def __init__(self):
qshort = display_knowl("ag.base_field", "base field")
q = TextBox(
"q",
label="Cardinality of the %s" % (qshort),
short_label=qshort,
example="81",
example_span="81 or 3-49",
)
pshort = display_knowl("ag.base_field", "Base char.")
p = TextBox(
"p",
label="Characteristic of the %s" % (qshort),
short_label=pshort,
example="3",
example_span="3 or 2-5",
)
g = TextBox(
"g",
label="Dimension",
knowl="ag.dimension",
example="2",
example_span="2 or 3-5"
)
p_rank = TextBox(
"p_rank",
label="$p$-rank",
knowl="av.fq.p_rank",
example="2"
)
p_rank_deficit = TextBox(
"p_rank_deficit",
label="$p$-rank deficit",
knowl="av.fq.p_rank",
example="2",
advanced=True,
)
angle_rank = TextBox(
"angle_rank",
label="Angle rank",
knowl="av.fq.angle_rank",
example="3",
example_col=False,
advanced=True,
)
newton_polygon = TextBox(
"newton_polygon",
label="Slopes of Newton polygon",
knowl="lf.newton_polygon",
example="[0,0,1/2]",
colspan=(1, 3, 1),
width=3*190 - 30,
short_width=160,
short_label="Slopes",
advanced=True,
)
initial_coefficients = TextBox(
"initial_coefficients",
label="Initial coefficients",
knowl="av.fq.initial_coefficients",
example="[2, -1, 3, 9]",
)
abvar_point_count = TextBox(
"abvar_point_count",
label="Point counts of the variety",
knowl="ag.fq.point_counts",
example="[75,7125]",
colspan=(1, 3, 1),
width=3*190 - 30,
short_width=160,
short_label="Points on variety",
advanced=True,
)
curve_point_count = TextBox(
"curve_point_count",
label="Point counts of the curve",
knowl="av.fq.curve_point_counts",
example="[9,87]",
colspan=(1, 3, 1),
width=3*190 - 30,
short_width=160,
short_label="Points on curve",
advanced=True,
)
def nbsp(knowl, label):
return " " + display_knowl(knowl, label)
number_field = TextBox(
"number_field",
label=nbsp("av.fq.number_field", "Number field"),
short_label=display_knowl("av.fq.number_field", "Number field"),
example="4.0.29584.2",
example_span="4.0.29584.2 or Qzeta8",
colspan=(1, 3, 1),
width=3*190 - 30,
short_width=160,
advanced=True,
)
galois_group = TextBox(
"galois_group",
label=nbsp("nf.galois_group", "Galois group"),
short_label=display_knowl("nf.galois_group", "Galois group"),
example="4T3",
example_span="C4, or 8T12, a list of "
+ display_knowl("nf.galois_group.name", "group names"),
colspan=(1, 3, 1),
width=3*190 - 30,
short_width=160,
advanced=True,
)
#size = TextBox(
# "size",
# label="Isogeny class size",
# knowl="av.fq.isogeny_class_size",
# example="1",
# example_col=False,
# advanced=True,
#)
gdshort = display_knowl("av.endomorphism_field", "End.") + " degree"
gdlong = "Degree of " + display_knowl("av.endomorphism_field", "endomorphism_field")
geom_deg = TextBox(
"geom_deg",
label=gdlong,
short_label=gdshort,
example="168",
example_span="6-12, 168",
advanced=True,
)
jac_cnt = TextBox(
"jac_cnt",
label="Number of Jacobians",
knowl="av.jacobian_count",
example="6",
short_label="# Jacobians",
advanced=True,
)
hyp_cnt = TextBox(
"hyp_cnt",
label="Number of hyperelliptic Jacobians",
knowl="av.hyperelliptic_count",
example="6",
example_col=False,
short_label="# Hyp. Jacobians",
advanced=True,
)
tcshort = display_knowl("av.twist", "# twists")
tclong = "Number of " + display_knowl("av.twist", "twists")
twist_count = TextBox(
"twist_count",
label=tclong,
short_label=tcshort,
example="390",
advanced=True,
)
max_twist_degree = TextBox(
"max_twist_degree",
label="Max twist degree",
knowl="av.twist",
example="16",
example_col=False,
advanced=True,
)
simple = YesNoBox(
"simple",
label="Simple",
knowl="av.simple",
)
geom_simple = YesNoBox(
