Rapid mathematical programming

All numerals in this text are recycled. Preface Avoid reality at all costs — fortune() As the inclined reader will find out soon enough, this thesis is not about deeply involved mathematics as a mean in itself, but about how to apply mathematics to solve real-world problems. We will show how to shape, forge, and yield our tool of choice to rapidly answer questions of concern to people outside the world of mathematics. But there is more to it. Our tool of choice is software. This is not unusual, since it has become standard practice in science to use software as part of experiments and sometimes even for proofs. But in order to call an experiment scientific it must be reproducible. Is this the case? Regarding software experiments, we have first to distinguish between reproducing and repeating results. The latter means that given the same data and the same programs, running on a similar computer, the results are identical. Reproducing results means to use the same data, but different programs and an arbitrary computer. Today we can reproduce experiments conducted by Leonardo da Vinci in the fif-teenth century. But can we expect even to repeat an experiment that involves a -year-old (commercial) program? Or in case we try to reproduce it, using different software and get dissenting results, can we make any conclusions why the results differ? Software is getting more complex all the time. And by no means it is usually possible to prove the correctness of a specific implementation even if the algorithm employed is known to be correct. But what can we do if the source code of the program is not available at all? How could we assert what the program is really doing? Science is about using the work of fellows. If a proof or experiment is published anybody can use it as part of their work, assumed due credit is given to the author. But how can we build on software that is not freely available? The same questions can be asked for the input data. Without the precise data, computational experiments can neither be repeated nor reproduced. Surely part of the problem is that there is no accepted or even adequate way to publish software and data for review in the same way as articles are published. While this thesis by no means gives answers to the above questions  , considerable efforts …