Theorems · Theorem · commutative algebra
MvPolynomial.coeff_map
∀ {R : Type u} {S₁ : Type v} {σ : Type u_1} [inst : CommSemiring R] [inst_1 : CommSemiring S₁] (f : R →+* S₁)
(p : MvPolynomial σ R) (m : σ →₀ ℕ), MvPolynomial.coeff m ((MvPolynomial.map f) p) = f (MvPolynomial.coeff m p)- Defined in
- Mathlib.Algebra.MvPolynomial.Eval
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 90 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.
Cites20
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 and proof · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- Finsupp.singleproof · cited by 943
- Finsupp.supportproof · cited by 828
- MvPolynomial.Xproof · cited by 552
- MvPolynomial.Cproof · cited by 400
- MvPolynomial.coeffstatement and proof · cited by 315
- MvPolynomial.mapstatement and proof · cited by 147
- RingHom.map_zeroproof · cited by 47
Cited by13
Results whose statement or proof uses this declaration.
- MvPolynomial.map_injectiveproof · cited by 19
- map_wittStructureIntproof · cited by 13
- MvPolynomial.ker_mapproof · cited by 3
- MvPolynomial.support_map_subsetproof · cited by 3
- MvPolynomial.constantCoeff_mapproof · cited by 2
- MvPolynomial.C_dvd_iff_map_hom_eq_zeroproof · cited by 1
- MvPolynomial.support_map_of_injectiveproof · cited by 1
- TensorProduct.toIntegralClosure_mvPolynomial_bijectiveproof · cited by 1
- MvPolynomial.map_mapRange_eq_iffproof · cited by 1
- MvPolynomial.mem_image_comap_C_basicOpenproof · cited by 1
- MvPolynomial.IsHomogeneous.of_mapproof · cited by 0
- MvPolynomial.map_surjective_iffproof · cited by 0