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"),
)
def dirichlet_character_search(info, query):
info=info,
learnmore=learnmore_list())
# For the search order-parsing
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,
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=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)
])
@search_wrap(
table=db.g2c_curves,
title="Genus 2 curve search results",
err_title="Genus 2 curves search input error",
shortcuts={
"jump": genus2_jump,
"download": G2C_download()
},
columns=g2c_columns,
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),