.elliptic.newform', title='newforms')
#stats_url = url_for(".statistics")
self.short_summary = r'The database currently contains %s (Galois orbits of) %s of %s \(k\) and %s \(N\) satisfying \(Nk^2 \le %s\), corresponding to %s modular forms over the complex numbers.' % (
nforms, newform_knowl, weight_knowl, level_knowl, Nk2_bound(),
ndim)
self.summary = r"The database currently contains %s (Galois orbits of) %s and %s spaces of %s \(k\) and %s \(N\) satisfying \(Nk^2 \le %s\), corresponding to %s modular forms over the complex numbers." % (
nforms, newform_knowl, nspaces, weight_knowl, level_knowl,
Nk2_bound(), ndim)
def ALdim_table(al_dims, level, weight):
# Assume that the primes always appear in the same order
al_dims = sorted(al_dims, key=lambda x:tuple(-ev for (p,ev) in x[0]))
header = []
first_row = al_dims[0][0]
primes = [p for (p,ev) in first_row]
num_primes = len(primes)
for p, ev in first_row:
header.append(r'<th>\(%s\)</th>'%p)
if len(first_row) > 1:
header.append(r"<th class='right'>%s</th>"%(display_knowl('cmf.fricke', title='Fricke').replace('"',"'")))
header.append('<th>Dim.</th>')
rows = []
fricke = {1:0,-1:0}
for i, (vec, dim, cnt) in enumerate(al_dims):
row = []
sign = 1
s = ''
for p, ev in vec:
if ev == 1:
s += '%2B'
symb = '+'
else:
sign = -sign
s += '-'
symb = '-'
row.append(r'<td>\(%s\)</td>'%(symb))
if len(vec) > 1:
row.append(r"<td class='right'>\(%s\)</td>"%('+' if sign == 1 else '-'))
query = {'level':level, 'weight':weight, 'char_order':1, 'atkin_lehner_string':s}
if cnt == 1:
query['jump'] = 'yes'
link = newform_search_link(r'\(%s\)'%dim, **query)
row.append(r'<td>%s</td>'%(link))
fricke[sign] += dim
if i == len(al_dims) - 1 and len(vec) > 1:
tr = "<tr class='endsection'>"
else:
tr = "<tr>"
rows.append(tr + ''.join(row) + '</tr>')
if num_primes > 1:
plus_knowl = display_knowl('cmf.plus_space',title='Plus space').replace('"',"'")
plus_link = newform_search_link(r'\(%s\)'%fricke[1], level=level, weight=weight, char_order=1, fricke_eigenval=1)
minus_knowl = display_knowl('cmf.minus_space',title='Minus space').replace('"',"'")
minus_link = newform_search_link(r'\(%s\)'%fricke[-1], level=level, weight=weight, char_order=1, fricke_eigenval=-1)
rows.append(r"<tr><td colspan='%s'>%s</td><td class='right'>\(+\)</td><td>%s</td></tr>"%(num_primes, plus_knowl, plus_link))
rows.append(r"<tr><td colspan='%s'>%s</td><td class='right'>\(-\)</td><td>%s</td></tr>"%(num_primes, minus_knowl, minus_link))
return ("<table class='ntdata'><thead><tr>%s</tr></thead><tbody>%s</tbody></table>" %
(''.join(header), ''.join(rows)))
def __init__(self):
parity = ParityBox(name="parity", label="Parity", knowl="gg.parity")
cyc = YesNoBox(name="cyc", label="Cyclic", knowl="group.cyclic")
solv = YesNoBox(name="solv", label="Solvable", knowl="group.solvable")
prim = YesNoBox(name="prim", label="Primitive", knowl="gg.primitive")
n = TextBox(name="n",
label="Degree",
knowl="gg.degree",
example="6",
example_span="6 or 4,6 or 2..5 or 4,6..8")
t = TextBox(name="t",
label="$T$-number",
knowl="gg.tnumber",
example="3",
example_span="3 or 4,6 or 2..5 or 4,6..8")
