implement string formatting for elements in RR and CC

[mwageringel]

Following #29514 (see also #27788 and #29212), this ticket implements __format__ for real and complex numbers.

sage: '{:.4f}'.format(1.2)
'1.2000'
sage: '{:.4f}'.format(CC(1.2, 0))
'1.2000 + 0.0000*I'

The complex case is implemented by reusing the code from CDF.

The real case is implemented by delegating to Python's arbitrary precision Decimal numbers. This works quite well, but has the caveat that the output is not completely the same as for the repr of real numbers. Compare for example:

sage: from decimal import Decimal
sage: '{!r} {!s}'.format(RR(oo), Decimal(float(oo)))
'+infinity Infinity'
sage: '{!r} {!s}'.format(RR(-oo), Decimal(float(-oo)))
'-infinity -Infinity'
sage: '{!r} {!s}'.format(RR(0), Decimal(str(RR(0))))
'0.00000000000000 0E-15'
sage: '{!r} {:.10}'.format(RR(1e10), Decimal(float(1e10)))
'1.00000000000000e10 1.000000000E+10'

It looks like this can only be avoided by a custom implementation of the format specification, rather than delegating to Decimal, which is quite a complex task.

CC: @slel @jcamp0x2a

Component: misc

Keywords: format

Author: Markus Wageringel

Branch: c118bf2

Reviewer: Dima Pasechnik

Issue created by migration from https://trac.sagemath.org/ticket/30515

[mwageringel]

Commit: c118bf2

[mwageringel]

Author: Markus Wageringel

[mwageringel]

Replying to @mwageringel:

It looks like this can only be avoided by a custom implementation of the format specification, rather than delegating to Decimal, which is quite a complex task.

As those differences are small, I would suggest to leave that for a follow-up ticket and merge this ticket as is.

---

New commits:

c118bf2

30515: implement formatting for elements of RR and CC

[mwageringel]

Branch: u/gh-mwageringel/30515

[mwageringel]

Changed keywords from none to format

[dimpase]

Reviewer: Dima Pasechnik

[dimpase]

comment:2

lgtm

[mwageringel]

comment:3

Thanks.

[vbraun]

Changed branch from u/gh-mwageringel/30515 to c118bf2

[antonio-rojas]

comment:5

I'm getting two test failures on my distro package, using system python 3.8.5

sage -t --long --random-seed=0 /usr/lib/python3.8/site-packages/sage/rings/complex_number.pyx
**********************************************************************
File "/usr/lib/python3.8/site-packages/sage/rings/complex_number.pyx", line 574, in sage.rings.complex_number.ComplexNumber.__format__
Failed example:
    format(CC(3, 0), '#.4g')
Expected:
    Traceback (most recent call last):
    ...
    ValueError: invalid format string
Got:
    '3.000 + 0.e-15*I'
**********************************************************************
File "/usr/lib/python3.8/site-packages/sage/rings/complex_number.pyx", line 578, in sage.rings.complex_number.ComplexNumber.__format__
Failed example:
    format(CC(0, 0), '+#.4')
Expected:
    Traceback (most recent call last):
    ...
    ValueError: invalid format string
Got:
    '+0.E-15'
**********************************************************************

[antonio-rojas]

Changed commit from c118bf2 to none

[mwageringel]

comment:6

#30689 should fix this. It is nice to see that the format specification seems to be more fully implemented in your Python version. On my end, I cannot reproduce it with 3.8.5 though.