def hilbert_modular_form_jump(info):
lab = info['jump'].strip()
info['label'] = lab
try:
split_full_label(lab)
return hilbert_modular_form_by_label(lab)
except ValueError:
return redirect(url_for(".hilbert_modular_form_render_webpage"))
hmf_columns = SearchColumns([
MultiProcessedCol(
"label",
"mf.hilbert.label",
"Label", ["field_label", "label", "short_label"],
lambda fld, label, short: '<a href="%s">%s</a>' % (url_for(
'hmf.render_hmf_webpage', field_label=fld, label=label), short),
default=True),
ProcessedCol("field_label",
"nf",
"Base field",
lambda fld: nf_display_knowl(fld, field_pretty(fld)),
default=True),
MathCol("deg", "nf.degree", "Field degree"),
MathCol("disc", "nf.discriminant", "Field discriminant"),
ProcessedCol("level_ideal",
"mf.hilbert.level_norm",
"Level",
teXify_pol,
mathmode=True,
@search_parser
def parse_cm_list(inp, query, qfield):
query[qfield] = {'$in': make_cm_query(inp)}
ecnf_columns = SearchColumns([
MultiProcessedCol(
"label",
"ec.curve_label",
"Label", [
"short_label", "field_label", "conductor_label", "iso_label",
"number"
],
lambda label, field, conductor, iso, number: '<a href="%s">%s</a>' %
(url_for('.show_ecnf',
nf=field,
conductor_label=conductor,
class_label=iso,
number=number), label),
default=True,
align="center"),
ProcessedCol("field_label",
"nf",
"Base field",
lambda field: nf_display_knowl(field, field_pretty(field)),
default=True,
align="center"),
MultiProcessedCol(
"conductor",
def url_for_label(label):
if label.count("_") == 2:
ab, t = label.rsplit("_", 1)
return url_for(".by_label", label=ab, t=t)
else:
return url_for(".by_family_label", label=label)
hgm_columns = SearchColumns([
MultiProcessedCol(
"label",
None,
"Label", ["A", "B", "t"],
lambda A, B, t: '<a href="%s">%s</a>' %
(url_for('.by_family_label', label=ab_label(A, B))
if t is None else url_for('.by_label',
label=ab_label(A, B),
t=make_t_label(t)), ab_label(A, B)
if t is None else make_abt_label(A, B, t)),
default=True),
MathCol("A", None, "$A$", default=True),
MathCol("B", None, "$B$", default=True),
ProcessedCol("t",
None,
"$t$",
display_t,
contingent=lambda info: info["search_type"] == "Motive",
default=True,
mathmode=True,
align="center"),
def url_for_label(label):
return url_for(".render_bmf_webpage",
**dict(zip(
['field_label', 'level_label', 'label_suffix'],
label.split('-')
)))
bmf_columns = SearchColumns([
ProcessedCol("field_label", "nf", "Base field",
lambda fld: nf_display_knowl(fld, field_pretty(fld)),
default=True),
MultiProcessedCol("level", "mf.bianchi.level", "Level", ["field_label", "level_label"],
lambda fld, lvl: '<a href="{}">{}</a>'.format(
url_for("bmf.render_bmf_space_webpage",
field_label=fld,
level_label=lvl),
lvl),
default=True), # teXify_pol(v['level_ideal'])
MultiProcessedCol("label", "mf.bianchi.labels", "Label", ["field_label", "level_label", "label_suffix", "short_label"],
lambda fld, lvl, suff, short: '<a href="{}">{}</a>'.format(
url_for("bmf.render_bmf_webpage",
field_label=fld,
level_label=lvl,
label_suffix=suff),
short),
default=True),
MathCol("dimension", "mf.bianchi.newform", "Dimension", default=True),
ProcessedCol("sfe", "mf.bianchi.sign", "Sign",
lambda v: "$+1$" if v == 1 else ("$-1$" if v == -1 else "?"),
default=True, align="center"),
return url_for(".render_Dirichletwebpage", modulus=modulus, number=number)
def display_galois_orbit(orbit, modulus):
trunc = (len(orbit) > 5)
if trunc:
orbit = [orbit[0], orbit[-1]]
