Theorems · Theorem · algebraic geometry
WeierstrassCurve.Projective.addZ_eq
∀ {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 → W.addZ P Q = (P 0 * Q 2 - Q 0 * P 2) ^ 3 / (P 2 * Q 2)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 99 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.
Cites7
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
- WeierstrassCurve.Projectivestatement and proof · cited by 244
- mul_ne_zeroproof · cited by 178
- WeierstrassCurve.Projective.Equationstatement and proof · cited by 88
- mul_div_cancel_right₀proof · cited by 70
- WeierstrassCurve.Projective.addZstatement and proof · cited by 29
- WeierstrassCurve.Projective.addZ_eq'proof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Projective.addX_of_Z_ne_zeroproof · cited by 2
- WeierstrassCurve.Projective.negAddY_of_Z_ne_zeroproof · cited by 1