units: fixed convert_to() bug and added some tests

[JotacBravo]

References to other Issues or PRs

Fixes #21463

Brief description of what is fixed or changed

Fixed a convert_to() function bug where the result for some inverse sums duplicated the expression units incorrectly.
I found that by using the together() function, these duplicates are prevented when the expression is a function.

Examples:

• Before

In [1]: convert_to(1/(betameter+meter), 1/meter)
Out [1]: 1/(meter(meter*beta + meter))

• After

In [2]: convert_to(1/(betameter+meter), 1/meter)
Out [2]: 1/(meterbeta + meter)

Other comments

Release Notes

• physics.units
  • Fixed a bug with convert_to function.

[sympy-bot]

✅

Hi, I am the SymPy bot. I'm here to help you write a release notes entry. Please read the guide on how to write release notes.

Your release notes are in good order.

Here is what the release notes will look like:

• physics.units
  • Fixed a bug with convert_to function. (#26612 by @JotacBravo and @smichr)

This will be added to https://github.com/sympy/sympy/wiki/Release-Notes-for-1.13.

Click here to see the pull request description that was parsed.

<!-- Your title above should be a short description of what
was changed. Do not include the issue number in the title. -->

#### References to other Issues or PRs
<!-- If this pull request fixes an issue, write "Fixes #NNNN" in that exact
format, e.g. "Fixes #1234" (see
https://tinyurl.com/auto-closing for more information). Also, please
write a comment on that issue linking back to this pull request once it is
open. -->

Fixes #21463

#### Brief description of what is fixed or changed

Fixed a convert_to() function bug where the result for some inverse sums duplicated the expression units incorrectly.
I found that by using the together() function, these duplicates are prevented when the expression is a function.

Examples:

- Before

In [1]: convert_to(1/(beta*meter+meter), 1/meter)
Out [1]: 1/(meter*(meter*beta + meter))

- After

In [2]: convert_to(1/(beta*meter+meter), 1/meter) 
Out [2]: 1/(meter*beta + meter)

#### Other comments


#### Release Notes

<!-- Write the release notes for this release below between the BEGIN and END
statements. The basic format is a bulleted list with the name of the subpackage
and the release note for this PR. For example:

* solvers
  * Added a new solver for logarithmic equations.

* functions
  * Fixed a bug with log of integers. Formerly, `log(-x)` incorrectly gave `-log(x)`.

* physics.units
  * Corrected a semantical error in the conversion between volt and statvolt which
    reported the volt as being larger than the statvolt.

or if no release note(s) should be included use:

NO ENTRY

See https://github.com/sympy/sympy/wiki/Writing-Release-Notes for more
information on how to write release notes. The bot will check your release
notes automatically to see if they are formatted correctly. -->

<!-- BEGIN RELEASE NOTES -->
* physics.units
  * Fixed a bug with convert_to function.
<!-- END RELEASE NOTES -->

Update

The release notes on the wiki have been updated.

