Theorems · Definition · algebraic geometry
WeierstrassCurve.Affine.negY
{R : Type r} → [CommRing R] → WeierstrassCurve.Affine R → R → R → RThe Y-coordinate of -(x, y) for a nonsingular affine point (x, y) on a Weierstrass curve
W.
This depends on W, and has argument order: x, y.
- Cited by
- 56 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- WeierstrassCurve.a₁proof · cited by 272
- WeierstrassCurve.a₃proof · cited by 210
- WeierstrassCurve.Affinestatement and proof · cited by 174
Cited by61
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Affine.slopeproof · cited by 54
- WeierstrassCurve.Affine.addYproof · cited by 30
- WeierstrassCurve.Affine.CoordinateRing.XYIdeal'proof · cited by 7
- WeierstrassCurve.Affine.nonsingular_addstatement and proof · cited by 5
- WeierstrassCurve.Affine.nonsingular_negstatement and proof · cited by 4
- WeierstrassCurve.Affine.nonsingular_negAddstatement and proof · cited by 4
- WeierstrassCurve.Jacobian.negY_of_Z_ne_zerostatement and proof · cited by 4
- WeierstrassCurve.Projective.negY_of_Z_ne_zerostatement and proof · cited by 4
- WeierstrassCurve.Projective.neg_of_Z_ne_zerostatement and proof · cited by 3
- WeierstrassCurve.Affine.Y_eq_of_Y_nestatement and proof · cited by 3
- WeierstrassCurve.Affine.addPolynomial_slopestatement and proof · cited by 3
- WeierstrassCurve.Affine.Point.add_of_Y_eqstatement and proof · cited by 3