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.
Cites11
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
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement and proof · cited by 10,189
- Finsuppstatement · cited by 5,255
- MvPolynomialstatement · cited by 2,140
- Finsupp.singleproof · cited by 943
- map_oneproof · cited by 861
- MvPolynomial.Xstatement · cited by 552
- MvPolynomial.monomialproof · cited by 253
- MvPolynomial.mapstatement · cited by 147
- MvPolynomial.map_monomialproof · cited by 7
Cited by42
Results whose statement or proof uses this declaration.
- MvPolynomial.coeff_mapproof · cited by 13
- MvPolynomial.eval_mapproof · cited by 9
- MvPolynomial.pderiv_mapproof · cited by 8
- MvPolynomial.map_renameproof · cited by 8
- WeierstrassCurve.Jacobian.map_polynomialproof · cited by 6
- WeierstrassCurve.Projective.map_polynomialproof · cited by 6
- MvPolynomial.mem_range_map_iff_coeffs_subsetproof · cited by 5
- MvPolynomial.transcendental_supported_polynomial_aeval_Xproof · cited by 4
- AlgebraicIndependent.restrictScalarsproof · cited by 3
- MvPolynomial.eval₂_comp_rightproof · cited by 3
- MvPolynomial.map_expandproof · cited by 3
- AlgebraicIndependent.sumElim_iffproof · cited by 2