Theorems · Theorem · commutative algebra
MvPolynomial.totalDegree_eq
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] (p : MvPolynomial σ R),
p.totalDegree = p.support.sup fun m => (Finsupp.toMultiset m).card- Defined in
- Mathlib.Algebra.MvPolynomial.Degrees
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 74 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.
Cites16
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
- Finsetproof · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement and proof · cited by 5,255
- AddMonoidHomstatement · cited by 3,230
- Multisetstatement · cited by 2,627
- MvPolynomialstatement and proof · cited by 2,140
- OrderBotproof · cited by 1,055
- SemilatticeSupproof · cited by 785
- Finset.supstatement and proof · cited by 530
- Finsupp.sumproof · cited by 481
- Multiset.cardstatement and proof · cited by 375
Cited by3
Results whose statement or proof uses this declaration.
- MvPolynomial.totalDegree_add_eq_left_of_totalDegree_ltproof · cited by 1
- MvPolynomial.totalDegree_le_degrees_cardproof · cited by 1
- MvPolynomial.totalDegree_expandproof · cited by 0