def __init__(self):
field = TextBox(
name='field_label',
label='Base field',
knowl='nf',
example='2.0.4.1',
example_span=
r'either a field label, e.g. 2.0.4.1 for \(\mathbb{Q}(\sqrt{-1})\), or a nickname, e.g. Qsqrt-1',
example_span_colspan=4)
level = TextBox(name='level_norm',
label='Level norm',
knowl='mf.bianchi.level',
example='1',
example_span='e.g. 1 or 1-100')
# See Issue #4170
# dimension = TextBox(
# name='dimension',
# label='Dimension',
# knowl='mf.bianchi.spaces',
# example='1',
# example_span='e.g. 1 or 2')
sign = SelectBox(name='sfe',
label='Sign',
knowl='mf.bianchi.sign',
options=[("", ""), ("+1", "+1"), ("-1", "-1")],
example_col=True)
base_change = ExcludeOnlyBox(name='include_base_change',
label='Base change',
knowl='mf.bianchi.base_change',
example="exclude")
CM = ExcludeOnlyBox(name='include_cm',
label='CM',
knowl='mf.bianchi.cm')
field_bad_quant = SubsetBox(name="field_bad_quantifier")
field_bad_primes = TextBoxWithSelect(name="field_bad_primes",
label="Field bad primes",
knowl="nf.ramified_primes",
example="5,13",
select_box=field_bad_quant)
level_bad_quant = SubsetBox(name="level_bad_quantifier")
level_bad_primes = TextBoxWithSelect(name="level_bad_primes",
label="Level bad primes",
knowl="mf.bianchi.level",
example="5,13",
select_box=level_bad_quant)
count = CountBox()
self.browse_array = [[field], [level, sign], [base_change, CM],
[field_bad_primes, level_bad_primes], [count]]
self.refine_array = [[field, level, CM],
[
sign, base_change, field_bad_primes,
level_bad_primes
]]
def __init__(self):
field = TextBox(
name='field_label',
label='Base field',
knowl='nf',
example='2.0.4.1',
example_span=
r'either a field label, e.g. 2.0.4.1 for \(\mathbb{Q}(\sqrt{-1})\), or a nickname, e.g. Qsqrt-1',
example_span_colspan=4)
degree = TextBox(name='deg',
label='Base field degree',
knowl='nf.degree',
example='2',
example_span='2, 2..3')
discriminant = TextBox(name='disc',
label='Base field discriminant',
knowl='nf.discriminant',
example='5',
example_span='5 or 1-100')
weight = TextBox(name='weight',
label='Weight',
knowl='mf.hilbert.weight_vector',
example='[2,2]',
example_span='2 or [2,2]')
level = TextBox(name='level_norm',
label='Level norm',
knowl='mf.hilbert.level_norm',
example='1',
example_span='1 or 1-100')
dimension = TextBox(name='dimension',
label='Dimension',
knowl='mf.hilbert.dimension',
example='1',
example_span='1 or 2')
base_change = ExcludeOnlyBox(
name='bc',
label='Base change',
knowl='mf.base_change',
)
CM = ExcludeOnlyBox(
name='cm',
label='CM',
knowl='mf.cm',
)
field_bad_quant = SubsetBox(name="field_bad_quantifier")
field_bad_primes = TextBoxWithSelect(name="field_bad_primes",
label="Field bad primes",
knowl="nf.ramified_primes",
example="5,13",
select_box=field_bad_quant)
level_bad_quant = SubsetBox(name="level_bad_quantifier")
level_bad_primes = TextBoxWithSelect(name="level_bad_primes",
label="Level bad primes",
knowl="mf.hilbert.level_norm",
example="5,13",
select_box=level_bad_quant)
count = CountBox()
self.browse_array = [[field], [degree, discriminant], [level, weight],
[dimension, base_change], [count, CM],
[field_bad_primes, level_bad_primes]]
self.refine_array = [
[field, degree, discriminant, CM, field_bad_primes],
[weight, level, dimension, base_change, level_bad_primes],
]
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",
)
geom_squarefree = SelectBox(name="geom_squarefree",
knowl="av.geometrically_squarefree",
label="(Geometrically) Squarefree",
short_label="(Geom.) Sq.free",
options=[('', ''), ('Yes', 'yes'),
('YesAndGeom', 'yes; and geom.'),
('YesNotGeom', 'yes; not geom.'),
('No', 'no'),
('NotGeom', 'not geom.')],
advanced=True)
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],
[simple, geom_simple, primitive, polarizable, jacobian],
[
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, geom_squarefree],
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, geom_squarefree],
[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):
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="isogeny_degrees",
label="Cyclic isogeny degree",
knowl="ec.isogeny",
example="16")
class_size = TextBox(
name="class_size",
label="Isogeny class size",
knowl="ec.isogeny",
example="4")
class_deg = TextBox(
name="class_deg",
label="Isogeny class 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",
example="all, one",
options=[("", "all"),
("on", "one")])
surj_quant = SubsetNoExcludeBox(
name="surj_quantifier")
nonsurj_primes = TextBoxWithSelect(
name="nonsurj_primes",
label="Nonmax $p$",
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)
sha_quant = SubsetBox(
name="sha_quantifier")
sha_primes = TextBoxWithSelect(
name="sha_primes",
label="$p$ dividing |Ш|",
short_label="$p$ 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")
semistable = YesNoBox(
name="semistable",
label="Semistable",
example="Yes",
knowl="ec.semistable")
potentially_good = YesNoBox(
name="potential_good_reduction",
label="Potential good reduction",
example="Yes",
knowl="ec.potential_good_reduction")
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, sha_primes],
[surj_primes, nonsurj_primes],
[isodeg, bad_primes],
[class_size, num_int_pts],
[class_deg, semistable],
[optimal, potentially_good],
[count]
