Theorems · Theorem · algebraic geometry
WeierstrassCurve.Jacobian.add_of_Z_eq_zero
∀ {F : Type u} [inst : Field F] {W : WeierstrassCurve.Jacobian F} {P Q : Fin 3 → F},
W.Nonsingular P → W.Nonsingular Q → P 2 = 0 → Q 2 = 0 → W.add P Q = P 0 ^ 2 • ![1, 1, 0]- Cited by
- 4 results in Mathlib
- Foundations
- Depth 106 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.
Cites9
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.Jacobianstatement and proof · cited by 232
- WeierstrassCurve.Jacobian.Nonsingularstatement and proof · cited by 40
- WeierstrassCurve.Jacobian.addstatement · cited by 20
- WeierstrassCurve.Jacobian.add_of_equivproof · cited by 6
- WeierstrassCurve.Jacobian.equiv_of_Z_eq_zeroproof · cited by 3
- WeierstrassCurve.Jacobian.dblXYZ_of_Z_eq_zeroproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Jacobian.nonsingular_addproof · cited by 1
- WeierstrassCurve.Jacobian.Point.toAffine_addproof · cited by 1
- WeierstrassCurve.Jacobian.addMap_of_Z_eq_zero_leftproof · cited by 0
- WeierstrassCurve.Jacobian.addMap_of_Z_eq_zero_rightproof · cited by 0