Defined Singularity Functions for Negative Integer Exponents.

[mvg2002]

References to other Issues or PRs

This PR follows from a conversation in this PR #26576
These functions are necessary to implement the mechanics described in this issue #26570

Brief description of what is fixed or changed

Defined Singularity Functions for negative integer exponents.

Other comments

It is now possible to use Singularity Functions with any negative integer exponent. Untill now the lowest possible exponent was -2.

Release Notes

• functions
  • Defined singularity functions for all negative integer exponents.

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• functions
  • Defined singularity functions for all negative integer exponents. (#26589 by @mvg2002)

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#### References to other Issues or PRs
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This PR follows from a conversation in this PR #26576
These functions are necessary to implement the mechanics described in this issue #26570 

#### Brief description of what is fixed or changed
Defined Singularity Functions for negative integer exponents.

#### Other comments
It is now possible to use Singularity Functions with any negative integer exponent. Untill now the lowest possible exponent was -2.

#### Release Notes

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* 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
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<!-- BEGIN RELEASE NOTES -->
* functions
    * Defined singularity functions for all negative integer exponents. 
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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 [b412fa4b]    |   Ratio | Benchmark (Parameter)                                                |
|----------|----------------------|---------------------|---------|----------------------------------------------------------------------|
| -        | 69.9±2ms             | 44.0±0.5ms          |    0.63 | integrate.TimeIntegrationRisch02.time_doit(10)                       |
| -        | 69.8±1ms             | 42.7±0.2ms          |    0.61 | integrate.TimeIntegrationRisch02.time_doit_risch(10)                 |
| +        | 18.8±0.3μs           | 30.0±0.2μs          |    1.59 | integrate.TimeIntegrationRisch03.time_doit(1)                        |
| -        | 5.26±0.02ms          | 2.94±0.02ms         |    0.56 | logic.LogicSuite.time_load_file                                      |
| -        | 73.4±0.4ms           | 28.5±0.06ms         |    0.39 | polys.TimeGCD_GaussInt.time_op(1, 'dense')                           |
| -        | 26.0±0.3ms           | 16.9±0.09ms         |    0.65 | polys.TimeGCD_GaussInt.time_op(1, 'expr')                            |
| -        | 73.9±0.4ms           | 28.6±0.09ms         |    0.39 | polys.TimeGCD_GaussInt.time_op(1, 'sparse')                          |
| -        | 258±2ms              | 123±0.5ms           |    0.48 | polys.TimeGCD_GaussInt.time_op(2, 'dense')                           |
| -        | 256±2ms              | 124±0.2ms           |    0.48 | polys.TimeGCD_GaussInt.time_op(2, 'sparse')                          |
| -        | 654±6ms              | 367±2ms             |    0.56 | polys.TimeGCD_GaussInt.time_op(3, 'dense')                           |
| -        | 660±7ms              | 367±1ms             |    0.56 | polys.TimeGCD_GaussInt.time_op(3, 'sparse')                          |
| -        | 501±4μs              | 284±2μs             |    0.57 | polys.TimeGCD_LinearDenseQuadraticGCD.time_op(1, 'dense')            |
| -        | 1.78±0ms             | 1.05±0ms            |    0.59 | polys.TimeGCD_LinearDenseQuadraticGCD.time_op(2, 'dense')            |
| -        | 5.78±0.02ms          | 3.01±0.02ms         |    0.52 | polys.TimeGCD_LinearDenseQuadraticGCD.time_op(3, 'dense')            |
| -        | 448±2μs              | 229±30μs            |    0.51 | polys.TimeGCD_QuadraticNonMonicGCD.time_op(1, 'dense')               |
| -        | 1.50±0.01ms          | 661±7μs             |    0.44 | polys.TimeGCD_QuadraticNonMonicGCD.time_op(2, 'dense')               |
| -        | 4.95±0.02ms          | 1.65±0ms            |    0.33 | polys.TimeGCD_QuadraticNonMonicGCD.time_op(3, 'dense')               |
| -        | 380±3μs              | 206±0.7μs           |    0.54 | polys.TimeGCD_SparseGCDHighDegree.time_op(1, 'dense')                |
| -        | 2.44±0ms             | 1.23±0ms            |    0.5  | polys.TimeGCD_SparseGCDHighDegree.time_op(3, 'dense')                |
| -        | 10.1±0.1ms           | 4.31±0.02ms         |    0.43 | polys.TimeGCD_SparseGCDHighDegree.time_op(5, 'dense')                |
| -        | 366±1μs              | 169±0.7μs           |    0.46 | polys.TimeGCD_SparseNonMonicQuadratic.time_op(1, 'dense')            |
| -        | 2.55±0.01ms          | 891±4μs             |    0.35 | polys.TimeGCD_SparseNonMonicQuadratic.time_op(3, 'dense')            |
