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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 R

The 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.

MvPowerSeries.coeff_truncTotal · cited by 10MvPowerSeries.coeff_trunc…MvPowerSeries.coeff_truncTotal_eq_zero · cited by 4MvPowerSeries.coeff_trunc…MvPowerSeries.HasSubst.truncTotal · cited by 3HasSubst.truncTotalMvPowerSeries.truncTotalAlgHom · cited by 3MvPowerSeries.truncTotalA…MvPowerSeries.coeff_truncTotal_eq_ite · cited by 3MvPowerSeries.coeff_trunc…MvPowerSeries.truncTotal_eq_sum · cited by 2MvPowerSeries.truncTotal_…MvPowerSeries.coeff_truncTotal_pow · cited by 2MvPowerSeries.coeff_trunc…MvPowerSeries.truncTotal_subst_eq_truncTotal_subst_sum · cited by 2MvPowerSeries.truncTotal_…MvPowerSeries.truncTotal_subst_eq_truncTotal_sum_subst_truncTotal_of_le · cited by 2MvPowerSeries.truncTotal_…MvPowerSeries.constantCoeff_truncTotal_eq_ite · cited by 2MvPowerSeries.constantCoe…MvPowerSeries.toAdicCompletion_apply_eq_mk_truncTotal · cited by 1MvPowerSeries.toAdicCompl…MvPowerSeries.truncTotalAlgHom_apply · cited by 1MvPowerSeries.truncTotalA…MvPowerSeries.coeff_truncTotal_mul_truncTotal_eq_coeff_mul · cited by 1MvPowerSeries.coeff_trunc…MvPowerSeries.truncTotal_subst_eq_truncTotal_subst_truncTotal_of_le · cited by 1MvPowerSeries.truncTotal_…MvPowerSeries.truncTotal_subst_eq_truncTotal_sum_subst · cited by 1MvPowerSeries.truncTotal_…RingHom.id · cited by 18349RingHom.idCommSemiring · cited by 10911CommSemiringLinearMap · cited by 10215LinearMapFinsupp · cited by 5255FinsuppFinite · cited by 3029FiniteMvPolynomial · cited by 2140MvPolynomialMvPowerSeries · cited by 659MvPowerSeriesSet.Finite.toFinset · cited by 351Finite.toFinsetMvPowerSeries.truncFinset · cited by 18MvPowerSeries.truncFinsetFinsupp.finite_of_degree_lt · cited by 5Finsupp.finite_of_degree_…MvPowerSeries.truncTotalCITED BYCITES

Cites10

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Cited by29

Results whose statement or proof uses this declaration.