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"
])
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"),
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"
])
# 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)
rec["class_group_desc"] = wnf.class_group_invariants()
return res
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=[
"bound_siblings", "gapid", "label", "name",
"order", "parity", "pretty", "siblings", "solv",
"subfields"
])
gg_columns.dummy_download = True
def url_for_label(label):
if label == "random":
return url_for(".random_abstract_group")
return url_for(".by_label", label=label)
def get_url(label):
return url_for(".by_label", label=label)
glnQ_columns = SearchColumns([
LinkCol("label", "group.label", "Label", get_url, default=True),
MathCol("tex_name", "group.name", "Name", default=True),
MathCol("order", "group.order", "Order", default=True),
MathCol("dim", "group.dimension", "Dimension", default=True)
],
db_cols=["label", "group", "order", "dim"])
glnQ_columns.dummy_download = True
def glnQ_postprocess(res, info, query):
tex_names = {
rec["label"]: rec["tex_name"]
for rec in db.gps_groups.search(
{"label": {
"$in": [gp["group"] for gp in res]
}}, ["label", "tex_name"])
}
for gp in res:
return 'a' + cremona_letter_code(-c)
return cremona_letter_code(c)
jump_box = "%s.%s.%s" % (g, q, "_".join(
extended_code(cdict.get(i, 0)) for i in range(1, g + 1)))
return by_label(jump_box)
abvar_columns = SearchColumns([
LinkCol("label", "ab.fq.lmfdb_label", "Label", url_for_label,
default=True),
MathCol("g", "ag.dimension", "Dimension", default=True),
MathCol("field", "ag.base_field", "Base field", default=True),
MathCol("formatted_polynomial",
"av.fq.l-polynomial",
"L-polynomial",
default=True),
MathCol("p_rank", "av.fq.p_rank", "$p$-rank", default=True),
SearchCol("decomposition_display_search", "av.decomposition",
"Isogeny factors")
], [
"label", "g", "q", "poly", "p_rank", "is_simple", "simple_distinct",
"simple_multiplicities", "is_primitive", "primitive_models"
])
@search_wrap(
table=db.av_fq_isog,
title="Abelian variety search results",
err_title="Abelian variety search input error",
columns=abvar_columns,
shortcuts={
except ValueError:
flash_error ("%s is not valid input. Expected a label or Weil polynomial.", jump_box)
return redirect(url_for(".abelian_varieties"))
def extended_code(c):
if c < 0:
return 'a' + cremona_letter_code(-c)
return cremona_letter_code(c)
jump_box = "%s.%s.%s" % (g, q, "_".join(extended_code(cdict.get(i, 0)) for i in range(1, g+1)))
return by_label(jump_box)
abvar_columns = SearchColumns([
LinkCol("label", "ab.fq.lmfdb_label", "Label", url_for_label, default=True),
MathCol("g", "ag.dimension", "Dimension", default=True),
MathCol("field", "ag.base_field", "Base field", default=True),
MathCol("p", "ag.base_field", "Base char.", short_title="base characteristic"),
MathCol("formatted_polynomial", "av.fq.l-polynomial", "L-polynomial", short_title="L-polynomial", default=True),
MathCol("p_rank", "av.fq.p_rank", "$p$-rank", default=True),
MathCol("p_rank_deficit", "av.fq.p_rank", "$p$-rank deficit"),
MathCol("curve_count", "av.fq.curve_point_counts", "points on curve"),
MathCol("abvar_count", "ag.fq.point_counts", "points on variety"),
SearchCol("decomposition_display_search", "av.decomposition", "Isogeny factors", default=True)],
db_cols=["label", "g", "q", "poly", "p_rank", "p_rank_deficit", "is_simple", "simple_distinct", "simple_multiplicities", "is_primitive", "primitive_models", "curve_count", "abvar_count"])
@search_wrap(
table=db.av_fq_isog,