"geom_simple",
label="Geometrically simple",
knowl="av.geometrically_simple",
short_label="Geom. simple",
)
primitive = YesNoBox(
"primitive",
label="Primitive",
knowl="ag.primitive",
)
polarizable = YesNoMaybeBox(
"polarizable",
label="Principally polarizable",
knowl="av.princ_polarizable",
short_label="Princ polarizable",
)
jacobian = YesNoMaybeBox(
"jacobian",
label="Jacobian",
knowl="ag.jacobian"
)
uglabel = "Use %s in the following inputs" % display_knowl("av.decomposition", "Geometric decomposition")
use_geom_decomp = CheckBox(
"use_geom_decomp",
label=uglabel,
short_label=uglabel
)
use_geom_index = CheckboxSpacer(use_geom_decomp, colspan=4, advanced=True)
use_geom_refine = CheckboxSpacer(use_geom_decomp, colspan=5, advanced=True)
def long_label(d):
return nbsp("av.decomposition", "Dimension %s factors" % d)
def short_label(d):
return display_knowl("av.decomposition", "Dim %s factors" % d)
dim1 = TextBox(
"dim1_factors",
label=long_label(1),
example="1-3",
example_col=False,
short_label=short_label(1),
advanced=True,
)
dim1d = TextBox(
"dim1_distinct",
label="Distinct factors",
knowl="av.decomposition",
example="1-2",
example_span="2 or 1-3",
short_label="(distinct)",
advanced=True,
)
dim2 = TextBox(
"dim2_factors",
label=long_label(2),
example="1-3",
example_col=False,
short_label=short_label(2),
advanced=True,
)
dim2d = TextBox(
"dim2_distinct",
label="Distinct factors",
knowl="av.decomposition",
example="1-2",
example_span="2 or 1-3",
short_label="(distinct)",
advanced=True,
)
dim3 = TextBox(
"dim3_factors",
label=long_label(3),
example="2",
example_col=False,
short_label=short_label(3),
advanced=True,
)
dim3d = TextBox(
"dim3_distinct",
label="Distinct factors",
knowl="av.decomposition",
example="1",
example_span="2 or 0-1",
short_label="(distinct)",
advanced=True,
)
dim4 = TextBox(
"dim4_factors",
label=long_label(4),
example="2",
example_col=False,
short_label=short_label(4),
advanced=True,
)
dim5 = TextBox(
"dim5_factors",
label=long_label(5),
example="2",
example_col=False,
short_label=short_label(5),
advanced=True,
)
dim4d = dim5d = SkipBox(example_span="0 or 1", advanced=True)
simple_quantifier = SubsetBox(
"simple_quantifier",
)
simple_factors = TextBoxWithSelect(
"simple_factors",
label="Simple factors",
select_box=simple_quantifier,
knowl="av.decomposition",
colspan=(1, 3, 2),
width=3*190 - 30,
short_width=2*190 - 30,
example="1.2.b,1.2.b,2.2.a_b",
advanced=True,
)
count = CountBox()
self.refine_array = [
[q, p, g, p_rank, initial_coefficients],
[newton_polygon, abvar_point_count, curve_point_count, simple_factors],
[angle_rank, jac_cnt, hyp_cnt, twist_count, max_twist_degree],
[geom_deg, p_rank_deficit],
#[size],
[simple, geom_simple, primitive, polarizable, jacobian],
use_geom_refine,
[dim1, dim2, dim3, dim4, dim5],
[dim1d, dim2d, dim3d, number_field, galois_group],
]
self.browse_array = [
[q, primitive],
[p, simple],
[g, geom_simple],
[initial_coefficients, polarizable],
[p_rank, jacobian],
[p_rank_deficit],
[jac_cnt, hyp_cnt],
[geom_deg, angle_rank],
[twist_count, max_twist_degree],
[newton_polygon],
[abvar_point_count],
[curve_point_count],
[simple_factors],
use_geom_index,
[dim1, dim1d],
[dim2, dim2d],
[dim3, dim3d],
[dim4, dim4d],
[dim5, dim5d],
[number_field],
[galois_group],
[count],
]
def __init__(self):
degree = TextBox(
name="degree",
label="Degree",
knowl="nf.degree",
example=3)
signature = TextBox(
name="signature",
label="Signature",
knowl="nf.signature",
example="[1,1]")
discriminant = TextBox(
name="discriminant",
