Theorems · Definition · commutative algebra
PowerSeries.toMvPowerSeries
{R : Type u_1} → {σ : Type u_2} → [inst : CommSemiring R] → σ → PowerSeries R →ₐ[R] MvPowerSeries σ RGiven a power series p : R⟦X⟧ and an index i, we may view it as a
multivariate power series toMvPowerSeries i p : MvPowerSeries σ R.
- Defined in
- Mathlib.RingTheory.MvPowerSeries.Equiv
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 100 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- AlgHomstatement · cited by 3,236
- PowerSeriesstatement · cited by 797
- MvPowerSeriesstatement · cited by 659
- MvPowerSeries.renameproof · cited by 26
Cited by11
Results whose statement or proof uses this declaration.
- PowerSeries.toMvPowerSeries_applystatement · cited by 4
- PowerSeries.toMvPowerSeries_injectivestatement · cited by 1
- MvPowerSeries.rename_comp_toMvPowerSeriesstatement · cited by 1
- PowerSeries.toMvPowerSeries_coeff_eq_zerostatement · cited by 1
- PowerSeries.toMvPowerSeries_eq_subststatement · cited by 1
- PowerSeries.subst_toMvPowerSeriesstatement · cited by 0
- PowerSeries.toMvPowerSeries_Cstatement · cited by 0
- PowerSeries.toMvPowerSeries_Xstatement · cited by 0
- MvPowerSeries.rename_toMvPowerSeriesstatement · cited by 0
- PowerSeries.toMvPowerSeries_injstatement · cited by 0
- MvPowerSeries.HasSubst.toMvPowerSeriesstatement · cited by 0