Theorems · Theorem · algebraic geometry
WeierstrassCurve.Affine.evalEval_polynomialX
∀ {R : Type r} [inst : CommRing R] {W : WeierstrassCurve.Affine R} (x y : R),
Polynomial.evalEval x y W.polynomialX = W.a₁ * y - (3 * x ^ 2 + 2 * W.a₂ * x + W.a₄)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- Polynomial.evalproof · cited by 796
- WeierstrassCurve.a₁statement and proof · cited by 272
- WeierstrassCurve.a₂statement and proof · cited by 216
- WeierstrassCurve.a₄statement and proof · cited by 187
- WeierstrassCurve.Affinestatement and proof · cited by 174
- Polynomial.eval_Xproof · cited by 172
- Polynomial.eval_Cproof · cited by 145
- Polynomial.eval_mulproof · cited by 127
Cited by5
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Affine.nonsingular_iff'proof · cited by 3
- WeierstrassCurve.Jacobian.eval_polynomialX_of_Z_ne_zeroproof · cited by 1
- WeierstrassCurve.Projective.eval_polynomialX_of_Z_ne_zeroproof · cited by 1
- WeierstrassCurve.Affine.evalEval_polynomialX_zeroproof · cited by 1
- WeierstrassCurve.Affine.slope_of_Y_ne_eq_evalEvalproof · cited by 0