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17709 bytes, as of the version from 2026-10-28 12:16 (current). Recorded here, not run.
"""Checks a table-building run should not have to write again.
Each of these caught a real error, or would have. They are here rather than in
the prompt because prose asking an agent to "make sure the arithmetic is exact"
gets a confident answer; a function that inspects the coefficients does not.
from check import exactness, measure, agrees_with, names_its_rings
Nothing here talks to the database. `stored` reads a table back so that the
values can be checked as published rather than as computed, which is the one
check `verify()` cannot do -- it compares a table with the generator that made
it and so cannot catch a generator wrong in the same way twice.
"""
import os
import re
def exactness(values):
"""Refuse anything that is not exactly what it claims to be.
The trap this exists for: in `sage -python` there is no preparser, so
`factorial(30)` is a Python int and `factorial(n) / k` is float division --
exact to 2^53 and quietly wrong after it. A Bessel polynomial built that
way was right to n = 15 and wrong from n = 16, in its last two digits.
`c in ZZ` does not catch it, because that is true of a float that happens
to be integral. This looks at the type.
Returns a list of complaints; empty means every coefficient is a Sage
integer or rational.
"""
complaints = []
for key, value in _pairs(values):
for coefficient in _coefficients(value):
name = type(coefficient).__name__
if _is_integer_interval_text(coefficient):
#The one string an exact table returns on purpose: `[43, 48]`
#for a Ramsey number, `[40, 44]` for a kissing number -- an
#integer known to lie between two integers. It is an
#enclosure in the database's own spelling, and the client
#writes a string verbatim, which is the only way to store it:
#a RealInterval with those endpoints is written in decimal
#form. The first version of this check reported it as
#"unexpected type str", and the run that met that wrapped
#the string in a subclass carrying its endpoints so that the
#check would pass -- which the client's YAML writer then
#serialised as a Python object, storing eighteen entries as
#mappings. A check that refuses the right answer teaches
#people to disguise it.
continue
if _is_ball_text(coefficient):
#The other string a table returns on purpose: `0.7478008 +/-
#2e-7`, a published estimate with the paper's uncertainty as
#its radius, in the database's own spelling -- what the table
#of the fine-structure constant stores and what a `measured`
#table of percolation thresholds returns for each transcribed
#row. The client writes it verbatim and reads the digits it
#claims from the radius. Plain `str` and a positive radius,
#for the same reasons as the integer interval above.
continue
if _is_decimal_text(coefficient):
#And the first spelling of the four in the skill: a plain
#decimal, `1.5030480824753322643220663294755536893857810`,
#which denotes the interval one unit of its last place wide.
#It is what a table returns for a value transcribed from a
#paper that states its digits and no separate uncertainty --
#Baxter's 43 decimals of the hard-square constant -- and the
#client stores it verbatim and counts the digits it carries.
#Plain `str`, with a point, for the same reasons as above; a
#string without a point is an exact integer and is not this.
continue
if isinstance(coefficient, float) or 'float' in name.lower():
complaints.append(
'%s: coefficient %r is a %s, not exact -- something '
'divided with / where both sides were Python ints'
% (key, coefficient, name))
break
if _is_enclosure(coefficient):
#A ball or an interval is not a failure of exactness, it is
#the strongest thing an inexact value can carry: the error
#bound travels with the number. What must not pass is one
#that encloses everything -- a nan ball compares true against
#any interval, so letting one through turns every later
#agreement check into a formality that cannot fail. A
#polygamma generator produced exactly that, from arb taking a
#negative base to a negative power, and a control "passed"
#while establishing nothing.
if not _is_finite(coefficient):
complaints.append(
'%s: value %r is not finite -- an enclosure this wide '
'contains every answer, so nothing compared against '
'it can fail' % (key, coefficient))
break
continue
if _is_p_adic(coefficient):
#A p-adic value is exact modulo its stated O(p^n), and the
#precision is part of the Sage object that the client writes.
#Treat it like a finite enclosure rather than like a stray
#coefficient type.
continue
if name not in ('Integer', 'Rational', 'int'):
complaints.append('%s: coefficient of unexpected type %s'
% (key, name))
break
return complaints
def exact_in_disguise(values):
"""Decimals whose digits suggest the value may be known exactly.
`3.000000000000000000000000000000` is *evidence* and not proof: the value
could be 3, or it could be 3 + 10^-40 rounded, and no number of zeros
decides between them. What decides it is the mathematics -- the logistic
map's first bifurcation is at r = 3 because the fixed point loses
stability when |f'| = 1, which is an argument and not a measurement.
