Theorems · Theorem · commutative algebra
MvPolynomial.coeff_rename_embDomain
∀ {σ : Type u_1} {τ : Type u_2} {R : Type u_4} [inst : CommSemiring R] (f : σ ↪ τ) (φ : MvPolynomial σ R) (d : σ →₀ ℕ),
MvPolynomial.coeff (Finsupp.embDomain f d) ((MvPolynomial.rename ⇑f) φ) = MvPolynomial.coeff d φ- Defined in
- Mathlib.Algebra.MvPolynomial.Rename
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 89 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.
Cites12
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
- Finsuppstatement and proof · cited by 5,255
- AlgHomstatement · cited by 3,236
- MvPolynomialstatement and proof · cited by 2,140
- Function.Embeddingstatement and proof · cited by 988
- MvPolynomial.coeffstatement and proof · cited by 315
- MvPolynomial.renamestatement and proof · cited by 168
- Function.Embedding.injectiveproof · cited by 111
- Finsupp.embDomainstatement · cited by 69
- Finsupp.embDomain_eq_mapDomainproof · cited by 13
- MvPolynomial.coeff_rename_mapDomainproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- MvPolynomial.isNilpotent_iffproof · cited by 0