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Theorems · Definition · algebraic geometry

WeierstrassCurve.Projective.polynomialZ

{R : Type r} → [inst : CommRing R] → WeierstrassCurve.Projective R → MvPolynomial (Fin 3) R

The partial derivative W_Z(X, Y, Z) with respect to Z of the polynomial W(X, Y, Z) associated to a Weierstrass curve W in projective coordinates.

Defined in
Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Basic
Cited by
7 results in Mathlib
Foundations
Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRing
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

WeierstrassCurve.Projective.Nonsingular · cited by 37Projective.NonsingularWeierstrassCurve.Projective.map_polynomialZ · cited by 2Projective.map_polynomialZWeierstrassCurve.Projective.eval_polynomialZ · cited by 2Projective.eval_polynomia…WeierstrassCurve.Projective.polynomialZ_eq · cited by 1Projective.polynomialZ_eqWeierstrassCurve.Projective.nonsingular_iff · cited by 1Projective.nonsingular_iffWeierstrassCurve.Projective.map_nonsingular · cited by 1Projective.map_nonsingularWeierstrassCurve.Projective.polynomial_relation · cited by 0Projective.polynomial_rel…WeierstrassCurve.Projective.baseChange_polynomialZ · cited by 0Projective.baseChange_pol…DFunLike.coe · cited by 62936DFunLike.coeCommRing · cited by 17173CommRingMvPolynomial · cited by 2140MvPolynomialWeierstrassCurve.Projective · cited by 244WeierstrassCurve.Projecti…MvPolynomial.pderiv · cited by 71MvPolynomial.pderivWeierstrassCurve.Projective.polynomial · cited by 10Projective.polynomialProjective.polynomialZCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by8

Results whose statement or proof uses this declaration.