Theorems · Definition · commutative algebra
MvPowerSeries.truncTotal
{σ : Type u_1} → [Finite σ] → {R : Type u_4} → [inst : CommSemiring R] → ℕ → MvPowerSeries σ R →ₗ[R] MvPolynomial σ RThe truncation of a multivariate formal power series at a total degree n
when the index σ is finite.
- Defined in
- Mathlib.RingTheory.MvPowerSeries.Trunc
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FiniteCommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Finsuppstatement · cited by 5,255
- Finitestatement and proof · cited by 3,029
- MvPolynomialstatement · cited by 2,140
- MvPowerSeriesstatement · cited by 659
- Set.Finite.toFinsetproof · cited by 351
- MvPowerSeries.truncFinsetproof · cited by 18
- Finsupp.finite_of_degree_ltproof · cited by 5
Cited by29
Results whose statement or proof uses this declaration.
- MvPowerSeries.coeff_truncTotalstatement · cited by 10
- MvPowerSeries.coeff_truncTotal_eq_zerostatement · cited by 4
- MvPowerSeries.HasSubst.truncTotalstatement and proof · cited by 3
- MvPowerSeries.truncTotalAlgHomproof · cited by 3
- MvPowerSeries.coeff_truncTotal_eq_itestatement and proof · cited by 3
- MvPowerSeries.truncTotal_eq_sumstatement · cited by 2
- MvPowerSeries.coeff_truncTotal_powstatement and proof · cited by 2
- MvPowerSeries.truncTotal_subst_eq_truncTotal_subst_sumstatement and proof · cited by 2
- MvPowerSeries.truncTotal_subst_eq_truncTotal_sum_subst_truncTotal_of_lestatement and proof · cited by 2
- MvPowerSeries.constantCoeff_truncTotal_eq_itestatement · cited by 2
- MvPowerSeries.toAdicCompletion_apply_eq_mk_truncTotalstatement · cited by 1
- MvPowerSeries.truncTotalAlgHom_applystatement · cited by 1