Theorems · Inductive type · algebraic geometry
WeierstrassCurve.Affine.Point
{R : Type r} → [CommRing R] → WeierstrassCurve.Affine R → Type rA nonsingular point on a Weierstrass curve W in affine coordinates. This is either the unique
point at infinity WeierstrassCurve.Affine.Point.zero or a nonsingular affine point
WeierstrassCurve.Affine.Point.some (x, y) satisfying the Weierstrass equation of W.
- Cited by
- 99 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 4 definitions · uses no axioms
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement · cited by 17,173
- WeierstrassCurve.Affinestatement · cited by 174
Cited by132
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Jacobian.Point.toAffinestatement · cited by 10
- WeierstrassCurve.Projective.Point.toAffinestatement · cited by 10
- WeierstrassCurve.Affine.Point.casesOnstatement and proof · cited by 9
- WeierstrassCurve.Affine.Point.sym2xstatement and proof · cited by 8
- WeierstrassCurve.Affine.Point.xRepstatement and proof · cited by 8
- WeierstrassCurve.Jacobian.Point.toAffineLiftstatement · cited by 8
- WeierstrassCurve.Projective.Point.toAffineLiftstatement · cited by 8
- WeierstrassCurve.Affine.Point.mkstatement · cited by 7
- WeierstrassCurve.Affine.Point.mapstatement and proof · cited by 6
- WeierstrassCurve.Affine.Point.toClassstatement and proof · cited by 5
- WeierstrassCurve.Jacobian.Point.toAffine_of_Z_eq_zerostatement and proof · cited by 5
- WeierstrassCurve.Jacobian.Point.toAffine_of_Z_ne_zerostatement and proof · cited by 5