Raymond Toy

The link you provided for Mathematica has a definition in terms of log. I find it's notation a bit confusing as well. But https://functions.wolfram.com/ElementaryFunctions/ArcTan2/19/ has formulas for the real and imaginary parts. These are quite messy. I didn't check to see if these are equivalent to the log definition when using complex values.

Your version of maxima is too old. This was fixed a while ago. I get: (%i31) rectform(atan2(x,%i)); Evaluation took 0.0100 seconds (0.0000 elapsed) using 302.539 KB. 2 2 atan2(x + 1, 0) - atan2(0, x - 1) abs(x + 1) (%o31) ──────────────────────────────────── - %i log(──────────────) 2 │ 2 │ sqrt(│x - 1│) Didn't check to see if that's correct, though.

integrate, asksign, part of answer doesn't use result

We could look at the operators property. For gamma, it's simp-%gamma. Using Lisp (trace simp-%gamma) does something reasonable. I don't know how to hook up Maxima's tracing functions for this, though.

Looking at the code for trigsolve, I see it calls to_poly_solve. But it doesn't load that, so results are funny. I get just {0} for trigsolve(sin(100*x)=0,0,10*%pi). But after loading to_poly_solve, I get your results. Also, there's this line in trigsolve: (makelist(ev(s[i],%z0=k),k,-10,10), I think that explains the fact that only 10 results are returned. (Well, 21 at most.) We could probably make this smarter figuring out an appropriate range of k values based on the limits a and b, assuming they're...

Agreed. For just about any user, trigeval does everything needed. trigvalue is basically an internal function that users don't really need to know. Since this was all written by Aleksas Domarkas, I defer to him on this. But the online documentation should probably remove references to trigvalue.

Ah, the difference between trigvalue and trigeval is the argument. The documentation isn't super clear about this, but trigvalue takes one trig function of the form trig(m*%pi/n). trigeval can handler expressions containing many trig functions. The docs need to make this distinction clearer, even though it does mention this.

Ah, looks like I missed some items. The first line of the example for trigeval shows that you need to load the package. I'm also not sure what the difference is between trigvalue and trigeval. I'll have to look at the code. There are some other bugs in the docs as well. trigsolve shows only one arg, but it actually takes 3. So we need to mention that the package to load and these other issues need to be fixed.