Theorems · Theorem · commutative algebra
MvPolynomial.coeff_rename_mapDomain
∀ {σ : Type u_1} {τ : Type u_2} {R : Type u_4} [inst : CommSemiring R] (f : σ → τ),
Function.Injective f →
∀ (φ : MvPolynomial σ R) (d : σ →₀ ℕ),
MvPolynomial.coeff (Finsupp.mapDomain f d) ((MvPolynomial.rename f) φ) = MvPolynomial.coeff d φ- Defined in
- Mathlib.Algebra.MvPolynomial.Rename
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 88 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.
Cites16
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
- AddCommMonoidproof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement and proof · cited by 5,255
- AlgHomstatement · cited by 3,236
- MvPolynomialstatement and proof · cited by 2,140
- map_addproof · cited by 964
- MvPolynomial.coeffstatement and proof · cited by 315
- MvPolynomial.monomialproof · cited by 253
- Finsupp.mapDomainstatement and proof · cited by 168
- MvPolynomial.renamestatement and proof · cited by 168
- MvPolynomial.coeff_monomialproof · cited by 32
Cited by6
Results whose statement or proof uses this declaration.
- MvPolynomial.IsHomogeneous.rename_isHomogeneous_iffproof · cited by 2
- MvPolynomial.isUnit_iffproof · cited by 2
- MvPolynomial.coeff_toPolynomialAdjoinImageCompl_ne_zeroproof · cited by 2
- MvPolynomial.IsSymmetric.antitone_supDegreeproof · cited by 1
- MvPolynomial.isIntegral_iff_isIntegral_coeffproof · cited by 1
- MvPolynomial.coeff_rename_embDomainproof · cited by 1