Reliability of high level scientific softwares

Yes, Mathematica and your new release with more than 700 new functions, I am hinting at you. I am wondering how programs so advance as you can be reliable.
Other softwares are in the same case, but S. Wolfram is rather explicit in his blog about making Mathematica the second, more advanced brain, of every scientist (for a small transfer of money).

The question that I have when I use this kind of software is the following:

How am I a sure that the software gives the right answer to my question?

 

This question has two parts:

  • first, how does Wolfram insures that the program has no bug? It is a closed proprietary system. Of course, you have a feedback system, but still, you need the bug to be obvious to detect it. When you do science, you are in quicksands: you are sure of nothing and you need some stable ground to progress.
  • second, these codes offer more and more advanced functions: how can I be sure that I use the function in the proper way. The problem is that for a same function, the code can branch on different algorithms depending on the range of your parameters and it is not always obvious to understand the limitations of each algorithm. Of course, you can call the hotline, you can follow trainings but it costs money, added to the initital cost of the license.

In my opinion, this kind of general purpose software should be kept for basic general computing; a kind of enhanced pocket calculator. As soon as you need to do more complex things, you need anyway to understand what happens under the hoot; so you have to use an open code, so that you can check if everything goes right during the simulation.

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