Theorems · Theorem · commutative algebra
PowerSeries.eq_X_pow_mul_shift_add_trunc
∀ {R : Type u_1} [inst : Semiring R] (n : ℕ) (f : PowerSeries R),
f = (PowerSeries.X ^ n * PowerSeries.mk fun i => (PowerSeries.coeff (i + n)) f) + ↑((PowerSeries.trunc n) f)Split off the first n coefficients.
- Defined in
- Mathlib.RingTheory.PowerSeries.Trunc
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 105 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.
Cites14
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
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- Polynomialstatement · cited by 5,681
- PowerSeriesstatement and proof · cited by 797
- PowerSeries.coeffstatement and proof · cited by 324
- PowerSeries.Xstatement · cited by 183
- Polynomial.toPowerSeriesstatement and proof · cited by 96
- Commute.eqproof · cited by 91
- PowerSeries.mkstatement and proof · cited by 52
- PowerSeries.truncstatement and proof · cited by 41
Cited by2
Results whose statement or proof uses this declaration.
- PowerSeries.IsWeierstrassDivisorAt.coeff_seq_memproof · cited by 2
- PowerSeries.IsWeierstrassDivisorAt.eq_zero_of_mul_eqproof · cited by 1