disp = [r'<a href="{0}/{1}">\(\chi_{{{0}}}({1}, \cdot)\)</a>'.format(modulus, o) for o in orbit]
if trunc:
disp = r"$, \cdots ,$".join(disp)
else:
disp = "$,$ ".join(disp)
return f'<p style="margin-top: 0px;margin-bottom:0px;">\n{disp}\n</p>'
character_columns = SearchColumns([
LinkCol("label", "character.dirichlet.galois_orbit_label", "Orbit label", lambda label: label.replace(".", "/"), default=True, align="center"),
MultiProcessedCol("conrey", "character.dirichlet.conrey'", "Conrey labels", ["galois_orbit", "modulus"],
display_galois_orbit, default=True, align="center"),
MathCol("modulus", "character.dirichlet.modulus", "Modulus", default=True),
MathCol("conductor", "character.dirichlet.conductor", "Conductor", default=True),
MathCol("order", "character.dirichlet.order", "Order", default=True),
ProcessedCol("parity", "character.dirichlet.primitive", "Parity", lambda parity: "even" if parity == 1 else "odd", default=True),
CheckCol("is_primitive", "character.dirichlet.primitive", "Primitive", default=True)])
character_columns.dummy_download = True
@search_wrap(
table=db.char_dir_orbits,
title="Dirichlet character search results",
err_title="Dirichlet character search input error",
columns=character_columns,
shortcuts={"jump": jump},
url_for_label=url_for_label,
lf_columns = SearchColumns([
LinkCol("label", "lf.field.label", "Label", url_for_label, default=True),
ProcessedCol("coeffs",
"lf.defining_polynomial",
"Polynomial",
format_coeffs,
default=True),
MathCol("p", "lf.qp", "$p$", default=True),
MathCol("e", "lf.ramification_index", "$e$", default=True),
MathCol("f", "lf.residue_field_degree", "$f$", default=True),
MathCol("c", "lf.discriminant_exponent", "$c$", default=True),
MultiProcessedCol(
"gal",
"nf.galois_group",
"Galois group", ["n", "gal", "cache"],
lambda n, t, cache: group_pretty_and_nTj(n, t, cache=cache),
default=True),
MultiProcessedCol("slopes",
"lf.slope_content",
"Slope content", ["slopes", "t", "u"],
show_slope_content,
default=True,
mathmode=True)
],
db_cols=[
"c", "coeffs", "e", "f", "gal", "label", "n",
"p", "slopes", "t", "u"
])
del query['$or']
elif level_field in query:
if not contains_level(query[level_field]):
raise ValueError(
"The modulus is not consistent with the specified level.")
query[level_field] = level
query[conrey_index_field] = conrey_index
maass_columns = SearchColumns([
MathCol("level", "mf.maass.mwf.level", "Level", default=True),
MathCol("weight", "mf.maass.mwf.weight", "Weight", default=True),
MultiProcessedCol("character",
"mf.maass.mwf.character",
"Char", ["level", "conrey_index"],
character_link,
short_title="character",
default=True,
align="center"),
MultiProcessedCol("spectral",
"mf.maass.mwf.spectralparameter",
"Spectral parameter", ["maass_id", "spectral_parameter"],
lambda mid, param: '<a href="%s">%s</a>' %
(url_for('.by_label', label=mid), param),
default=True),
ProcessedCol("symmetry",
"mf.maass.mwf.symmetry",
"Symmetry",
symmetry_pretty,
default=True,
align="center"),
def make_order_key(order):
order1 = int(ZZ(order).log(10))
return '%03d%s' % (order1, str(order))
gg_columns = SearchColumns([
LinkCol("label", "gg.label", "Label", url_for_label, default=True),
SearchCol("pretty", "gg.simple_name", "Name", default=True),
MathCol("order", "group.order", "Order", default=True, align="right"),
MathCol("parity", "gg.parity", "Parity", default=True, align="right"),
CheckCol("solv", "group.solvable", "Solvable", default=True),
