Theorems · Theorem · commutative algebra
MvPolynomial.le_totalDegree
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] {p : MvPolynomial σ R} {s : σ →₀ ℕ},
s ∈ p.support → (s.sum fun x e => e) ≤ p.totalDegree- Defined in
- Mathlib.Algebra.MvPolynomial.Degrees
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 61 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement and proof · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- Finsupp.sumstatement · cited by 481
- MvPolynomial.supportstatement and proof · cited by 220
- Finset.le_supproof · cited by 112
- MvPolynomial.totalDegreestatement · cited by 76
Cited by6
Results whose statement or proof uses this declaration.
- MvPolynomial.totalDegree_rename_leproof · cited by 2
- MvPolynomial.coeff_toPolynomialAdjoinImageCompl_ne_zeroproof · cited by 2
- MvPolynomial.exists_degree_ltproof · cited by 1
- MvPolynomial.degreeOf_le_totalDegreeproof · cited by 1
- MvPolynomial.degree_degLexDegreeproof · cited by 1
- MvPolynomial.totalDegree_coeff_finSuccEquiv_add_leproof · cited by 0