Mathlib Map

Theorems · Definition · algebraic geometry

WeierstrassCurve.Affine.CoordinateRing.XYIdeal

{R : Type r} → [inst : CommRing R] → (W' : WeierstrassCurve.Affine R) → R → Polynomial R → Ideal W'.CoordinateRing

The ideal ⟨X - x, Y - y(X)⟩ of R[W] for some x in R and y(X) in R[X].

Defined in
Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point
Cited by
9 results in Mathlib
Foundations
Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRing

Around this declaration

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

WeierstrassCurve.Affine.CoordinateRing.XYIdeal' · cited by 7CoordinateRing.XYIdeal'WeierstrassCurve.Affine.CoordinateRing.quotientXYIdealEquiv · cited by 1CoordinateRing.quotientXY…WeierstrassCurve.Affine.Point.toClass_eq_zero · cited by 1Point.toClass_eq_zeroWeierstrassCurve.Affine.CoordinateRing.mk_XYIdeal'_neg_mul · cited by 1CoordinateRing.mk_XYIdeal…WeierstrassCurve.Affine.CoordinateRing.XYIdeal'_eq · cited by 1CoordinateRing.XYIdeal'_eqWeierstrassCurve.Affine.CoordinateRing.XYIdeal_add_eq · cited by 1CoordinateRing.XYIdeal_ad…WeierstrassCurve.Affine.CoordinateRing.XYIdeal_eq₁ · cited by 1CoordinateRing.XYIdeal_eq₁WeierstrassCurve.Affine.CoordinateRing.XYIdeal_eq₂ · cited by 1CoordinateRing.XYIdeal_eq₂WeierstrassCurve.Affine.CoordinateRing.XYIdeal_mul_XYIdeal · cited by 1CoordinateRing.XYIdeal_mu…WeierstrassCurve.Affine.CoordinateRing.XYIdeal_neg_mul · cited by 1CoordinateRing.XYIdeal_ne…WeierstrassCurve.Affine.CoordinateRing.mk_XYIdeal'_mul_mk_XYIdeal' · cited by 0CoordinateRing.mk_XYIdeal…CommRing · cited by 17173CommRingPolynomial · cited by 5681PolynomialIdeal · cited by 4748IdealIdeal.span · cited by 948Ideal.spanWeierstrassCurve.Affine · cited by 174WeierstrassCurve.AffineWeierstrassCurve.Affine.polynomial · cited by 61Affine.polynomialWeierstrassCurve.Affine.CoordinateRing · cited by 39Affine.CoordinateRingWeierstrassCurve.Affine.CoordinateRing.XClass · cited by 5CoordinateRing.XClassWeierstrassCurve.Affine.CoordinateRing.YClass · cited by 3CoordinateRing.YClassCoordinateRing.XYIdealCITED BYCITES

Cites9

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

Cited by11

Results whose statement or proof uses this declaration.