LAZY POWER SERIES RINGS

DETAILS

 
Introduction

 
Creation of Lazy Series Rings
      LazyPowerSeriesRing(C, n) : Rng, RngIntElt -> RngPowLaz
      ChangeRing(L, C) : RngPowLaz, Rng -> RngPowLaz, Map
      Example RngLaz_ring_create (H50E1)

 
Functions on Lazy Series Rings
      R . i : RngPowLaz, RngIntElt -> RngPowLazElt
      AssignNames(~R, S) : RngPowLaz, [MonStgElt] ->
      BaseRing(R) : RngPowLaz -> Rng
      Rank(R) : RngPowLaz -> RngIntElt
      R1 eq R2 : RngPowLaz, RngPowLaz -> BoolElt
      Example RngLaz_ring-ops (H50E2)

 
Elements

      Creation of Finite Lazy Series
            R ! c : RngPowLaz, RngElt -> RngPowLazElt
            R ! s : RngPowLaz, RngPowLazElt -> RngPowLazElt
            R ! S : RngPowLaz, [RngElt] -> RngPowLazElt
            LazySeries(R, f) : RngPowLaz, RngMPolElt -> RngPowLazElt
            Example RngLaz_elt-create-fin (H50E3)

            Creation of Lazy Series from Maps
                  elt<R | m> : RngPowLaz, Map -> RngPowLazElt
                  Example RngLaz_maps-uni (H50E4)
                  Example RngLaz_maps-multi (H50E5)

      Arithmetic with Lazy Series
            s + t : RngPowLazElt, RngPowLazElt -> RngPowLazElt
            - s : RngPowLazElt -> RngPowLazElt
            s - t : RngPowLazElt, RngPowLazElt -> RngPowLazElt
            s * t : RngPowLazElt, RngPowLazElt -> RngPowLazElt
            s + r : RngPowLazElt, RngElt -> RngPowLazElt
            c * s : RngElt, RngPowLazElt -> RngPowLazElt
            s * n : RngPowLazElt, [RngIntElt] -> RngPowLazElt
            s ^ n : RngPowLazElt, RngIntElt -> RngPowLazElt
            Example RngLaz_elt_arith (H50E6)

      Finding Coefficients of Lazy Series
            Coefficient(s, i) : RngPowLazElt, RngIntElt -> RngElt
            Coefficient(s, T) : RngPowLazElt, SeqEnum -> RngElt
            Coefficients(s, n) : RngPowLazElt, RngIntElt -> [RngElt]
            Valuation(s) : RngPowLazElt -> Any
            PrintToPrecision(s, n) : RngPowLazElt, RngIntElt ->
            PrintTermsOfDegree(s, l, n) : RngPowLazElt, RngIntElt, RngIntElt ->
            LeadingCoefficient(s) : RngPowLazElt -> RngElt
            LeadingTerm(s) : RngPowLazElt -> RngPowLazElt
            Example RngLaz_elt_coeffs_spiral (H50E7)
            CoefficientsNonSpiral(s, n) : RngPowLazElt, [RngIntElt] -> SeqEnum
            Index(s, i, n) : RngPowLazElt, [RngIntElt], [RngIntElt] -> RngIntElt
            Example RngLaz_coeff_non_spiral (H50E8)

      Predicates on Lazy Series
            s eq t : RngPowLazElt, RngPowLazElt -> BoolElt
            IsZero(s) : RngPowLazElt -> BoolElt
            IsOne(s) : RngPowLazElt -> BoolElt
            IsMinusOne(s) : RngPowLazElt -> BoolElt
            IsUnit(s) : RngPowLazElt -> BoolElt
            IsWeaklyZero(s, n) : RngPowLazElt, RngIntElt -> BoolElt
            IsWeaklyEqual(s, t, n) : RngPowLazElt, RngPowLazElt, RngIntElt -> BoolElt

      Other Functions on Lazy Series
            Derivative(s) : RngPowLazElt -> RngPowLazElt
            Integral(s) : RngPowLazElt -> RngPowLazElt
            Evaluate(s, t) : RngPowLazElt, RngPowLazElt -> RngPowLazElt
            Example RngLaz_eval (H50E9)
            SquareRoot(s) : RngPowLazElt -> RngPowLazElt
            IsSquare(s) : RngPowLazElt -> BoolElt, RngPowLazElt
            PolynomialCoefficient(s, i) : RngPowLazElt, RngIntElt -> RngPowLazElt

[Next][Prev] [Right] [____] [Up] [Index] [Root]
Version: V2.19 of Wed Apr 24 15:09:57 EST 2013