[tombouctou]

Part of step 6 of the outline in #2047. On top of the hyperbolic PR, #2056 (and the PRs below it): SetPrecision evaluates after setting the numbers, so SetPrecision[Sin[2], 20] needs Sin's rule.

SetPrecision and SetAccuracy did not exist; they came back unevaluated. They now work as in WMA 15:

Input	WMA 15 and this PR
SetPrecision[1/3, 20]	0.33333333333333333333
SetPrecision[0.1, 20]	0.10000000000000000555: an inexact number keeps its binary value
SetPrecision[f[Pi, x], 20]	f[3.1415926535897932385, x]: numeric constants are evaluated
SetPrecision[0.1, Infinity]	3602879701896397 / 36028797018963968
SetPrecision[1.520, MachinePrecision]`	1.5
Precision[SetPrecision[Sin[2], 20]]	20.0384: the numbers are set, then the expression is evaluated
Precision[SetPrecision[Sqrt[2], 20]]	20.301: an exact exponent stays exact
SetPrecision[0., 20]	0: a machine or arbitrary-precision zero becomes an exact 0
Precision /@ {Re[#], Im[#]} &[SetPrecision[1.5 + 2.5 I, 20.3]]	{20.1619, 20.3837}: both parts get the same accuracy, so that the number has precision 20.3
Precision[SetAccuracy[150.5, 20]]	22.1775
Accuracy[SetAccuracy[0.001, 2]]	2.: no digit left, so a zero
SetPrecision[1.5, a]	SetPrecision::precbd
SetPrecision[1.5, -1]	SetPrecision::precsm, then $MinPrecision is used
SetAccuracy[1.5, a]	SetAccuracy::accbd

Changes

• SetPrecision and SetAccuracy in mathics/builtin/atomic/numbers.py, next to Precision and Accuracy. The work is in a new module, mathics/eval/numbers/precision.py.
• Complex: the object cache was keyed on the parts' values and whole-bit precision. Since PrecisionReal: keep a real-valued precision, as WMA does (#2047) #2050, two complex numbers that differ only in a real-valued precision were the same object: SetAccuracy[1.5 + 2.5 I, 20] returned the result of SetPrecision[1.5 + 2.5 I, 20.3] evaluated just before it. The key now has the parts' precisions, as PrecisionReal's key does.
• number._get_float_inf becomes get_float_inf, used by SetPrecision for $MinPrecision and $MaxPrecision.

Tests

test_set_precision, test_set_accuracy and test_set_precision_messages in test/builtin/atomic/test_numbers.py, with WMA 15 values, and doctests. Full run on kimmy: doctests all pass. The pytest failures are the ones that depend on the order the tests run in; the failing files that touch numbers pass on their own.

🤖 Generated with Claude Code

[rocky]

Small nit: for constants like this, we've been using

from typing import Final
LOG10_2: Final[float] = math.log10(2)

[tombouctou]

Done in a88806c: LOG10_2: Final[float] = math.log10(2). I did the same for the constants #2060 adds to number.py (MIN_STORED_BITS, EXTENDED_DIGITS), which match the Final ones already there.

[rocky]

LGTM - if you want to address the nit, that's up to you. Merge when you feel ready.