The last functions to be added were the Coulomb wavefunctions (relevant for studying quantum scattering processes). And over the years in the development of Wolfram Language we’ve steadily been checking off more functions from Abramowitz & Stegun.Īnd in Version 13.0 we’re finally done! All the functions in Abramowitz & Stegun are now fully computable in the Wolfram Language. It listed hundreds of functions, some widely used, others less so. When I first started using special functions about 45 years ago, the book that was the standard reference was Abramowitz & Stegun’s 1964 Handbook of Mathematical Functions.
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In the Wolfram Language, we’ve always taken special functions very seriously, not only supporting a vast collection of them, but also making it possible to evaluate them to any numerical precision, and to have them participate in a full range of symbolic mathematical operations. Special functions are in a sense a way of packaging mathematical knowledge: once you know that the solution to your equation is a Lamé function, that immediately tells you lots of mathematical things about it. Mathematical Functions: A Milestone Is Reachedīack when one still had to do integrals and the like by hand, it was always a thrill when one discovered that one’s problem could be solved in terms of some exotic “ special function” that one hadn’t even heard of before. In Version 12.3 the same integral could still be done, but only in terms of elliptic integrals: Here’s an integral that couldn’t be done “in closed form” before, but in Version 13.0 it can: And a third of a century later-in Version 13.0-we’re delivering another jump forward. Over the years, we’ve gradually increased the range of integrals that can be done. Don’t Forget Integrals!īack in 1988 one of the features of Mathematica 1.0 that people really liked was the ability to do integrals symbolically. But here I’ll just concentrate on what’s new in Version 13.0 relative to Version 12.3 I’ve written before about Version 12.1, Version 12.2 and Version 12.3. The complete span of what’s new in Version 13 relative to Version 12 is very large and impressive. And, of course, today we can and do write perhaps a hundred times more extensive and detailed documentation than would have ever fit in the (printed) Mathematica Book of 1988. Because when we add a function today the expectations are so much higher than in 1988-because there’s so much more automation we can do, and so much more in the whole system that we have to connect to and integrate with. And it’s actually even more impressive than that. Yet between Version 12.0 and Version 13.0 we’ve now added a total of 635 new functions (in addition to the 702 functions that have been updated and upgraded). In Version 1.0 there were a total of 554 functions altogether. And that is why we’re able to reach so far, automate so much-and invent so much. What we build today is not built from scratch it is built on top of the huge tower of capabilities that we have built before. Because those are what have allowed what is now a huge system to maintain its coherence and consistency-and to grow ever stronger. But it also reflects something else: the success of the core design principles of the Wolfram Language. And now we can see the results of all those individual ideas and projects and pieces of work: a steady drumbeat of innovation sustained now over the course of more than a third of a century: And I’m pleased to say that in that short time an impressive amount of R&D has come to fruition: not only a total of 117 completely new functions, but also many hundreds of updated and upgraded functions, several thousand bug fixes and small enhancements, and a host of new ideas to make the system ever easier and smoother to use.Įvery day, every week, every month for the past third of a century we’ve been pushing hard to add more to the vast integrated framework that is Mathematica and the Wolfram Language. It’s 207 days-or a little over 6 months-since we released Version 12.3. (Yes, the 1, 3 theme-complete with the fact that it’s the 13th of the month today-is amusing, if coincidental.) Today I’m excited to announce the latest results of our long-running R&D pipeline: Version 13 of Wolfram Language and Mathematica. Just a few weeks ago it was 1/3 of a century since Mathematica 1.0 was released.
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