Very cool. It feel like a bit of a shame that Dual isn't just a the first order instance of PowerSeries, but I think for now that's probably for the best. But maybe down the line some time in future they could be merged? Or are there fundamental differences that make that impractical?
On Sat, Jan 18, 2014 at 3:42 PM, John Myles White <[email protected]>wrote: > This is so cool, Jason. Really excited to try this out. > > — John > > P.S. Sorry for missing your talk the other. Had to take a job candidate > out for dinner. > > On Jan 18, 2014, at 12:28 PM, Jason Merrill <[email protected]> wrote: > > > 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 > >