title="Abelian variety search results",
err_title="Abelian variety search input error",
columns=abvar_columns,
shortcuts={
"jump": jump,
"download": download_search,
},
query['gram'] = gram
proj = lattice_search_projection
count = parse_count(info)
start = parse_start(info)
res = db.lat_lattices.search(query, proj, limit=count, offset=start, info=info)
break
return res
def url_for_label(label):
return url_for(".render_lattice_webpage", label=label)
lattice_columns = SearchColumns([
LinkCol("label", "lattice.label", "Label", url_for_label, default=True),
MathCol("dim", "lattice.dimension", "Dimension", default=True),
MathCol("det", "lattice.determinant", "Determinant", default=True),
MathCol("level", "lattice.level", "Level", default=True),
MathCol("class_number", "lattice.class_number", "Class number", default=True),
MathCol("minimum", "lattice.minimal_vector", "Minimal vector", default=True),
MathCol("aut", "lattice.group_order", "Aut. group order", default=True)])
@search_wrap(table=db.lat_lattices,
title='Integral lattices search results',
err_title='Integral lattices search error',
columns=lattice_columns,
shortcuts={'download':download_search,
'label':lambda info:lattice_by_label_or_name(info.get('label'))},
postprocess=lattice_search_isometric,
url_for_label=url_for_label,
bread=lambda: get_bread("Search results"),
learnmore=learnmore_list,
properties=lambda: [])
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]),
default=lambda info: info.get("nonmax_primes"), short_title="nonmaximal primes", mathmode=True, align="center"),
ProcessedCol("elladic_images", "ec.galois_rep_elladic_image", r"$\ell$-adic images", lambda v: ", ".join([display_knowl('gl2.subgroup_data', title=s, kwargs={'label':s}) for s in v]),
short_title="ℓ-adic images", default=lambda info: info.get("nonmax_primes") or info.get("galois_image"), align="center"),
ProcessedCol("modell_images", "ec.galois_rep_modell_image", r"mod-$\ell$ images", lambda v: ", ".join([display_knowl('gl2.subgroup_data', title=s, kwargs={'label':s}) for s in v]),
short_title="mod-ℓ images", default=lambda info: info.get("nonmax_primes") or info.get("galois_image"), align="center"),
ProcessedCol("regulator", "ec.regulator", "Regulator", lambda v: str(v)[:11], mathmode=True),
MathCol("sha", "ec.analytic_sha_order", r"$Ш_{\textrm{an}}$", short_title="analytic Ш"),
ProcessedCol("sha_primes", "ec.analytic_sha_order", "Ш primes", lambda primes: ", ".join(str(p) for p in primes),
default=lambda info: info.get("sha_primes"), mathmode=True, align="center"),
MathCol("num_int_pts", "ec.q.integral_points", "Integral points",
default=lambda info: info.get("num_int_pts"), align="center"),
MathCol("degree", "ec.q.modular_degree", "Modular degree", align="center"),
ProcessedCol("faltings_height", "ec.q.faltings_height", "Faltings height", lambda v: "%.6f"%(RealField(20)(v)), short_title="Faltings height",
default=lambda info: info.get("faltings_height"), mathmode=True, align="right"),
ProcessedCol("jinv", "ec.q.j_invariant", "j-invariant", lambda v: r"$%s/%s$"%(v[0],v[1]) if v[1] > 1 else r"$%s$"%v[0],
short_title="j-invariant", align="center"),
MathCol("ainvs", "ec.weierstrass_coeffs", "Weierstrass coefficients", short_title="Weierstrass coeffs", align="left"),
ProcessedCol("equation", "ec.q.minimal_weierstrass_equation", "Weierstrass equation", latex_equation, default=True, short_title="Weierstrass equation", align="left", orig="ainvs"),
])
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_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"),
MultiProcessedCol("cremona_iso",
