field-cat 0.1.0

Finite field algebra shared across plonkish-cat, proof-cat, and stark-cat
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# field-cat

Finite field algebra shared across the `*-cat` proof-system ecosystem.

`field-cat` owns the [`Field`] trait, the [`FieldBytes`] serialization trait, and a small library of concrete finite fields used by [plonkish-cat](https://github.com/MavenRain/plonkish-cat), [proof-cat](https://github.com/MavenRain/proof-cat), and `stark-cat`.

## Why a separate crate

The `Field` trait was previously defined in `plonkish-cat`.  That coupling forces any downstream proof system (modern STARK, FRI, plain polynomial commitment schemes) to depend on the entire `plonkish-cat` constraint vocabulary (`ConstraintSet`, `Expression`, `Wire`, `CopyConstraint`) just to use field arithmetic.  Lifting the trait into its own crate lets each downstream pick exactly the layer it needs.

## Provided fields

| Field | Modulus | Width | Typical use |
|---|---|---|---|
| [`F101`] | `101` | 7-bit | toy field for tests and small inspectable examples |
| [`BabyBear`] | `2^31 - 1` (Mersenne prime) | 31-bit | Plonky3, SP1, modern STARK frontends |
| [`BFieldElement`] | `2^64 - 2^32 + 1` (Goldilocks prime) | 64-bit | Triton VM, Plonky3 (when wider field needed), Risc0 base |

Adding a new field is a matter of defining a newtype, implementing the `std::ops` arithmetic, implementing [`Field`] (`zero` / `one` / `inv`), and implementing [`FieldBytes`] if the element will be absorbed into a Fiat-Shamir transcript.

## Quick start

```rust
use field_cat::{BabyBear, BFieldElement, Field};

let a = BabyBear::new(7);
let b = BabyBear::new(11);
assert_eq!((a * b).value(), 77);

let g = BFieldElement::new(42);
let g_inv = g.inv()?;
assert_eq!(g * g_inv, BFieldElement::one());
# Ok::<(), field_cat::Error>(())
```

## Building

```bash
cargo build
cargo test
RUSTFLAGS="-D warnings" cargo clippy
cargo doc --no-deps --open
```

## Conventions

See [`CLAUDE.md`](CLAUDE.md): functional, type-driven, hand-rolled error enum, no `unwrap`, no `as` casts, no `mut`, no `dyn`, no `loop`/`for`.  Linter is run with `RUSTFLAGS="-D warnings"`.

## License

MIT