label="Discriminant",
knowl="nf.discriminant",
example="-1000..-1",
example_span="-3 or 1000-2000")
rd = TextBox(
name="rd",
label="Root discriminant",
knowl="nf.root_discriminant",
example="1..4.3",
example_span="a range such as 1..4.3 or 3-10")
cm_field = YesNoBox(
name="cm_field",
label="CM field",
knowl="nf.cm_field")
gal = TextBox(
name="galois_group",
label="Galois group",
knowl="nf.galois_search",
example="C5",
example_span="[8,3], C5 or 7T2")
is_galois = YesNoBox(
name="is_galois",
label="Is Galois",
knowl="nf.galois_group")
regulator = TextBox(
name="regulator",
label="Regulator",
knowl="nf.regulator",
example="1..3.5",
example_span="a range such as 1..3.5")
class_number = TextBox(
name="class_number",
label="Class number",
knowl="nf.class_number",
example="5")
class_group = TextBox(
name="class_group",
label="Class group structure",
knowl="nf.ideal_class_group",
example="[2,4]",
example_span="[ ], [3], or [2,4]")
num_ram = TextBox(
name="num_ram",
label="Ramified prime count",
knowl="nf.ramified_primes",
example=2)
ram_quantifier = SubsetNoExcludeBox(
name="ram_quantifier")
ram_primes = TextBoxWithSelect(
name="ram_primes",
label="Ramified",
knowl="nf.ramified_primes",
example="2,3",
select_box=ram_quantifier)
ur_primes = TextBox(
name="ur_primes",
label="Unramified primes",
knowl="nf.unramified_prime",
example="2,3")
subfield = TextBox(
name="subfield",
label="Intermediate field",
knowl="nf.intermediate_fields",
example_span="2.2.5.1 or x^2-5 or a "+
display_knowl("nf.nickname", "field nickname"),
example="x^2-5")
completion = TextBox(
name="completions",
label="$p$-adic completions",
knowl="nf.padic_completion.search",
example_span="2.4.10.7 or 2.4.10.7,3.2.1.2",
example="2.4.10.7")
count = CountBox()
self.browse_array = [
[degree, signature],
[discriminant, rd],
[gal, is_galois],
[class_number, class_group],
[num_ram, cm_field],
[ram_primes, ur_primes],
[regulator, subfield],
[count, completion]]
self.refine_array = [
[degree, signature, class_number, class_group, cm_field],
[num_ram, ram_primes, ur_primes, gal, is_galois],
[discriminant, rd, regulator, subfield, completion]]
def __init__(self):
geometric_invariants_type = SelectBox(
name="geometric_invariants_type",
width=108,
options=[("", "Igusa-Clebsh"), ("igusa_inv", "Igusa"),
("g2_inv", "G2")],
)
geometric_invariants = TextBoxWithSelect(
name="geometric_invariants",
knowl="g2c.geometric_invariants",
label=r"\(\overline{\Q}\)-invariants",
example="[8,3172,30056,-692224]",
select_box=geometric_invariants_type,
width=689,
colspan=(1, 4, 1),
example_col=False,
) # the last 1 is irrelevant
conductor = TextBox(
name="cond",
knowl="ag.conductor",
label="Conductor",
example="169",
example_span="169, 100-1000",
)
discriminant = TextBox(
name="abs_disc",
knowl="g2c.abs_discriminant",
label="Absolute discriminant",
short_label="Discriminant",
example="169",
example_span="169, 0-1000",
)
rational_points = TextBox(
name="num_rat_pts",
knowl="g2c.num_rat_pts",
label="Rational points*",
example="1",
example_span="0, 20-26",
)
rational_weirstrass_points = TextBox(
name="num_rat_wpts",
knowl="g2c.num_rat_wpts",
label="Rational Weierstrass points",
short_label="Weierstrass",
example="1",
example_span="1, 0-6",
)
torsion_order = TextBox(
name="torsion_order",
knowl="g2c.torsion_order",
label="Torsion order",
example="2",
)
torsion_structure = TextBox(
name="torsion",
knowl="g2c.torsion",
label="Torsion structure",
short_label="Torsion",
example="[2,2,2]",
)
two_selmer_rank = TextBox(
name="two_selmer_rank",
