Add convexity check for multivariate functions

[Emilius12]

• calculus
  • Added convexity check for multivariate functions

[sympy-bot]

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• calculus
  • Added convexity check for multivariate functions (#26450 by @Emilius12 and @smichr)

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<!-- BEGIN RELEASE NOTES -->
* calculus
   * Added convexity check for multivariate functions

<!-- END RELEASE NOTES -->

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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 [521193b7]    |   Ratio | Benchmark (Parameter)                                                |
|----------|----------------------|---------------------|---------|----------------------------------------------------------------------|
| -        | 70.0±0.8ms           | 43.8±0.2ms          |    0.63 | integrate.TimeIntegrationRisch02.time_doit(10)                       |
| -        | 67.9±0.6ms           | 43.1±0.2ms          |    0.63 | integrate.TimeIntegrationRisch02.time_doit_risch(10)                 |
| +        | 18.3±0.3μs           | 30.5±0.3μs          |    1.67 | integrate.TimeIntegrationRisch03.time_doit(1)                        |
| -        | 5.43±0.03ms          | 2.90±0.01ms         |    0.53 | logic.LogicSuite.time_load_file                                      |
| -        | 73.8±0.3ms           | 28.8±0.1ms          |    0.39 | polys.TimeGCD_GaussInt.time_op(1, 'dense')                           |
| -        | 25.6±0.2ms           | 17.0±0.06ms         |    0.66 | polys.TimeGCD_GaussInt.time_op(1, 'expr')                            |
| -        | 73.2±0.4ms           | 28.8±0.1ms          |    0.39 | polys.TimeGCD_GaussInt.time_op(1, 'sparse')                          |
| -        | 253±0.7ms            | 125±0.2ms           |    0.49 | polys.TimeGCD_GaussInt.time_op(2, 'dense')                           |
| -        | 255±2ms              | 125±0.3ms           |    0.49 | polys.TimeGCD_GaussInt.time_op(2, 'sparse')                          |
| -        | 644±3ms              | 373±2ms             |    0.58 | polys.TimeGCD_GaussInt.time_op(3, 'dense')                           |
| -        | 647±4ms              | 372±2ms             |    0.57 | polys.TimeGCD_GaussInt.time_op(3, 'sparse')                          |
| -        | 490±2μs              | 288±3μs             |    0.59 | polys.TimeGCD_LinearDenseQuadraticGCD.time_op(1, 'dense')            |
| -        | 1.79±0.01ms          | 1.06±0.01ms         |    0.59 | polys.TimeGCD_LinearDenseQuadraticGCD.time_op(2, 'dense')            |
| -        | 5.74±0.06ms          | 3.08±0.03ms         |    0.54 | polys.TimeGCD_LinearDenseQuadraticGCD.time_op(3, 'dense')            |
| -        | 442±6μs              | 232±3μs             |    0.52 | polys.TimeGCD_QuadraticNonMonicGCD.time_op(1, 'dense')               |
| -        | 1.47±0.01ms          | 677±2μs             |    0.46 | polys.TimeGCD_QuadraticNonMonicGCD.time_op(2, 'dense')               |
| -        | 4.82±0.06ms          | 1.67±0.02ms         |    0.35 | polys.TimeGCD_QuadraticNonMonicGCD.time_op(3, 'dense')               |
| -        | 371±1μs              | 208±0.8μs           |    0.56 | polys.TimeGCD_SparseGCDHighDegree.time_op(1, 'dense')                |
| -        | 2.38±0.02ms          | 1.23±0.01ms         |    0.52 | polys.TimeGCD_SparseGCDHighDegree.time_op(3, 'dense')                |
| -        | 9.85±0.06ms          | 4.36±0.03ms         |    0.44 | polys.TimeGCD_SparseGCDHighDegree.time_op(5, 'dense')                |
| -        | 357±2μs              | 170±2μs             |    0.48 | polys.TimeGCD_SparseNonMonicQuadratic.time_op(1, 'dense')            |
| -        | 2.47±0.01ms          | 899±5μs             |    0.36 | polys.TimeGCD_SparseNonMonicQuadratic.time_op(3, 'dense')            |
| -        | 9.52±0.04ms          | 2.66±0.02ms         |    0.28 | polys.TimeGCD_SparseNonMonicQuadratic.time_op(5, 'dense')            |
| -        | 1.02±0.01ms          | 433±3μs             |    0.42 | polys.TimePREM_LinearDenseQuadraticGCD.time_op(3, 'dense')           |
| -        | 1.72±0.01ms          | 503±1μs             |    0.29 | polys.TimePREM_LinearDenseQuadraticGCD.time_op(3, 'sparse')          |
| -        | 5.83±0.04ms          | 1.81±0.01ms         |    0.31 | polys.TimePREM_LinearDenseQuadraticGCD.time_op(5, 'dense')           |