order = TextBox(name="order",
label="Order",
knowl="group.order",
example="6",
example_span="6 or 4,6 or 2..35 or 4,6..80")
gal = TextBoxNoEg(
name="gal",
label="Group",
knowl="group",
example_span_colspan=8,
example="[8,3]",
example_span=
"list of %s, e.g. [8,3] or [16,7], group names from the %s, e.g. C5 or S12, and %s, e.g., 7T2 or 11T5"
% (display_knowl("group.small_group_label", "GAP id's"),
display_knowl("nf.galois_group.name", "list of group labels"),
display_knowl("gg.label", "transitive group labels")))
nilpotency = TextBox(name="nilpotency",
label="Nilpotency class",
knowl="group.nilpotent",
example="1..100",
example_span="-1, or 1..3")
arith_equiv = TextBox(name="arith_equiv",
label="Equivalent siblings",
knowl="gg.arithmetically_equiv_input",
example="1",
example_span="1 or 2,3 or 1..5 or 1,3..10")
count = CountBox()
self.browse_array = [[n, parity], [t, cyc], [order, solv],
[nilpotency, prim], [gal], [arith_equiv], [count]]
self.refine_array = [[parity, cyc, solv, prim, arith_equiv],
[n, t, order, gal, nilpotency]]
def ALdim_table(al_dims, level, weight):
# Assume that the primes always appear in the same order
al_dims = sorted(al_dims, key=lambda x:tuple(-ev for (p,ev) in x[0]))
header = []
first_row = al_dims[0][0]
primes = [p for (p,ev) in first_row]
num_primes = len(primes)
for p, ev in first_row:
header.append(r'<th>\(%s\)</th>'%p)
if len(first_row) > 1:
header.append(r"<th class='right'>%s</th>"%(display_knowl('cmf.fricke', title='Fricke').replace('"',"'")))
header.append('<th>Dim.</th>')
rows = []
fricke = {1:0,-1:0}
for i, (vec, dim, cnt) in enumerate(al_dims):
row = []
sign = 1
s = ''
for p, ev in vec:
if ev == 1:
s += '%2B'
symb = '+'
else:
sign = -sign
s += '-'
symb = '-'
row.append(r'<td>\(%s\)</td>'%(symb))
if len(vec) > 1:
row.append(r"<td class='right'>\(%s\)</td>"%('+' if sign == 1 else '-'))
query = {'level':level, 'weight':weight, 'char_order':1, 'atkin_lehner_string':s}
if cnt == 1:
query['jump'] = 'yes'
link = newform_search_link(r'\(%s\)'%dim, **query)
row.append(r'<td>%s</td>'%(link))
fricke[sign] += dim
if i == len(al_dims) - 1 and len(vec) > 1:
tr = "<tr class='endsection'>"
else:
tr = "<tr>"
rows.append(tr + ''.join(row) + '</tr>')
if num_primes > 1:
plus_knowl = display_knowl('cmf.plus_space',title='Plus space').replace('"',"'")
plus_link = newform_search_link(r'\(%s\)'%fricke[1], level=level, weight=weight, char_order=1, fricke_eigenval=1)
minus_knowl = display_knowl('cmf.minus_space',title='Minus space').replace('"',"'")
minus_link = newform_search_link(r'\(%s\)'%fricke[-1], level=level, weight=weight, char_order=1, fricke_eigenval=-1)
rows.append(r"<tr><td colspan='%s'>%s</td><td class='right'>\(+\)</td><td>%s</td></tr>"%(num_primes, plus_knowl, plus_link))
rows.append(r"<tr><td colspan='%s'>%s</td><td class='right'>\(-\)</td><td>%s</td></tr>"%(num_primes, minus_knowl, minus_link))
return ("<table class='ntdata'><thead><tr>%s</tr></thead><tbody>%s</tbody></table>" %
(''.join(header), ''.join(rows)))
def __init__(self):
self.genus_max = db.hgcwa_passports.max('genus')
self.dim_max = db.hgcwa_passports.max('dim')