knowl="g2c.two_selmer_rank",
label="2-Selmer rank",
example="1",
)
analytic_sha = TextBox(
name="analytic_sha",
knowl="g2c.analytic_sha",
label="Analytic order of Ш*",
short_label="Analytic Ш*",
example="2",
)
analytic_rank = TextBox(
name="analytic_rank",
knowl="g2c.analytic_rank",
label="Analytic rank*",
example="1",
)
bad_quantifier = SelectBox(
name="bad_quantifier",
width=85,
options=[
("", "include"),
("exclude", "exclude"),
("exactly", "exactly"),
("subset", "subset"),
],
)
bad_primes = TextBoxWithSelect(
name="bad_primes",
knowl="g2c.good_reduction",
label="Bad primes",
short_label=r"Bad \(p\)",
example="5,13",
select_box=bad_quantifier,
)
is_gl2_type = SelectBox(
name="is_gl2_type",
knowl="g2c.gl2type",
label=r"$\GL_2$-type",
options=[("", ""), ("True", "True"), ("False", "False")],
)
st_group = SelectBox(
name="st_group",
knowl="g2c.st_group",
label="Sato-Tate group",
short_label=r"\(\mathrm{ST}\)",
options=([("", "")] + [(elt, st_group_dict[elt])
for elt in st_group_list]),
)
st_group_identity_component = SelectBox(
name="real_geom_end_alg",
knowl="g2c.st_group_identity_component",
label="Sate-Tate identity component",
short_label=r"\(\mathrm{ST}^0\)",
options=([("", "")] + [(elt, real_geom_end_alg_to_ST0_dict[elt])
for elt in real_geom_end_alg_list]),
)
Q_automorphism = SelectBox(
name="aut_grp_id",
knowl="g2c.aut_grp",
label=r"\(\Q\)-automorphism group",
short_label=r"\(\mathrm{Aut}(X)\)",
options=([("", "")] + [(elt, aut_grp_dict[elt])
for elt in aut_grp_list]),
)
geometric_automorphism = SelectBox(
name="geom_aut_grp_id",
knowl="g2c.aut_grp",
label=r"\(\overline{\Q}\)-automorphism group",
short_label=r"\(\mathrm{Aut}(X_{\overline{\Q}})\)",
options=([("", "")] + [(elt, geom_aut_grp_dict[elt])
for elt in geom_aut_grp_list]),
)
geometric_endomorphism = SelectBox(
name="geom_end_alg",
knowl="g2c.geom_end_alg",
label=r"\(\overline{\Q}\)-endomorphism algebra",
short_label=r"\(\overline{\Q}\)-end algebra",
options=([("", "")] + [(elt, geom_end_alg_dict[elt])
for elt in geom_end_alg_list]),
)
locally_solvable = SelectBox(
name="locally_solvable",
knowl="g2c.locally_solvable",
label="Locally solvable",
options=[("", ""), ("True", "True"), ("False", "False")],
)
has_square_sha = SelectBox(
name="has_square_sha",
knowl="g2c.analytic_sha",
label=r"Order of Ш is square*",
short_label=r"Square Ш*",
options=[("", ""), ("True", "True"), ("False", "False")],
)
geometrically_simple = SelectBox(
name="is_simple_geom",
knowl="ag.geom_simple",
label="Geometrically simple",
short_label=r"\(\overline{\Q}\)-simple",
options=[("", ""), ("True", "True"), ("False", "False")],
)
count = TextBox("count",
label="Results to display",
example=50,
example_col=False)
browse_array = [
[geometric_invariants],
[conductor, is_gl2_type],
[discriminant, st_group],
[rational_points, st_group_identity_component],
[rational_weirstrass_points, Q_automorphism],
[torsion_order, geometric_automorphism],
[torsion_structure, geometric_endomorphism],
[two_selmer_rank, locally_solvable],
[analytic_sha, has_square_sha],
[analytic_rank, geometrically_simple],
[bad_primes, count],
]
refine_array = [
[
conductor,
discriminant,
rational_points,
rational_weirstrass_points,
torsion_order,
],
[
bad_primes,
two_selmer_rank,
analytic_rank,
analytic_sha,
torsion_structure,
],
[
is_gl2_type,
st_group,
Q_automorphism,
has_square_sha,
geometrically_simple,
],
[
geometric_endomorphism,
st_group_identity_component,
geometric_automorphism,
locally_solvable,
],
]
SearchArray.__init__(self, browse_array, refine_array)
