Function prove 

pub fn prove<A, P, Channel>(
    alloc: &A,
    packed_witness: FieldSlice<'_, P>,
    eval_point: &[B128],
    channel: &mut Channel,
) -> RingSwitchOutput<A, P>
where
    A: Allocator,
    P: PackedField<Scalar = B128>,
    Channel: IPProverChannel<B128>,

Prove the ring-switching reduction.

Takes the packed witness and evaluation point from shift reduction, and:

1. Computes partial evaluations s_hat_v
2. Sends s_hat_v to verifier via channel
3. Samples row-batching challenges
4. Computes the ring-switching equality indicator and sumcheck claim

Returns the transparent polynomial and sumcheck claim for BaseFold.

Arguments

• alloc - the allocator the ring-switching equality indicator is drawn from
• packed_witness - the packed witness buffer (B1 polynomial packed into P elements)
• eval_point - the evaluation point from shift reduction
• channel - the prover channel for sending/sampling

Preconditions

• packed_witness.log_len() + log_packing == eval_point.len() where log_packing is the base-2 log of the extension degree of B128 over B1 (= 7)