Implement matrix truncation for latex to enhance the display of large matrices

[SamLubelsky]

References to other Issues or PRs

Fixes #16251.

Brief description of what is fixed or changed

I fixed the merge conflict for PR#26284 which seems to have been abandoned. It should auto-merge into master now.

Other comments

Original Author: mohamedrezk122

Release Notes

• printing
  • Large matrices printed in LaTeX are now automatically condensed(can be disabled)

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• printing
  • Large matrices printed in LaTeX are now automatically condensed(can be disabled) (#26526 by @mohamedrezk122 and @SamLubelsky)

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Fixes #16251. 


#### Brief description of what is fixed or changed
I fixed the merge conflict for PR#26284 which seems to have been abandoned.  It should auto-merge into master now.

#### Other comments
Original Author: mohamedrezk122

#### Release Notes

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* printing
  * Large matrices printed in LaTeX are now automatically condensed(can be disabled)

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[github-actions]

Benchmark results from GitHub Actions

Lower numbers are good, higher numbers are bad. A ratio less than 1
means a speed up and greater than 1 means a slowdown. Green lines
beginning with + are slowdowns (the PR is slower then master or
master is slower than the previous release). Red lines beginning
with - are speedups.

Significantly changed benchmark results (PR vs master)

Significantly changed benchmark results (master vs previous release)

| Change   | Before [2487dbb5]    | After [bd0b3e6f]    |   Ratio | Benchmark (Parameter)                                                |
|----------|----------------------|---------------------|---------|----------------------------------------------------------------------|
| -        | 67.2±1ms             | 43.0±0.2ms          |    0.64 | integrate.TimeIntegrationRisch02.time_doit_risch(10)                 |
| +        | 18.4±0.2μs           | 30.2±0.04μs         |    1.64 | integrate.TimeIntegrationRisch03.time_doit(1)                        |
| -        | 5.36±0.03ms          | 2.89±0.05ms         |    0.54 | logic.LogicSuite.time_load_file                                      |
| -        | 73.3±0.3ms           | 29.0±0.2ms          |    0.4  | polys.TimeGCD_GaussInt.time_op(1, 'dense')                           |
| -        | 25.7±0.1ms           | 16.9±0.03ms         |    0.66 | polys.TimeGCD_GaussInt.time_op(1, 'expr')                            |
| -        | 73.2±0.6ms           | 29.5±0.1ms          |    0.4  | polys.TimeGCD_GaussInt.time_op(1, 'sparse')                          |
| -        | 260±2ms              | 125±0.4ms           |    0.48 | polys.TimeGCD_GaussInt.time_op(2, 'dense')                           |
| -        | 258±1ms              | 126±0.7ms           |    0.49 | polys.TimeGCD_GaussInt.time_op(2, 'sparse')                          |
| -        | 657±5ms              | 377±3ms             |    0.57 | polys.TimeGCD_GaussInt.time_op(3, 'dense')                           |
| -        | 662±4ms              | 374±3ms             |    0.57 | polys.TimeGCD_GaussInt.time_op(3, 'sparse')                          |
| -        | 497±5μs              | 291±3μs             |    0.58 | polys.TimeGCD_LinearDenseQuadraticGCD.time_op(1, 'dense')            |
| -        | 1.81±0.02ms          | 1.06±0ms            |    0.58 | polys.TimeGCD_LinearDenseQuadraticGCD.time_op(2, 'dense')            |
| -        | 5.77±0.04ms          | 3.08±0.01ms         |    0.53 | polys.TimeGCD_LinearDenseQuadraticGCD.time_op(3, 'dense')            |
| -        | 452±2μs              | 231±2μs             |    0.51 | polys.TimeGCD_QuadraticNonMonicGCD.time_op(1, 'dense')               |
| -        | 1.48±0ms             | 696±10μs            |    0.47 | polys.TimeGCD_QuadraticNonMonicGCD.time_op(2, 'dense')               |
| -        | 4.92±0.02ms          | 1.67±0.01ms         |    0.34 | polys.TimeGCD_QuadraticNonMonicGCD.time_op(3, 'dense')               |
| -        | 374±1μs              | 206±1μs             |    0.55 | polys.TimeGCD_SparseGCDHighDegree.time_op(1, 'dense')                |
| -        | 2.41±0.01ms          | 1.25±0.01ms         |    0.52 | polys.TimeGCD_SparseGCDHighDegree.time_op(3, 'dense')                |
| -        | 9.97±0.09ms          | 4.45±0.05ms         |    0.45 | polys.TimeGCD_SparseGCDHighDegree.time_op(5, 'dense')                |
| -        | 357±2μs              | 169±0.9μs           |    0.47 | polys.TimeGCD_SparseNonMonicQuadratic.time_op(1, 'dense')            |
| -        | 2.49±0.03ms          | 917±4μs             |    0.37 | polys.TimeGCD_SparseNonMonicQuadratic.time_op(3, 'dense')            |
| -        | 9.47±0.1ms           | 2.64±0.01ms         |    0.28 | polys.TimeGCD_SparseNonMonicQuadratic.time_op(5, 'dense')            |
| -        | 1.02±0.01ms          | 431±4μs             |    0.42 | polys.TimePREM_LinearDenseQuadraticGCD.time_op(3, 'dense')           |
| -        | 1.72±0.02ms          | 501±3μs             |    0.29 | polys.TimePREM_LinearDenseQuadraticGCD.time_op(3, 'sparse')          |
| -        | 5.80±0.04ms          | 1.83±0.01ms         |    0.32 | polys.TimePREM_LinearDenseQuadraticGCD.time_op(5, 'dense')           |
| -        | 8.46±0.05ms          | 1.48±0ms            |    0.18 | polys.TimePREM_LinearDenseQuadraticGCD.time_op(5, 'sparse')          |
| -        | 286±2μs              | 65.4±0.2μs          |    0.23 | polys.TimePREM_QuadraticNonMonicGCD.time_op(1, 'sparse')             |
| -        | 3.43±0.03ms          | 396±3μs             |    0.12 | polys.TimePREM_QuadraticNonMonicGCD.time_op(3, 'dense')              |
| -        | 3.96±0.02ms          | 275±1μs             |    0.07 | polys.TimePREM_QuadraticNonMonicGCD.time_op(3, 'sparse')             |
| -        | 6.98±0.07ms          | 1.29±0.01ms         |    0.18 | polys.TimePREM_QuadraticNonMonicGCD.time_op(5, 'dense')              |
| -        | 8.71±0.07ms          | 834±10μs            |    0.1  | polys.TimePREM_QuadraticNonMonicGCD.time_op(5, 'sparse')             |
| -        | 5.08±0.04ms          | 3.32±0.01ms         |    0.65 | polys.TimeSUBRESULTANTS_LinearDenseQuadraticGCD.time_op(2, 'sparse') |
| -        | 12.0±0.04ms          | 6.69±0.01ms         |    0.56 | polys.TimeSUBRESULTANTS_LinearDenseQuadraticGCD.time_op(3, 'dense')  |
| -        | 22.8±0.2ms           | 9.03±0.02ms         |    0.4  | polys.TimeSUBRESULTANTS_LinearDenseQuadraticGCD.time_op(3, 'sparse') |
| -        | 5.49±0.01ms          | 870±5μs             |    0.16 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(1, 'sparse')    |
| -        | 12.6±0.03ms          | 6.98±0.02ms         |    0.55 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(2, 'sparse')    |
| -        | 101±0.7ms            | 26.0±0.1ms          |    0.26 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(3, 'dense')     |
| -        | 173±2ms              | 54.0±0.2ms          |    0.31 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(3, 'sparse')    |
| -        | 175±0.7μs            | 114±0.4μs           |    0.65 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(1, 'dense')      |
| -        | 368±1μs              | 213±2μs             |    0.58 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(1, 'sparse')     |
| -        | 4.25±0.03ms          | 846±7μs             |    0.2  | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(3, 'dense')      |
| -        | 5.24±0.04ms          | 379±2μs             |    0.07 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(3, 'sparse')     |
| -        | 19.8±0.2ms           | 2.83±0.01ms         |    0.14 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(5, 'dense')      |
| -        | 22.8±0.09ms          | 624±1μs             |    0.03 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(5, 'sparse')     |
| -        | 498±2μs              | 136±1μs             |    0.27 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(1, 'sparse') |
| -        | 4.69±0.03ms          | 623±2μs             |    0.13 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(3, 'dense')  |
| -        | 5.28±0.02ms          | 137±1μs             |    0.03 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(3, 'sparse') |
| -        | 13.1±0.2ms           | 1.28±0ms            |    0.1  | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(5, 'dense')  |
| -        | 13.8±0.07ms          | 140±1μs             |    0.01 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(5, 'sparse') |
| -        | 132±1μs              | 73.5±0.3μs          |    0.56 | solve.TimeMatrixOperations.time_rref(3, 0)                           |
| -        | 252±5μs              | 87.1±0.3μs          |    0.35 | solve.TimeMatrixOperations.time_rref(4, 0)                           |
| -        | 24.0±0.3ms           | 10.2±0.02ms         |    0.43 | solve.TimeSolveLinSys189x49.time_solve_lin_sys                       |
| -        | 29.1±0.1ms           | 15.5±0.04ms         |    0.53 | solve.TimeSparseSystem.time_linsolve_Aaug(20)                        |
| -        | 54.8±0.1ms           | 25.0±0.2ms          |    0.46 | solve.TimeSparseSystem.time_linsolve_Aaug(30)                        |
| -        | 28.2±0.1ms           | 15.3±0.1ms          |    0.54 | solve.TimeSparseSystem.time_linsolve_Ab(20)                          |
| -        | 54.7±0.3ms           | 24.5±0.2ms          |    0.45 | solve.TimeSparseSystem.time_linsolve_Ab(30)                          |

