implement formatting of elements in RDF/CDF

[mwageringel]

This ticket implements __format__ for elements in RDF and CDF. See also #29212 for a related discussion.

The real number format immediately delegates to float, whereas the complex format matches the usual repr of elements in CDF as closely as possible (unlike Python's type complex).

sage: '{:.4e}'.format(RDF(2/3))
'6.6667e-01'

sage: format(CDF(32/3, 0), ' .4f')
' 10.6667 + 0.0000*I'

sage: format(CDF(-2/3, -2/3), '.4e')
'-6.6667e-01 - 6.6667e-01*I'

sage: format(CDF(0, 2/3), '.4')
'0.6667*I'

sage: format(CDF(2, 0), '.4')
'2.0'

For reference: the format specification in Python.

Component: misc

Author: Markus Wageringel

Branch/Commit: 51a9736

Reviewer: Eric Gourgoulhon

Issue created by migration from https://trac.sagemath.org/ticket/29514

[mwageringel]

Author: Markus Wageringel

[mwageringel]

Branch: u/gh-mwageringel/29514

[mwageringel]

New commits:

f89ae6e

29514: implement formatting of RDF/CDF elements

[mwageringel]

Commit: f89ae6e

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

829bcc0

29514: implement formatting of RDF/CDF elements

[sagetrac-git]

Changed commit from f89ae6e to 829bcc0

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

51a9736

29514: implement custom `__format__` matching the CDF representation

[sagetrac-git]

Changed commit from 829bcc0 to 51a9736

[mwageringel]

comment:4

Actually, here is a much better version that very closely matches the usual representation of elements in CDF.

[mwageringel]

comment:5

A possible use case is reducing the number of digits in matrices:

sage: print(matrix.random(CDF, 4).str(' {:.4f}'.format))
[ -0.6482 + 0.4684*I   0.7523 + 0.9738*I   0.0076 - 0.5470*I   0.4949 + 0.5821*I]
[  0.6205 + 0.5834*I  -0.0394 + 0.3852*I  -0.3764 - 0.9199*I   0.3162 - 0.2032*I]
[ -0.0436 + 0.5112*I  -0.3949 + 0.2829*I   0.2733 + 0.4865*I   0.3938 - 0.0825*I]
[  0.0763 + 0.6577*I  -0.9444 + 0.4760*I   0.0951 + 0.6043*I  -0.4464 + 0.4081*I]

[egourgoulhon]

comment:6

LGTM. Thank you!

[egourgoulhon]

Reviewer: Eric Gourgoulhon

[mwageringel]

comment:7

Thank you for the review.

[vbraun]

Changed branch from u/gh-mwageringel/29514 to 51a9736