class LFStats(StatsDisplay):
table = db.lf_fields
baseurl_func = ".index"
short_display = {
'galois_label': 'Galois group',
'n': 'degree',
'e': 'ramification index',
'c': 'discriminant exponent'
}
sort_keys = {'galois_label': galdata}
formatters = {'galois_label': galformatter}
query_formatters = {
'galois_label': (lambda gal: r'gal=%s' % (galunformatter(gal)))
}
stat_list = [
ramdisp(2),
ramdisp(3),
discdisp(2),
discdisp(3),
galdisp(2, 4),
galdisp(2, 6),
galdisp(2, 8),
galdisp(2, 10),
galdisp(2, 12),
galdisp(2, 14),
galdisp(3, 6),
galdisp(3, 9),
galdisp(3, 12),
galdisp(3, 15),
galdisp(5, 10),
galdisp(5, 15),
galdisp(7, 14)
]
def __init__(self):
self.numfields = db.lf_fields.count()
@property
def short_summary(self):
return self.summary + ' Here are some <a href="%s">further statistics</a>.' % (
url_for(".statistics"))
@property
def summary(self):
return r'The database currently contains %s %s, including all with $p < 200$ and %s $n < 16$.' % (
comma(self.numfields),
display_knowl("lf.padic_field", r"$p$-adic fields"),
display_knowl("lf.degree", "degree"))
class ArtinStats(StatsDisplay):
table = db.artin_reps
baseurl_func = ".index"
stat_list = [
{"cols": ["Dim", "Conductor"],
"constraint": {"Hide": 0},
"totaler": totaler(),
"proportioner": proportioners.per_row_total},
{"cols": ["Dim", "NumBadPrimes"],
"constraint": {"Hide": 0},
"totaler": totaler(),
"proportioner": proportioners.per_row_total},
{"cols": ["Indicator", "Dim"],
"constraint": {"Hide": 0}},
{"cols": ["Is_Even", "Dim"],
"constraint": {"Hide": 0}},
{"cols": ["GaloisLabel"],
"constraint": {"Hide": 0}},
{"cols": ["Proj_nTj"],
"constraint": {"Hide": 0}},
{"cols": ["Container"],
"constraint": {"Hide": 0}}
]
knowls = {"Dim": "artin.dimension",
"Conductor": "artin.conductor",
"GaloisLabel": "artin.gg_quotient",
"Is_Even": "artin.parity",
"Proj_nTj": "artin.projective_image",
"NumBadPrimes": "artin.ramified_primes",
"Container": "artin.permutation_container",
"Indicator": "artin.frobenius_schur_indicator"}
top_titles = {"Indicator": "Frobenius-Schur indicators",
"Container": "smallest permutation containers",
"Is_Even": "parities"}
short_display = {"Dim": "dimension",
"Conductor": "conductor",
"GaloisLabel": "Galois group",
"Is_Even": "parity",
"Proj_nTj": "projective image",
"Container": "container",
"NumBadPrimes": "number of ramified primes",
"Indicator": "indicator"}
sort_keys = {"GaloisLabel": galdata,
"Proj_nTj": galdata,
"Container": galdata}
formatters = {"Conductor": lambda N: scinot(range_formatter(N)),
"Is_Even": lambda x: "even" if x in ["even", True] else "odd",
"GaloisLabel": galformatter,
"Container": contformatter,
"Proj_nTj": projformatter}
query_formatters = {
"Dim": (lambda d: "dimension=%s" % range_formatter(d)),
"Conductor": (lambda N: "conductor=%s" % (unsci(range_formatter(N)))),
"NumBadPrimes": (lambda N: "num_ram=%s" % range_formatter(N)),
"GaloisLabel": (lambda gal: r"group=%s" % (galunformatter(gal))),
"Proj_nTj": (lambda proj: r"projective_image=%s" % (galunformatter(proj))),
"Container": (lambda cont: r"container=%s" % (galunformatter(cont))),
"Is_Even": (lambda x: r"parity=%s" % ("even" if x in ["even", True] else "odd")),
"Indicator": (lambda ind: r"frobenius_schur_indicator=%s" % ind),
}
buckets = {
"Conductor": [trange(a, b) for (a,b) in intervals(0,8,2) + intervals(8,24,4) + intervals(24,56,8) + intervals(56,88,16)] + [trange(88,None)],
"Dim": [str(x) for x in range(1,13)] + ["14-21", "24-30", "35", "40-70"]
}
def __init__(self):
hide = {"Hide": 0}
self.nreps = db.artin_reps.count(hide)
self.nfields = db.artin_reps.count_distinct("NFGal", hide)
self.ngroups = db.artin_reps.count_distinct("GaloisLabel", hide)
self.maxdim = db.artin_reps.max("Dim")
maxcond = ZZ(db.artin_reps.max("Conductor"))
self.maxcond = maxcond.factor()._latex_()
self.amaxcond = maxcond.n(digits=2)._latex_()
@property
def summary(self):
return r"The database currently contains {nreps} Galois conjugacy classes of {repknowl}, for a total of {nfields} {nfknowl} with {ngroups} {gpknowl}. The largest {dimknowl} is ${mdim}$ and the largest {condknowl} is ${mcond} \approx {amcond}$.".format(
nreps=comma(self.nreps),
repknowl=display_knowl("artin", "Artin representations"),
nfields=comma(self.nfields),
nfknowl=display_knowl("artin.number_field", "number fields"),
ngroups=self.ngroups,
gpknowl=display_knowl("artin.gg_quotient", "Galois groups"),
dimknowl=display_knowl("artin.dimension", "dimension"),
mdim=self.maxdim,
condknowl=display_knowl("artin.conductor", "conductor"),
mcond=self.maxcond,
amcond=self.amaxcond)
@property
def short_summary(self):
return r'The database currently contains {nreps} Galois conjugacy classes of {repknowl}, for a total of {nfields} {nfknowl}. Here are some <a href="{url}">further statistics</a>.'.format(
nreps=comma(self.nreps),
repknowl=display_knowl("artin", "Artin representations"),
nfields=comma(self.nfields),
nfknowl=display_knowl("artin.number_field", "number fields"),
url=url_for(".statistics"))