self.g0_max = db.hgcwa_passports.max('g0')
self.refined_passports_knowl = display_knowl(
'curve.highergenus.aut.refinedpassport', title='refined passports')
self.generating_vectors_knowl = display_knowl(
'curve.highergenus.aut.generatingvector',
title='generating vectors')
self.dimension_knowl = display_knowl('curve.highergenus.aut.dimension',
title='dimension'),
self.distinct_generating_vectors = comma(db.hgcwa_passports.count())
self.distinct_refined_passports = comma(compute_total_refined_pp())
self.by_genus_data = init_by_genus_data()
def __init__(self):
self.ncurves = db.ec_curvedata.count()
self.ncurves_c = comma(self.ncurves)
self.nclasses = db.ec_classdata.count()
self.nclasses_c = comma(self.nclasses)
self.max_N_Cremona = 500000
self.max_N_Cremona_c = comma(500000)
self.max_N = db.ec_curvedata.max('conductor')
self.max_N_c = comma(self.max_N)
self.max_rank = db.ec_curvedata.max('rank')
self.max_rank_c = comma(self.max_rank)
self.cond_knowl = display_knowl('ec.q.conductor', title="conductor")
self.rank_knowl = display_knowl('ec.rank', title="rank")
self.ec_knowl = display_knowl('ec.q', title='elliptic curves')
self.cl_knowl = display_knowl('ec.isogeny', title="isogeny classes")
def __init__(self):
degree = TextBox(name='n',
label='Degree',
knowl='lf.degree',
example='6',
example_span='6, or a range like 3..5')
qp = TextBox(name='p',
label=r'Prime $p$ for base field $\Q_p$',
short_label='Prime $p$',
knowl='lf.qp',
example='3',
example_span='3, or a range like 3..7')
c = TextBox(name='c',
label='Discriminant exponent $c$',
knowl='lf.discriminant_exponent',
example='8',
example_span='8, or a range like 2..6')
e = TextBox(name='e',
label='Ramification index $e$',
knowl='lf.ramification_index',
example='3',
example_span='3, or a range like 2..6')
topslope = TextBox(
name='topslope',
label='Top slope',
knowl='lf.top_slope',
example='4/3',
example_span='0, 1, 2, 4/3, 3.5, or a range like 3..5')
gal = TextBoxNoEg(
name='gal',
label='Galois group $G$',
short_label='Galois group',
knowl='nf.galois_group',
example='5T3',
example_span=
'list of %s, e.g. [8,3] or [16,7], group names from the %s, e.g. C5 or S12, and %s, e.g., 7T2 or 11T5'
% (display_knowl('group.small_group_label', "GAP id's"),
display_knowl('nf.galois_group.name', 'list of group labels'),
display_knowl('gg.label', 'transitive group labels')))
results = TextBox(
"count",
label="Results to display",
example=50,
)
self.browse_array = [[degree], [qp], [c], [e], [topslope], [gal],
[results]]
self.refine_array = [[degree, c, gal], [qp, e, topslope]]
def short_summary(self):
stats_url = url_for(".statistics")
g2c_knowl = display_knowl("g2c.g2curve", title="genus 2 curves")
return (
r'The database currently contains %s %s over $\Q$ of %s up to %s. Here are some <a href="%s">further statistics</a>.'
%
(self.ncurves, g2c_knowl, self.disc_knowl, self.max_D, stats_url))
def __init__(self):
self.ncurves = db.ec_curves.count()
self.ncurves_c = comma(db.ec_curves.count())
self.max_N = db.ec_curves.max('conductor')
# round up to nearest multiple of 1000
self.max_N = 1000 * int((self.max_N / 1000) + 1)
