Misfortunes of a mathematicians' trio using Computer Algebra Systems: Can we trust?
Antonio J. Durán, Mario Pérez, Juan L. Varona
TL;DR
This paper is a sample of the current state of the art of what mathematicians can expect when they use this kind of software, and aims to improve some results of Karlin and Szegő related to orthogonal polynomials on the real line.
Abstract
Computer algebra systems are a great help for mathematical research but sometimes unexpected errors in the software can also badly affect it. As an example, we show how we have detected an error of Mathematica computing determinants of matrices of integer numbers: not only it computes the determinants wrongly, but also it produces different results if one evaluates the same determinant twice.