Theorems · Theorem · commutative algebra
MvPolynomial.totalDegree_pow
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] (a : MvPolynomial σ R) (n : ℕ),
(a ^ n).totalDegree ≤ n * a.totalDegree- Defined in
- Mathlib.Algebra.MvPolynomial.Degrees
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 85 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement and proof · cited by 5,255
- Finset.prodproof · cited by 2,356
- MvPolynomialstatement and proof · cited by 2,140
- Finset.rangeproof · cited by 1,341
- MvPolynomial.totalDegreestatement and proof · cited by 76
- Finsupp.sum_add_index'proof · cited by 14
- Nat.nsmul_eq_mulproof · cited by 7
- Finset.pow_eq_prod_constproof · cited by 4
- AddMonoidAlgebra.supDegree_prod_leproof · cited by 3
- Finset.nsmul_eq_sum_constproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- char_dvd_card_solutions_of_sum_ltproof · cited by 2