NewtonGF is a Maple package, developed with Carine Pivoteau and Pablo Rotondo, which provides tools based on the combinatorial Newton iteration described in

C. Pivoteau, B. Salvy, and M. Soria, “Algorithms for Combinatorial Structures: Well-founded systems and Newton iterations,” Journal of Combinatorial Theory, Series A, vol. 119, pp. 1711–1773, 2012.

In particular, it implements the oracle required by the famous Boltzmann samplers of

P. Duchon, P. Flajolet, G. Louchard, and G. Schaeffer, “Boltzmann Samplers for the Random Generation of Combinatorial Structures,” Combinatorics, Probability and Computing, vol. 13, no. 4–5, pp. 577–625, 2004.

Download

 The latest version is NewtonGF 2.21 (Feb. 2018).

Once downloaded, see the help page of libname to understand how to make them available from Maple. Typically, your session will contain something like libname:="NewtonGF_path",libname:

You can check that this worked by asking NewtonGF:-version; that should return the number above.

Help Pages

The help pages distributed with the package work with the Maple help system for version 18 (and will hopefully work with later versions). Here are readable pdf versions of these pages. The package itself has been tested with earlier versions (Maple16 is the oldest we’ve tried).

• NewtonGF

• GFSeries

• SeriesNewtonIteration

• NumericalNewtonIteration

• Radius

• BoltzmannExpectedSize

• BoltzmannParameter