Theorems · Definition · commutative algebra
PowerSeries.constantCoeff
{R : Type u_1} → [inst : Semiring R] → PowerSeries R →+* RThe constant coefficient of a formal power series.
- Defined in
- Mathlib.RingTheory.PowerSeries.Basic
- Cited by
- 126 results in Mathlib
- Foundations
- Depth 94 from the axioms, rests on 2,226 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- RingHomstatement · cited by 10,189
- PowerSeriesstatement · cited by 797
- MvPowerSeries.constantCoeffproof · cited by 98
Cited by128
Results whose statement or proof uses this declaration.
- PowerSeries.coeff_zero_eq_constantCoeffstatement and proof · cited by 41
- PowerSeries.constantCoeff_Xstatement · cited by 16
- PowerSeries.constantCoeff_expstatement · cited by 9
- PowerSeries.coeff_zero_eq_constantCoeff_applystatement and proof · cited by 8
- PowerSeries.HasSubst.of_constantCoeff_zero'statement and proof · cited by 7
- ArithmeticFunction.ofPowerSeriesproof · cited by 7
- PowerSeries.X_dvd_iffstatement and proof · cited by 5
- ArithmeticFunction.ofPowerSeries_applyproof · cited by 4
- PowerSeries.isUnit_iff_constantCoeffstatement · cited by 3
- PowerSeries.rescale_zerostatement and proof · cited by 3
- PowerSeries.subst_substInv_leftstatement and proof · cited by 3
- PowerSeries.constantCoeff_substInvstatement · cited by 3