| -        | 9.57±0.05ms          | 2.64±0.02ms         |    0.28 | polys.TimeGCD_SparseNonMonicQuadratic.time_op(5, 'dense')            |
| -        | 1.03±0.01ms          | 422±3μs             |    0.41 | polys.TimePREM_LinearDenseQuadraticGCD.time_op(3, 'dense')           |
| -        | 1.73±0.01ms          | 507±5μs             |    0.29 | polys.TimePREM_LinearDenseQuadraticGCD.time_op(3, 'sparse')          |
| -        | 5.92±0.03ms          | 1.78±0.01ms         |    0.3  | polys.TimePREM_LinearDenseQuadraticGCD.time_op(5, 'dense')           |
| -        | 8.50±0.03ms          | 1.52±0.01ms         |    0.18 | polys.TimePREM_LinearDenseQuadraticGCD.time_op(5, 'sparse')          |
| -        | 287±2μs              | 65.7±0.3μs          |    0.23 | polys.TimePREM_QuadraticNonMonicGCD.time_op(1, 'sparse')             |
| -        | 3.54±0.03ms          | 392±4μs             |    0.11 | polys.TimePREM_QuadraticNonMonicGCD.time_op(3, 'dense')              |
| -        | 4.09±0.01ms          | 283±3μs             |    0.07 | polys.TimePREM_QuadraticNonMonicGCD.time_op(3, 'sparse')             |
| -        | 7.09±0.04ms          | 1.25±0.01ms         |    0.18 | polys.TimePREM_QuadraticNonMonicGCD.time_op(5, 'dense')              |
| -        | 8.82±0.08ms          | 848±3μs             |    0.1  | polys.TimePREM_QuadraticNonMonicGCD.time_op(5, 'sparse')             |
| -        | 5.02±0.02ms          | 3.01±0.01ms         |    0.6  | polys.TimeSUBRESULTANTS_LinearDenseQuadraticGCD.time_op(2, 'sparse') |
| -        | 12.1±0.07ms          | 6.59±0.06ms         |    0.55 | polys.TimeSUBRESULTANTS_LinearDenseQuadraticGCD.time_op(3, 'dense')  |
| -        | 22.5±0.08ms          | 9.14±0.03ms         |    0.41 | polys.TimeSUBRESULTANTS_LinearDenseQuadraticGCD.time_op(3, 'sparse') |
| -        | 5.24±0.03ms          | 878±5μs             |    0.17 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(1, 'sparse')    |
| -        | 12.5±0.05ms          | 7.04±0.06ms         |    0.56 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(2, 'sparse')    |
| -        | 104±0.7ms            | 25.5±0.06ms         |    0.25 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(3, 'dense')     |
| -        | 168±1ms              | 53.8±0.1ms          |    0.32 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(3, 'sparse')    |
| -        | 173±0.6μs            | 113±0.8μs           |    0.65 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(1, 'dense')      |
| -        | 359±2μs              | 217±2μs             |    0.6  | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(1, 'sparse')     |
| -        | 4.40±0.02ms          | 861±7μs             |    0.2  | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(3, 'dense')      |
| -        | 5.34±0.1ms           | 384±1μs             |    0.07 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(3, 'sparse')     |
| -        | 20.5±0.4ms           | 2.82±0.02ms         |    0.14 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(5, 'dense')      |
| -        | 23.5±0.3ms           | 632±1μs             |    0.03 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(5, 'sparse')     |
| -        | 480±1μs              | 136±0.6μs           |    0.28 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(1, 'sparse') |
| -        | 4.76±0.02ms          | 618±4μs             |    0.13 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(3, 'dense')  |
| -        | 5.38±0.02ms          | 140±1μs             |    0.03 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(3, 'sparse') |
| -        | 13.6±0.05ms          | 1.29±0ms            |    0.1  | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(5, 'dense')  |
| -        | 14.3±0.1ms           | 143±1μs             |    0.01 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(5, 'sparse') |
| -        | 134±0.2μs            | 75.6±1μs            |    0.56 | solve.TimeMatrixOperations.time_rref(3, 0)                           |
| -        | 250±0.7μs            | 89.0±0.3μs          |    0.36 | solve.TimeMatrixOperations.time_rref(4, 0)                           |
| -        | 24.1±0.1ms           | 10.1±0.02ms         |    0.42 | solve.TimeSolveLinSys189x49.time_solve_lin_sys                       |
| -        | 28.4±0.2ms           | 15.5±0.09ms         |    0.54 | solve.TimeSparseSystem.time_linsolve_Aaug(20)                        |
| -        | 55.7±0.2ms           | 24.9±0.1ms          |    0.45 | solve.TimeSparseSystem.time_linsolve_Aaug(30)                        |
| -        | 28.5±0.2ms           | 15.4±0.07ms         |    0.54 | solve.TimeSparseSystem.time_linsolve_Ab(20)                          |
| -        | 55.4±0.4ms           | 24.7±0.1ms          |    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).

[mvg2002]

I see #26576 has been merged into master. This has led to merge conflicts in this pull request. Is this change still wanted or can I close this pull request?

[moorepants]

I wasn't aware of this PR when I merged the other one and don't know the difference. In the future, work in one PR as the review is occurring.