]
self.refine_array = [
[cond, jinv, rank, torsion, torsion_struct],
[sha, sha_primes, surj_primes, nonsurj_primes, bad_primes],
[num_int_pts, regulator, cm, cm_disc, semistable],
[optimal, isodeg, class_size, class_deg, potentially_good]
]
def __init__(self):
geometric_invariants_type = SelectBox(
name="geometric_invariants_type",
min_width=115,
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_span="",
) # the last 1 is irrelevant
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="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",
)
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_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]),
)
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,
],
]
def __init__(self):
field = TextBox(name="field",
label="Base field",
knowl="ag.base_field",
example="2.2.5.1",
example_span="2.2.5.1 or Qsqrt5")
include_base_change = ExcludeOnlyBox(name="include_base_change",
label="Base change curves",
knowl="ec.base_change")
include_Q_curves = ExcludeOnlyBox(name="include_Q_curves",
label=r"\(\Q\)-curves",
knowl="ec.q_curve")
conductor_norm = TextBox(name="conductor_norm",
label="Conductor norm",
knowl="ec.conductor",
example="31",
example_span="31 or 1-100")
one = SelectBox(name="one",
label="Curves per isogeny class",
knowl="ec.isogeny_class",
example="all, one",
options=[("", "all"), ("yes", "one")])
include_cm = SelectBox(name="include_cm",
label="CM",
knowl="ec.complex_multiplication",
options=[('', ''), ('PCM', 'potential CM'),
('PCMnoCM', 'potential CM but no CM'),
('CM', 'CM'),
('noPCM', 'no potential CM')])
cm_disc = TextBox(name="cm_disc",
label="CM discriminant",
example="-4",
example_span="-4 or -3,-8",
knowl="ec.complex_multiplication")
jinv = TextBox(name="jinv",
label="j-invariant",
knowl="ec.j_invariant",
width=685,
short_width=160,
colspan=(1, 4, 1),
example_span_colspan=2,
example="105474/49 + a*34213/49",
example_span="")
rank = TextBox(name="rank",
label="Rank*",
knowl="ec.rank",
example="2")
torsion = TextBox(name="torsion",
label="Torsion order",
knowl="ec.torsion_order",
example="2")
bf_deg = SelectBox(name="bf_deg",
label="Base field degree",
knowl="nf.degree",
options=[("", ""), ("2", "2"), ("3", "3"),
("4", "4"), ("5", "5"), ("6", "6")])
tor_opts = (
[("", ""), ("[]", "trivial")] +
[disp_tor(tuple(t)) for t in ECNF_stats().torsion_counts if t])
torsion_structure = SelectBox(name="torsion_structure",
label="Torsion structure",
knowl="ec.torsion_subgroup",
options=tor_opts)
sha = TextBox(name="sha",
label="Analytic order* of Ш",
knowl="ec.analytic_sha_order",
example="4")
regulator = TextBox(name="regulator",
label="Regulator*",
knowl="ec.regulator",
example="8.4-9.1")
bad_quant = SubsetBox(name="bad_quantifier")
bad_primes = TextBoxWithSelect(name="conductor_norm_factors",
label="Bad primes",
knowl="ec.reduction_type",
example="5,13",
select_box=bad_quant)
isodeg = TextBox(name="isodeg",
label="Cyclic isogeny degree",
knowl="ec.isogeny",
example="16")
semistable = YesNoBox(name="semistable",
label="Semistable",
example="Yes",
knowl="ec.semistable")
potential_good_reduction = YesNoBox(
name="potential_good_reduction",
label="Potential good reduction",
example="Yes",
knowl="ec.potential_good_reduction")
class_size = TextBox(name="class_size",
label="Isogeny class size",
knowl="ec.isogeny",
example="4")
class_deg = TextBox(name="class_deg",
label="Isogeny class degree",
knowl="ec.isogeny",
example="16")
count = CountBox()
self.browse_array = [[field, bf_deg],
[conductor_norm, include_base_change],
[rank, include_Q_curves],
[torsion, torsion_structure],
[cm_disc, include_cm], [sha, regulator],
[isodeg, one], [class_size, class_deg],
[semistable, potential_good_reduction], [jinv],
[count, bad_primes]]
self.refine_array = [
[field, conductor_norm, rank, torsion, cm_disc],
[
bf_deg, include_base_change, include_Q_curves,
torsion_structure, include_cm
],
[sha, isodeg, class_size, semistable, jinv],
[regulator, one, class_deg, potential_good_reduction, bad_primes],
]
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 = TextBoxNoEg(
name="galois_group",
label="Galois group",
knowl="nf.galois_group",
example="C5",
example_span_colspan=4,
example_span=
"list of %s, e.g. [8,3] or [16,7], group names from the %s, e.g. C5 or S12, and %s, e.g., 7T2 or 11T5"
% (display_knowl("group.small_group_label", "GAP id's"),
display_knowl("nf.galois_group.name", "list of group labels"),
display_knowl("gg.label", "transitive group labels")))
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="Number of ramified primes",
knowl="nf.ramified_primes",
example=2)
ram_quantifier = SubsetBox(name="ram_quantifier", width=50)
ram_primes = TextBoxWithSelect(name="ram_primes",
label="Ram. primes",
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")
count = TextBox(name="count", label="Results to display", example=50)
self.browse_array = [[degree, signature], [discriminant, rd], [gal],
[class_number, class_group], [num_ram, cm_field],
[ram_primes, ur_primes], [regulator], [count]]
self.refine_array = [[
degree, signature, gal, class_number, class_group
], [regulator, num_ram, ram_primes, ur_primes, cm_field],
[discriminant, rd]]
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]
]
