Theorems · Theorem · algebraic geometry
WeierstrassCurve.Jacobian.neg_of_Z_ne_zero
∀ {F : Type u} [inst : Field F] {W : WeierstrassCurve.Jacobian F} {P : Fin 3 → F},
P 2 ≠ 0 → W.neg P = P 2 • ![P 0 / P 2 ^ 2, W.toAffine.negY (P 0 / P 2 ^ 2) (P 1 / P 2 ^ 3), 1]- Cited by
- 3 results in Mathlib
- Foundations
- Depth 48 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.
Cites13
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
- mul_oneproof · cited by 3,885
- Matrix.vecConsstatement and proof · cited by 852
- Matrix.vecEmptystatement and proof · cited by 832
- WeierstrassCurve.Jacobianstatement and proof · cited by 232
- pow_ne_zeroproof · cited by 208
- mul_div_cancel₀proof · cited by 77
- WeierstrassCurve.Affine.negYstatement and proof · cited by 56
- WeierstrassCurve.Jacobian.negYproof · cited by 56
- WeierstrassCurve.Jacobian.toAffinestatement and proof · cited by 47
- WeierstrassCurve.Jacobian.negstatement · cited by 19
- WeierstrassCurve.Jacobian.smul_fin3proof · cited by 9
Cited by3
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Jacobian.nonsingular_negproof · cited by 2
- WeierstrassCurve.Jacobian.Point.toAffine_negproof · cited by 1
- WeierstrassCurve.Jacobian.negMap_of_Z_ne_zeroproof · cited by 0