> > > > OK, let's try with a being the imaginary unity. > > > > I thought that by default FriCAS assumes that variables are real.
Users requently try to use complex expressions and when possible FriCAS tries to accomodate this. > I just found out that the exact same question was asked 7 years ago: > https://groups.google.com/d/topic/fricas-devel/jTeaKzcEJgs/discussion > > It is surprising that nothing has been done to correct this problem. But > reading that thread > explains why. It is not a matter of mathematics or computer science, but a > matter of sociology. Well, concerning "nothing has been done" it depends what "this problem" is. If you mean exact expression appearing in the report, it is just one of several thousends of possible inputs. If you mean problem Juanjo raised (better support of special functions), then a lot happened. In particular FriCAS is now quite good at _indefinite_ integrals with result involving 'erf'. Concerning sociology, any specific integral could be added via pattern matching (FriCAS has special pattern matcher for definite integrals), that is about 40 lines of code. That is great for benchmarketing (you can show 100% success rate on any small testsuite). However, if you want comprehensive support in that way you would need to add hundreds or thousends of integrals meaning several thoushends of lines of code. Tedious and still it would be easy to find integrals which are not handled. I prefer algorithms that handle _all_ functions in given relatively large class. To put is differently, if I thought that handling of this specific Gaussian integral is most imporant feature for FriCAS I would implement it. But fixing via special cases several such "most imporant features" would soak all time that I can spent on FriCAS developement and IMO would result in much weaker system compared to current FriCAS. > To us physicists, Juanjo in that thread and myself, a CAS should be a tool > that helps us save > time by performing the calculations that come up in our work. But to the > current maintainers of > the big three: Maxima, FriCAS and Reduce, it does not matter that their > programs cannot calculate > Gaussian integrals (all three have failed my tests). World is not black and white. You write "Gaussian integrals" in the plural here, so maybe you mean things like (indefinite) integrate(x^16*exp(-x^2), x) In the past FriCAS could not do them, now it is handled by general routine. So it matters. But fixing _one_ definite integral is not very significant when there are thousends of similar cases. Now, solutions that handle large classes take time to develop. IMO seeking general solutions pays in longer time. Extra remark about "does not matter": if I would serioulsy worry about every similar problem/bug I would quickly end up in a madhouse with serious mental ilness. And the same applies to other sofware. Mathematica and Maple are very secretive about their problems, but there are enough reports to know that they have a lot of problems. > In the Axiom/FriCAS wiki it is claimed that this CAS boasts the most > complete implementation of the > Risch algorithm. And I am sure that it can calculate thousands of > integrals. But what is the purpose of > having a sophisticated integrator if it cannot calculate the simplest > integrals? In the thread above > Waldek replies: do not use it for calculating integrals you already know. > Seriously? Read carefuly, it is not what I wrote. Hint: I was discussing possible _pragmatic_ approches given current FriCAS limitations. And in this disscussion you were given IMHO reasonable workaround (using fourth power of parameter), so this problem is not a "killer" in sense that stops you from doing serious work. Annoying, yes, so I understand why you are annoyed... -- Waldek Hebisch -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
