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,
default=True),
MathCol("level_norm", "mf.level_norm", "Level norm"),
MathCol("weight", "mf.hilbert.weight_vector", "Weight"),
MathCol("dimension", "mf.hilbert.dimension", "Dimension", default=True),
ProcessedCol("is_CM",
"mf.cm",
"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",
"ec.conductor_label",
"Conductor", ["field_label", "conductor_label"],
lambda field, conductor: '<a href="%s">%s</a>' %
(url_for('.show_ecnf_conductor', nf=field, conductor_label=conductor),
conductor),
default=True,
align="center"),
MultiProcessedCol(
"iso_class",
"ec.isogeny_class",
"Isogeny class",
"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"),
ProcessedCol("cond",
None,
"Conductor",
factorint,
contingent=lambda info: info["search_type"] == "Motive",
default=True,
mathmode=True,
align="center"),
MathCol("degree", None, "Degree", default=True),
MathCol("weight", None, "Weight", default=True),
MathCol("famhodge", None, "Hodge", default=True)
])
info['field_pretty_name'] = field_pretty(res[0]['field_label'])
else:
info['field_pretty_name'] = ''
res.sort(key=lambda x: [x['level_norm'], int(x['level_number']), x['label_suffix']])
return res
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),
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,
learnmore=learn,
random_projection="label",
bread=lambda: bread("Search results"),
)
'Prec := 100; // Default precision of 100',
'return [LocalField( pAdicField(r[1], Prec) , PolynomialRing(pAdicField(r[1], Prec))![c : c in r[2]] ) : r in data];'
],
'sage': [
'Prec = 100 # Default precision of 100',
"return [pAdicExtension(Qp(r[0], Prec), PolynomialRing(Qp(r[0], Prec),'x')(r[1]), var_name='x') for r in data]"
],
'gp': ['[[c[1], Polrev(c[2])]|c<-data];']
}
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"],
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"),
ProcessedCol("fricke_eigenvalue",
"cmf.fricke",
"Fricke",
fricke_pretty,
short_title="Fricke",
default=True,
align="center")
],
db_cols=[
"maass_id", "level", "weight",
"conrey_index", "spectral_parameter",
"symmetry", "fricke_eigenvalue"
])
def parse_group_order(inp, query, qfield, parse_singleton=int):
if LIST_RE.match(inp):
collapse_ors(parse_range2_extend(inp, qfield, parse_singleton), query)
else:
raise ValueError("It needs to be an integer (such as 25), \
a range of integers (such as 2-10 or 2..10), \
a linear function of variable g for genus (such as 84(g-1), 84g-84, 84g, or g-1), \
or a comma-separated list of these (such as 4,9,16 or 4-25, 81-121).")
hgcwa_columns = SearchColumns([
LinkCol("passport_label", "dq.curve.highergenus.aut.label", "Refined passport label",
lambda label: f"/HigherGenus/C/Aut/{label}",
default=True),
MathCol("genus", "ag.curve.genus", "Genus", default=True),
MathCol("g0", "curve.highergenus.aut.quotientgenus", "Quotient genus"),
ProcessedCol("group", "group.small_group_label", "Group", group_display, mathmode=True, align="center", default=True),
MathCol("group_order", "group.order", "Group order", default=True),
MathCol("dim", "curve.highergenus.aut.dimension", "Dimension", default=True),
ProcessedCol("signature", "curve.highergenus.aut.signature", "Signature", lambda sig: sign_display(ast.literal_eval(sig)), default=True, mathmode=True)])
hgcwa_columns.languages = ['gap', 'magma']
@search_wrap(
table=db.hgcwa_passports,
title='Family of higher genus curves with automorphisms search results',
err_title='Family of higher genus curves with automorphisms search input error',
columns=hgcwa_columns,
per_page=50,
url_for_label=url_for_label,
random_projection="passport_label",
shortcuts={'jump': higher_genus_w_automorphisms_jump,
'download': hgcwa_code_download_search },
raise ValueError("A CM discriminant must be a fundamental discriminant of an imaginary quadratic field.")
