Theorems · Theorem · commutative algebra
MvPolynomial.IsWeightedHomogeneous.weightedHomogeneousComponent_same
∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] {σ : Type u_3} [inst_1 : AddCommMonoid M] {w : σ → M} {m : M}
{p : MvPolynomial σ R},
MvPolynomial.IsWeightedHomogeneous w p m → (MvPolynomial.weightedHomogeneousComponent w m) p = p- Cited by
- 1 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringAddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- 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
- MvPolynomialstatement and proof · cited by 2,140
- MvPolynomial.coeffproof · cited by 315
- Finsupp.weightproof · cited by 90
- MvPolynomial.extproof · cited by 61
- MvPolynomial.IsWeightedHomogeneousstatement and proof · cited by 31
- MvPolynomial.weightedHomogeneousComponentstatement and proof · cited by 25
Cited by1
Results whose statement or proof uses this declaration.
- MvPolynomial.weightedHomogeneousComponent_directSumproof · cited by 0