Struct TestUairFqLargePrime 

pub struct TestUairFqLargePrime<R, P>(/* private fields */);

A UAIR exercising the Flavor-1 $F_{q}[X]$-constraint surface for multiple large primes.

Single arbitrary-poly witness column a. Two $F_{q_i}[X]$- constraints, one per declared prime $q_i$:

$$ \phi_{q_0}(a) \in (X - 0) \quad \text{in } F_{q_0}[X], \qquad \phi_{q_1}(a) \in (X - 0) \quad \text{in } F_{q_1}[X], $$

i.e. the constant term of a is zero modulo each of $q_0$ and $q_1$. The trace generator builds a with its $X^0$ coefficient set to integer zero, so both constraints hold simultaneously regardless of the chosen primes.

Used to exercise the per-prime $F_{q_i}[X]$ ideal-check family of the Zinc$+$ protocol end-to-end with multiple primes, including the lockstep multi-family sumcheck/MP-eval driver.

Trait Implementations

impl<R: Clone, P: Clone> Clone for TestUairFqLargePrime<R, P>

fn clone(&self) -> TestUairFqLargePrime<R, P>

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<R: Debug, P: Debug> Debug for TestUairFqLargePrime<R, P>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<R, P> GenerateRandomTrace<32> for TestUairFqLargePrime<R, P>

where R: ConstSemiring + From<i32> + 'static, P: Semiring + From<u64> + 'static,

type PolyCoeff = R

type Int = R

fn generate_random_trace<G: Rng + ?Sized>( num_vars: usize, rng: &mut G, ) -> UairTrace<'static, R, R, 32, 32>

impl<R, P> Uair for TestUairFqLargePrime<R, P>

where R: ConstSemiring + From<i32> + 'static, P: Semiring + From<u64> + 'static,

type Ideal = ImpossibleIdeal

The ideal type the AIR operates with. Since a ConstraintBuilder is “opaque” for a Uair a Uair has to have a means to create ideals so ideals are fixed by this associated types. At the constrain* methods a Uair is given a way to convert its own ideals into builder’s ideals via the FromRef trait.

type FqIdeal = RotationIdeal<R, 1>

The ideal type for $F_{q_i}[X]$-constraints emitted via [ConstraintBuilder::assert_in_fq_ideal]. UAIRs that do not declare any primes should set this to [ideal::ImpossibleIdeal].

type Scalar = DensePolynomial<R, 32>

The type of scalars of the UAIR. For now, we assume they are of the type “arbitrary polynomials”.

type Prime = P

Type of primes defined in signature. Must be compatible with the field type we’re using.

fn signature() -> UairSignature<Self::Prime>

Signature of the UAIR.

fn constrain_general<C, B, FromR, MulByScalar, IFromR, IFqFromR>( b: &mut B, _expr_cfg: &C, up: TraceRow<'_, C::Element>, _down: TraceRow<'_, C::Element>, _from_ref: FromR, _mbs: MulByScalar, _ideal_from_ref: IFromR, fq_ideal_from_ref: IFqFromR, )

where C: SemiringConfig, B: ConstraintBuilder<Expr = C::Element>, FromR: Fn(&Self::Scalar) -> C::Element, MulByScalar: Fn(&C::Element, &Self::Scalar) -> Option<C::Element>, IFqFromR: Fn(&Self::FqIdeal) -> B::FqIdeal,

A general method for describing constraints.