Theorems · Theorem · commutative algebra

PowerSeries.eq_X_mul_shift_add_const

∀ {R : Type u_1} [inst : Semiring R] (φ : PowerSeries R),
  φ =
    (PowerSeries.X * PowerSeries.mk fun p => (PowerSeries.coeff (p + 1)) φ) +
      PowerSeries.C (PowerSeries.constantCoeff φ)

Split off the constant coefficient.

Defined in: Mathlib.RingTheory.PowerSeries.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Semiring

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

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Cited by2

Results whose statement or proof uses this declaration.

PowerSeries.sub_const_eq_X_mul_shiftproof · cited by 2
PowerSeries.map_constantCoeff_le_self_of_X_memproof · cited by 0