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How to handle big expressions in Mathematica

5 Replies

After 9 days, no reaction from Wolfram developers ?! Why I am not surprised...

I am really not sure if WR already knows who is the Mathematica main user group, which is using Mathematica for serious symbolic (!!!) computations trying to solve huge and challenging problems. Because only this user group is able to point out on serious performance issues with basic symbolic functionality.

From my point of view, the WR is now focused mainly on non-important "whistles and bells" improvements (GUI, AI and other irrelevant functionalities), without any significant impact on the core symbolic functionalities and its performance.

Current typical Mathematica use case scenario in HEP and other theoretical physics research use the Mathematica only as the comfortable pre-post processor for external specialized symbolic solvers (like FORM, ...). This is definitely not a way expected from Mathematica by theoretical physicists.

Any significant performance improvement on core level symbolic functionalities would have definitely great positive impact on all use case scenarios in general, even on high school and undergrad math education.

Current common status of Mathematica in the theoretical physics research community is as follows:

  • very nice GUI + Documentation
  • a lot of functionalities, covering nearly all domains of mathematics... but effective often only on the trivial introductory level (toy problems)
  • in a case of more complex (size, dimension, generality) problems, the usefulness of Mathematica terribly fast decreasing up to totally unusable tool
  • nobody (!!!) at theoretical physics community is really officially sure if Mathematica is worth for the money ... This is the main reason why only Universities buy global licenses. Separate small research groups do not buy Mathematica and use other more specialized but far more effective (open-source) tools and Mathematica play only sometimes a role of tool-in-between

Thanks for writing this up, I will certainly have a look to see whether the methods/workarounds you present here could be used in my research, though of course I run most computationally expensive calculations in FORM.

I think your conclusions nicely summarize the feelings of the theoretical physics community; we spend a lot of money on Mathematica licenses, while the development efforts and direction hardly benefit us at all (here I acknowledge at least recent efforts to improve polynomial arithmetic performance through the use of FLINT). It is quite discouraging to see some of the new features introduced lately when some core functionality is so inadequate for our needs. If Mathematica 15 were simply "Mathematica 14, but much faster, and no regressions in Series" I think we would consider this to be a release actually worth paying for.

I would also be very interested to hear any opinions of the developers on this topic.

POSTED BY: Josh Davies
Posted 2 months ago

As someone who uses Mathematica every day for my own research, I can strongly relate to the ideas mentioned in this post. I prefer working with Mathematica, but it is always frustrating when I have to switch to other tools because handling symbolic expressions becomes too difficult or counterintuitive.

I would definitely support the directions for future development that were mentioned.

POSTED BY: Leonid Shumilov
Posted 2 months ago

Good read! +1

POSTED BY: Zoltán Péli

Excellent post!!! I agree with all your conclusions and recommendations!!! I am really very curious how will react community and mainly WR staff.

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