Dear James (and Joachim), Of course, I know, people working with GAP and so on are mainly professors and dr.'s, and they are programming it. I am not a prof dr. so I won't ever say that gap, sage, pari etc. etc. are not good. What I meant is: Can't there be a danger in using these programs? If you trust them so much (They are open source and programmed by the world's finest professors etc.) there is always a chance of big accidents. I don't want to fly in an airplane designed with possibly faulty software. That's my point. I already see it happen on television: "Yes yes, we designed our planes (of which on crashed that day) with the best software available... So that cannot be the reason." No, but very seriously speaking now: There is always a danger that we trust software too much. If we do so there will always be security risks that could have been avoided.
Lisette > > GAP, Sage, and most of Magma include the source files to the software > which means that if you are interested you can read the way that > computations are performed. That is hard to do if you don't have a > background in the details of these platforms. But most of the authors > of these algorithms also publish academic papers describing their > algorithms. These publications receive peer review and the most used > routines receive a lot of testing before they are distributed. You can > see this in the documentation. Most of the documentation include > references to published papers where you can read about the theorems > behind the algorithms, and examples that show you the correct behavior > is being produced on well-known examples. > > Are their mistakes? Of course, both in the programming and in the > design of some algorithms. But this is likely to happen at least as > often when you do similar computations by hand. Furthermore, many > computations just cannot be done by hand because of their size, e.g. > proof of the 4 color theorem. Others could be done by hand but rather > inconsistently because of their complexity. > > Some people think of these tools as the microscope for mathematics. It > lets you see things you couldn't see before. But you don't just except > the data, you need to go in to each experiment with a hypothesis of what > you expect and then process the results against what you understand. So > if you get a result that doesn't make sense you should endeavor to > explain it, redo it, and try to discover if there is a problem with the > microscope. Overtime we will build even better microscopes and others > will redo important computations with their own tools to see if they get > the same thing. > > For most things I trust these platforms. It has been my (limited) > experience that most of the incorrect outputs are a result of my failure > to ask the question in the right way and not the result of the computer > doing something contrary to what it claims it would do. > > You are permitted and encouraged to doubt anything in these algorithms, > but hopefully that simply spurs you to get more information on what they > do rather than give up on them :) > > > > -James > > > > Lisette Brillemans wrote: > > Dear forum, > > > > I'm exploring the exiting possibilities of the wonderful GAP and there > > is quite a lot to explore there but... > > > > How can I trust that everything GAP calculates is correct? I'm sure I > > can't. > > And then we're only talking about GAP. GAP has also been added to > > another, much bigger, software package calles SAGE, where many > > opensource packages and libraries can be used in one interface. But so > > many libraries, so many programs, so many packages, this cannot all be > > correct. There must have been programming mistakes leading to wrong > > calculations. > > > > But I would say that one cannot rely on it without recalculating > > everyting, or is that preposterous? I hope that I may ask this here... > > > > I wish you a nice day and am continuing to learn to use gap (and sage > > too). > > > > Lisette > > > > > > _______________________________________________ > > Forum mailing list > > Forum@mail.gap-system.org > > http://mail.gap-system.org/mailman/listinfo/forum > > > _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
