Theorems · Theorem · commutative algebra
MvPolynomial.totalDegree_zero_iff_isHomogeneous
∀ (σ : Type u_1) {R : Type u_3} [inst : CommSemiring R] {p : MvPolynomial σ R}, p.totalDegree = 0 ↔ p.IsHomogeneous 0- Cited by
- 3 results in Mathlib
- Foundations
- Depth 82 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
- MvPolynomialstatement and proof · cited by 2,140
- MvPolynomial.totalDegreestatement · cited by 76
- MvPolynomial.IsHomogeneousstatement and proof · cited by 68
- MvPolynomial.IsWeightedHomogeneousproof · cited by 31
- MvPolynomial.weightedTotalDegree_oneproof · cited by 2
- MvPolynomial.isWeightedHomogeneous_zero_iff_weightedTotalDegree_eq_zeroproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- MvPolynomial.homogeneousSubmodule_zeroproof · cited by 1
- MvPolynomial.isHomogeneous_of_totalDegree_zeroproof · cited by 0
- MvPolynomial.IsHomogeneous.pderivproof · cited by 0