[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 [3cc42c49]    |   Ratio | Benchmark (Parameter)                                                |
|----------|----------------------|---------------------|---------|----------------------------------------------------------------------|
| -        | 70.1±2ms             | 46.6±2ms            |    0.66 | integrate.TimeIntegrationRisch02.time_doit(10)                       |
| -        | 68.3±0.7ms           | 44.7±2ms            |    0.65 | integrate.TimeIntegrationRisch02.time_doit_risch(10)                 |
| +        | 18.3±0.1μs           | 30.6±0.5μs          |    1.67 | integrate.TimeIntegrationRisch03.time_doit(1)                        |
| -        | 5.35±0.07ms          | 2.96±0.08ms         |    0.55 | logic.LogicSuite.time_load_file                                      |
| -        | 72.8±0.3ms           | 29.0±0.3ms          |    0.4  | polys.TimeGCD_GaussInt.time_op(1, 'dense')                           |
| -        | 72.9±0.3ms           | 29.0±0.2ms          |    0.4  | polys.TimeGCD_GaussInt.time_op(1, 'sparse')                          |
| -        | 255±0.6ms            | 126±0.6ms           |    0.49 | polys.TimeGCD_GaussInt.time_op(2, 'dense')                           |
| -        | 256±0.6ms            | 127±0.7ms           |    0.5  | polys.TimeGCD_GaussInt.time_op(2, 'sparse')                          |
| -        | 662±4ms              | 373±0.8ms           |    0.56 | polys.TimeGCD_GaussInt.time_op(3, 'dense')                           |
| -        | 649±2ms              | 372±2ms             |    0.57 | polys.TimeGCD_GaussInt.time_op(3, 'sparse')                          |
| -        | 494±2μs              | 296±1μs             |    0.6  | polys.TimeGCD_LinearDenseQuadraticGCD.time_op(1, 'dense')            |
| -        | 1.79±0.02ms          | 1.07±0ms            |    0.6  | polys.TimeGCD_LinearDenseQuadraticGCD.time_op(2, 'dense')            |
| -        | 5.86±0.03ms          | 3.13±0.03ms         |    0.53 | polys.TimeGCD_LinearDenseQuadraticGCD.time_op(3, 'dense')            |
| -        | 448±1μs              | 235±3μs             |    0.52 | polys.TimeGCD_QuadraticNonMonicGCD.time_op(1, 'dense')               |
| -        | 1.48±0.01ms          | 696±5μs             |    0.47 | polys.TimeGCD_QuadraticNonMonicGCD.time_op(2, 'dense')               |
| -        | 4.90±0.04ms          | 1.69±0.01ms         |    0.34 | polys.TimeGCD_QuadraticNonMonicGCD.time_op(3, 'dense')               |
| -        | 371±2μs              | 208±3μs             |    0.56 | polys.TimeGCD_SparseGCDHighDegree.time_op(1, 'dense')                |
| -        | 2.44±0.03ms          | 1.26±0.01ms         |    0.51 | polys.TimeGCD_SparseGCDHighDegree.time_op(3, 'dense')                |
| -        | 10.0±0.07ms          | 4.38±0.01ms         |    0.44 | polys.TimeGCD_SparseGCDHighDegree.time_op(5, 'dense')                |
| -        | 362±2μs              | 174±2μs             |    0.48 | polys.TimeGCD_SparseNonMonicQuadratic.time_op(1, 'dense')            |
| -        | 2.53±0.01ms          | 916±6μs             |    0.36 | polys.TimeGCD_SparseNonMonicQuadratic.time_op(3, 'dense')            |
| -        | 9.55±0.09ms          | 2.72±0.02ms         |    0.28 | polys.TimeGCD_SparseNonMonicQuadratic.time_op(5, 'dense')            |
| -        | 1.02±0.01ms          | 432±3μs             |    0.42 | polys.TimePREM_LinearDenseQuadraticGCD.time_op(3, 'dense')           |
| -        | 1.71±0.01ms          | 517±2μs             |    0.3  | polys.TimePREM_LinearDenseQuadraticGCD.time_op(3, 'sparse')          |
| -        | 6.06±0.03ms          | 1.80±0.02ms         |    0.3  | polys.TimePREM_LinearDenseQuadraticGCD.time_op(5, 'dense')           |
| -        | 8.43±0.02ms          | 1.53±0.01ms         |    0.18 | polys.TimePREM_LinearDenseQuadraticGCD.time_op(5, 'sparse')          |
| -        | 284±1μs              | 67.5±0.2μs          |    0.24 | polys.TimePREM_QuadraticNonMonicGCD.time_op(1, 'sparse')             |
| -        | 3.43±0.03ms          | 394±2μs             |    0.11 | polys.TimePREM_QuadraticNonMonicGCD.time_op(3, 'dense')              |
