Theorems · Theorem · commutative algebra
MvPolynomial.weightedHomogeneousComponent_eq_zero_of_notMem
∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] {σ : Type u_3} (w : σ → M) [inst_1 : AddCommMonoid M]
[inst_2 : DecidableEq M] (φ : MvPolynomial σ R),
∀ i ∉ Finset.image (⇑(Finsupp.weight w)) φ.support, (MvPolynomial.weightedHomogeneousComponent w i) φ = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
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
- RingHom.idstatement · cited by 18,349
- Finsetstatement · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Finsuppstatement and proof · cited by 5,255
- AddMonoidHomstatement · cited by 3,230
- MvPolynomialstatement and proof · cited by 2,140
- Finset.imagestatement and proof · cited by 910
- MvPolynomial.supportstatement and proof · cited by 220
- Finsupp.weightstatement and proof · cited by 90
Cited by1
Results whose statement or proof uses this declaration.
- MvPolynomial.decompose'_applyproof · cited by 1