Theorems · Definition · commutative algebra
MvPolynomial.degreesLE
(R : Type u) → (σ : Type u_1) → [inst : CommSemiring R] → Multiset σ → Submodule R (MvPolynomial σ R)
The submodule of multivariate polynomials of degrees bounded by a monomial s.
- Defined in
- Mathlib.Algebra.MvPolynomial.Degrees
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 87 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.
Cites7
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
- Submodulestatement · cited by 7,192
- Set.ofPredproof · cited by 6,101
- Finsuppstatement · cited by 5,255
- Multisetstatement and proof · cited by 2,627
- MvPolynomialstatement and proof · cited by 2,140
- MvPolynomial.degreesproof · cited by 51
Cited by6
Results whose statement or proof uses this declaration.
- MvPolynomial.degreesLE_nsmulstatement · cited by 2
- ChevalleyThm.chevalley_mvPolynomialCstatement and proof · cited by 1
- MvPolynomial.mem_degreesLEstatement · cited by 1
- chevalley_mvPolynomial_mvPolynomialproof · cited by 0
- MvPolynomial.degreesLE_addstatement and proof · cited by 0
- MvPolynomial.degreesLE_zerostatement and proof · cited by 0