| -        | 4.05±0.01ms          | 287±1μs             |    0.07 | polys.TimePREM_QuadraticNonMonicGCD.time_op(3, 'sparse')             |
| -        | 6.90±0.09ms          | 1.25±0.01ms         |    0.18 | polys.TimePREM_QuadraticNonMonicGCD.time_op(5, 'dense')              |
| -        | 8.81±0.02ms          | 865±4μs             |    0.1  | polys.TimePREM_QuadraticNonMonicGCD.time_op(5, 'sparse')             |
| -        | 5.03±0.01ms          | 3.15±0.02ms         |    0.63 | polys.TimeSUBRESULTANTS_LinearDenseQuadraticGCD.time_op(2, 'sparse') |
| -        | 12.2±0.09ms          | 6.70±0.04ms         |    0.55 | polys.TimeSUBRESULTANTS_LinearDenseQuadraticGCD.time_op(3, 'dense')  |
| -        | 22.4±0.08ms          | 9.92±0.02ms         |    0.44 | polys.TimeSUBRESULTANTS_LinearDenseQuadraticGCD.time_op(3, 'sparse') |
| -        | 5.26±0.02ms          | 894±10μs            |    0.17 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(1, 'sparse')    |
| -        | 12.6±0.03ms          | 7.21±0.02ms         |    0.57 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(2, 'sparse')    |
| -        | 103±0.7ms            | 26.6±0.09ms         |    0.26 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(3, 'dense')     |
| -        | 168±1ms              | 54.5±0.2ms          |    0.32 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(3, 'sparse')    |
| -        | 172±1μs              | 114±0.5μs           |    0.66 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(1, 'dense')      |
| -        | 360±4μs              | 223±2μs             |    0.62 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(1, 'sparse')     |
| -        | 4.27±0.02ms          | 855±3μs             |    0.2  | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(3, 'dense')      |
| -        | 5.31±0.03ms          | 388±0.8μs           |    0.07 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(3, 'sparse')     |
| -        | 19.8±0.1ms           | 2.86±0.03ms         |    0.14 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(5, 'dense')      |
| -        | 23.0±0.2ms           | 649±2μs             |    0.03 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(5, 'sparse')     |
| -        | 484±4μs              | 139±0.7μs           |    0.29 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(1, 'sparse') |
| -        | 4.74±0.02ms          | 636±5μs             |    0.13 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(3, 'dense')  |
| -        | 5.26±0.03ms          | 143±0.5μs           |    0.03 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(3, 'sparse') |
| -        | 13.1±0.05ms          | 1.33±0ms            |    0.1  | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(5, 'dense')  |
| -        | 14.1±0.09ms          | 144±1μs             |    0.01 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(5, 'sparse') |
| -        | 134±0.5μs            | 76.5±0.3μs          |    0.57 | solve.TimeMatrixOperations.time_rref(3, 0)                           |
| -        | 249±4μs              | 90.0±0.5μs          |    0.36 | solve.TimeMatrixOperations.time_rref(4, 0)                           |
| -        | 24.2±0.2ms           | 10.2±0.03ms         |    0.42 | solve.TimeSolveLinSys189x49.time_solve_lin_sys                       |
| -        | 28.8±0.3ms           | 16.0±0.07ms         |    0.55 | solve.TimeSparseSystem.time_linsolve_Aaug(20)                        |
| -        | 55.3±0.5ms           | 25.3±0.1ms          |    0.46 | solve.TimeSparseSystem.time_linsolve_Aaug(30)                        |
| -        | 28.3±0.2ms           | 15.4±0.09ms         |    0.54 | solve.TimeSparseSystem.time_linsolve_Ab(20)                          |
| -        | 54.9±0.2ms           | 24.9±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).

[smichr]

Just used the preferred format for creation of symbols in the test suite.

[smichr]

We can wait to see if there are any other comments.

Should cancel be used or is together sufficient?

[JotacBravo]

We can wait to see if there are any other comments.

Should cancel be used or is together sufficient?

I did some more tests and for all of them, cancel and together gave the same results, so together seemed sufficient to me.

[smichr]

Nice to have this old issue fixed. Thanks!