Update to MultivariatePolynomials v0.5

[blegat]

Most of the breaking changes were done in order to make it faster notably to resolve https://github.com/JuliaAlgebra/MultivariatePolynomials.jl/issues/194 (I should update the benchmarks in this issue by the way, they should be much better now). The performance of multivariate gcd should be much better now.

[shashi]

CI is erroring with:

  `variable_union_type` not implemented for MultivariatePolynomials.AbstractVariable.

[github-actions[bot]]

Benchmark Results

	master	c6ffe2f1bd77d6...	t[master]/t[c6ffe2f1bd77d6...]
overhead/acrule/a+2	1.2 ± 0.2 μs	1.18 ± 0.19 μs	1.02
overhead/acrule/a+2+b	1.19 ± 0.2 μs	1.17 ± 0.21 μs	1.02
overhead/acrule/a+b	0.401 ± 0.0055 μs	0.396 ± 0.007 μs	1.01
overhead/acrule/noop:Int	27.2 ± 0.4 ns	25.1 ± 0.2 ns	1.08
overhead/acrule/noop:Sym	0.0436 ± 0.0067 μs	0.0396 ± 0.0064 μs	1.1
overhead/rule/noop:Int	0.0421 ± 0.0026 μs	0.0397 ± 0.0022 μs	1.06
overhead/rule/noop:Sym	0.0528 ± 0.0014 μs	0.0517 ± 0.0023 μs	1.02
overhead/rule/noop:Term	0.0528 ± 0.0015 μs	0.0514 ± 0.0016 μs	1.03
overhead/ruleset/noop:Int	0.157 ± 0.0018 μs	0.145 ± 0.0021 μs	1.08
overhead/ruleset/noop:Sym	0.179 ± 0.0024 μs	0.187 ± 0.0039 μs	0.957
overhead/ruleset/noop:Term	4.47 ± 0.2 μs	4.56 ± 0.23 μs	0.981
overhead/simplify/noop:Int	0.206 ± 0.0071 μs	0.196 ± 0.0093 μs	1.05
overhead/simplify/noop:Sym	0.213 ± 0.0031 μs	0.218 ± 0.003 μs	0.978
overhead/simplify/noop:Term	0.0417 ± 0.0012 ms	0.0421 ± 0.0021 ms	0.991
overhead/simplify/randterm (+, *):serial	0.111 ± 0.0016 s	0.113 ± 0.0015 s	0.99
overhead/simplify/randterm (+, *):thread	0.0756 ± 0.011 s	0.0734 ± 0.012 s	1.03
overhead/simplify/randterm (/, *):serial	0.251 ± 0.005 ms	0.252 ± 0.0057 ms	0.995
overhead/simplify/randterm (/, *):thread	0.292 ± 0.0069 ms	0.296 ± 0.0071 ms	0.987
overhead/substitute/a	0.0955 ± 0.0013 ms	0.0936 ± 0.0013 ms	1.02
overhead/substitute/a,b	0.0844 ± 0.0012 ms	0.0836 ± 0.0013 ms	1.01
overhead/substitute/a,b,c	0.0409 ± 0.0008 ms	0.0406 ± 0.0007 ms	1.01
polyform/easy_iszero	0.0413 ± 0.0017 ms	0.0417 ± 0.0019 ms	0.99
polyform/isone	2.8 ± 0.1 ns	3.6 ± 0.1 ns	0.778
polyform/iszero	1.62 ± 0.026 ms	1.68 ± 0.027 ms	0.964
polyform/simplify_fractions	2.47 ± 0.034 ms	2.55 ± 0.04 ms	0.969
time_to_load	5.15 ± 0.0052 s	5.09 ± 0.0065 s	1.01

Benchmark Plots

A plot of the benchmark results have been uploaded as an artifact to the workflow run for this PR. Go to "Actions"->"Benchmark a pull request"->[the most recent run]->"Artifacts" (at the bottom).

[schillic]

If this looks good to you, could you please merge and tag a new release? This is holding back changes in other packages.

[shashi]

Thanks!