changes for fixing branch-cuts

[arnabnandikgp]

References to other Issues or PRs

Fixes #23843

Brief description of what is fixed or changed

Fixed eval_aseries for atan and acot for fixing conflicting results at branch cuts

Release Notes

• functions
  • fixed the eval_aseries method for atan and acot in order to ensure their correct working at the branch cuts.

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• functions
  • fixed the eval_aseries method for atan and acot in order to ensure their correct working at the branch cuts. (#25852 by @arnabnandikgp)

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#### References to other Issues or PRs
Fixes #23843 

#### Brief description of what is fixed or changed
Fixed  `eval_aseries` for atan and acot for fixing conflicting results at branch cuts 

#### Release Notes

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* functions
  * fixed the eval_aseries method for atan and acot in order to ensure their correct working at the branch cuts.

<!-- END RELEASE NOTES -->

Update

The release notes on the wiki have been updated.

[anutosh491]

Hey @arnabnandikgp I shall review the PR tomorrow and get back to you. Untill then could you please fix the authors check. The instructions for the same have been noted down here https://docs.sympy.org/dev/contributing/new-contributors-guide/workflow-process.html#mailmap-instructions

[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 [a00718ba]    | After [39594aac]    |   Ratio | Benchmark (Parameter)                                                |
|----------|----------------------|---------------------|---------|----------------------------------------------------------------------|
| -        | 67.0±0.2ms           | 44.3±0.4ms          |    0.66 | integrate.TimeIntegrationRisch02.time_doit(10)                       |
| -        | 67.0±1ms             | 43.0±0.1ms          |    0.64 | integrate.TimeIntegrationRisch02.time_doit_risch(10)                 |
| +        | 17.9±0.2μs           | 28.9±0.2μs          |    1.62 | integrate.TimeIntegrationRisch03.time_doit(1)                        |
| -        | 5.34±0.05ms          | 2.87±0.03ms         |    0.54 | logic.LogicSuite.time_load_file                                      |
| -        | 72.3±0.4ms           | 28.3±0.09ms         |    0.39 | polys.TimeGCD_GaussInt.time_op(1, 'dense')                           |
| -        | 25.2±0.1ms           | 16.7±0.04ms         |    0.66 | polys.TimeGCD_GaussInt.time_op(1, 'expr')                            |
| -        | 71.6±0.6ms           | 28.5±0.1ms          |    0.4  | polys.TimeGCD_GaussInt.time_op(1, 'sparse')                          |
| -        | 251±1ms              | 124±0.3ms           |    0.49 | polys.TimeGCD_GaussInt.time_op(2, 'dense')                           |
| -        | 253±1ms              | 125±1ms             |    0.49 | polys.TimeGCD_GaussInt.time_op(2, 'sparse')                          |
| -        | 647±3ms              | 374±4ms             |    0.58 | polys.TimeGCD_GaussInt.time_op(3, 'dense')                           |
| -        | 644±5ms              | 369±1ms             |    0.57 | polys.TimeGCD_GaussInt.time_op(3, 'sparse')                          |
| -        | 493±2μs              | 286±2μs             |    0.58 | polys.TimeGCD_LinearDenseQuadraticGCD.time_op(1, 'dense')            |
| -        | 1.76±0.01ms          | 1.04±0ms            |    0.59 | polys.TimeGCD_LinearDenseQuadraticGCD.time_op(2, 'dense')            |
| -        | 5.67±0.02ms          | 3.02±0.01ms         |    0.53 | polys.TimeGCD_LinearDenseQuadraticGCD.time_op(3, 'dense')            |
| -        | 444±2μs              | 231±0.6μs           |    0.52 | polys.TimeGCD_QuadraticNonMonicGCD.time_op(1, 'dense')               |
| -        | 1.44±0.03ms          | 672±7μs             |    0.47 | polys.TimeGCD_QuadraticNonMonicGCD.time_op(2, 'dense')               |
| -        | 4.87±0.05ms          | 1.63±0.01ms         |    0.34 | polys.TimeGCD_QuadraticNonMonicGCD.time_op(3, 'dense')               |
| -        | 368±1μs              | 206±2μs             |    0.56 | polys.TimeGCD_SparseGCDHighDegree.time_op(1, 'dense')                |
| -        | 2.37±0.04ms          | 1.20±0.01ms         |    0.5  | polys.TimeGCD_SparseGCDHighDegree.time_op(3, 'dense')                |
| -        | 9.89±0.08ms          | 4.25±0.02ms         |    0.43 | polys.TimeGCD_SparseGCDHighDegree.time_op(5, 'dense')                |
| -        | 353±2μs              | 165±1μs             |    0.47 | polys.TimeGCD_SparseNonMonicQuadratic.time_op(1, 'dense')            |
| -        | 2.47±0.01ms          | 866±5μs             |    0.35 | polys.TimeGCD_SparseNonMonicQuadratic.time_op(3, 'dense')            |
