Theorems · Theorem · commutative algebra
MvPolynomial.monomial_eq
∀ {R : Type u} {σ : Type u_1} {a : R} {s : σ →₀ ℕ} [inst : CommSemiring R],
(MvPolynomial.monomial s) a = MvPolynomial.C a * s.prod fun n e => MvPolynomial.X n ^ e- Defined in
- Mathlib.Algebra.MvPolynomial.Basic
- Cited by
- 20 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.
Cites14
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
- RingHom.idstatement · cited by 18,349
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- RingHomstatement · cited by 10,189
- Finsuppstatement and proof · cited by 5,255
- MvPolynomialstatement · cited by 2,140
- Finsupp.singleproof · cited by 943
- MvPolynomial.Xstatement · cited by 552
- MvPolynomial.Cstatement and proof · cited by 400
- MvPolynomial.monomialstatement and proof · cited by 253
- Finsupp.prodstatement and proof · cited by 231
Cited by20
Results whose statement or proof uses this declaration.
- wittPolynomial_eq_sum_C_mul_X_powproof · cited by 8
- MvPolynomial.finSuccEquiv_coeff_coeffproof · cited by 5
- MvPolynomial.bind₁_monomialproof · cited by 3
- MvPowerSeries.monomial_one_eqproof · cited by 3
- MvPolynomial.expand_monomialproof · cited by 3
- Algebra.Generators.ofComp_kerCompPreimageproof · cited by 2
- MvPolynomial.coeff_X_powproof · cited by 2
- MvPolynomial.uniqueAlgEquiv_symm_monomialproof · cited by 1
- MvPolynomial.bind₂_monomialproof · cited by 1
- Polynomial.homogenize_eq_of_isHomogeneousproof · cited by 1
- MvPolynomial.aeval_ite_mem_eq_selfproof · cited by 1
- Algebra.Generators.ofComp_toAlgHom_monomial_sumElimproof · cited by 1