Theorems · Theorem · algebraic geometry
WeierstrassCurve.Projective.add_of_Y_ne
∀ {F : Type u} [inst : Field F] {W : WeierstrassCurve.Projective F} {P Q : Fin 3 → F},
W.Equation P →
W.Equation Q →
P 2 ≠ 0 →
Q 2 ≠ 0 →
P 0 * Q 2 = Q 0 * P 2 → P 1 * Q 2 ≠ Q 1 * P 2 → W.add P Q = WeierstrassCurve.Projective.addU P Q • ![0, 1, 0]- Cited by
- 3 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Matrix.vecConsstatement and proof · cited by 852
- Matrix.vecEmptystatement and proof · cited by 832
- WeierstrassCurve.Projectivestatement and proof · cited by 244
- WeierstrassCurve.Projective.Equationstatement and proof · cited by 88
- WeierstrassCurve.Projective.addstatement · cited by 20
- WeierstrassCurve.Projective.addUstatement and proof · cited by 10
- WeierstrassCurve.Projective.add_of_not_equivproof · cited by 6
- WeierstrassCurve.Projective.addXYZ_of_X_eqproof · cited by 1
- WeierstrassCurve.Projective.not_equiv_of_Y_neproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Projective.Point.toAffine_addproof · cited by 1
- WeierstrassCurve.Projective.nonsingular_addproof · cited by 1
- WeierstrassCurve.Projective.addMap_of_Y_eqproof · cited by 0