Comparing the computation of Chebyshev polynomials in computer algebra systems

Abstract. In this article we compare the efficiency of the computer algebra systems Maple and Sage, using as benchmark the calculation of Chebyshev polynomials with various methods. In most tests, Maple performed better, but Sage is also capable of doing the calculations. We conclude that Sage, although still inferior to Maple in functionality and performance, has by now become a reasonable open-source alternative of commercial computer algebra systems.