In: Boulier, F., Mou, C., Sadykov, T.M., Vorozhtsov, E.V. (eds).
CASC'24. LNCS, vol 14938. Springer, Cham.
DOI:https://doi.org/10.1007/978-3-031-69070-9_18.
I developed the following mathematical software packages. Follow the link for further details. I am going to spend more time with NLDE as there seems to be a convergence in my research for problems and applications related to the use of nonlinear algebra for difference and differential equations.
The differential equation in ADE encodes the Weierstrass elliptic functions. The command invDalg from the package NLDE computes a differential equation for the functional inverses of Weirstrass elliptic functions.
The FPS command from the FPS package is used to find a closed-form representation for the power series expansion of the expression in the argument. This yields a formula in the variable z and the summation index n, as provided in the arguments. Note that this is purely symbolic algebra: it consists of finding and solving differential equations.
The first command solves the recurrence equation with the initial values in the list, and the second command simplifies the given trigonometric expression. The terms denoted with the Greek symbols represent the interlacements (or interleavings) involved in these sequences. The commands are from my package HyperTypeSeq.
Research Notes