Theorems · Theorem · algebraic geometry
WeierstrassCurve.Projective.addXYZ_of_Z_eq_zero_right
∀ {R : Type r} [inst : CommRing R] {W' : WeierstrassCurve.Projective R} [NoZeroDivisors R] {P Q : Fin 3 → R},
W'.Equation Q → Q 2 = 0 → W'.addXYZ P Q = -(Q 1 ^ 2 * P 2) • P- Cited by
- 1 results in Mathlib
- Foundations
- Depth 103 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.
Cites13
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
- Matrix.vecConsproof · cited by 852
- Matrix.vecEmptyproof · cited by 832
- NoZeroDivisorsstatement and proof · cited by 545
- WeierstrassCurve.Projectivestatement and proof · cited by 244
- WeierstrassCurve.Projective.Equationstatement and proof · cited by 88
- WeierstrassCurve.Projective.addZproof · cited by 29
- WeierstrassCurve.Projective.addYproof · cited by 19
- WeierstrassCurve.Projective.addXYZstatement · cited by 15
- WeierstrassCurve.Projective.smul_fin3proof · cited by 14
- WeierstrassCurve.Projective.addX_of_Z_eq_zero_rightproof · cited by 2
- WeierstrassCurve.Projective.addZ_of_Z_eq_zero_rightproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Projective.add_of_Z_eq_zero_rightproof · cited by 3