Theorems · Theorem · algebraic geometry
WeierstrassCurve.Jacobian.nonsingular_of_Z_eq_zero
∀ {R : Type r} [inst : CommRing R] {W' : WeierstrassCurve.Jacobian R} {P : Fin 3 → R},
P 2 = 0 → (W'.Nonsingular P ↔ W'.Equation P ∧ (3 * P 0 ^ 2 ≠ 0 ∨ 2 * P 1 ≠ 0 ∨ W'.a₁ * P 0 * P 1 ≠ 0))- Cited by
- 2 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- add_zeroproof · cited by 2,707
- MulZeroClass.mul_zeroproof · cited by 2,091
- sub_zeroproof · cited by 938
- MonoidWithZeroproof · cited by 456
- Nat.AtLeastTwoproof · cited by 405
- zero_powproof · cited by 361
- zero_subproof · cited by 335
- WeierstrassCurve.a₁statement and proof · cited by 272
- WeierstrassCurve.Jacobianstatement and proof · cited by 232
- WeierstrassCurve.a₂proof · cited by 216
- WeierstrassCurve.a₃proof · cited by 210
Cited by2
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Jacobian.X_ne_zero_of_Z_eq_zeroproof · cited by 2
- WeierstrassCurve.Jacobian.Y_ne_zero_of_Z_eq_zeroproof · cited by 1