So this reports and does not conclude. Both readings are worth a person's
attention before the table exists, and they need opposite fixes:
* the value is exactly a rational, and a decimal understates what is
known -- return it exactly;
* the value is not exact, and the digits are a rounding presented as
sixty significant places -- return fewer digits, or a ball.
A run of trailing zeros is what makes either likely: a genuine irrational
computed to sixty places does not end in ten of them by chance.
Returns a list of remarks; empty means nothing looked suspicious.
"""
import re
from fractions import Fraction
suspect = re.compile(r'^-?\d+\.\d*?0{10,}$')
remarks = []
for key, value in _pairs(values):
for text in _flatten(value):
text = str(text).strip()
if not suspect.match(text):
continue
try:
nearby = Fraction(text).limit_denominator(10 ** 6)
except (ValueError, ZeroDivisionError):
nearby = None
remarks.append(
'%s: %s ends in a run of zeros%s. Either it is exact, and a '
'decimal understates it -- return the exact value; or it is '
'not, and sixty places claim more than is known -- return '
'fewer digits or a ball. The digits cannot tell you which: '
'the definition can.'
% (key, text[:24] + '...',
', suggesting %s' % (nearby,) if nearby is not None else ''))
return remarks
def prose(values):
"""Refuse an entry comment that will read wrongly on the page.
Two things the value checks cannot see. A comment written in a raw
Python string with an escaped apostrophe, ``r"Onsager\\'s"``, keeps the
backslash: the client stores it as written, every check passed, and the
page of the Ising couplings showed "Onsager\\'s" until a person read it.
And "below" or "above" in a comment points at a position the page does
not keep, which `audit_table` refuses in the document but not in the
entries.
Returns a list of complaints; empty means nothing was found.
"""
complaints = []
for key, value in _pairs(values):
if not isinstance(value, dict):
continue
comment = value.get('comment')
if not isinstance(comment, str):
continue
if "\\'" in comment or '\\"' in comment:
complaints.append('%s: the comment carries a backslash before a quote -- an escaped '
'apostrophe in a raw string is stored as written' % key)
for word in ('below', 'above'):
if re.search(r'\b%s\b' % word, comment):
complaints.append('%s: the comment says "%s", which points at a position the page '
'does not keep' % (key, word))
return complaints
def _is_integer_interval_text(value):
"""Whether this is the string `[a, b]` with integers a < b: the interval
an exact table stores for an integer that is only known to lie between
two others. Must be a plain string -- a subclass is what the client
serialises as an object -- and must have nonzero width, since `[2, 2]`
is an integer pretending to be uncertain."""
if type(value) is not str:
return False
found = re.fullmatch(r'\[(-?\d+), (-?\d+)\]', value)
return bool(found) and int(found.group(1)) < int(found.group(2))
def _is_ball_text(value):
"""Whether this is the string `centre +/- radius` with a decimal centre
and a positive radius: the form a measured value is stored in. Must be
a plain string, and the radius must be positive, since `x +/- 0` is a
point pretending to be an enclosure."""
if type(value) is not str:
return False
found = re.fullmatch(
r'(-?\d+(?:\.\d+)?(?:[eE]-?\d+)?) \+/- (\d+(?:\.\d+)?(?:[eE]-?\d+)?)', value)
if not found:
return False
from decimal import Decimal, InvalidOperation
try:
return Decimal(found.group(2)) > 0
except InvalidOperation:
return False
def _is_decimal_text(value):
"""Whether this is a plain decimal string, `1.5030480824753322`, with
digits on both sides of the point and at most a sign and an exponent:
the interval a written real denotes, its last digit uncertain by one.
Must be a plain string, as above, and must carry a point, since a string
of digits alone is an exact integer."""
if type(value) is not str:
return False
return bool(re.fullmatch(r'-?\d+\.\d+(?:[eE]-?\d+)?', value))
def _is_enclosure(value):
"""Whether this carries its own error bound: a ball or an interval."""
name = type(value).__name__
return ('Ball' in name or 'IntervalFieldElement' in name
or 'Interval' in name)
def _is_finite(value):
"""Whether an enclosure actually pins something down."""
try:
if hasattr(value, 'is_finite'):
return bool(value.is_finite())
if hasattr(value, 'is_NaN'):
return not bool(value.is_NaN())
except Exception: # noqa: BLE001
return False
return True
def _is_p_adic(value):
"""Whether this is a Sage p-adic element carrying finite precision."""
parent = getattr(value, 'parent', None)
if not callable(parent):
return False
try:
if 'adic' not in str(parent()).lower():
return False
precision = value.precision_absolute()
except Exception: # noqa: BLE001
return False
return precision is not None
def measure(values):
"""How long the entries get, so a range is chosen from data.
