Theorems · Definition · commutative algebra
MvPolynomial.IsHomogeneous
{σ : Type u_1} → {R : Type u_3} → [inst : CommSemiring R] → MvPolynomial σ R → ℕ → PropA multivariate polynomial φ is homogeneous of degree n
if all monomials occurring in φ have degree n.
- Cited by
- 68 results in Mathlib
- Foundations
- Depth 80 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.
Cites3
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.IsWeightedHomogeneousproof · cited by 31
Cited by69
Results whose statement or proof uses this declaration.
- MvPolynomial.homogeneousSubmoduleproof · cited by 23
- MvPolynomial.isHomogeneous_Cstatement · cited by 7
- MvPolynomial.isHomogeneous_monomialstatement · cited by 6
- MvPolynomial.IsHomogeneous.mulstatement and proof · cited by 5
- MvPolynomial.IsHomogeneous.sumstatement and proof · cited by 5
- MvPolynomial.isHomogeneous_Xstatement · cited by 5
- MvPolynomial.IsHomogeneous.C_mulstatement and proof · cited by 3
- MvPolynomial.IsHomogeneous.degree_eq_sum_deg_supportstatement and proof · cited by 3
- MvPolynomial.IsHomogeneous.eq_zero_of_forall_eval_eq_zero_of_le_cardstatement and proof · cited by 3
- MvPolynomial.IsHomogeneous.eval₂statement and proof · cited by 3
- MvPolynomial.IsHomogeneous.prodstatement and proof · cited by 3
- Height.mulHeight_eval_lestatement and proof · cited by 3