Commit 2022-12-19 09:05 b7487a0e
View on Github →feat(algebraic_geometry/EllipticCurve/weierstrass): define Weierstrass polynomials and prove basic facts (#17631)
Define the Weierstrass polynomial and its partial derivatives, as well as properties of their evaluations (the Weierstrass equation and nonsingularity). Prove that a Weierstrass curve is nonsingular at every point if its discriminant is non-zero, and its coordinate ring is an integral domain (because the associated polynomial is irreducible). Fix minor issues (rename the variable C
with the variable W
to avoid a clash with polynomial.C
, and generalise two_torsion_polynomial_disc_ne_zero
).