Theorems · Definition · commutative algebra
PowerSeries.substInvFun
{R : Type u_2} → [inst : CommRing R] → (P : PowerSeries R) → [Invertible ((PowerSeries.coeff 1) P)] → ℕ → RGiven a power series P = u • X + O(X²) with u invertible,
this is the construction of a power series Q such that P(Q(X)) = X.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingInvertible
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- Finset.sumproof · cited by 5,195
- Finset.univproof · cited by 3,473
- PowerSeriesstatement and proof · cited by 797
- Invertiblestatement and proof · cited by 549
- PowerSeries.coeffstatement and proof · cited by 324
- Invertible.invOfproof · cited by 268
- PowerSeries.Xproof · cited by 183
- PowerSeries.Cproof · cited by 76
Cited by5
Results whose statement or proof uses this declaration.
- PowerSeries.substInvproof · cited by 9
- PowerSeries.subst_substInv_rightproof · cited by 2
- PowerSeries.coeff_one_substInvproof · cited by 2
- PowerSeries.coeff_subst_sum_C_substInvFun_mul_X_pow_sub_Xstatement and proof · cited by 1
- PowerSeries.substInvFun.eq_defstatement and proof · cited by 0