Theorems · Theorem · algebraic geometry

WeierstrassCurve.Projective.dblX_of_Y_eq

∀ {R : Type r} [inst : CommRing R] {W' : WeierstrassCurve.Projective R} [NoZeroDivisors R] {P Q : Fin 3 → R},
  W'.Equation P →
    P 2 ≠ 0 → Q 2 ≠ 0 → P 0 * Q 2 = Q 0 * P 2 → P 1 * Q 2 = Q 1 * P 2 → P 1 * Q 2 = W'.negY Q * P 2 → W'.dblX P = 0

Defined in: Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Formula
Cited by: 2 results in Mathlib
Foundations: Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing NoZeroDivisors

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Cites15

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

DFunLike.coeproof · cited by 62,936
CommRingstatement and proof · cited by 17,173
Nat.cast_zeroproof · cited by 1,870
NoZeroDivisorsstatement and proof · cited by 545
WeierstrassCurve.a₁proof · cited by 272
WeierstrassCurve.Projectivestatement and proof · cited by 244
WeierstrassCurve.a₂proof · cited by 216
MvPolynomial.evalproof · cited by 157
WeierstrassCurve.Projective.Equationstatement and proof · cited by 88
WeierstrassCurve.Projective.negYstatement and proof · cited by 56
WeierstrassCurve.Projective.polynomialXproof · cited by 19
WeierstrassCurve.Projective.dblXstatement · cited by 17

Cited by2

Results whose statement or proof uses this declaration.

WeierstrassCurve.Projective.dblY_of_Y_eq'proof · cited by 1
WeierstrassCurve.Projective.dblXYZ_of_Y_eqproof · cited by 1