"ec.q.cremona_label",
"Cremona label", ["Ciso", "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),
MathCol("ainvs",
"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", ""),
default=True,
align="center"),
ProcessedCol("nonmax_primes",
"ec.maximal_elladic_galois_rep",
"Nonmax primes",
lambda primes: ",".join(str(p) for p in primes),
contingent=lambda info: info.get("nonmax_primes"),
default=True,
mathmode=True,
align="center"),
ProcessedCol("elladic_images",
"ec.galois_rep_elladic_image",
"Galois images",
",".join,
contingent=lambda info: info.get("galois_image"),
default=True,
align="center"),
MathCol("num_int_pts",
"ec.q.integral_points",
"Integral points",
contingent=lambda info: info.get("num_int_pts"),
default=True,
align="center")
],
tr_class=["bottom-align", ""])
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',
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"),
MathCol("num_rat_pts", "g2c.all_rational_points", r"$\Q$-points", short_title="Q-points*"),
MathCol("num_rat_wpts", "g2c.num_rat_wpts", r"$\Q$-Weierstrass points", short_title="Q-Weierstrass points"),
CheckCol("locally_solvable", "g2c.locally_solvable", "Locally solvable"),
CheckCol("has_square_sha", "g2c.analytic_sha", "Square ле*"),
MathCol("analytic_sha", "g2c.analytic_sha", "Analytic ле*"),
ProcessedCol("tamagawa_product", "g2c.tamagawa", "Tamagawa", lambda v: web_latex(factor(v)), short_title="Tamagawa product", align="center"),
ProcessedCol("regulator", "g2c.regulator", "Regulator", lambda v: r"\(%.6f\)"%v, align="right"),
ProcessedCol("real_period", "g2c.real_period", "Real period", lambda v: r"\(%.6f\)"%v, align="right"),
ProcessedCol("leading_coeff", "g2c.bsd_invariants", "Leading coefficient", lambda v: r"\(%.6f\)"%v, align="right"),
ProcessedCol("igusa_clebsch_inv", "g2c.igusa_clebsch_invariants", "Igusa-Clebsch invariants", lambda v: v.replace("'",""), short_title="Igusa-Clebsch invariants", mathmode=True),
ProcessedCol("igusa_inv", "g2c.igusa_invariants", "Igusa invariants", lambda v: v.replace("'",""), short_title="Igusa invariants", mathmode=True),
ProcessedCol("g2_inv", "g2c.g2_invariants", "G2-invariants", lambda v: v.replace("'",""), short_title="G2-invariants", mathmode=True),
ProcessedCol("eqn", "g2c.minimal_equation", "Equation", lambda v: min_eqn_pretty(literal_eval(v)), default=True, mathmode=True),
])
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"),
ProcessedCol("bc", "mf.bianchi.base_change", "Base change", bc_info, default=True, align="center"),
ProcessedCol("CM", "mf.bianchi.cm", "CM", cm_info, default=True, align="center")])
bmf_columns.dummy_download = True
artin_columns = SearchColumns([
SearchCol("galois_links", "artin.label", "Label", default=True),
MathCol("dimension", "artin.dimension", "Dimension", default=True),
MathCol("factored_conductor_latex",
"artin.conductor",
"Conductor",
default=True),
MathCol("num_ramps", "artin.ramified_primes", "Ramified prime count"),
SearchCol("field_knowl",
"artin.stem_field",
"Artin stem field",
default=True,
short_title="Artin stem field"),
SearchCol("pretty_galois_knowl",
"artin.gg_quotient",
"$G$",
default=True,
align="center",
short_title="image"),
SearchCol("projective_group",
"artin.projective_image",
"Projective image",
align="center"),
SearchCol("container",
"artin.permutation_container",
"Container",
align="center"),
MathCol("indicator",
"artin.frobenius_schur_indicator",
"Ind",
default=True,
short_title="indicator"),
MathCol("trace_complex_conjugation",
"artin.trace_of_complex_conj",
r"$\chi(c)$",
default=True,
short_title="trace of complex conj.")
