Theorems · Theorem · commutative algebra
MvPolynomial.totalDegree_monomial
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] (s : σ →₀ ℕ) {c : R},
c ≠ 0 → ((MvPolynomial.monomial s) c).totalDegree = s.sum fun x e => e- Defined in
- Mathlib.Algebra.MvPolynomial.Degrees
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 83 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.
Cites13
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
- Finsetproof · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Finsuppstatement and proof · cited by 5,255
- MvPolynomialstatement · cited by 2,140
- Finset.supproof · cited by 530
- Finsupp.sumstatement and proof · cited by 481
- MvPolynomial.monomialstatement · cited by 253
- MvPolynomial.totalDegreestatement · cited by 76
- Finset.sup_singletonproof · cited by 42
Cited by2
Results whose statement or proof uses this declaration.
- MvPolynomial.totalDegree_monomial_leproof · cited by 0
- MvPolynomial.totalDegree_X_powproof · cited by 0