MultiProcessedCol(
"subfields",
"gg.subfields",
"Subfields", ["subfields", "cache"],
lambda subs, cache: WebGaloisGroup(None, {
"subfields": subs
}).subfields(cache=cache),
contingent=lambda info: info["show_subs"],
default=True),
MultiProcessedCol(
"siblings",
"gg.other_representations",
"Low Degree Siblings", ["siblings", "bound_siblings", "cache"],
lambda sibs, bnd, cache: WebGaloisGroup(None, {
"siblings": sibs,
"bound_siblings": bnd
}).otherrep_list(givebound=False, cache=cache),
default=True)
],
db_cols=[
else:
return abort(404, f"Invalid label {label}")
return datapage(labels, tables, title=f"Belyi map data - {label}", bread=bread, label_cols=label_cols)
def url_for_label(label):
return url_for(".by_url_belyi_search_url", smthorlabel=label)
belyi_columns = SearchColumns([
LinkCol("label", "belyi.label", "Label", url_for_belyi_galmap_label, default=True),
MathCol("deg", "belyi.degree", "Degree", default=True),
SearchCol("group", "belyi.group", "Group", default=True),
MathCol("abc", "belyi.abc", "abc", default=True, align="left", short_title="abc triple"),
MathCol("lambdas", "belyi.ramification_type", "Ramification type", default=True, align="left"),
MathCol("g", "belyi.genus", "Genus", default=True),
MathCol("orbit_size", "belyi.orbit_size", "Orbit Size", default=True),
MultiProcessedCol("field", "belyi.base_field", "Base field", ["base_field_label", "base_field"], lambda label, disp: field_display_gen(label, disp, truncate=16), default=True)])
@search_wrap(
table=db.belyi_galmaps_fixed,
title="Belyi map search results",
err_title="Belyi map search input error",
columns=belyi_columns,
shortcuts={"jump": belyi_jump, "download": Belyi_download()},
url_for_label=url_for_label,
bread=lambda: get_bread("Search results"),
learnmore=learnmore_list,
)
def belyi_search(info, query):
if "group" in query:
info["group"] = query["group"]
data_description = "defining the elliptic curve y^2 + a1xy + a3y = x^3 + a2x^2 + a4x + a6."
function_body = {
"magma": [
"return [EllipticCurve([a:a in ai]):ai in data];", # convert ai from list to sequence
],
"sage": [
"return [EllipticCurve(ai) for ai in data]",
],
"gp": ["[ellinit(ai)|ai<-data];"],
}
ec_columns = SearchColumns([
LinkCol("lmfdb_label", "ec.q.lmfdb_label", "Label", lambda label: url_for(".by_ec_label", label=label),
default=True, align="center", short_title="LMFDB curve label"),
MultiProcessedCol("cremona_label", "ec.q.cremona_label", "Cremona label",
["Clabel", "conductor"],
lambda label, conductor: '<a href="%s">%s</a>' % (url_for(".by_ec_label", label=label), label) if conductor < CREMONA_BOUND else " - ",
align="center", short_title="Cremona curve label"),
LinkCol("lmfdb_iso", "ec.q.lmfdb_label", "Class", lambda label: url_for(".by_ec_label", label=label),
default=True, align="center", short_title="LMFDB class label"),
MultiProcessedCol("cremona_iso", "ec.q.cremona_label", "Cremona class",
["Ciso", "conductor"],
lambda label, conductor: '<a href="%s">%s</a>' % (url_for(".by_ec_label", label=label), label) if conductor < CREMONA_BOUND else " - ",
align="center", short_title="Cremona class label"),
MathCol("class_size", "ec.isogeny_class", "Class size", align="center", default=lambda info: info.get("class_size") or info.get("optimal") == "on"),
MathCol("class_deg", "ec.isogeny_class_degree", "Class degree", align="center", default=lambda info: info.get("class_deg")),