def __init__(self):
conductor_quantifier = SelectBox(name='conductor_type',
options=[
('', ''),
('prime', 'prime'),
('prime_power', 'p-power'),
('squarefree', 'sq-free'),
('divides', 'divides'),
],
min_width=85)
cond = TextBoxWithSelect(name="conductor",
label="Conductor",
knowl="ec.q.conductor",
example="389",
example_span="389 or 100-200",
select_box=conductor_quantifier)
disc = TextBox(name="discriminant",
label="Discriminant",
knowl="ec.discriminant",
example="389",
example_span="389 or 100-200")
rank = TextBox(name="rank", label="Rank", knowl="ec.rank", example="0")
sha = TextBox(name="sha",
label="Analytic order of Ш",
knowl="ec.analytic_sha_order",
example="4")
isodeg = TextBox(name="isogeny_degrees",
label="Cyclic isogeny degree",
knowl="ec.isogeny",
example="16")
class_size = TextBox(name="class_size",
label="Isogeny class size",
knowl="ec.isogeny_class",
example="4")
class_deg = TextBox(name="class_deg",
label="Isogeny class degree",
knowl="ec.isogeny_class_degree",
example="16")
num_int_pts = TextBox(name="num_int_pts",
label="Integral points",
knowl="ec.q.integral_points",
example="2",
example_span="2 or 4-15")
jinv = TextBox(name="jinv",
label="j-invariant",
knowl="ec.q.j_invariant",
example="1728",
example_span="1728 or -4096/11")
torsion_opts = ([("", ""),
("[]", "trivial")] + [("%s" % n, "order %s" % n)
for n in range(4, 16, 4)] +
[("[%s]" % n, "C%s" % n)
for n in range(2, 13) if n != 11] +
[("[2,%s]" % n, "C2×C%s" % n)
for n in range(2, 10, 2)])
torsion = SelectBox(name="torsion",
label="Torsion",
knowl="ec.torsion_subgroup",
example="C3",
options=torsion_opts)
optimal = SelectBox(name="optimal",
label="Curves per isogeny class",
knowl="ec.isogeny_class",
example="all, one",
options=[("", "all"), ("on", "one")])
bad_quant = SubsetBox(name="bad_quantifier")
bad_primes = TextBoxWithSelect(name="bad_primes",
label="Bad primes $p$",
short_label=r"Bad$\ p$",
knowl="ec.q.reduction_type",
example="5,13",
select_box=bad_quant)
sha_quant = SubsetBox(name="sha_quantifier")
sha_primes = TextBoxWithSelect(name="sha_primes",
label="$p$ dividing |Ш|",
short_label=r"$p\ $div$\ $|Ш|",
knowl="ec.analytic_sha_order",
example="3,5",
select_box=sha_quant)
regulator = TextBox(name="regulator",
label="Regulator",
knowl="ec.q.regulator",
example="8.4-9.1")
faltings_height = TextBox(name="faltings_height",
label="Faltings height",
knowl="ec.q.faltings_height",
example="-1-2")
reduction_opts = ([("", ""), ("semistable", "semistable"),
("not semistable", "not semistable"),
("potentially good", "potentially good"),
("not potentially good", "not potentially good")])
reduction = SelectBox(name="reduction",
label="Reduction",
example="semistable",
knowl="ec.reduction",
options=reduction_opts)
galois_image = TextBox(name="galois_image",
label=r"Galois image",
short_label=r"Galois image",
example="13S4 or 13.91.3.2",
knowl="ec.galois_image_search")
nonmax_quant = SubsetBox(name="nonmax_quantifier")
nonmax_primes = TextBoxWithSelect(
name="nonmax_primes",
label=r"Nonmaximal $\ell$",
short_label=r"Nonmax$\ \ell$",
knowl="ec.maximal_elladic_galois_rep",
example="2,3",
select_box=nonmax_quant)
cm_opts = (
[('', ''), ('noCM', 'no potential CM'),
('CM', 'potential CM')] + [('-4,-16', 'CM field Q(sqrt(-1))'),
('-3,-12,-27', 'CM field Q(sqrt(-3))'),
('-7,-28', 'CM field Q(sqrt(-7))')] +
[('-%d' % d, 'CM discriminant -%d' % d)
for d in [3, 4, 7, 8, 11, 12, 16, 19, 27, 38, 43, 67, 163]])
cm = SelectBox(name="cm",
label="Complex multiplication",
example="potential CM by Q(i)",
