Theorems · Theorem · commutative algebra
MvPolynomial.aeval_monomial
∀ {R : Type u} {S₁ : Type v} {σ : Type u_1} [inst : CommSemiring R] [inst_1 : CommSemiring S₁] [inst_2 : Algebra R S₁]
(g : σ → S₁) (d : σ →₀ ℕ) (r : R),
(MvPolynomial.aeval g) ((MvPolynomial.monomial d) r) = (algebraMap R S₁) r * d.prod fun i k => g i ^ k- Defined in
- Mathlib.Algebra.MvPolynomial.Eval
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- RingHomstatement · cited by 10,189
- Finsuppstatement and proof · cited by 5,255
- Algebra.algebraMapstatement and proof · cited by 4,706
- AlgHomstatement · cited by 3,236
- MvPolynomialstatement · cited by 2,140
- MvPolynomial.aevalstatement · cited by 298
- MvPolynomial.monomialstatement · cited by 253
Cited by11
Results whose statement or proof uses this declaration.
- aeval_wittPolynomialproof · cited by 3
- Algebra.Generators.H1Cotangent.δAux_mulproof · cited by 2
- Algebra.Generators.Hom.toAlgHom_monomialproof · cited by 2
- MvPowerSeries.substAlgHom_monomialproof · cited by 2
- MvPolynomial.esymmAlgHomMonomial_singleproof · cited by 1
- WittVector.pow_dvd_ghostComponent_of_dvd_coeffproof · cited by 1
- MvPolynomial.killCompl_monomial_eq_zero_of_notMem_rangeproof · cited by 1
- Polynomial.homogenize_eq_of_isHomogeneousproof · cited by 1
- MvPolynomial.optionEquivLeft_monomialproof · cited by 1
- MvPolynomial.aeval_ite_mem_eq_selfproof · cited by 1
- Algebra.Generators.ofComp_toAlgHom_monomial_sumElimproof · cited by 1