2014/02/27 by Kwong, Man Kam
#Classical Analysis and ODEs (math.CA) #FOS: Computer and information sciences #FOS: Mathematics #Symbolic Computation (cs.SC)
paper · doi:10.48550/arxiv.1402.6778
In this paper, we explain a procedure based on a classical result of Sturm that can be used to determine rigorously whether a given trigonometric polynomial is nonnegative in a certain interval or not. Many examples are given. This technique has been employed by the author in several recent works. The procedure often involves tedious computations that are time-consuming and error-prone. Fortunately, symbolic computation software is available to automate the procedure. In this paper, we give the details of its implementation in MAPLE 13. Some who are strongly attached to a more traditional theoretical research framework may find such details boring or even consider computer-assisted proofs suspicious. However, we emphasize again that the procedure is completely mathematically rigorous.