Theorems · Theorem · commutative algebra
MvPolynomial.map_expand
∀ {σ : Type u_1} {R : Type u_3} {S : Type u_4} [inst : CommSemiring R] [inst_1 : CommSemiring S] (p : ℕ) (f : R →+* S)
(φ : MvPolynomial σ R),
(MvPolynomial.map f) ((MvPolynomial.expand p) φ) = (MvPolynomial.expand p) ((MvPolynomial.map f) φ)- Defined in
- Mathlib.Algebra.MvPolynomial.Expand
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 100 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.
Cites13
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
- AlgHomstatement · cited by 3,236
- MvPolynomialstatement and proof · cited by 2,140
- MvPolynomial.Xproof · cited by 552
- map_powproof · cited by 503
- MvPolynomial.mapstatement and proof · cited by 147
- MvPolynomial.bind₁proof · cited by 70
- MvPolynomial.expandstatement · cited by 44
- MvPolynomial.map_Xproof · cited by 42
Cited by3
Results whose statement or proof uses this declaration.
- MvPowerSeries.map_frobenius_expandproof · cited by 1
- C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sumproof · cited by 1
- bind₁_rename_expand_wittPolynomialproof · cited by 1