# NB while we only have the Cremona database, the upper bound
# will always be a multiple of 1000, but it looks funny to
# show the maximum condictor as something like 399998; there
# are no elliptic curves whose conductor is a multiple of
# 1000.
self.max_N_c = comma(self.max_N)
self.max_rank = db.ec_curves.max('rank')
self.max_rank_c = comma(self.max_rank)
self.cond_knowl = display_knowl('ec.q.conductor', title="conductor")
self.rank_knowl = display_knowl('ec.rank', title="rank")
def __init__(self):
ngalmaps = comma(db.belyi_galmaps.stats.count())
npassports = comma(db.belyi_passports.stats.count())
max_deg = comma(db.belyi_passports.max('deg'))
deg_knowl = display_knowl('belyi.degree', title = "degree")
belyi_knowl = '<a title="Belyi maps (up to Galois conjugation) [belyi.galmap]" knowl="belyi.galmap" kwargs="">Belyi maps</a>'
stats_url = url_for(".statistics")
self.short_summary = 'The database currently contains %s %s of %s up to %s. Here are some <a href="%s">further statistics</a>.' % (ngalmaps, belyi_knowl, deg_knowl, max_deg, stats_url)
self.summary = "The database currently contains %s Galois orbits of Belyi maps in %s passports, with %s at most %s." % (ngalmaps, npassports, deg_knowl, max_deg)
def __init__(self):
ngalmaps = comma(db.belyi_galmaps.stats.count())
npassports = comma(db.belyi_passports.stats.count())
max_deg = comma(db.belyi_passports.max('deg'))
deg_knowl = display_knowl('belyi.degree', title="degree")
belyi_knowl = '<a title="Belyi maps (up to Galois conjugation) [belyi.galmap]" knowl="belyi.galmap" kwargs="">Belyi maps</a>'
stats_url = url_for(".statistics")
self.short_summary = 'The database currently contains %s %s of %s up to %s. Here are some <a href="%s">further statistics</a>.' % (
ngalmaps, belyi_knowl, deg_knowl, max_deg, stats_url)
self.summary = "The database currently contains %s Galois orbits of Belyi maps in %s passports, with %s at most %s." % (
ngalmaps, npassports, deg_knowl, max_deg)
def __init__(self):
self.nlats = comma(db.lat_lattices.count())
self.max_cn = db.lat_lattices.max("class_number")
self.max_dim = db.lat_lattices.max("dim")
self.max_det = db.lat_lattices.max("det")
self.kposdef = display_knowl('lattice.postive_definite',
'positive definite')
self.kintegral = display_knowl('lattice.definition',
'integral lattices')
self.kcatalogue = display_knowl('lattice.catalogue_of_lattices',
'Catalogue of Lattices')
self.kcn = display_knowl('lattice.class_number', 'class number')
self.kdim = display_knowl('lattice.dimension', 'dimension')
self.kdet = display_knowl('lattice.determinant', 'determinant')
self.kpri = display_knowl('lattice.primitive', 'primitive')
def display_hecke_cutters(self):
polynomials = [bigpoly_knowl(F, var='T%s'%p) for p,F in self.hecke_cutters]
title = 'linear operator'
if len(polynomials) > 1:
title += 's'
knowl = display_knowl('cmf.hecke_cutter', title=title)
desc = "<p>This newform can be constructed as the "
if len(polynomials) > 1:
desc += "intersection of the kernels of the following %s acting on %s:</p>\n<table>"
desc = desc % (knowl, self.display_newspace())
desc += "\n".join("<tr><td>%s</td></tr>" % F for F in polynomials) + "\n</table>"
elif len(polynomials) == 1:
desc += "kernel of the %s %s acting on %s."
desc = desc % (knowl, polynomials[0], self.display_newspace())
else:
desc = r"<p>There are no other newforms in %s.</p>"%(self.display_newspace())
return desc
def display_inner_twists(self):
if self.inner_twist_count == -1:
# Only CM data available
if self.is_cm:
discriminant = self.cm_discs[0]
return '<p>Only self twists have been computed for this newform, which has CM by %s.</p>' % (quad_field_knowl(discriminant))
else:
return '<p>This newform does not have CM; other inner twists have not been computed.</p>'
def th_wrap(kwl, title):
return ' <th>%s</th>' % display_knowl(kwl, title=title)
def td_wrap(val):
return ' <td>%s</th>' % val
twists = ['<table class="ntdata">', '<thead>', ' <tr>',
th_wrap('character.dirichlet.galois_orbit_label', 'Char. orbit'),
th_wrap('character.dirichlet.parity', 'Parity'),
#th_wrap('character.dirichlet.order', 'Order'),
th_wrap('cmf.inner_twist_multiplicity', 'Mult.'),
th_wrap('cmf.self_twist_col', 'Type'),
