Theorems · Definition · commutative algebra
MvPolynomial.degrees
{R : Type u} → {σ : Type u_1} → [inst : CommSemiring R] → MvPolynomial σ R → Multiset σThe maximal degrees of each variable in a multi-variable polynomial, expressed as a multiset.
(For example, degrees (x^2 * y + y^3) would be {x, x, y, y, y}.)
- Defined in
- Mathlib.Algebra.MvPolynomial.Degrees
- Cited by
- 51 results in Mathlib
- Foundations
- Depth 73 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.
- DFunLike.coeproof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- Finsuppproof · cited by 5,255
- Multisetstatement · cited by 2,627
- MvPolynomialstatement and proof · cited by 2,140
- Finset.supproof · cited by 530
- MvPolynomial.supportproof · cited by 220
- Finsupp.toMultisetproof · cited by 44
Cited by54
Results whose statement or proof uses this declaration.
- MvPolynomial.varsproof · cited by 79
- MvPolynomial.degreeOfproof · cited by 53
- MvPolynomial.vars_defstatement and proof · cited by 11
- MvPolynomial.degrees_Cstatement · cited by 8
- MvPolynomial.degrees_defstatement · cited by 8
- MvPolynomial.degreeOf_zeroproof · cited by 7
- MvPolynomial.degreeOf_defstatement and proof · cited by 7
- MvPolynomial.degreesLEproof · cited by 6
- MvPolynomial.degrees_mul_lestatement · cited by 6
- MvPolynomial.vars_mulproof · cited by 6
- MvPolynomial.degrees_onestatement · cited by 5
- MvPolynomial.degrees_X'statement · cited by 3