Theorems · Theorem · commutative algebra
MvPolynomial.eval_X
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] {f : σ → R} (n : σ),
(MvPolynomial.eval f) (MvPolynomial.X n) = f n- Defined in
- Mathlib.Algebra.MvPolynomial.Eval
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idproof · cited by 18,349
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Finsuppstatement · cited by 5,255
- MvPolynomialstatement · cited by 2,140
- MvPolynomial.Xstatement · cited by 552
- MvPolynomial.evalstatement · cited by 157
- MvPolynomial.eval₂_Xproof · cited by 36
Cited by23
Results whose statement or proof uses this declaration.
- MvPolynomial.eval_mapproof · cited by 9
- WeierstrassCurve.Projective.eval_polynomialXproof · cited by 6
- WeierstrassCurve.Projective.eval_polynomialYproof · cited by 4
- WeierstrassCurve.Jacobian.eval_polynomialXproof · cited by 4
- WeierstrassCurve.Jacobian.eval_polynomialYproof · cited by 4
- WeierstrassCurve.Jacobian.eval_polynomialproof · cited by 3
- WeierstrassCurve.Projective.eval_polynomialproof · cited by 3
- WeierstrassCurve.Projective.eval_polynomialZproof · cited by 2
- WeierstrassCurve.Jacobian.eval_polynomialZproof · cited by 2
- WeierstrassCurve.addSubMapCoeff_conditionproof · cited by 2
- MvPolynomial.expand_zeroproof · cited by 2
- Ideal.span_eq_map_homogeneousSubmoduleproof · cited by 2