Full benchmark results can be found as artifacts in GitHub Actions
(click on checks at the top of the PR).

[oscarbenjamin]

This looks good although I am not sure about the option names.

There should be tests for what happens under different settings.

Ideally all printers would have this option and in fact displaying large matrices should not be done by default. I wonder about having something like a symbolic ShowAll(expr) to handle this rather than a printer option.

[oscarbenjamin]

I don't think that this many matrix specific options are warranted.

Let's start with something basic: we can have an option like truncate that defaults to true. It could be used for more than just matrices but for now it could be implemented only for matrices. Ideally other printers like str/repr should support the same and it should be controllable via init_printing.

[SamLubelsky]

Ok, I just made the changes for latex printing. I agree truncation should also work for the other printers and I will try to get that working. Should I put that in this PR or open a new one?

Also, do you think there is a way to implement this for many of the printers simultaneously(srepr, unicode, etc), or will it have to be a new implementation for each individual printer?

[oscarbenjamin]

I still don't think mat_compact is the right kind of option to add. Rather there should be a general option for shortening all possible outputs (not just matrices). Its purpose should be to avoid producing absurdly large output in general even if for now it is only applied to matrices.

[SamLubelsky]

I agree, just forgot to change mat_compact to truncate in a few spots. The docstring specifies that truncate currently only truncates matrix but might be extended to truncate other things in the future.

[oscarbenjamin]

Using truncate=False expresses what is wanted in a negated sense. Maybe what would be better is the opposite like full_output=True (default is False) or something like that...