Implement batch_inverse_and_mul

[ValarDragon]

Description

Implement batch inverse and mul, and add tests for both batch inverse and batch inverse & mul.

closes: #98

---

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• Targeted PR against correct branch (main)
• Linked to Github issue with discussion and accepted design OR have an explanation in the PR that describes this work.
• Wrote unit tests
• Updated relevant documentation in the code
• Added a relevant changelog entry to the Pending section in CHANGELOG.md
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[Pratyush]

Thanks for the PR! To get the test to compile you need to add a dev-dependency on ark-test-curves.

[ValarDragon]

Thanks! Just realized I was testing it incorrectly locally (forgot to use all features)

I'll try to fix the remaining build errors later tonight

[ValarDragon]

I'm running into an error that doesn't really make sense to me:

484 | pub fn batch_inversion<F: Field>(v: &mut [F]) {
    |                           ----- required by this bound in `fields::batch_inversion`
...
559 |         batch_inversion::<Fr>(&mut random_coeffs_inv);
    |                               ^^^^^^^^^^^^^^^^^^^^^^ the trait `fields::Field` is not implemented for `ark_ff::fields::models::Fp256<FrParameters>`

Not sure how to fix it

[Pratyush]

I'm running into an error that doesn't really make sense to me:

484 | pub fn batch_inversion<F: Field>(v: &mut [F]) {
    |                           ----- required by this bound in `fields::batch_inversion`
...
559 |         batch_inversion::<Fr>(&mut random_coeffs_inv);
    |                               ^^^^^^^^^^^^^^^^^^^^^^ the trait `fields::Field` is not implemented for `ark_ff::fields::models::Fp256<FrParameters>`

Not sure how to fix it

Hmm this is probably because of some circular dependency issues: test-curves is using a different "version" of ff in the dependency tree than ff's tests are. Ugh this is annoying. If you'd like you can just copy paste bls12_381's Fr into a private module of ark-ff (and similarly for ark-ec).

[ValarDragon]

Oh cool, that worked!

[Pratyush]

@ValarDragon Is this ready to merge?

[ValarDragon]

Yes!

[ValarDragon]

Thanks for the help in debugging this!

[Pratyush]

np, thanks for the PR!