Formal polynomials.

[Alon-Ti]

This change is 

[Alon-Ti]

• Formal polynomial evaluator. #836
• Formal polynomials. #835 👈
• Change Eval Framework Copy requirement to Clone. #834
• dev

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[codecov-commenter]

Codecov Report

Attention: Patch coverage is 73.22835% with 68 lines in your changes missing coverage. Please review.

Project coverage is 91.53%. Comparing base (6e649fc) to head (5a971e9).

Files with missing lines	Patch %	Lines
crates/prover/src/constraint_framework/poly.rs	73.22%	61 Missing and 7 partials ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##              dev     #835      +/-   ##
==========================================
- Coverage   91.91%   91.53%   -0.38%     
==========================================
  Files          90       91       +1     
  Lines       12375    12629     +254     
  Branches    12375    12629     +254     
==========================================
+ Hits        11374    11560     +186     
- Misses        892      953      +61     
- Partials      109      116       +7     

Flag	Coverage Δ
	91.53% <73.22%> (-0.38%)	⬇️

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[andrewmilson]

Reviewable status: 0 of 2 files reviewed, 4 unresolved discussions (waiting on @Alon-Ti)

---

crates/prover/src/constraint_framework/poly.rs line 12 at r2 (raw file):

/// A monic monomial consists of a list of variables and their exponents.
#[derive(Debug, Hash, PartialEq, PartialOrd, Eq, Ord, Clone)]

Nit: is hash needed?

Suggestion:

#[derive(Debug, PartialEq, PartialOrd, Eq, Ord, Clone)]

---

crates/prover/src/constraint_framework/poly.rs line 31 at r2 (raw file):

/// A polynomial consists of a list of monomials with coefficients.
#[derive(Debug, Hash, PartialEq, PartialOrd, Eq, Ord, Clone)]

Same here.

Suggestion:

#[derive(Debug, PartialEq, PartialOrd, Eq, Ord, Clone)]

---

crates/prover/src/constraint_framework/poly.rs line 46 at r2 (raw file):

impl<F: From<BaseField>> From<F> for Polynomial<F>
where
    F: One + Clone,

Suggestion:

impl<F: One + Clone + From<BaseField>> From<F> for Polynomial<F>

---

crates/prover/src/constraint_framework/poly.rs line 151 at r2 (raw file):

impl<F: Zero + Clone + From<BaseField>> Zero for Polynomial<F> {
    fn is_zero(&self) -> bool {
        self.monomials.is_empty()

Can multiple zero representations not returning true here? i.e. x0^0 - x1^0
Is it a problem?

Code quote:

self.monomials.is_empty()