Length is what decides these tables, not the stated size limits. The
Fibonacci polynomials stop where the longest is 1107 characters; `h_6` in
six variables would be 6969, which nobody reads.
`longest` is the written value alone. `block_kb` is what the server
measures against its limit: the YAML of the flat records, annotations
included -- a comment on every entry is part of the block, and a table of
607 hundred-digit values found that out by coming in at 166 KB rather
than the 75 KB its numbers alone would make.
"""
lengths = {key: len(str(_number_of(value))) for key, value in _pairs(values)}
if not lengths:
return {'entries': 0, 'longest': 0, 'block_kb': 0.0, 'longest_at': None}
longest_at = max(lengths, key=lambda k: lengths[k])
return {
'entries': len(lengths),
'longest': lengths[longest_at],
'longest_at': longest_at,
'block_kb': _block_bytes(values) / 1024.0,
}
def _number_of(value):
"""The value inside an entry, whether it came bare or as a mapping.
A generator may return ``{'number': x, 'comment': '...'}``, which the
skill says it may; the first version of these checks reported that as
"coefficient of unexpected type dict" and measured the comment's length
as the value's.
"""
if isinstance(value, dict) and 'number' in value:
return value['number']
return value
def _block_bytes(values):
"""The size of the entries block as the server serialises it.
The same `yaml.dump` of the same flat records as `numberdb_app/limits.py`;
without PyYAML, the old estimate of 24 bytes of overhead per entry.
"""
records = []
for key, value in _pairs(values):
record = {'params': {'key': str(key)}}
if isinstance(value, dict):
record.update({k: (str(v) if k == 'number' else v)
for k, v in value.items()})
else:
record['number'] = str(value)
records.append(record)
try:
import yaml
except ImportError:
return sum(len(str(_number_of(v))) + 24 for _, v in _pairs(values))
return len(yaml.dump(records, default_flow_style=False,
allow_unicode=True).encode('utf8'))
def agrees_with(values, other):
"""Compare against a computation that shares no code with the generator.
A generator checked against its own definition proves nothing. `other` is
called with the same key and must return the same value.
"""
disagreements = []
for key, value in _pairs(values):
try:
expected = other(key)
except Exception as trouble: # noqa: BLE001
disagreements.append('%s: the independent computation raised %s: %s'
% (key, type(trouble).__name__, trouble))
continue
if expected != value:
disagreements.append('%s: %s here, %s independently'
% (key, str(value)[:60], str(expected)[:60]))
return disagreements
def names_its_rings(path):
"""A generator should name the rings it uses rather than import sage.all.
`sage.all` does not exist in a modular passagemath, and the same source
then runs in both. Returns a list of complaints.
"""
with open(path, encoding='utf8') as handle:
source = handle.read()
complaints = []
for line in source.splitlines():
stripped = line.strip()
if stripped.startswith(('from sage.all import', 'import sage.all')):
complaints.append('imports sage.all: %s' % stripped)
if 'import numberdb.sage' not in source:
complaints.append('does not import numberdb.sage, which is what '
'initialises Sage before a ring can be imported')
return complaints
def stored(tid):
"""The table as published: {params tuple or string: written value}.
Read back so the identities can be checked on what a reader will see.
Needs the Django app; call it from `manage.py shell`.
"""
from numberdb_app.editing import tree_of
from numberdb_app.models import Table
tree = tree_of(Table.objects.get(tid=tid).head_revision)
out = {}
for entry in tree.get('Numbers') or []:
if not isinstance(entry, dict) or not entry.get('number'):
continue
params = entry.get('params') or {}
key = tuple(sorted(params.items())) if len(params) > 1 \
else (list(params.values()) or [None])[0]
out[key] = entry['number']
return out
def _pairs(values):
if isinstance(values, dict):
return list(values.items())
return list(enumerate(values))
def _coefficients(value):
"""Every number inside a value, whatever shape it arrives in.
A polynomial, a bare list of coefficients, a nested list, or a single
number: the check is about the numbers, and the first version of it
reported "unexpected type list" for a list of floats instead of reporting
the floats -- which is a check stumbling on the shape rather than doing
its job.
"""
value = _number_of(value)
getter = getattr(value, 'coefficients', None)
if callable(getter):
try:
return _flatten(getter())
except Exception: # noqa: BLE001
pass
return _flatten(value)
def _flatten(value):
if isinstance(value, (list, tuple)):
out = []
for item in value:
out.extend(_flatten(item))
return out
return [value]