Research proof index

If a non-zero bivariate polynomial f divides a non-zero bivariate polynomial g, then all the coefficients of the quoetient are non-zero. -/ @[grind .] lemma coeff_ne_zero {f q : F[X][Y]} (hg : q * f ≠ 0) : q.coeff ≠ 0 := (ne_zero_iff_coeffs_ne_zero q).1 (quotient_nezero hg) /- If q * f ≠ 0, then the X-degree of q is bounded above by the differen...

There exists a maximal Y-index achieving totalDegree. Above it, total-degree contributions are strictly smaller or the coefficient vanishes.

The total degree of the product of two bivariate polynomials is the sum of their total degrees.