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={
"jump": jump,
"download": download_search,
},
dih_list = [{qfield: z} for z in dihedrals]
query[qfield] = {'$or': dih_list}
#query[qfield] = {'$in': dihedrals}
if current and current not in dihedrals:
raise ValueError(
'Projective image and projective image type are inconsistent')
elif current:
query[qfield] = current
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",
return render_template("gg-index.html",
title="Galois groups",
bread=bread,
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",
tables = ["belyi_passports_fixed", "belyi_galmaps_fixed"]
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"),
dih_list = [{qfield: z} for z in dihedrals]
query[qfield] = {'$or': dih_list}
#query[qfield] = {'$in': dihedrals}
if current and current not in dihedrals:
raise ValueError(
'Projective image and projective image type are inconsistent')
elif current:
query[qfield] = current
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),
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,
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,
},
postprocess=lambda res, info, query: [AbvarFq_isoclass(x) for x in res],
url_for_label=url_for_label,
learnmore=learnmore_list,
bread=lambda: get_bread(("Search results", " ")),
"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,
# 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