| -        | 8.41±0.06ms          | 1.49±0.01ms         |    0.18 | polys.TimePREM_LinearDenseQuadraticGCD.time_op(5, 'sparse')          |
| -        | 287±2μs              | 65.6±0.8μs          |    0.23 | polys.TimePREM_QuadraticNonMonicGCD.time_op(1, 'sparse')             |
| -        | 3.39±0.06ms          | 389±3μs             |    0.11 | polys.TimePREM_QuadraticNonMonicGCD.time_op(3, 'dense')              |
| -        | 3.96±0.02ms          | 278±1μs             |    0.07 | polys.TimePREM_QuadraticNonMonicGCD.time_op(3, 'sparse')             |
| -        | 6.97±0.06ms          | 1.27±0.01ms         |    0.18 | polys.TimePREM_QuadraticNonMonicGCD.time_op(5, 'dense')              |
| -        | 8.65±0.05ms          | 828±3μs             |    0.1  | polys.TimePREM_QuadraticNonMonicGCD.time_op(5, 'sparse')             |
| -        | 5.07±0.02ms          | 3.00±0.02ms         |    0.59 | polys.TimeSUBRESULTANTS_LinearDenseQuadraticGCD.time_op(2, 'sparse') |
| -        | 11.9±0.1ms           | 6.58±0.01ms         |    0.55 | polys.TimeSUBRESULTANTS_LinearDenseQuadraticGCD.time_op(3, 'dense')  |
| -        | 22.0±0.05ms          | 9.10±0.01ms         |    0.41 | polys.TimeSUBRESULTANTS_LinearDenseQuadraticGCD.time_op(3, 'sparse') |
| -        | 5.29±0.02ms          | 871±4μs             |    0.16 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(1, 'sparse')    |
| -        | 12.7±0.05ms          | 6.97±0.05ms         |    0.55 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(2, 'sparse')    |
| -        | 101±0.7ms            | 26.1±0.04ms         |    0.26 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(3, 'dense')     |
| -        | 166±0.7ms            | 54.0±0.4ms          |    0.33 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(3, 'sparse')    |
| -        | 175±0.7μs            | 111±0.6μs           |    0.63 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(1, 'dense')      |
| -        | 360±3μs              | 221±0.9μs           |    0.61 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(1, 'sparse')     |
| -        | 4.20±0.04ms          | 848±3μs             |    0.2  | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(3, 'dense')      |
| -        | 5.33±0.02ms          | 386±1μs             |    0.07 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(3, 'sparse')     |
| -        | 19.8±0.2ms           | 2.80±0.01ms         |    0.14 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(5, 'dense')      |
| -        | 22.7±0.1ms           | 629±2μs             |    0.03 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(5, 'sparse')     |
| -        | 476±2μs              | 139±1μs             |    0.29 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(1, 'sparse') |
| -        | 4.60±0.03ms          | 618±2μs             |    0.13 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(3, 'dense')  |
| -        | 5.28±0.07ms          | 143±0.9μs           |    0.03 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(3, 'sparse') |
| -        | 13.1±0.04ms          | 1.32±0ms            |    0.1  | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(5, 'dense')  |
| -        | 13.8±0.2ms           | 147±0.7μs           |    0.01 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(5, 'sparse') |
| -        | 134±1μs              | 75.5±0.5μs          |    0.56 | solve.TimeMatrixOperations.time_rref(3, 0)                           |
| -        | 250±0.9μs            | 89.9±0.8μs          |    0.36 | solve.TimeMatrixOperations.time_rref(4, 0)                           |
| -        | 24.5±0.07ms          | 10.3±0.06ms         |    0.42 | solve.TimeSolveLinSys189x49.time_solve_lin_sys                       |
| -        | 28.6±0.2ms           | 15.5±0.1ms          |    0.54 | solve.TimeSparseSystem.time_linsolve_Aaug(20)                        |
| -        | 55.7±0.5ms           | 24.8±0.09ms         |    0.44 | solve.TimeSparseSystem.time_linsolve_Aaug(30)                        |
| -        | 28.7±0.4ms           | 15.2±0.04ms         |    0.53 | solve.TimeSparseSystem.time_linsolve_Ab(20)                          |
| -        | 54.9±0.1ms           | 24.7±0.3ms          |    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).

[1e9abhi1e10]

@Emilius12 Please ensure the pull request title indicates the fix without including issue numbers. Issue numbers belong in the PR description.