Theorems · Theorem · algebraic geometry

WeierstrassCurve.Jacobian.polynomialX_eq

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

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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Cites28

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
one_ne_zeroproof · cited by 885
map_subproof · cited by 565

Cited by1

Results whose statement or proof uses this declaration.

WeierstrassCurve.Jacobian.eval_polynomialXproof · cited by 4