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Property Tests #2

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Property Tests #2

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curiecrypt
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This PR includes the proptests. Tests cover the following cases:

  • fft_mul
    • Single coefficient polynomials
    • Polynomials with different lengths
    • Empty polynomials
    • Zero and Non-zero polynomials with varying sizes
    • Polynomial multiplication with random inputs and large sizes
  • get_coeff_from_roots
    • TBA
  • get_poly_commitment_g1
    • TBA

Closes #1

}

// Test: Empty polynomials
proptest! {
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For the record

@perturbing We might want to cover the case for empty polynomials in fft_mul, since we get the following fail:

thread 'tests::test_fft_mul_empty_polys' panicked at src/lib.rs:201:5:
Test failed: assertion failed: `(left == right)` 
  left: `[]`, 
 right: `[Scalar(0x0000000000000000000000000000000000000000000000000000000000000000)]`: Failed on case left = empty, right = non-empty with right.len() = 1 at src/lib.rs:209.
minimal failing input: non_empty_vec = [
    Scalar(0x0000000000000000000000000000000000000000000000000000000000000000),
]
	successes: 0
	local rejects: 0
	global rejects: 0

Yeah, sounds good.

It's also a balance between safety and speed. In the code as it is now, I highly favored speed and less complexity.

But we can also make the interface safer, in that we introduce a type for a polynomial and create an interface where polynomials are always normalized and no trailing zero's etc. Then the zero is uniquely the empty list.

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Implement Property Tests
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