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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.

MvPolynomial.eval_map · cited by 9MvPolynomial.eval_mapWeierstrassCurve.Projective.eval_polynomialX · cited by 6Projective.eval_polynomia…WeierstrassCurve.Projective.eval_polynomialY · cited by 4Projective.eval_polynomia…WeierstrassCurve.Jacobian.eval_polynomialX · cited by 4Jacobian.eval_polynomialXWeierstrassCurve.Jacobian.eval_polynomialY · cited by 4Jacobian.eval_polynomialYWeierstrassCurve.Jacobian.eval_polynomial · cited by 3Jacobian.eval_polynomialWeierstrassCurve.Projective.eval_polynomial · cited by 3Projective.eval_polynomialWeierstrassCurve.Projective.eval_polynomialZ · cited by 2Projective.eval_polynomia…WeierstrassCurve.Jacobian.eval_polynomialZ · cited by 2Jacobian.eval_polynomialZWeierstrassCurve.addSubMapCoeff_condition · cited by 2WeierstrassCurve.addSubMa…MvPolynomial.expand_zero · cited by 2MvPolynomial.expand_zeroIdeal.span_eq_map_homogeneousSubmodule · cited by 2Ideal.span_eq_map_homogen…Matrix.eval_det_mvPolynomialX · cited by 1Matrix.eval_det_mvPolynom…MvPolynomial.combinatorial_nullstellensatz_exists_linearCombination · cited by 1MvPolynomial.combinatoria…MvPolynomial.eval_indicator_apply_eq_one · cited by 1MvPolynomial.eval_indicat…DFunLike.coe · cited by 62936DFunLike.coeRingHom.id · cited by 18349RingHom.idCommSemiring · cited by 10911CommSemiringRingHom · cited by 10189RingHomFinsupp · cited by 5255FinsuppMvPolynomial · cited by 2140MvPolynomialMvPolynomial.X · cited by 552MvPolynomial.XMvPolynomial.eval · cited by 157MvPolynomial.evalMvPolynomial.eval₂_X · cited by 36MvPolynomial.eval₂_XMvPolynomial.eval_XCITED BYCITES

Cites9

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Cited by23

Results whose statement or proof uses this declaration.