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Theorems · Theorem · commutative algebra

MvPolynomial.map_X

∀ {R : Type u} {S₁ : Type v} {σ : Type u_1} [inst : CommSemiring R] [inst_1 : CommSemiring S₁] (f : R →+* S₁) (n : σ),
  (MvPolynomial.map f) (MvPolynomial.X n) = MvPolynomial.X n
Defined in
Mathlib.Algebra.MvPolynomial.Eval
Cited by
42 results in Mathlib
Foundations
Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommSemiringCommSemiring

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MvPolynomial.coeff_map · cited by 13MvPolynomial.coeff_mapMvPolynomial.eval_map · cited by 9MvPolynomial.eval_mapMvPolynomial.pderiv_map · cited by 8MvPolynomial.pderiv_mapMvPolynomial.map_rename · cited by 8MvPolynomial.map_renameWeierstrassCurve.Jacobian.map_polynomial · cited by 6Jacobian.map_polynomialWeierstrassCurve.Projective.map_polynomial · cited by 6Projective.map_polynomialMvPolynomial.mem_range_map_iff_coeffs_subset · cited by 5MvPolynomial.mem_range_ma…MvPolynomial.transcendental_supported_polynomial_aeval_X · cited by 4MvPolynomial.transcendent…AlgebraicIndependent.restrictScalars · cited by 3AlgebraicIndependent.rest…MvPolynomial.eval₂_comp_right · cited by 3MvPolynomial.eval₂_comp_r…MvPolynomial.map_expand · cited by 3MvPolynomial.map_expandAlgebraicIndependent.sumElim_iff · cited by 2AlgebraicIndependent.sumE…LinearMap.polyCharpolyAux_baseChange · cited by 2LinearMap.polyCharpolyAux…Algebra.FinitePresentation.of_restrict_scalars_finitePresentation · cited by 2FinitePresentation.of_res…MvPolynomial.map_eq_eval₂Hom_C_comp · cited by 2MvPolynomial.map_eq_eval₂…DFunLike.coe · cited by 62936DFunLike.coeCommSemiring · cited by 10911CommSemiringRingHom · cited by 10189RingHomFinsupp · cited by 5255FinsuppMvPolynomial · cited by 2140MvPolynomialFinsupp.single · cited by 943Finsupp.singlemap_one · cited by 861map_oneMvPolynomial.X · cited by 552MvPolynomial.XMvPolynomial.monomial · cited by 253MvPolynomial.monomialMvPolynomial.map · cited by 147MvPolynomial.mapMvPolynomial.map_monomial · cited by 7MvPolynomial.map_monomialMvPolynomial.map_XCITED BYCITES

Cites11

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Cited by42

Results whose statement or proof uses this declaration.