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Theorems · Definition · algebraic geometry

WeierstrassCurve.Projective.addZ

{R : Type r} → [CommRing R] → WeierstrassCurve.Projective R → (Fin 3 → R) → (Fin 3 → R) → R

The 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.

Defined in
Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Formula
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.

WeierstrassCurve.Projective.addY · cited by 19Projective.addYWeierstrassCurve.Projective.addXYZ · cited by 15Projective.addXYZWeierstrassCurve.Projective.isUnit_addZ_of_X_ne · cited by 4Projective.isUnit_addZ_of…WeierstrassCurve.Projective.addZ_eq' · cited by 3Projective.addZ_eq'WeierstrassCurve.Projective.add_of_X_ne · cited by 3Projective.add_of_X_neWeierstrassCurve.Projective.map_addXYZ · cited by 2Projective.map_addXYZWeierstrassCurve.Projective.map_addY · cited by 2Projective.map_addYWeierstrassCurve.Projective.map_addZ · cited by 2Projective.map_addZWeierstrassCurve.Projective.addX_of_Z_ne_zero · cited by 2Projective.addX_of_Z_ne_z…WeierstrassCurve.Projective.addZ_eq · cited by 2Projective.addZ_eqWeierstrassCurve.Projective.addZ_ne_zero_of_X_ne · cited by 2Projective.addZ_ne_zero_o…WeierstrassCurve.Projective.addZ_neg · cited by 2Projective.addZ_negWeierstrassCurve.Projective.addZ_of_X_eq · cited by 2Projective.addZ_of_X_eqWeierstrassCurve.Projective.addZ_of_Z_eq_zero_left · cited by 2Projective.addZ_of_Z_eq_z…WeierstrassCurve.Projective.addZ_of_Z_eq_zero_right · cited by 2Projective.addZ_of_Z_eq_z…CommRing · cited by 17173CommRingWeierstrassCurve.a₁ · cited by 272WeierstrassCurve.a₁WeierstrassCurve.Projective · cited by 244WeierstrassCurve.Projecti…WeierstrassCurve.a₂ · cited by 216WeierstrassCurve.a₂WeierstrassCurve.a₃ · cited by 210WeierstrassCurve.a₃WeierstrassCurve.a₄ · cited by 187WeierstrassCurve.a₄Projective.addZCITED BYCITES

Cites6

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Cited by31

Results whose statement or proof uses this declaration.