th_wrap('cmf.inner_twist_proved', 'Proved'),
' </tr>', '</thead>', '<tbody>']
trivial = [elt for elt in self.inner_twists if elt[6] == 1]
CMRM = sorted([elt for elt in self.inner_twists if elt[6] not in [0,1]],
key = lambda elt: elt[2])
other = sorted([elt for elt in self.inner_twists if elt[6] == 0],
key = lambda elt: (elt[2],elt[3]))
self.inner_twists = trivial + CMRM + other
for proved, mult, modulus, char_orbit_index, parity, order, discriminant in self.inner_twists:
label = '%s.%s' % (modulus, cremona_letter_code(char_orbit_index-1))
parity = 'Even' if parity == 1 else 'Odd'
proved = 'yes' if proved == 1 else 'no'
link = display_knowl('character.dirichlet.orbit_data', title=label, kwargs={'label':label})
if discriminant == 0:
field = ''
elif discriminant == 1:
field = 'trivial'
else:
cmrm = 'CM by ' if discriminant < 0 else 'RM by '
field = cmrm + quad_field_knowl(discriminant)
twists.append(' <tr>')
twists.extend(map(td_wrap, [link, parity, mult, field, proved])) # add order back eventually
twists.append(' </tr>')
twists.extend(['</tbody>', '</table>'])
return '\n'.join(twists)
def display_hecke_cutters(self):
polynomials = []
truncated = False
for p,F in self.hecke_cutters:
cut = len(F) - 1
count = 0
while cut >= 0 and count < 8:
if F[cut]:
count += 1
cut -= 1
if count < 8 or cut == 0 and abs(F[0]) < 100:
F = latex(coeff_to_poly(F, 'T%s'%p))
else:
# truncate to the first 8 nonzero coefficients
F = [0]*(cut+1) + F[cut+1:]
F = latex(coeff_to_poly(F, 'T%s'%p)) + r' + \cdots'
truncated = True
polynomials.append(web_latex_split_on_pm(F))
title = 'linear operator'
if len(polynomials) > 1:
title += 's'
knowl = display_knowl('mf.elliptic.hecke_cutter', title=title)
desc = "<p>This newform can be constructed as the "
if truncated or len(polynomials) > 1:
if len(polynomials) > 1:
desc += "intersection of the kernels "
else:
desc += "kernel "
desc += "of the following %s acting on %s:</p>\n<table>"
desc = desc % (knowl, self.display_newspace())
desc += "\n".join("<tr><td>%s</td></tr>" % F for F in polynomials) + "\n</table>"
elif len(polynomials) == 1:
desc += "kernel of the %s %s acting on %s."
desc = desc % (knowl, polynomials[0], self.display_newspace())
else:
desc = r"<p>There are no other newforms in %s.</p>"%(self.display_newspace())
return desc
def __init__(self):
degree = TextBox(name="degree",
label="Degree",
knowl="nf.degree",
example=3)
signature = TextBox(name="signature",
label="Signature",
knowl="nf.signature",
example="[1,1]")
discriminant = TextBox(name="discriminant",
label="Discriminant",
knowl="nf.discriminant",
example="-1000..-1",
example_span="-3 or 1000-2000")
rd = TextBox(name="rd",
label="Root discriminant",
knowl="nf.root_discriminant",
example="1..4.3",
example_span="a range such as 1..4.3 or 3-10")
cm_field = YesNoBox(name="cm_field",
label="CM field",
knowl="nf.cm_field")
gal = TextBoxNoEg(
name="galois_group",
label="Galois group",
knowl="nf.galois_group",
example="C5",
example_span_colspan=4,
example_span=
"%s, e.g. [8,3] or [16,7]; %s, e.g. C5 or S12; %s, e.g., 7T2 or 11T5"
% (display_knowl("group.small_group_label", "GAP id's"),
display_knowl("nf.galois_group.name", "group names"),
display_knowl("gg.label", "transitive group labels")))
regulator = TextBox(name="regulator",
label="Regulator",
knowl="nf.regulator",
example="1..3.5",
example_span="a range such as 1..3.5")
class_number = TextBox(name="class_number",
label="Class number",
knowl="nf.class_number",
example="5")
class_group = TextBox(name="class_group",
label="Class group structure",
knowl="nf.ideal_class_group",
example="[2,4]",
example_span="[ ], [3], or [2,4]")
num_ram = TextBox(name="num_ram",
label="Ramified prime count",
knowl="nf.ramified_primes",
example=2)
ram_quantifier = SubsetNoExcludeBox(name="ram_quantifier")
ram_primes = TextBoxWithSelect(name="ram_primes",
label="Ramified",
knowl="nf.ramified_primes",
example="2,3",
select_box=ram_quantifier)
ur_primes = TextBox(name="ur_primes",
label="Unramified primes",
knowl="nf.unramified_prime",
example="2,3")
subfield = TextBox(name="subfield",
label="Intermediate field",
knowl="nf.intermediate_fields",
example_span="2.2.5.1 or x^2-5 or a " +
