control the number of digits to display in matrices via IPython's %precision magic

[mwageringel]

Based on #30552, this ticket adds options for customizing the number of floating point digits to display in matrices. This is particularly useful for numeric computations involving large matrices.

The option is linked to the IPython magic %precision. (The IPython magic also sets the corresponding option in NumPy.)

sage: %precision 4
'%.4f'
sage: A = matrix.random(RDF, 5); A
[-0.01337  -0.9269  -0.0893   0.1784    0.975]
[  0.2152   0.6165   0.4195   0.7558  -0.9292]
[  0.8234  -0.2305     0.83  -0.9375   0.4938]
[ -0.6378   0.7058   0.1209  -0.9081  -0.9551]
[  0.9217  -0.3054  -0.2997   0.5871  -0.5642]
sage: %precision
'%r'
sage: A
[-0.013365510514271595   -0.9268868721196306  -0.08930150422327143   0.17839999989498323    0.9750196839071508]
[  0.21517169403284941    0.6165223907365385    0.4195049240955384    0.7557760012777428   -0.9291629307331721]
[   0.8233703740645537  -0.23053733934301857    0.8299695817296515   -0.9375095363818953    0.4937640499860838]
[  -0.6378186095056861    0.7057551432596336   0.12087801033553447   -0.9080993678019631   -0.9551440194578318]
[   0.9216765622236254  -0.30541498083145413  -0.29967291645930083    0.5871367386637378   -0.5642041854379536]

CC: @slel @DavidAyotte

Component: numerical

Author: Markus Wageringel

Branch/Commit: f7cc8c9

Reviewer: David Ayotte

Issue created by migration from https://trac.sagemath.org/ticket/30755

[mwageringel]

Commit: 98e0926

[mwageringel]

Author: Markus Wageringel

[mwageringel]

New commits:

7d0b548	30552: implement global options for matrices
98e0926	30755: implement precision for display of matrices

[mwageringel]

Branch: u/gh-mwageringel/30755

[mwageringel]

Dependencies: #30552

[sagetrac-git]

Changed commit from 98e0926 to ec5440b

[sagetrac-git]

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

5fe9b2c	30552: reset options after examples
ec5440b	30755: implement precision for display of matrices

[mkoeppe]

comment:4

Setting new milestone based on a cursory review of ticket status, priority, and last modification date.

[sagetrac-git]

Changed commit from ec5440b to f7cc8c9

[sagetrac-git]

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

f7cc8c9

30755: implement precision for display of matrices

[mwageringel]

comment:6

Rebased on 9.3.rc5.

[mwageringel]

Changed dependencies from #30552 to none

[DavidAyotte]

comment:7

Hello Markus,

Thanks for this enhancement. I have reviewed it and everything is correct. However, I got two unrelated errors when testing the whole documentation:

Running doctests with ID 2021-06-28-14-01-05-7ec3f02e.
Git branch: HEAD
Using --optional=build,debian,dochtml,pip,sage,sage_spkg
Doctesting 1 file.
sage -t --long --warn-long 160.0 --random-seed=0 src/sage/modules/fg_pid/fgp_module.py
**********************************************************************
File "src/sage/modules/fg_pid/fgp_module.py", line 1274, in sage.modules.fg_pid.fgp_module.FGP_Module_class.coordinate_vector
Failed example:
    Q.coordinate_vector(Q.0 - Q.1)
Expected:
    (1, -1)
Got:
    (1, 47)
**********************************************************************
File "src/sage/modules/fg_pid/fgp_module.py", line 1294, in sage.modules.fg_pid.fgp_module.FGP_Module_class.coordinate_vector
Failed example:
    Q.coordinate_vector(x)
Expected:
    (0, -1)
Got:
    (0, 11)
**********************************************************************
1 item had failures:
   2 of  23 in sage.modules.fg_pid.fgp_module.FGP_Module_class.coordinate_vector
    [397 tests, 2 failures, 2.04 s]
----------------------------------------------------------------------
sage -t --long --warn-long 160.0 --random-seed=0 src/sage/modules/fg_pid/fgp_module.py  # 2 doctests failed
----------------------------------------------------------------------
Total time for all tests: 2.1 seconds
    cpu time: 2.0 seconds
    cumulative wall time: 2.0 seconds

I tested this module outside of your ticket (on the develop branch) and I also got the same error, so it is definitely not related with your code. Do you know if there is already a ticket about this?

EDIT: this issue is already known and is covered in ticket #32048

[DavidAyotte]

Reviewer: David Ayotte

[mwageringel]

comment:9

Thank you for the review, David.

[vbraun]

Changed branch from u/gh-mwageringel/30755 to f7cc8c9