cm_list += [-el for el in cm_list]
return cm_list
@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", "ec.conductor_label", "Conductor",
["field_label", "conductor_label"],
lambda field, conductor: '<a href="%s">%s</a>' %(
url_for('.show_ecnf_conductor', nf=field, conductor_label=conductor),
conductor),
default=True, align="center"),
MultiProcessedCol("iso_class", "ec.isogeny_class", "Isogeny class",
["field_label", "conductor_label", "iso_label", "short_class_label"],
lambda field, conductor, iso, short_class_label: '<a href="%s">%s</a>' % (
url_for('.show_ecnf_isoclass', nf=field, conductor_label=conductor, class_label=iso),
short_class_label),
default=True, align="center"),
MultiProcessedCol("ainvs", "ec.weierstrass_coeffs", "Weierstrass coefficients",
["field_label", "conductor_label", "iso_label", "number", "ainvs"],
lambda field, conductor, iso, number, ainvs: '<a href="%s">%s</a>' % (
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"),
ProcessedCol("geom_end_alg", "ag.endomorphism_algebra", r"$\textrm{End}^0(E_{\overline\Q})$",
lambda v: r"$\Q$" if not v else r"$\Q(\sqrt{%d})$"%(integer_squarefree_part(v)),
short_title="Qbar-end algebra", align="center", orig="cm"),
ProcessedCol("cm_discriminant", "ec.complex_multiplication", "CM", lambda v: "" if v == 0 else v,
short_title="CM discriminant", mathmode=True, align="center", default=True, orig="cm"),
ProcessedCol("sato_tate_group", "st_group.definition", "Sato-Tate", lambda v: st_display_knowl('1.2.A.1.1a' if v==0 else '1.2.B.2.1a'),
short_title="Sato-Tate group", align="center", orig="cm"),
CheckCol("semistable", "ec.reduction", "Semistable"),
CheckCol("potential_good_reduction", "ec.reduction", "Potentially good"),
ProcessedCol("nonmax_primes", "ec.maximal_elladic_galois_rep", r"Nonmax $\ell$", lambda primes: ", ".join([str(p) for p in primes]),
query["__sort__"] = d[info.get("sort_order")]
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("eqn",
"g2c.minimal_equation",
"Equation",
lambda v: min_eqn_pretty(literal_eval(v)),
default=True,
mathmode=True),
ProcessedCol("st_group",
"g2c.st_group",
"Sato-Tate",
lambda v: st_link_by_name(1, 4, v),
default=True,
align="center"),
CheckCol("is_simple_geom",
"ag.geom_simple",
r"\(\overline{\Q}\)-simple",
default=True),
CheckCol("is_gl2_type", "g2c.gl2type", r"\(\GL_2\)", default=True),
MathCol("analytic_rank", "g2c.analytic_rank", "Rank*", default=True)
])
"ec.weierstrass_coeffs",
"Weierstrass coefficients",
default=True,
align="left"),
MultiProcessedCol("disc",
"ec.discriminant",
"Discriminant", ["signD", "absD"],
lambda s, a: f"+{a}" if s == 1 else "-{a}",
contingent=lambda info: info.get("discriminant"),
default=True,
mathmode=True,
align="center"),
ProcessedCol("faltings_height",
"ec.q.faltings_height",
"Faltings height",
RealField(20),
contingent=lambda info: info.get("faltings_height"),
default=True,
align="center"),
MathCol("rank", "ec.rank", "Rank", default=True),
ProcessedCol("torsion_structure",
"ec.torsion_subgroup",
"Torsion",
lambda tors: f"${tors}$" if tors else "trivial",
default=True,
align="center"),
SearchCol("cm",
"ec.complex_multiplication",
"CM disc",
contingent=lambda info: info.get("cm") == "CM" or "," in info.
get("cm", ""),
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),
ProcessedCol("level_ideal",
"mf.hilbert.level_norm",
"Level",
teXify_pol,
mathmode=True,
default=True),
MathCol("dimension", "mf.hilbert.dimension", "Dimension", default=True)
])
hmf_columns.dummy_download = True
@search_wrap(table=db.hmf_forms,
title='Hilbert modular form search results',
function_body = {
"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"),
return redirect(url_for(".number_field_render_webpage"))
# This doesn't seem to be used currently
#def number_field_algebra(info):
# fields = info['algebra'].split('_')
# fields2 = [WebNumberField.from_coeffs(a) for a in fields]
# for j in range(len(fields)):
# if fields2[j] is None:
# fields2[j] = WebNumberField.fakenf(fields[j])
# t = 'Number field algebra'
# info = {'results': fields2}
# return render_template("number_field_algebra.html", info=info, title=t, bread=bread)
nf_columns = SearchColumns([
ProcessedCol("label", "nf.label", "Label",
lambda label: '<a href="%s">%s</a>' % (url_for_label(label), nf_label_pretty(label)),
default=True),
SearchCol("poly", "nf.defining_polynomial", "Polynomial", default=True),
MathCol("disc", "nf.discriminant", "Discriminant", default=True, align="left"),
SearchCol("galois", "nf.galois_group", "Galois group", default=True),
SearchCol("class_group_desc", "nf.ideal_class_group", "Class group", default=True)],
db_cols=["class_group", "coeffs", "degree", "disc_abs", "disc_sign", "galois_label", "label", "ramps", "used_grh"])
def nf_postprocess(res, info, query):
galois_labels = [rec["galois_label"] for rec in res if rec.get("galois_label")]
cache = knowl_cache(list(set(galois_labels)))
for rec in res:
wnf = WebNumberField.from_data(rec)
rec["poly"] = wnf.web_poly()
rec["disc"] = wnf.disc_factored_latex()
rec["galois"] = wnf.galois_string(cache=cache)
query["__sort__"] = d[info.get("sort_order")]
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("eqn",
"g2c.minimal_equation",
"Equation",
lambda v: min_eqn_pretty(literal_eval(v)),
default=True,
mathmode=True),
ProcessedCol("st_group",
"g2c.st_group",
"Sato-Tate",
lambda v: st_link_by_name(1, 4, v),
default=True,
align="center"),
ProcessedCol("end_alg",
"g2c.end_alg",
r"\(\Q\)-end algebra",
lambda v: r"\(%s\)" % end_alg_name(v),
short_title="Q-end algebra",
align="center"),
ProcessedCol("geom_end_alg",