the preliminaries so far seems to give a fully self-contained description of polynomials (in one variable), but the soundness reduction ends up (both Case 1 and Case 2) requires multivariable polynomials, with the latter also invoking Schwartz-Zippel lemma. In the interest of giving a consistent level of self-containedness, we should state the relative facts about multivariable polynomials. S-Z lemma itself is not hard to prove by induction
the preliminaries so far seems to give a fully self-contained description of polynomials (in one variable), but the soundness reduction ends up (both Case 1 and Case 2) requires multivariable polynomials, with the latter also invoking Schwartz-Zippel lemma. In the interest of giving a consistent level of self-containedness, we should state the relative facts about multivariable polynomials. S-Z lemma itself is not hard to prove by induction