knowl="ec.complex_multiplication",
options=cm_opts)
count = CountBox()
self.browse_array = [[cond, bad_primes], [disc, jinv], [torsion, cm],
[rank, sha], [regulator, sha_primes],
[galois_image, nonmax_primes],
[class_size, class_deg], [num_int_pts, isodeg],
[optimal, reduction], [count, faltings_height]]
self.refine_array = [
[cond, jinv, rank, torsion, cm],
[bad_primes, disc, regulator, sha, galois_image],
[class_size, class_deg, isodeg, sha_primes, nonmax_primes],
[optimal, reduction, num_int_pts, faltings_height]
]
def __init__(self):
cond = TextBox(name="conductor",
label="Conductor",
knowl="ec.q.conductor",
example="389",
example_span="389 or 100-200")
rank = TextBox(name="rank", label="Rank", knowl="ec.rank", example="0")
torsion = TextBox(name="torsion",
label="Torsion order",
knowl="ec.torsion_order",
example="2")
sha = TextBox(name="sha",
label="Analytic order of Ш",
knowl="ec.q.analytic_sha_order",
example="4")
surj_primes = TextBox(name="surj_primes",
label="Maximal primes",
knowl="ec.maximal_galois_rep",
example="2,3")
isodeg = TextBox(name="isodeg",
label="Cyclic isogeny degree",
knowl="ec.isogeny",
example="16")
num_int_pts = TextBox(
name="num_int_pts",
label="Number of %s" %
display_knowl("ec.q.integral_points", "integral points"),
example="2",
example_span="2 or 4-15")
jinv = TextBox(name="jinv",
label="j-invariant",
knowl="ec.q.j_invariant",
example="1728",
example_span="1728 or -4096/11")
cm = IncludeOnlyBox(name="include_cm",
label="CM",
knowl="ec.complex_multiplication")
tor_opts = ([("", "any"),
("[]", "trivial")] + [("[%s]" % n, "C%s" % n)
for n in range(2, 13) if n != 11] +
[("[2,%s]" % n, "C2×C%s" % n)
for n in range(2, 10, 2)])
torsion_struct = SelectBox(name="torsion_structure",
label="Torsion structure",
knowl="ec.torsion_subgroup",
options=tor_opts)
optimal = SelectBox(name="optimal",
label="Curves per isogeny class",
knowl="ec.isogeny_class",
options=[("", "all"), ("on", "one")])
surj_quant = SelectBox(name="surj_quantifier",
options=[("", "include"),
("exactly", "exactly")],
width=75)
nonsurj_primes = TextBoxWithSelect(name="nonsurj_primes",
label="Non-maximal primes",
short_label="Non-max. $p$",
knowl="ec.maximal_galois_rep",
example="2,3",
select_box=surj_quant)
bad_quant = SelectBox(name="bad_quantifier",
options=[("", "include"), ("exclude", "exclude"),
("exactly", "exactly"),
("subset", "subset of")],
width=75)
bad_primes = TextBoxWithSelect(name="bad_primes",
label="Bad primes",
knowl="ec.q.reduction_type",
example="5,13",
select_box=bad_quant)
regulator = TextBox(name="regulator",
label="Regulator",
knowl="ec.q.regulator",
example="8.4-9.1")
count = TextBox(name="count", label="Results to display", example=50)
self.browse_array = [[cond, jinv], [rank,
cm], [torsion, torsion_struct],
[sha, optimal], [surj_primes, nonsurj_primes],
[isodeg, bad_primes], [num_int_pts, regulator],
[count]]
self.refine_array = [[cond, jinv, rank, torsion, torsion_struct],
[
sha, isodeg, surj_primes, nonsurj_primes,
bad_primes
], [num_int_pts, regulator, cm, optimal]]
def __init__(self):
cond = TextBox(name="conductor",
label="Conductor",
knowl="ec.q.conductor",
example="389",
example_span="389 or 100-200")
rank = TextBox(name="rank", label="Rank", knowl="ec.rank", example="0")
torsion = TextBox(name="torsion",
label="Torsion order",
knowl="ec.torsion_order",
example="2")
sha = TextBox(name="sha",
label="Analytic order of Ш",
knowl="ec.analytic_sha_order",
example="4")
surj_primes = TextBox(name="surj_primes",
label="Maximal primes",
knowl="ec.maximal_galois_rep",
