Theorems · Theorem · algebraic geometry
WeierstrassCurve.Jacobian.X_ne_zero_of_Z_eq_zero
∀ {R : Type r} [inst : CommRing R] {W' : WeierstrassCurve.Jacobian R} [NoZeroDivisors R] {P : Fin 3 → R},
W'.Nonsingular P → P 2 = 0 → P 0 ≠ 0- Cited by
- 2 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingNoZeroDivisors
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- NoZeroDivisorsstatement and proof · cited by 545
- MonoidWithZeroproof · cited by 456
- Nat.AtLeastTwoproof · cited by 405
- zero_powproof · cited by 361
- WeierstrassCurve.a₁proof · cited by 272
- two_ne_zeroproof · cited by 251
- WeierstrassCurve.Jacobianstatement and proof · cited by 232
- WeierstrassCurve.Jacobian.Nonsingularstatement and proof · cited by 40
- OfNat.ofNat_ne_zeroproof · cited by 20
Cited by2
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Jacobian.isUnit_X_of_Z_eq_zeroproof · cited by 9
- WeierstrassCurve.Jacobian.Y_ne_zero_of_Z_eq_zeroproof · cited by 1