A practical approach to testing random number generators in computer algebra systems

This paper has a practical aim. For a long time, implementations of pseudorandom number generators in standard libraries of programming languages had poor quality. The situation started to improve only recently. Up to now, a large number of libraries and weakly supported mathematical packages use outdated algorithms for random number generation. Four modern sets of statistical tests that can be used for verifying random number generators are described. It is proposed to use command line utilities, which makes it possible to avoid low-level programming in such languages as C or C++. Only free open source systems are considered.