Theorems · Theorem · commutative algebra
MvPolynomial.IsHomogeneous.degree_eq_sum_deg_support
∀ {σ : Type u_1} {R : Type u_3} [inst : CommSemiring R] {φ : MvPolynomial σ R} {n : ℕ},
φ.IsHomogeneous n → ∀ {s : σ →₀ ℕ}, s ∈ φ.support → n = ∑ i ∈ s.support, s i- Cited by
- 3 results in Mathlib
- Foundations
- Depth 81 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.
Cites12
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
- Finsetstatement · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement and proof · cited by 5,255
- Finset.sumstatement · cited by 5,195
- MvPolynomialstatement and proof · cited by 2,140
- Finsupp.supportstatement · cited by 828
- MvPolynomial.supportstatement and proof · cited by 220
- Finsupp.weightproof · cited by 90
- MvPolynomial.IsHomogeneousstatement and proof · cited by 68
- MvPolynomial.mem_support_iffproof · cited by 37
- Finsupp.degree_eq_weight_oneproof · cited by 26
Cited by3
Results whose statement or proof uses this declaration.
- AbsoluteValue.eval_mvPolynomial_leproof · cited by 1
- IsNonarchimedean.eval_mvPolynomial_leproof · cited by 1
- Polynomial.sum_eq_natDegree_of_mem_support_homogenizeproof · cited by 1