Theorems · Theorem · commutative algebra
MvPolynomial.IsHomogeneous.rename_isHomogeneous_iff
∀ {σ : Type u_1} {τ : Type u_2} {R : Type u_3} [inst : CommSemiring R] {φ : MvPolynomial σ R} {n : ℕ} {f : σ → τ},
Function.Injective f → (((MvPolynomial.rename f) φ).IsHomogeneous n ↔ φ.IsHomogeneous n)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 89 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.
Cites15
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
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement and proof · cited by 5,255
- mul_oneproof · cited by 3,885
- AlgHomstatement · cited by 3,236
- MvPolynomialstatement and proof · cited by 2,140
- Finsupp.sumproof · cited by 481
- MvPolynomial.coeffproof · cited by 315
- Finsupp.mapDomainproof · cited by 168
- MvPolynomial.renamestatement and proof · cited by 168
- Finsupp.weightproof · cited by 90
- MvPolynomial.IsHomogeneousstatement and proof · cited by 68
Cited by2
Results whose statement or proof uses this declaration.
- MvPolynomial.IsHomogeneous.eq_zero_of_forall_eval_eq_zero_of_le_cardproof · cited by 3
- MvPolynomial.IsHomogeneous.coeff_isHomogeneous_of_optionEquivLeft_symmproof · cited by 1