I have been so busy this week, I forgot to blog about our latest Maxima release, 5.39. Nothing spectacular, just incremental improvements over 5.38; for me, this was a big milestone though as this was the first time that I used a CentOS platform to prepare the release. (Which, incidentally, is why I haven’t done this months ago.)

And SourceForge, kindly enough, once again designated Maxima as one of the site’s Projects of the Week.

Sometime last year, I foolishly volunteered to manage new releases of the Maxima computer algebra system (CAS).

For the past several weeks, I’ve been promising to do my first release, but I kept putting it off as I had other, more pressing work obligations.

Well, not anymore… today, I finally found the time, after brushing up on the Git version management system, and managed to put together a release, 5.38.0.

Maxima is beautiful and incredibly powerful. I have been working on its tensor algebra packages for the past 15 years or so. As far as I know, Maxima is the only general purpose CAS that can derive the field equations of a Lagrangian field theory; for instance, it can derive Einstein’s field equations from the Einstein-Hilbert Lagrangian.

I use Maxima a lot for tensor algebra, though I admit that when it comes to integration, differential equations or plotting, I prefer Maple. Maple’s ODE/PDE solvers are unbeatable. But when it comes to tensor algebra, or just as a generic on-screen symbolic calculator, Maxima wins hands down. I prefer to use its command-line version: Nothing fancy, just ASCII art, but very snappy, very responsive, and does exactly what I want it to do.

So then, Maxima 5.38.0: Say hi to the world. World, this is the latest version of the oldest (nearly half a century old) continuously maintained CAS in existence.

I was having a discussion with a lawyer friend of mine. I was trying to illustrate the difference between the advocating done by lawyers and the scientist’s unbiased (or at least, not intentionally biased) search for the truth. One is about cherry-picking facts and arguments to prove a preconceived notion; the other about trying to understand the world around us.

I told him that anything and the opposite of anything can be proven by cherry-picking facts. Then it occurred to me that it is true even in math. For instance, by cherry-picking facts, I can easily prove that $$2\times 2=5$$. Let’s start with three variables, $$a$$, $$b$$ and $$c$$, for which it is true that $$a=b+c$$. Then, multiplying by 5 gives

$$5a=5b+5c.$$

Multiplying by 4 and switching the two sides gives

$$4b+4c=4a.$$

Adding these two equations together, we get

$$5a+4b+4c=4a+5b+5c.$$

Subtracting $$9a$$ from both sides, we obtain

$$4b+4c-4a=5b+5c-5a,$$

or

$$4(b+c-a)=5(b+c-a).$$

Dividing both sides by $$b+c-a$$ gives the final result:

$$4=5.$$

And no, I did not make some simple mistake in my derivation. In fact, I can use computer algebra to obtain the same result, and computers surely don’t lie. Here it is, with Maxima:

(%i1) eq1:5*a=5*b+5*c$(%i2) eq2:4*b+4*c=4*a$
(%i3) eq3:eq1+eq2$(%i4) eq4:eq3-9*a$
(%i5) eq5:factor(eq4)\$
(%i6) eq6:eq5/(b+c-a);
(%o6)                                4 = 5

All I had to do to make this happen was to ignore an inconvenient little fact, which is precisely what lawyers (not to mention politicians) do all the time. Surely, if I can prove that $$2\times 2=5$$, I can prove anything. So can lawyers and they know it.

Maxima is an open-source computer algebra system (CAS) and a damn good one at that if I may say so myself, being one of Maxima’s developers.

Among other things, Maxima has top-notch tensor algebra capabilities, which can be used, among other things, to work with Lagrangian field theories.

This week, I am pleased to report, SourgeForge chose Maxima as one of the featured open-source projects on their front page. No, it won’t make us rich and famous (not even rich or famous) but it is nice to be recognized.

An interesting anniversary today: 25 years ago, on March 15, 1985, the first ever .com domain name was registered, symbolics.com. The company, in addition to building their own brand of “Lisp Machine” computers, also happened to be selling the commercial version of the MACSYMA computer algebra software. The same software that, in the form of its open-source version, Maxima, continues to evolve thanks to a devoted team of developers… of which I happen to be one.

Alas, Symbolics is no longer, at least not the original company. A privately held company by the same name which obtained much of Symbolics’ assets still sells licenses of the old MACSYMA code.