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Theorems · Definition · algebraic geometry

WeierstrassCurve.Projective.addY

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

The Y-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
19 results in Mathlib
Foundations
Depth 32 from the axioms · uses propext
Assumes
CommRing

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

WeierstrassCurve.Projective.addXYZ · cited by 15Projective.addXYZWeierstrassCurve.Projective.map_addXYZ · cited by 2Projective.map_addXYZWeierstrassCurve.Projective.map_addY · cited by 2Projective.map_addYWeierstrassCurve.Projective.addXYZ_Y · cited by 1Projective.addXYZ_YWeierstrassCurve.Projective.addXYZ_of_X_eq · cited by 1Projective.addXYZ_of_X_eqWeierstrassCurve.Projective.addXYZ_of_Z_eq_zero_left · cited by 1Projective.addXYZ_of_Z_eq…WeierstrassCurve.Projective.addXYZ_of_Z_eq_zero_right · cited by 1Projective.addXYZ_of_Z_eq…WeierstrassCurve.Projective.addXYZ_of_Z_ne_zero · cited by 1Projective.addXYZ_of_Z_ne…WeierstrassCurve.Projective.addXYZ_smul · cited by 1Projective.addXYZ_smulWeierstrassCurve.Projective.addY_neg · cited by 1Projective.addY_negWeierstrassCurve.Projective.addY_of_X_eq · cited by 1Projective.addY_of_X_eqWeierstrassCurve.Projective.addY_of_X_eq' · cited by 1Projective.addY_of_X_eq'WeierstrassCurve.Projective.addY_of_Z_eq_zero_left · cited by 1Projective.addY_of_Z_eq_z…WeierstrassCurve.Projective.addY_of_Z_eq_zero_right · cited by 1Projective.addY_of_Z_eq_z…WeierstrassCurve.Projective.addY_of_Z_ne_zero · cited by 1Projective.addY_of_Z_ne_z…CommRing · cited by 17173CommRingMatrix.vecCons · cited by 852Matrix.vecConsMatrix.vecEmpty · cited by 832Matrix.vecEmptyWeierstrassCurve.Projective · cited by 244WeierstrassCurve.Projecti…WeierstrassCurve.Projective.negY · cited by 56Projective.negYWeierstrassCurve.Projective.addZ · cited by 29Projective.addZWeierstrassCurve.Projective.addX · cited by 21Projective.addXWeierstrassCurve.Projective.negAddY · cited by 18Projective.negAddYProjective.addYCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by20

Results whose statement or proof uses this declaration.