Express and check expression degree

When we write down constraints in our documentation we often will write something like
- $f \gets \mathsf{flag}( f_1, \ldots, f_n) \| \deg = d$
- $\mathsf{constraint}(v_1, \ldots, v_n) = 0 \| \deg = d$

These degree hints are very useful to ensure we are not blowing past the maximum supported degree (in our case 9). However, without actually implementing them, we have to manually check if they are correct and they might contain mistakes.

In AirScript, it could be useful to support syntax for specifying the expected degree and then have it be checked by the compiler.
- `let f = flag(v_1, ..., v_n) | deg d`
- `ev constraint([v_1, ..., v_n]) { ... } | deg = d`
- `enf constraint(v_1, ..., v_n) when f | deg = d`

The easy approach to checking the degree is by evaluating the expression graph and counting the multiplications. But this might erroneously complain if we specify a degree we know is correct but is technically lower than what would be computed in this naive way. For example the expression $s \cdot f + (1-s) \cdot f$ would have degree $\deg(s) + \deg(f)$ when in fact it has degree $\deg(f)$ since the $s$ cancel out.

It seems like there exists an established way of computing the actual degree of a multivariate expression using a randomized polynomial identity test which output the degree with high probability, thought I haven't taken the time to fully understand how it works. This is left as exercise to the assignee.

The issue is about adding degree checking to the AirScript compiler. Start by examining the expression graph evaluation in the compiler codebase. Research randomized polynomial identity tests for multivariate degree computation. The goal is to implement syntax for degree hints and verify them, ensuring they don't exceed the maximum degree of 9.

Scritto dal modello di indicizzazione a partire dal testo della issue.