Theorems · Theorem · algebraic geometry

WeierstrassCurve.Jacobian.polynomialZ_eq

∀ {R : Type r} [inst : CommRing R] {W' : WeierstrassCurve.Jacobian R},
  W'.polynomialZ =
    MvPolynomial.C W'.a₁ * MvPolynomial.X 0 * MvPolynomial.X 1 +
        MvPolynomial.C (3 * W'.a₃) * MvPolynomial.X 1 * MvPolynomial.X 2 ^ 2 -
      (MvPolynomial.C (2 * W'.a₂) * MvPolynomial.X 0 ^ 2 * MvPolynomial.X 2 +
          MvPolynomial.C (4 * W'.a₄) * MvPolynomial.X 0 * MvPolynomial.X 2 ^ 3 +
        MvPolynomial.C (6 * W'.a₆) * MvPolynomial.X 2 ^ 5)

Defined in: Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing

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Cites27

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

DFunLike.coestatement and proof · cited by 62,936
CommRingstatement and proof · cited by 17,173
CommSemiringproof · cited by 10,911
RingHomstatement · cited by 10,189
Finsuppstatement · cited by 5,255
Nat.cast_oneproof · cited by 2,501
MvPolynomialstatement and proof · cited by 2,140
Nat.cast_zeroproof · cited by 1,870
map_mulproof · cited by 1,137
map_addproof · cited by 964
map_subproof · cited by 565
MvPolynomial.Xstatement and proof · cited by 552

Cited by1

Results whose statement or proof uses this declaration.

WeierstrassCurve.Jacobian.eval_polynomialZproof · cited by 2