Theorems · Theorem · algebraic geometry
WeierstrassCurve.Jacobian.nonsingular_of_Z_ne_zero
∀ {F : Type u} [inst : Field F] {W : WeierstrassCurve.Jacobian F} {P : Fin 3 → F},
P 2 ≠ 0 → (W.Nonsingular P ↔ W.toAffine.Nonsingular (P 0 / P 2 ^ 2) (P 1 / P 2 ^ 3))- Cited by
- 7 results in Mathlib
- Foundations
- Depth 114 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.
Cites8
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.Jacobianstatement and proof · cited by 232
- WeierstrassCurve.Affine.Nonsingularstatement · cited by 76
- WeierstrassCurve.Jacobian.toAffinestatement · cited by 47
- WeierstrassCurve.Jacobian.Nonsingularstatement · cited by 40
- WeierstrassCurve.Jacobian.nonsingular_someproof · cited by 5
- WeierstrassCurve.Jacobian.equiv_some_of_Z_ne_zeroproof · cited by 2
- WeierstrassCurve.Jacobian.nonsingular_of_equivproof · cited by 1
Cited by7
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Jacobian.Point.toAffine_of_Z_ne_zerostatement and proof · cited by 5
- WeierstrassCurve.Jacobian.Point.toAffine_smulproof · cited by 3
- WeierstrassCurve.Jacobian.Point.toAffine_someproof · cited by 2
- WeierstrassCurve.Jacobian.Point.toAffine_addproof · cited by 1
- WeierstrassCurve.Jacobian.Point.toAffine_negproof · cited by 1
- WeierstrassCurve.Jacobian.nonsingular_iff_of_Z_ne_zeroproof · cited by 1
- WeierstrassCurve.Jacobian.Point.toAffineLift_of_Z_ne_zerostatement · cited by 0