[arith]: isSquare on 𝔽r

[mratsim]

Add isSquare on 𝔽r to unblock:

• WebGPU GPU compiler backend improvements (and small CUDA) #565
• Groth16 prover #463

[gemini-code-assist]

Summary of Changes

Hello @mratsim, I'm Gemini Code Assist¹! I'm currently reviewing this pull request and will post my feedback shortly. In the meantime, here's a summary to help you and other reviewers quickly get up to speed!

This pull request introduces a necessary extension to the isSquare utility, enabling its use across different finite field types. This foundational update is essential for advancing other features and ensures broader applicability of cryptographic operations within the codebase.

Highlights

• isSquare function generalization: The isSquare function in constantine/math/arithmetic/finite_fields_square_root.nim has been updated to work with 𝔽r (finite fields of prime order r) in addition to 𝔽p (finite fields of prime order p), by generalizing its type parameter from Fp to FF.
• Unblocking dependent features: This change is crucial for unblocking progress on related pull requests, specifically #565 and #463, which likely depend on the isSquare functionality for 𝔽r.
• New test coverage: New tests have been added in tests/math_fields/t_finite_fields_sqrt.nim to ensure the correctness and consistency of the isSquare function when applied to 𝔽r types, using specific Fr[BW6_761] examples.

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[gemini-code-assist]

Code Review

The pull request adds the isSquare function for finite field elements, specifically for 𝔽r, to determine if an element is a quadratic residue. This enhancement is intended to unblock issues #565 and #463. The code changes involve modifying the finite_fields_square_root.nim file to include the isSquare function and updating the t_finite_fields_sqrt.nim file to add tests for the new functionality.

[gemini-code-assist]

The test description "𝔽r[BW6_761] is consistent with 𝔽p[BLS12_381]" is vague. It doesn't clearly state what consistency is being tested. Clarify the test description to explain the expected behavior or relationship between 𝔽r[BW6_761] and 𝔽p[BLS12_381].