cppTPSA/pyTPSA: a C++/Python package for truncated power series algebra

Abstract

The truncated power series algebra (TPSA), also referred to as differential algebra (DA), is a well-established and widely used method in particle accelerator physics and astronomy. The most straightforward usage of TPSA/DA is to calculate the Taylor expansion of a given function at a specific point up to order 𝑛 . In recent years, as the application of TPSA/TA has been extended to other fields, a reusable implementation of TPSA/DA as a modern C++ library or other high level programming language like Python has become desirable. The cppTPSA package implements TPSA/DA in C++11 and provides developers a convenient library with which to build advanced TPSA/DA-based methods. A Python 3 library, pyTPSA, has also been developed based on the C++ lib.