example="2,3")
isodeg = TextBox(name="isodeg",
label="Cyclic isogeny degree",
knowl="ec.isogeny",
example="16")
num_int_pts = TextBox(
name="num_int_pts",
label="Number of %s" %
display_knowl("ec.q.integral_points", "integral points"),
example="2",
example_span="2 or 4-15")
jinv = TextBox(name="jinv",
label="j-invariant",
knowl="ec.q.j_invariant",
example="1728",
example_span="1728 or -4096/11")
cm = SelectBox(name="include_cm",
label="CM",
knowl="ec.complex_multiplication",
options=[('', ''), ('only', 'potential CM'),
('exclude', 'no potential CM')])
tor_opts = ([("", ""),
("[]", "trivial")] + [("[%s]" % n, "C%s" % n)
for n in range(2, 13) if n != 11] +
[("[2,%s]" % n, "C2×C%s" % n)
for n in range(2, 10, 2)])
torsion_struct = SelectBox(name="torsion_structure",
label="Torsion structure",
knowl="ec.torsion_subgroup",
options=tor_opts)
optimal = SelectBox(name="optimal",
label="Curves per isogeny class",
knowl="ec.isogeny_class",
options=[("", ""), ("on", "one")])
surj_quant = SubsetNoExcludeBox(name="surj_quantifier")
nonsurj_primes = TextBoxWithSelect(name="nonsurj_primes",
label="Non-max. $p$",
short_label="Non-max. $p$",
knowl="ec.maximal_galois_rep",
example="2,3",
select_box=surj_quant)
bad_quant = SubsetBox(name="bad_quantifier")
bad_primes = TextBoxWithSelect(name="bad_primes",
label="Bad $p$",
knowl="ec.q.reduction_type",
example="5,13",
select_box=bad_quant)
regulator = TextBox(name="regulator",
label="Regulator",
knowl="ec.q.regulator",
example="8.4-9.1")
semistable = YesNoBox(name="semistable",
label="Semistable",
example="Yes",
knowl="ec.semistable")
cm_opts = [('', ''), ('-3', '-3'), ('-4', '-4'), ('-7', '-7'),
('-8', '-8'), ('-11', '-11'), ('-12', '-12'),
('-16', '-16'), ('-19', '-19'), ('-27', '-27'),
('-28', '-28'), ('-43', '-43'), ('-67', '-67'),
('-163', '-163'), ('-3,-12,-27', '-3,-12,-27'),
('-4,-16', '-4,-16'), ('-7,-28', '-7,-28')]
cm_disc = SelectBox(name="cm_disc",
label="CM discriminant",
example="-3",
knowl="ec.complex_multiplication",
options=cm_opts)
count = CountBox()
self.browse_array = [[cond, jinv], [rank, regulator],
[torsion, torsion_struct], [cm_disc, cm],
[sha, optimal], [surj_primes, nonsurj_primes],
[isodeg, bad_primes], [num_int_pts, semistable],
[count]]
self.refine_array = [[cond, jinv, rank, torsion, torsion_struct],
[
sha, isodeg, surj_primes, nonsurj_primes,
bad_primes
],
[num_int_pts, regulator, cm, cm_disc, semistable],
[optimal]]
def __init__(self):
geometric_invariants = SneakyTextBox(
name="geometric_invariants",
knowl="g2c.geometric_invariants",
label=r"\(\overline{\Q}\)-invariants",
example="[8,3172,30056,-692224] or [-1/169,33/169,43/169]",
width=689,
short_width=190 * 3 - 10 * 3,
colspan=(1, 4, 3),
example_span="",
)
bad_quantifier = SubsetBox(
name="bad_quantifier",
min_width=115,
)
bad_primes = TextBoxWithSelect(
name="bad_primes",
knowl="g2c.good_reduction",
label="Bad primes",
short_label=r"Bad \(p\)",
example="5,13",
example_span="2 or 2,3,5",
select_box=bad_quantifier,
)
conductor = TextBox(
name="cond",
knowl="ag.conductor",
label="Conductor",
example="169",
example_span="169, 100-1000",
)
discriminant = TextBox(
name="abs_disc",
knowl="g2c.abs_discriminant",
label="Absolute discriminant",
short_label="Absolute discriminant",
example="169",
example_span="169, 0-1000",
)
rational_points = TextBox(
name="num_rat_pts",
knowl="g2c.num_rat_pts",
label="Rational points*",
example="1",
example_span="0, 20-26",
)
rational_weirstrass_points = TextBox(
name="num_rat_wpts",
knowl="g2c.num_rat_wpts",
