Hi!

I'm new to Mathematica, and am trying to sum up some a function I've defined as so

f[x, k] = 4/Pi * (-4 k)/(1 - k^2)^2 * Cos[k*x]

Plot[Sum[f[x, k], {k, 2, 30}], {x, 0, Pi}]

If I take the body of the function and replace f[x, k] with it in the Sum call, then everything works fine

But when I do it this way, it gives me a blank graph. Could anyone please give some advice as to how I can fix this?

Thinking about a new MacBook Pro. How much does Mathematica take advantage of multicore?

macrumors.com/2021/10/23/8-core-14-inch-macbook-pro-benchmark

Beware of your license too, because eg the Home license only lets you use 4 parallel kernels (for Parallelize etc).

However the new M1X and etc chips look absolutely excellent for single-core use too, so I doubt you'd go far wrong if you did get one. Only thing might be neural network training (until they get that properly working on the new processor) and the odd architecture-related bug or incompatabillity.

here's my geekbench results in case it does anything for you, system spec is here: mathematica.stackexchange.com/a/238024/57593

I imagine Mathematica would absolutely fly with a single-core speed like the one the new Macbook processors have... almost enough to get me to switch back :D

@ChrisK It depends on license you use. At least home use license is for four cores (I wonder if one can get extra capacity nowadays by buying processor-hours, it can be done on AWS at least). I wonder if they're bumping up those license based numbers at some point...

@CarlLange @kirma Thanks for the info! So, outside explicitly using Parallelize (which I never do), Mathematica doesn't take advantage of extra cores? Sounds like cheaper = fine then.

I think the new entitlement system could be used to buy more parallelism for a specified amount of time. I think it costed something like a cent per core-hour, maybe? It's quite a while since I tested it last time.

CreateLicenseEntitlement etc.

Some parallelism (mostly on vector/matrix/tensor numerics) might be available independent of licensing... maybe.

Parallelism in symbolic computation is tricky anyway unless you can effectively transform it to ParallelMap or such.

@ChrisK the big (potential) benefit is in anything that happens at the MKL level/low library level/through Parallel->True in Compile. That's only really possible for numerical stuff, but can provide some dramatic benefits and that parallelism directly benefits from more cores/hardware threads

@b3m2a1 There's that certain level of inconvience on getting stuff compiled... I guess I resort to it only when problems are suitably numerical and run times without ocmpilation totally intolerable...

Although I see that there are horrible inefficiencies from time to time in Mma, I think I haven't really resorted to compilation this year. Waiting couple minutes to couple hours is usually just fine instead of spending timee on that effort.

@kirma depends on your problem/your familiarity with Compile. I've had numerically heavy workflows and compiling pieces of the flow has led to many hours of savings with lowish effort

I love the crazies in the chat of the Live CEOing videos but I gotta feel bad for the person who has to read through to find useful questions to promote. It's just a constant stream of nonsense