Theorems · Definition · commutative algebra
PowerSeries.invOneSubPow
(S : Type u_1) → [inst : CommRing S] → ℕ → (PowerSeries S)ˣ
Given a natural number d : ℕ and a commutative ring S, PowerSeries.invOneSubPow S d is the
multiplicative inverse of (1 - X) ^ d in S⟦X⟧ˣ. When d is 0, PowerSeries.invOneSubPow S d
will just be 1. When d is positive, PowerSeries.invOneSubPow S d will be the power series
mk fun n => Nat.choose (d - 1 + n) (d - 1).
- Defined in
- Mathlib.RingTheory.PowerSeries.WellKnown
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Unitsstatement and proof · cited by 2,804
- PowerSeriesstatement and proof · cited by 797
- Nat.chooseproof · cited by 494
- PowerSeries.Xproof · cited by 183
- PowerSeries.mkproof · cited by 52
Cited by16
Results whose statement or proof uses this declaration.
- Polynomial.coeff_mul_invOneSubPow_eq_hilbertPoly_evalstatement and proof · cited by 3
- PowerSeries.one_sub_pow_mul_invOneSubPow_val_add_eq_invOneSubPow_valstatement and proof · cited by 1
- Polynomial.existsUnique_hilbertPolystatement and proof · cited by 1
- Polynomial.eq_hilbertPoly_of_forall_coeff_eq_evalstatement and proof · cited by 1
- PowerSeries.invOneSubPow_addstatement · cited by 1
- PowerSeries.invOneSubPow_eq_inv_one_sub_powstatement and proof · cited by 1
- PowerSeries.invOneSubPow_inv_eq_one_sub_powstatement and proof · cited by 1
- PowerSeries.invOneSubPow_val_eq_mk_sub_one_add_choose_of_posstatement and proof · cited by 1
- PowerSeries.invOneSubPow_zerostatement · cited by 1
- Polynomial.hilbertPoly_mul_one_sub_succproof · cited by 1
- PowerSeries.one_sub_pow_add_mul_invOneSubPow_val_eq_one_sub_powstatement and proof · cited by 0
- PowerSeries.invOneSubPow_inv_zero_eq_onestatement · cited by 0