Theorems · Definition · algebraic geometry
WeierstrassCurve.Affine.CoordinateRing.XYIdeal
{R : Type r} → [inst : CommRing R] → (W' : WeierstrassCurve.Affine R) → R → Polynomial R → Ideal W'.CoordinateRingThe ideal ⟨X - x, Y - y(X)⟩ of R[W] for some x in R and y(X) in R[X].
- 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement and proof · cited by 5,681
- Idealstatement · cited by 4,748
- Ideal.spanproof · cited by 948
- WeierstrassCurve.Affinestatement and proof · cited by 174
- WeierstrassCurve.Affine.polynomialstatement · cited by 61
- WeierstrassCurve.Affine.CoordinateRingstatement · cited by 39
- WeierstrassCurve.Affine.CoordinateRing.XClassproof · cited by 5
- WeierstrassCurve.Affine.CoordinateRing.YClassproof · cited by 3
Cited by11
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Affine.CoordinateRing.XYIdeal'proof · cited by 7
- WeierstrassCurve.Affine.CoordinateRing.quotientXYIdealEquivstatement · cited by 1
- WeierstrassCurve.Affine.Point.toClass_eq_zeroproof · cited by 1
- WeierstrassCurve.Affine.CoordinateRing.mk_XYIdeal'_neg_mulproof · cited by 1
- WeierstrassCurve.Affine.CoordinateRing.XYIdeal'_eqstatement · cited by 1
- WeierstrassCurve.Affine.CoordinateRing.XYIdeal_add_eqstatement · cited by 1
- WeierstrassCurve.Affine.CoordinateRing.XYIdeal_eq₁statement · cited by 1
- WeierstrassCurve.Affine.CoordinateRing.XYIdeal_eq₂statement and proof · cited by 1
- WeierstrassCurve.Affine.CoordinateRing.XYIdeal_mul_XYIdealstatement and proof · cited by 1
- WeierstrassCurve.Affine.CoordinateRing.XYIdeal_neg_mulstatement · cited by 1
- WeierstrassCurve.Affine.CoordinateRing.mk_XYIdeal'_mul_mk_XYIdeal'proof · cited by 0