5 ms·

How good is symbolic math in comparison to Mathematica?

leephillips 8y ago
It's not a symbolic math program, although there is a symbolic math package for it, that I haven't tried.
cultus 8y ago
As leephilips said, there's a package, but it's nowhere near what Mathematica can do symbolically. Julia was more intended as a numerical Matlab replacement. However, it could have a lot of potential here. It is a fully homoiconic language with real macros, so it could be a very good fit for symbolic math, just as Maxima is built in Common Lisp. It would be great if there was a real effort towards that. Mathematica is still really the only game in town.
- waldrews 8y ago
  It's surprising to me that there isn't a good way to call Maxima from either Python/R/Julia or even a non-CL lisp. Since Maxima runs on top of Common Lisp, could it run on a JVM-based Common Lisp, and exchange objects with Clojure? Could the CLASP project, CL on the LLVM, lead to a Julia-Maxima bridge? Any other integration ideas from the Common Lisp folks?
cultus 8y ago
Replying to your other comment >It's surprising to me that there isn't a good way to call Maxima from either Python/R/Julia or even a non-CL lisp. There's Sage, which integrates Scipy/Numpy, Maxima, and some other things. However, I personally find Maxima to be pretty awful to use, and even it is nowhere close to Mathematica in functionality at this point. Mathematica itself is horrible to use (although extemely capable), so I'd love an open source, good alternative.
- ssivark 8y ago
  A general comment about Mathematica, not just a response to the comment above: Trying to use Mathematica like Python/Matlab is setting yourself up for failure. It took me a few months of getting frustrated with Mathematica till I suddenly "got" it [1]. But once I understood that it's programming model revolves around pattern matching and string replacement, things just clicked and it was very easy to write Mathematica code after that. [1] Coincidentally, I was reading a little bit about functional programming when Mathematica finally started making sense. In particular, IIRC, I was looking at "Learn You a Haskell" for fun, unrelated to Mathematica, which was for work.
  - cultus 8y ago
    The term-rewriting paradigm of Mathematica is very cool, kind of like lisp rotated a few degrees. I'd really like to see a more mainstream language adopt that approach. My complaints are more about everything else. Insane scoping rules and constructs (like variables shared between notebooks), and how it is difficult to productively use the language outside of the GUI, but yet the text editor is beyond awful (can't undo more than once, no redo). That and the cells and such drive me crazy. I'm no expert, but I've been forced to use it on a few occasions, and I've hated every minute of it. I'm fairly fluent in several of languages in different paradigms, but the frustration I experience with Mathematica is worse than any of them.
KenoFischer 8y ago
The project to watch here is http://nemocas.org/ http://nemocas.org/, which is built on top of Julia, but julia itself is not a CAS.

It's not a symbolic math program, although there is a symbolic math package for it, that I haven't tried.

As leephilips said, there's a package, but it's nowhere near what Mathematica can do symbolically. Julia was more intended as a numerical Matlab replacement. However, it could have a lot of potential here. It is a fully homoiconic language with real macros, so it could be a very good fit for symbolic math, just as Maxima is built in Common Lisp. It would be great if there was a real effort towards that. Mathematica is still really the only game in town.

waldrews 8y ago
It's surprising to me that there isn't a good way to call Maxima from either Python/R/Julia or even a non-CL lisp. Since Maxima runs on top of Common Lisp, could it run on a JVM-based Common Lisp, and exchange objects with Clojure? Could the CLASP project, CL on the LLVM, lead to a Julia-Maxima bridge? Any other integration ideas from the Common Lisp folks?

cultus 8y ago

Replying to your other comment >It's surprising to me that there isn't a good way to call Maxima from either Python/R/Julia or even a non-CL lisp. There's Sage, which integrates Scipy/Numpy, Maxima, and some other things. However, I personally find Maxima to be pretty awful to use, and even it is nowhere close to Mathematica in functionality at this point. Mathematica itself is horrible to use (although extemely capable), so I'd love an open source, good alternative.

ssivark 8y ago
A general comment about Mathematica, not just a response to the comment above: Trying to use Mathematica like Python/Matlab is setting yourself up for failure. It took me a few months of getting frustrated with Mathematica till I suddenly "got" it [1]. But once I understood that it's programming model revolves around pattern matching and string replacement, things just clicked and it was very easy to write Mathematica code after that. [1] Coincidentally, I was reading a little bit about functional programming when Mathematica finally started making sense. In particular, IIRC, I was looking at "Learn You a Haskell" for fun, unrelated to Mathematica, which was for work.
- cultus 8y ago
  The term-rewriting paradigm of Mathematica is very cool, kind of like lisp rotated a few degrees. I'd really like to see a more mainstream language adopt that approach. My complaints are more about everything else. Insane scoping rules and constructs (like variables shared between notebooks), and how it is difficult to productively use the language outside of the GUI, but yet the text editor is beyond awful (can't undo more than once, no redo). That and the cells and such drive me crazy. I'm no expert, but I've been forced to use it on a few occasions, and I've hated every minute of it. I'm fairly fluent in several of languages in different paradigms, but the frustration I experience with Mathematica is worse than any of them.

KenoFischer 8y ago

The project to watch here is http://nemocas.org/ http://nemocas.org/, which is built on top of Julia, but julia itself is not a CAS.