Theorems · Definition · commutative algebra
MvPowerSeries.homogeneousComponent
{σ : Type u_1} → {R : Type u_2} → [inst : Semiring R] → ℕ → MvPowerSeries σ R →ₗ[R] MvPowerSeries σ RThe homogeneous components of an MvPowerSeries
- Defined in
- Mathlib.RingTheory.MvPowerSeries.Order
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
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.
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- MvPowerSeriesstatement · cited by 659
- MvPowerSeries.weightedHomogeneousComponentproof · cited by 7
Cited by13
Results whose statement or proof uses this declaration.
- MvPowerSeries.truncTotal_eq_sumstatement 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.coeff_homogeneousComponentstatement and proof · cited by 2
- MvPowerSeries.truncTotal_subst_eq_truncTotal_sum_subststatement and proof · cited by 1
- MvPowerSeries.truncTotal_subst_of_leproof · cited by 1
- MvPowerSeries.homogeneousComponent_mul_of_le_orderstatement · cited by 0
- MvPowerSeries.homogeneousComponent_of_lt_order_eq_zerostatement · cited by 0
- MvPowerSeries.homogeneousComponent_of_orderstatement · cited by 0
- MvPowerSeries.truncTotal_subst_eq_truncTotal_sum_subst_truncTotalstatement · cited by 0
- MvPowerSeries.isHomogeneous_homogeneousComponentstatement · cited by 0
- MvPowerSeries.isHomogeneous_iff_eq_homogeneousComponentstatement · cited by 0