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Theorems · Theorem · algebraic geometry

WeierstrassCurve.Projective.dblXYZ_of_Z_eq_zero

∀ {R : Type r} [inst : CommRing R] {W' : WeierstrassCurve.Projective R} [NoZeroDivisors R] {P : Fin 3 → R},
  W'.Equation P → P 2 = 0 → W'.dblXYZ P = P 1 ^ 4 • ![0, 1, 0]
Defined in
Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Formula
Cited by
1 results in Mathlib
Foundations
Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingNoZeroDivisors
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Around this declaration

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

WeierstrassCurve.Projective.add_of_Z_eq_zero · cited by 4Projective.add_of_Z_eq_ze…CommRing · cited by 17173CommRingmul_one · cited by 3885mul_oneMulZeroClass.mul_zero · cited by 2091MulZeroClass.mul_zeroMatrix.vecCons · cited by 852Matrix.vecConsMatrix.vecEmpty · cited by 832Matrix.vecEmptyNoZeroDivisors · cited by 545NoZeroDivisorsWeierstrassCurve.Projective · cited by 244WeierstrassCurve.Projecti…WeierstrassCurve.Projective.Equation · cited by 88Projective.EquationWeierstrassCurve.Projective.dblZ · cited by 26Projective.dblZWeierstrassCurve.Projective.dblXYZ · cited by 14Projective.dblXYZWeierstrassCurve.Projective.smul_fin3 · cited by 14Projective.smul_fin3WeierstrassCurve.Projective.dblY · cited by 13Projective.dblYWeierstrassCurve.Projective.dblX_of_Z_eq_zero · cited by 2Projective.dblX_of_Z_eq_z…WeierstrassCurve.Projective.dblZ_of_Z_eq_zero · cited by 2Projective.dblZ_of_Z_eq_z…WeierstrassCurve.Projective.dblY_of_Z_eq_zero · cited by 1Projective.dblY_of_Z_eq_z…Projective.dblXYZ_of_Z_eq_zeroCITED BYCITES

Cites15

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Cited by1

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