Theorems · Definition · commutative algebra
Polynomial.toPowerSeries
{R : Type u_1} → [inst : Semiring R] → Polynomial R → PowerSeries RThe natural inclusion from polynomials into formal power series.
- Defined in
- Mathlib.RingTheory.PowerSeries.Basic
- Cited by
- 96 results in Mathlib
- Foundations
- Depth 60 from the axioms, rests on 881 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Polynomialstatement and proof · cited by 5,681
- Polynomial.coeffproof · cited by 1,045
- PowerSeriesstatement · cited by 797
- PowerSeries.mkproof · cited by 52
Cited by103
Results whose statement or proof uses this declaration.
- Polynomial.coeff_coestatement · cited by 25
- Polynomial.coe_Xstatement · cited by 12
- PowerSeries.IsWeierstrassDivisionAt.eq_mul_addstatement · cited by 11
- PowerSeries.IsWeierstrassDivisorAt.isWeierstrassDivisionAt_div_modproof · cited by 10
- PowerSeries.IsWeierstrassDivisorAt.eq_of_mul_add_eq_mul_addstatement and proof · cited by 7
- PowerSeries.IsWeierstrassFactorizationAt.eq_mulstatement · cited by 6
- Polynomial.coe_monomialstatement · cited by 5
- Polynomial.coe_powstatement · cited by 5
- Polynomial.coeToPowerSeries.ringHomproof · cited by 5
- Polynomial.coe_addstatement and proof · cited by 4
- Polynomial.coe_substatement · cited by 4
- Polynomial.gaussNorm_coe_powerSeriesstatement and proof · cited by 4