Theorems · Theorem · algebraic geometry
WeierstrassCurve.Jacobian.equation_of_Z_eq_zero
∀ {R : Type r} [inst : CommRing R] {W' : WeierstrassCurve.Jacobian R} {P : Fin 3 → R},
P 2 = 0 → (W'.Equation P ↔ P 1 ^ 2 = P 0 ^ 3)- Cited by
- 7 results in Mathlib
- Foundations
- Depth 99 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.
Cites14
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
- MonoidWithZeroproof · cited by 456
- Nat.AtLeastTwoproof · cited by 405
- zero_powproof · cited by 361
- WeierstrassCurve.a₁proof · cited by 272
- WeierstrassCurve.Jacobianstatement and proof · cited by 232
- WeierstrassCurve.a₂proof · cited by 216
- WeierstrassCurve.a₃proof · cited by 210
- WeierstrassCurve.a₄proof · cited by 187
- WeierstrassCurve.a₆proof · cited by 153
Cited by7
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Jacobian.neg_of_Z_eq_zeroproof · cited by 3
- WeierstrassCurve.Jacobian.X_ne_zero_of_Z_eq_zeroproof · cited by 2
- WeierstrassCurve.Jacobian.dblX_of_Z_eq_zeroproof · cited by 2
- WeierstrassCurve.Jacobian.negDblY_of_Z_eq_zeroproof · cited by 1
- WeierstrassCurve.Jacobian.negAddY_of_Z_eq_zero_leftproof · cited by 1
- WeierstrassCurve.Jacobian.negAddY_of_Z_eq_zero_rightproof · cited by 1
- WeierstrassCurve.Jacobian.Y_ne_zero_of_Z_eq_zeroproof · cited by 1