| -        | 9.29±0.07ms          | 2.60±0.03ms         |    0.28 | polys.TimeGCD_SparseNonMonicQuadratic.time_op(5, 'dense')            |
| -        | 1.00±0.01ms          | 427±5μs             |    0.43 | polys.TimePREM_LinearDenseQuadraticGCD.time_op(3, 'dense')           |
| -        | 1.70±0.01ms          | 511±2μs             |    0.3  | polys.TimePREM_LinearDenseQuadraticGCD.time_op(3, 'sparse')          |
| -        | 5.68±0.01ms          | 1.77±0.01ms         |    0.31 | polys.TimePREM_LinearDenseQuadraticGCD.time_op(5, 'dense')           |
| -        | 8.31±0.2ms           | 1.51±0ms            |    0.18 | polys.TimePREM_LinearDenseQuadraticGCD.time_op(5, 'sparse')          |
| -        | 283±0.9μs            | 63.6±0.6μs          |    0.22 | polys.TimePREM_QuadraticNonMonicGCD.time_op(1, 'sparse')             |
| -        | 3.33±0.02ms          | 389±6μs             |    0.12 | polys.TimePREM_QuadraticNonMonicGCD.time_op(3, 'dense')              |
| -        | 3.83±0.06ms          | 281±0.5μs           |    0.07 | polys.TimePREM_QuadraticNonMonicGCD.time_op(3, 'sparse')             |
| -        | 6.73±0.06ms          | 1.25±0.01ms         |    0.19 | polys.TimePREM_QuadraticNonMonicGCD.time_op(5, 'dense')              |
| -        | 8.38±0.04ms          | 853±8μs             |    0.1  | polys.TimePREM_QuadraticNonMonicGCD.time_op(5, 'sparse')             |
| -        | 4.99±0.02ms          | 3.01±0.01ms         |    0.6  | polys.TimeSUBRESULTANTS_LinearDenseQuadraticGCD.time_op(2, 'sparse') |
| -        | 11.9±0.08ms          | 6.35±0.03ms         |    0.54 | polys.TimeSUBRESULTANTS_LinearDenseQuadraticGCD.time_op(3, 'dense')  |
| -        | 22.1±0.09ms          | 9.16±0.02ms         |    0.41 | polys.TimeSUBRESULTANTS_LinearDenseQuadraticGCD.time_op(3, 'sparse') |
| -        | 5.27±0.01ms          | 866±5μs             |    0.16 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(1, 'sparse')    |
| -        | 12.6±0.05ms          | 7.10±0.02ms         |    0.56 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(2, 'sparse')    |
| -        | 99.7±0.5ms           | 25.4±0.08ms         |    0.25 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(3, 'dense')     |
| -        | 165±0.6ms            | 54.5±0.4ms          |    0.33 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(3, 'sparse')    |
| -        | 173±0.9μs            | 113±2μs             |    0.65 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(1, 'dense')      |
| -        | 355±1μs              | 215±2μs             |    0.61 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(1, 'sparse')     |
| -        | 4.13±0.04ms          | 842±4μs             |    0.2  | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(3, 'dense')      |
| -        | 5.10±0.02ms          | 383±2μs             |    0.07 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(3, 'sparse')     |
| -        | 19.0±0.05ms          | 2.76±0.01ms         |    0.15 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(5, 'dense')      |
| -        | 22.1±0.1ms           | 623±3μs             |    0.03 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(5, 'sparse')     |
| -        | 478±2μs              | 133±0.4μs           |    0.28 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(1, 'sparse') |
| -        | 4.57±0.03ms          | 609±2μs             |    0.13 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(3, 'dense')  |
| -        | 5.19±0.03ms          | 137±2μs             |    0.03 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(3, 'sparse') |
| -        | 12.8±0.06ms          | 1.27±0ms            |    0.1  | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(5, 'dense')  |
| -        | 13.7±0.07ms          | 139±1μs             |    0.01 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(5, 'sparse') |
| -        | 134±0.5μs            | 72.7±1μs            |    0.54 | solve.TimeMatrixOperations.time_rref(3, 0)                           |
| -        | 251±0.6μs            | 86.8±0.2μs          |    0.35 | solve.TimeMatrixOperations.time_rref(4, 0)                           |
| -        | 23.9±0.06ms          | 10.1±0.03ms         |    0.42 | solve.TimeSolveLinSys189x49.time_solve_lin_sys                       |

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

[arnabnandikgp]

@anutosh491 I verified your suggested changes and also added all combinations of tests for I and oo for both atan and acot.

[anutosh491]

Thanks a lot for working on this. Was a long time pending issue !

Could you please squash all the commits . 4 commits look unnecessary here. Once that is done I'll merge the PR @arnabnandikgp

[anutosh491]

Hey @arnabnandikgp I see that you have been addressing issues related to the series module. Here's another interesting issue which we should tackle #24266 :)
Let's try and fix this !