Notes on Chebyshev Series and Computer Algebra

A typical computer algebra system (CAS) represents formulas by (what amounts to) trees. By approximating a more general function as a univariate polynomial, it can be represented as an array of coefficients. Another common representation is as a set of values of the function at specified points. In either case, one can compute in this realm of “functions” further by combining such arrays. By taking advantage of the special properties of Chebyshev series, a number of facilities may be programmed especially neatly. These have been nicely pursued by the Chebfun project at Oxford University. Combining these ideas and reimplementing with computer algebra systems, we gain additional facilities.