Theorems · Theorem · commutative algebra
MvPolynomial.constantCoeff_map
∀ {R : Type u} {S₁ : Type v} {σ : Type u_1} [inst : CommSemiring R] [inst_1 : CommSemiring S₁] (f : R →+* S₁)
(φ : MvPolynomial σ R), MvPolynomial.constantCoeff ((MvPolynomial.map f) φ) = f (MvPolynomial.constantCoeff φ)- Defined in
- Mathlib.Algebra.MvPolynomial.Eval
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 91 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement and proof · cited by 10,189
- Finsuppstatement · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- MvPolynomial.mapstatement · cited by 147
- MvPolynomial.constantCoeffstatement · cited by 46
- MvPolynomial.coeff_mapproof · cited by 13
Cited by2
Results whose statement or proof uses this declaration.
- constantCoeff_wittStructureIntproof · cited by 6
- constantCoeff_wittStructureInt_zeroproof · cited by 0