Theorems · Definition · algebraic geometry
WeierstrassCurve.Projective.addZ
{R : Type r} → [CommRing R] → WeierstrassCurve.Projective R → (Fin 3 → R) → (Fin 3 → R) → RThe Z-coordinate of a representative of P + Q for two distinct projective point
representatives P and Q on a Weierstrass curve.
If the representatives of P and Q are equal, then this returns the value 0.
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- 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
Cited by31
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Projective.addYproof · cited by 19
- WeierstrassCurve.Projective.addXYZproof · cited by 15
- WeierstrassCurve.Projective.isUnit_addZ_of_X_nestatement · cited by 4
- WeierstrassCurve.Projective.addZ_eq'statement · cited by 3
- WeierstrassCurve.Projective.add_of_X_nestatement and proof · cited by 3
- WeierstrassCurve.Projective.map_addXYZproof · cited by 2
- WeierstrassCurve.Projective.map_addYproof · cited by 2
- WeierstrassCurve.Projective.map_addZstatement · cited by 2
- WeierstrassCurve.Projective.addX_of_Z_ne_zerostatement and proof · cited by 2
- WeierstrassCurve.Projective.addZ_eqstatement and proof · cited by 2
- WeierstrassCurve.Projective.addZ_ne_zero_of_X_nestatement · cited by 2
- WeierstrassCurve.Projective.addZ_negstatement · cited by 2