I'd like to announce the first public release of PowerSeries.jl [1], a package for computing with truncated power series. In PowerSeries, Series behave just like numbers, and you can do arithmetic on them and compute functions of them just as you would a Real or Complex number. Integration and differentiation are also supported.
[1] https://github.com/jwmerrill/PowerSeries.jl Truncated power series over floating point numbers have the nice property that the result of a long series of computations can be stored in the same amount of space as the input to the computation. This is in contrast with, e.g., Rational numbers, where the numerator and denominator typically grow exponentially as you compute with them, or non-truncated power series, where the number of terms grows linearly under multiplication, and (typically) infinitely under division. I intend for PowerSeries series to be a practical computation tool with very little overhead compared to code you might hand-write for a specific problem. This goal may not be completely realized yet--issues and pull requests welcome! One of my motivations for creating PowerSeries.jl was to extend automatic differentiation to higher order derivatives. You can implement forward-mode AD by overloading functions to operate on dual numbers [2], which are numbers of the form a + b*eps | eps^2 = 0 Truncated power series can be viewed as a natural extension of Dual numbers to numbers the form a + b*eps + c*eps^2 + d*eps^3 + ... | eps^n = 0 for some n that allow computing higher order derivatives. See the README for details. [2] see DualNumbers.jl, https://github.com/scidom/DualNumbers.jl