label="Rational Weierstrass points",
short_label="Weierstrass points",
example="1",
example_span="1, 0-6",
)
torsion_order = TextBox(
name="torsion_order",
knowl="g2c.torsion_order",
label="Torsion order",
example="2",
)
torsion_structure = TextBox(
name="torsion",
knowl="g2c.torsion",
label="Torsion structure",
short_label="Torsion",
example="[2,2,2]",
)
two_selmer_rank = TextBox(
name="two_selmer_rank",
knowl="g2c.two_selmer_rank",
label="2-Selmer rank",
example="1",
)
analytic_sha = TextBox(
name="analytic_sha",
knowl="g2c.analytic_sha",
label="Analytic order of Ш*",
short_label="Analytic Ш*",
example="2",
)
analytic_rank = TextBox(
name="analytic_rank",
knowl="g2c.analytic_rank",
label="Analytic rank*",
example="1",
)
is_gl2_type = YesNoBox(
name="is_gl2_type",
knowl="g2c.gl2type",
label=r"$\GL_2$-type",
)
st_group = SelectBox(
name="st_group",
knowl="g2c.st_group",
label="Sato-Tate group",
short_label=r"\(\mathrm{ST}(X)\)",
options=([("", "")] + [(elt, st_group_dict[elt])
for elt in st_group_list]),
)
st_group_identity_component = SelectBox(
name="real_geom_end_alg",
knowl="g2c.st_group_identity_component",
label="Sate-Tate identity component",
short_label=r"\(\mathrm{ST}^0(X)\)",
options=([("", "")] + [(elt, real_geom_end_alg_to_ST0_dict[elt])
for elt in real_geom_end_alg_list]),
)
Q_automorphism = SelectBox(
name="aut_grp_label",
knowl="g2c.aut_grp",
label=r"\(\Q\)-automorphism group",
short_label=r"\(\mathrm{Aut}(X)\)",
options=([("", "")] + [(elt, aut_grp_dict[elt])
for elt in aut_grp_list]),
)
geometric_automorphism = SelectBox(
name="geom_aut_grp_label",
knowl="g2c.aut_grp",
label=r"\(\overline{\Q}\)-automorphism group",
short_label=r"\(\mathrm{Aut}(X_{\overline{\Q}})\)",
options=([("", "")] + [(elt, geom_aut_grp_dict[elt])
for elt in geom_aut_grp_list]),
)
Q_endomorphism = SelectBox(
name="end_alg",
knowl="g2c.end_alg",
label=r"\(\Q\)-endomorphism algebra",
short_label=r"\(\Q\)-end algebra",
options=([("", "")] + [(elt, end_alg_dict[elt])
for elt in end_alg_list]),
)
geometric_endomorphism = SelectBox(
name="geom_end_alg",
knowl="g2c.geom_end_alg",
label=r"\(\overline{\Q}\)-endomorphism algebra",
short_label=r"\(\overline{\Q}\)-end algebra",
options=([("", "")] + [(elt, geom_end_alg_dict[elt])
for elt in geom_end_alg_list]),
)
locally_solvable = YesNoBox(
name="locally_solvable",
knowl="g2c.locally_solvable",
label="Locally solvable",
)
has_square_sha = YesNoBox(
name="has_square_sha",
knowl="g2c.analytic_sha",
label=r"Order of Ш is square*",
short_label=r"Square Ш*",
)
geometrically_simple = YesNoBox(
name="is_simple_geom",
knowl="ag.geom_simple",
label="Geometrically simple",
short_label=r"\(\overline{\Q}\)-simple",
)
count = CountBox()
self.browse_array = [
[geometric_invariants],
[bad_primes, geometrically_simple],
[conductor, is_gl2_type],
[discriminant, st_group],
[rational_points, st_group_identity_component],
[rational_weirstrass_points, Q_automorphism],
[torsion_order, geometric_automorphism],
[torsion_structure, Q_endomorphism],
[two_selmer_rank, geometric_endomorphism],
[analytic_sha, has_square_sha],
[analytic_rank, locally_solvable],
[count],
]
self.refine_array = [
[
conductor,
discriminant,
rational_points,
rational_weirstrass_points,
torsion_order,
],
[
bad_primes,
two_selmer_rank,
analytic_rank,
analytic_sha,
torsion_structure,
],
[
Q_endomorphism,
st_group,
Q_automorphism,
has_square_sha,
geometrically_simple,
],
[
geometric_endomorphism,
st_group_identity_component,
geometric_automorphism,
locally_solvable,
is_gl2_type,
],
[geometric_invariants],
]
