Theorems · Definition · commutative algebra
MvPolynomial.coeff
{R : Type u} → {σ : Type u_1} → [inst : CommSemiring R] → (σ →₀ ℕ) → MvPolynomial σ R → RThe coefficient of the monomial m in the multi-variable polynomial p.
- Defined in
- Mathlib.Algebra.MvPolynomial.Basic
- Cited by
- 315 results in Mathlib
- Foundations
- Depth 59 from the axioms, rests on 877 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement and proof · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- AddMonoidAlgebra.coeffproof · cited by 365
Cited by327
Results whose statement or proof uses this declaration.
- MonomialOrder.leadingCoeffproof · cited by 72
- MvPolynomial.extstatement and proof · cited by 61
- MvPolynomial.toMvPowerSeriesproof · cited by 59
- MvPolynomial.constantCoeffproof · cited by 46
- MvPolynomial.mem_support_iffstatement · cited by 37
- MvPolynomial.coeff_monomialstatement · cited by 32
- MvPolynomial.IsWeightedHomogeneousproof · cited by 31
- MvPolynomial.coeffsproof · cited by 24
- MvPolynomial.weightedHomogeneousSubmoduleproof · cited by 23
- MvPolynomial.coeff_addstatement · cited by 22
- MvPolynomial.map_injectiveproof · cited by 19
- MvPolynomial.coeffsInproof · cited by 18
Showing the 200 most cited of 327.