Theorems · Theorem · algebraic geometry
WeierstrassCurve.Projective.addZ_of_Z_eq_zero_left
∀ {R : Type r} [inst : CommRing R] {W' : WeierstrassCurve.Projective R} [NoZeroDivisors R] {P Q : Fin 3 → R},
W'.Equation P → P 2 = 0 → W'.addZ P Q = P 1 ^ 2 * Q 2 * Q 2- Cited by
- 2 results in Mathlib
- Foundations
- Depth 101 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.
Cites11
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
- Nat.cast_zeroproof · cited by 1,870
- NoZeroDivisorsstatement and proof · cited by 545
- WeierstrassCurve.a₁proof · cited by 272
- WeierstrassCurve.Projectivestatement and proof · cited by 244
- WeierstrassCurve.a₂proof · cited by 216
- WeierstrassCurve.a₃proof · cited by 210
- WeierstrassCurve.a₄proof · cited by 187
- WeierstrassCurve.Projective.Equationstatement and proof · cited by 88
- WeierstrassCurve.Projective.addZstatement · cited by 29
- WeierstrassCurve.Projective.X_eq_zero_of_Z_eq_zeroproof · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Projective.addY_of_Z_eq_zero_leftproof · cited by 1
- WeierstrassCurve.Projective.addXYZ_of_Z_eq_zero_leftproof · cited by 1