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chore: update ark-ff doc refs #710

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chore: update ark-ff doc refs #710

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24 changes: 12 additions & 12 deletions ff/README.md
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Expand Up @@ -17,26 +17,26 @@ This crate contains two types of traits:
The available field traits are:

- [`AdditiveGroup`](/ff/src/lib.rs) - Interface for additive groups that have a "scalar multiplication" operation with respect to the `Scalar` associated type. This applies to to prime-order fields, field extensions, and elliptic-curve groups used in cryptography.
- [`Field`](https://github.com/arkworks-rs/algebra/blob/master/ff/src/fields/mod.rs#L66) - Interface for a generic finite field.
- [`FftField`](https://github.com/arkworks-rs/algebra/blob/master/ff/src/fields/mod.rs#L419) - Exposes methods that allow for performing efficient FFTs on field elements.
- [`PrimeField`](https://github.com/arkworks-rs/algebra/blob/master/ff/src/fields/mod.rs#L523) - Field with a prime `p` number of elements, also referred to as `Fp`.
- [`Field`](https://github.com/arkworks-rs/algebra/blob/master/ff/src/fields/mod.rs#L161) - Interface for a generic finite field.
- [`FftField`](https://github.com/arkworks-rs/algebra/blob/master/ff/src/fields/fft_friendly.rs#L2) - Exposes methods that allow for performing efficient FFTs on field elements.
- [`PrimeField`](https://github.com/arkworks-rs/algebra/blob/master/ff/src/fields/prime.rs#L27) - Field with a prime `p` number of elements, also referred to as `Fp`.

The models implemented are:

- [`Quadratic Extension`](https://github.com/arkworks-rs/algebra/blob/master/ff/src/fields/models/quadratic_extension.rs)
- [`QuadExtField`](https://github.com/arkworks-rs/algebra/blob/master/ff/src/fields/models/quadratic_extension.rs#L140) - Struct representing a quadratic extension field, in this case holding two base field elements
- [`QuadExtConfig`](https://github.com/arkworks-rs/algebra/blob/master/ff/src/fields/models/quadratic_extension.rs#L27) - Trait defining the necessary parameters needed to instantiate a Quadratic Extension Field
- [`QuadExtField`](https://github.com/arkworks-rs/algebra/blob/master/ff/src/fields/models/quadratic_extension.rs#L113) - Struct representing a quadratic extension field, in this case holding two base field elements
- [`QuadExtConfig`](https://github.com/arkworks-rs/algebra/blob/master/ff/src/fields/models/quadratic_extension.rs#L29) - Trait defining the necessary parameters needed to instantiate a Quadratic Extension Field
- [`Cubic Extension`](https://github.com/arkworks-rs/algebra/blob/master/ff/src/fields/models/cubic_extension.rs)
- [`CubicExtField`](https://github.com/arkworks-rs/algebra/blob/master/ff/src/fields/models/cubic_extension.rs#L72) - Struct representing a cubic extension field, holds three base field elements
- [`CubicExtConfig`](https://github.com/arkworks-rs/algebra/blob/master/ff/src/fields/models/cubic_extension.rs#L27) - Trait defining the necessary parameters needed to instantiate a Cubic Extension Field
- [`CubicExtField`](https://github.com/arkworks-rs/algebra/blob/master/ff/src/fields/models/cubic_extension.rs#L97) - Struct representing a cubic extension field, holds three base field elements
- [`CubicExtConfig`](https://github.com/arkworks-rs/algebra/blob/master/ff/src/fields/models/cubic_extension.rs#L28) - Trait defining the necessary parameters needed to instantiate a Cubic Extension Field

The above two models serve as abstractions for constructing the extension fields `Fp^m` directly (i.e. `m` equal 2 or 3) or for creating extension towers to arrive at higher `m`. The latter is done by applying the extensions iteratively, e.g. cubic extension over a quadratic extension field.

- [`Fp2`](https://github.com/arkworks-rs/algebra/blob/master/ff/src/fields/models/fp2.rs#L103) - Quadratic extension directly on the prime field, i.e. `BaseField == BasePrimeField`
- [`Fp3`](https://github.com/arkworks-rs/algebra/blob/master/ff/src/fields/models/fp3.rs#L54) - Cubic extension directly on the prime field, i.e. `BaseField == BasePrimeField`
- [`Fp6_2over3`](https://github.com/arkworks-rs/algebra/blob/master/ff/src/fields/models/fp6_2over3.rs#L48) - Extension tower: quadratic extension on a cubic extension field, i.e. `BaseField = Fp3`, but `BasePrimeField = Fp`.
- [`Fp6_3over2`](https://github.com/arkworks-rs/algebra/blob/master/ff/src/fields/models/fp6_3over2.rs#L49) - Extension tower, similar to the above except that the towering order is reversed: it's a cubic extension on a quadratic extension field, i.e. `BaseField = Fp2`, but `BasePrimeField = Fp`. Only this latter one is exported by default as `Fp6`.
- [`Fp12_2over3over2`](https://github.com/arkworks-rs/algebra/blob/master/ff/src/fields/models/fp12_2over3over2.rs#L83) - Extension tower: quadratic extension of `Fp6_3over2`, i.e. `BaseField = Fp6`.
- [`Fp2`](https://github.com/arkworks-rs/algebra/blob/master/ff/src/fields/models/fp2.rs#L99) - Quadratic extension directly on the prime field, i.e. `BaseField == BasePrimeField`
- [`Fp3`](https://github.com/arkworks-rs/algebra/blob/master/ff/src/fields/models/fp3.rs#L72) - Cubic extension directly on the prime field, i.e. `BaseField == BasePrimeField`
- [`Fp6_2over3`](https://github.com/arkworks-rs/algebra/blob/master/ff/src/fields/models/fp6_2over3.rs#L59) - Extension tower: quadratic extension on a cubic extension field, i.e. `BaseField = Fp3`, but `BasePrimeField = Fp`.
- [`Fp6_3over2`](https://github.com/arkworks-rs/algebra/blob/master/ff/src/fields/models/fp6_3over2.rs#L64) - Extension tower, similar to the above except that the towering order is reversed: it's a cubic extension on a quadratic extension field, i.e. `BaseField = Fp2`, but `BasePrimeField = Fp`. Only this latter one is exported by default as `Fp6`.
- [`Fp12_2over3over2`](https://github.com/arkworks-rs/algebra/blob/master/ff/src/fields/models/fp12_2over3over2.rs#L66) - Extension tower: quadratic extension of `Fp6_3over2`, i.e. `BaseField = Fp6`.

## Usage

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