ProcessedCol("conductor", "ec.q.conductor", "Conductor", lambda v: web_latex_factored_integer(ZZ(v)), default=True, align="center"),
MultiProcessedCol("disc", "ec.discriminant", "Discriminant", ["signD", "absD"], lambda s, a: web_latex_factored_integer(s*ZZ(a)),
default=lambda info: info.get("discriminant"), align="center"),
MathCol("rank", "ec.rank", "Rank", default=True),
ProcessedCol("torsion_structure", "ec.torsion_subgroup", "Torsion",
lambda tors: r"\oplus".join([r"\Z/%s\Z"%n for n in tors]) if tors else r"\mathsf{trivial}", default=True, mathmode=True, align="center"),
ec_columns = SearchColumns([
ColGroup(
"curve_labels",
None,
"Curve", [
LinkCol("lmfdb_label",
"ec.q.lmfdb_label",
"LMFDB label",
lambda label: url_for(".by_ec_label", label=label),
default=True,
align="center"),
MultiProcessedCol("cremona_label",
"ec.q.cremona_label",
"Cremona label", ["Clabel", "conductor"],
lambda label, conductor: '<a href="%s">%s</a>' %
(url_for(".by_ec_label", label=label), label)
if conductor < CREMONA_BOUND else " - ",
default=True,
align="center")
],
default=True),
ColGroup(
"iso_labels",
"ec.isogeny_class",
"Isogeny class", [
LinkCol("lmfdb_iso",
"ec.q.lmfdb_label",
"LMFDB label",
lambda label: url_for(".by_ec_label", label=label),
default=True,
align="center"),
"magma": [
"R<x>:=PolynomialRing(Rationals());",
"return [HyperellipticCurve(R![c:c in r[1]],R![c:c in r[2]]):r in data];",
],
"sage": [
"R.<x>=PolynomialRing(QQ)",
"return [HyperellipticCurve(R(r[0]),R(r[1])) for r in data]",
],
"gp": ["[apply(Polrev,c)|c<-data];"],
}
g2c_columns = SearchColumns([
LinkCol("label", "g2c.label", "Label", url_for_curve_label, default=True),
ProcessedLinkCol("class", "g2c.isogeny_class", "Class", lambda v: url_for_isogeny_class_label(class_from_curve_label(v)), class_from_curve_label, default=True, orig="label"),
ProcessedCol("cond", "g2c.conductor", "Conductor", lambda v: web_latex(factor(v)), align="center", default=True),
MultiProcessedCol("disc", "ec.discriminant", "Discriminant", ["disc_sign", "abs_disc"], lambda s, a: web_latex_factored_integer(s*ZZ(a)),
default=lambda info: info.get("abs_disc"), align="center"),
MathCol("analytic_rank", "g2c.analytic_rank", "Rank*", default=True),
MathCol("two_selmer_rank", "g2c.two_selmer_rank", "2-Selmer rank"),
ProcessedCol("torsion_subgroup", "g2c.torsion", "Torsion",
lambda tors: r"\oplus".join([r"\Z/%s\Z"%n for n in literal_eval(tors)]) if tors != "[]" else r"\mathsf{trivial}",
default=True, mathmode=True, align="center"),
ProcessedCol("geom_end_alg", "g2c.geom_end_alg", r"$\textrm{End}^0(J_{\overline\Q})$", lambda v: r"\(%s\)"%geom_end_alg_name(v),
short_title="Qbar-end algebra", default=True, align="center"),
ProcessedCol("end_alg", "g2c.end_alg", r"$\textrm{End}^0(J)$", lambda v: r"\(%s\)"%end_alg_name(v), short_title="Q-end algebra", align="center"),
CheckCol("is_gl2_type", "g2c.gl2type", r"$\GL_2\textsf{-type}$", short_title="GL2-type"),
ProcessedCol("st_label", "g2c.st_group", "Sato-Tate", st_display_knowl, short_title='Sato-Tate group', align="center"),
CheckCol("is_simple_base", "ag.simple", r"$\Q$-simple", short_title="Q-simple"),
CheckCol("is_simple_geom", "ag.geom_simple", r"\(\overline{\Q}\)-simple", short_title="Qbar-simple"),
MathCol("aut_grp_tex", "g2c.aut_grp", r"\(\Aut(X)\)", short_title="Q-automorphisms"),
MathCol("geom_aut_grp_tex", "g2c.geom_aut_grp", r"\(\Aut(X_{\overline{\Q}})\)", short_title="Qbar-automorphisms"),