display_knowl("nf.nickname", "field nickname"),
example="x^2-5")
count = CountBox()
self.browse_array = [[degree, signature], [discriminant, rd], [gal],
[class_number, class_group], [num_ram, cm_field],
[ram_primes, ur_primes], [regulator, subfield],
[count]]
self.refine_array = [[
degree, signature, gal, class_number, class_group
], [regulator, num_ram, ram_primes, ur_primes, cm_field],
[discriminant, rd, subfield]]
def th_wrap(kwl, title):
return ' <th>%s</th>' % display_knowl(kwl, title=title)
def char_conrey_link(self):
if self.embedding_label is None:
raise ValueError
label = '%s.%s' % (self.level, self.embedding_label.split('.')[0])
return display_knowl('character.dirichlet.data', title=label, kwargs={'label':label})
def __init__(self):
degree = TextBox(name="degree",
label="Degree",
knowl="nf.degree",
example=3)
signature = TextBox(name="signature",
label="Signature",
knowl="nf.signature",
example="[1,1]")
discriminant = TextBox(name="discriminant",
label="Discriminant",
knowl="nf.discriminant",
example="-1000..-1",
example_span="-3 or 1000-2000")
rd = TextBox(name="rd",
label="Root discriminant",
knowl="nf.root_discriminant",
example="1..4.3",
example_span="a range such as 1..4.3 or 3-10")
cm_field = YesNoBox(name="cm_field",
label="CM field",
knowl="nf.cm_field")
gal = TextBox(name="galois_group",
label="Galois group",
knowl="nf.galois_search",
example="C5",
example_span="[8,3], C5 or 7T2")
is_galois = YesNoBox(name="is_galois",
label="Is Galois",
knowl="nf.galois_group")
regulator = TextBox(name="regulator",
label="Regulator",
knowl="nf.regulator",
example="1..3.5",
example_span="a range such as 1..3.5")
class_number = TextBox(name="class_number",
label="Class number",
knowl="nf.class_number",
example="5")
class_group = TextBox(name="class_group",
label="Class group structure",
knowl="nf.ideal_class_group",
example="[2,4]",
example_span="[ ], [3], or [2,4]")
num_ram = TextBox(name="num_ram",
label="Ramified prime count",
knowl="nf.ramified_primes",
example=2)
ram_quantifier = SubsetNoExcludeBox(name="ram_quantifier")
ram_primes = TextBoxWithSelect(name="ram_primes",
label="Ramified",
knowl="nf.ramified_primes",
example="2,3",
select_box=ram_quantifier)
ur_primes = TextBox(name="ur_primes",
label="Unramified primes",
knowl="nf.unramified_prime",
example="2,3")
subfield = TextBox(name="subfield",
label="Intermediate field",
knowl="nf.intermediate_fields",
example_span="2.2.5.1 or x^2-5 or a " +
display_knowl("nf.nickname", "field nickname"),
example="x^2-5")
count = CountBox()
self.browse_array = [[degree, signature], [discriminant, rd],
[gal, is_galois], [class_number, class_group],
[num_ram, cm_field], [ram_primes, ur_primes],
[regulator, subfield], [count]]
self.refine_array = [[
degree, signature, class_number, class_group, cm_field
], [num_ram, ram_primes, ur_primes, gal, is_galois],
[discriminant, rd, regulator, subfield]]
def short_label(d):
return display_knowl("av.decomposition", "Dim %s factors" % d)
def nbsp(knowl, label):
return " " + display_knowl(knowl, label)
def short_summary(self):
stats_url = url_for(".statistics")
g2c_knowl = display_knowl('g2c.g2curve', title='genus 2 curves')
return 'The database currently contains %s %s over $\Q$ of %s up to %s. Here are some <a href="%s">further statistics</a>.' % (self.ncurves, g2c_knowl, self.disc_knowl, self.max_D, stats_url)
def __init__(self):
self.ncurves = comma(db.g2c_curves.count())
self.max_D = comma(db.g2c_curves.max('abs_disc'))
self.disc_knowl = display_knowl('g2c.abs_discriminant', title = "absolute discriminant")
def th_wrap(kwl, title):
return ' <th>%s</th>' % display_knowl(kwl, title=title)
def __init__(self):
self.ngalmaps = comma(db.belyi_galmaps_fixed.stats.count())
self.npassports = comma(db.belyi_passports_fixed.stats.count())
self.max_deg = comma(db.belyi_passports_fixed.max("deg"))
self.deg_knowl = display_knowl("belyi.degree", title="degree")
self.belyi_knowl = '<a title="Belyi maps (up to Galois conjugation) [belyi.galmap]" knowl="belyi.galmap" kwargs="">Belyi maps</a>'
def char_orbit_link(self):
label = '%s.%s' % (self.level, self.char_orbit_label)
return display_knowl('character.dirichlet.orbit_data', title=label, kwargs={'label':label})
