Theorems · Theorem · commutative algebra
MvPowerSeries.truncFinset_apply
∀ {σ : Type u_1} {R : Type u_2} [inst : CommSemiring R] {s : Finset (σ →₀ ℕ)} (p : MvPowerSeries σ R),
(MvPowerSeries.truncFinset R s) p = ∑ x ∈ s, (MvPolynomial.monomial x) ((MvPowerSeries.coeff x) p)- Defined in
- Mathlib.RingTheory.MvPowerSeries.Trunc
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 84 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.
Cites12
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 and proof · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Finsuppstatement and proof · cited by 5,255
- Finset.sumstatement · cited by 5,195
- MvPolynomialstatement · cited by 2,140
- MvPowerSeriesstatement and proof · cited by 659
- MvPowerSeries.coeffstatement · cited by 273
- MvPolynomial.monomialstatement · cited by 253
- MvPowerSeries.truncFinsetstatement and proof · cited by 18
Cited by3
Results whose statement or proof uses this declaration.
- MvPowerSeries.coeff_truncFinset_eq_zeroproof · cited by 3
- MvPowerSeries.coeff_truncFinset_of_memproof · cited by 3
- MvPowerSeries.coeff_truncFinsetproof · cited by 2