], [
"Baselabel", "GaloisConjugates", "Dim", "Conductor", "BadPrimes", "NFGal",
"GaloisLabel", "Indicator", "Is_Even", "Container", "NumBadPrimes",
"Proj_GAP", "Proj_nTj"
])
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,
learnmore=learn,
elif label.count("-") == 2: # galmap label length
labels = [label, "-".join(label.split("-")[:-1]), label]
label_cols = ["label", "plabel", "label"]
tables = ["belyi_galmaps_fixed", "belyi_passports_fixed", "belyi_galmap_portraits"]
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,
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>' %
(url_for('.show_ecnf',
nf=field,
conductor_label=conductor,
class_label=iso,
number=number), web_ainvs(field, ainvs)))
])
def url_for_label(label):
return url_for(".render_artin_representation_webpage", label=label)
artin_columns = SearchColumns([
SearchCol("galois_links", "artin.label", "Label", default=True),
MathCol("dimension", "artin.dimension", "Dimension", default=True),
MathCol("factored_conductor_latex",
"artin.conductor",
"Conductor",
default=True),
SearchCol(
"field_knowl", "artin.stem_field", "Artin stem field", default=True),
SearchCol("pretty_galois_knowl",
"artin.gg_quotient",
"$G$",
default=True,
align="center"),
MathCol(
"indicator", "artin.frobenius_schur_indicator", "Ind", default=True),
MathCol("trace_complex_conjugation",
"artin.trace_of_complex_conj",
r"$\chi(c)$",
default=True)
], [
"Baselabel", "GaloisConjugates", "Dim", "Conductor", "BadPrimes", "NFGal",
"GaloisLabel", "Indicator", "Is_Even"
])
artin_columns.above_table = "<div>Galois conjugate representations are grouped into single lines.</div>"
artin_columns.dummy_download = True
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"),
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)
])
@search_parser(clean_info=True, prep_ranges=True)
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,
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",
"CM",
lambda cm: "✓" if cm == "yes" else "",
align="center"),
ProcessedCol("is_base_change",
"mf.base_change",
"Base change",
lambda bc: "✓" if bc == "yes" else "",
align="center")
])
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",
"g2c.geom_end_alg",
r"\(\overline{\Q}\)-end algebra",
lambda v: r"\(%s\)" % geom_end_alg_name(v),
short_title="Qbar-end algebra",
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",
default=True),
CheckCol("is_gl2_type",
"g2c.gl2type",
r"\(\GL_2\)-type",
short_title="GL2-type",
default=True),
MathCol("analytic_rank", "g2c.analytic_rank", "Rank*", default=True),
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"),
CheckCol("locally_solvable", "g2c.locally_solvable", "Locally solvable"),
MathCol("num_rat_pts", "g2c.all_rational_points", "Q-points*"),
MathCol("num_rat_wpts", "g2c.num_rat_wpts", "Q-Weierstrass pts"),
CheckCol("has_square_sha", "g2c.analytic_sha", "Square ле*"),
MathCol("analytic_sha", "g2c.analytic_sha", "Analytic ле*"),
ProcessedCol("torsion_subgroup",
"g2c.torsion",
"Torsion subgroup",
lambda v: "trivial" if v == "[]" else r"\(%s\)" % v,
align="center"),
MathCol("two_selmer_rank", "g2c.two_selmer_rank", "2-Selmer rank"),
MathCol("tamagawa_product", "g2c.tamagawa", "Tamagawa product"),
ProcessedCol("regulator",
"g2c.regulator",
"Regulator",
lambda v: r"\(%.6f\)" % v,
align="right"),
ProcessedCol("real_period",
"g2c.real_period",
"Real period",
lambda v: r"\(%.6f\)" % v,
align="right"),
ProcessedCol("leading_coeff",
"g2c.bsd_invariants",
"Leading coeff",
lambda v: r"\(%.6f\)" % v,
align="right"),
])
