4 ms·

> I think Fricas is more powerful than Maxima (maybe much more) regarding symbolic integration and its type system Citations or proofs?

• muizelaar 6y ago
  https://www.12000.org/my_notes/CAS_integration_tests/reports/rubi_4_16_1_graded/inch1.htm#x2-30001.2 https://www.12000.org/my_notes/CAS_integration_tests/reports... gives Fricas solving 68% of the integrals vs. Maxima's 43%
• nsajko 6y ago
  The linked Wikipedia page already mentions the Risch-Bronstein-Trager algorithm, which is supposedly implemented most fully in Fricas (i.e. Fricas or Axiom should, modulo bugs, be able to find an elementary function integral for any function that has an elementary function integral). But note that even in Fricas, there are still unimplemented cases of the "Risch algorithm" (and bugs), as the problem is hard and requires a lot of work and knowledge. You probably want something more concrete, so take a look at this effort to test symbolic integration software using a common testsuite: https://www.12000.org/my_notes/CAS_integration_tests/reports/rubi_4_16_1_graded/inch1.htm#x2-10001 https://www.12000.org/my_notes/CAS_integration_tests/reports... Fricas scores quite a bit better than Maxima there, but note that there are big problems with the test, although there is a somewhat active effort to improve its accuracy. It is problematic (but understandable) that the test uses Sage, as the Sage interface to Fricas, at least, is imperfect. I.e., AFAIK some of the integration tests will fail simply because Sage fails to communicate with Fricas successfully. Main page of the integration tests: https://www.12000.org/my_notes/CAS_integration_tests/index.htm https://www.12000.org/my_notes/CAS_integration_tests/index.h... Fricas (and Axiom) also has a more well thought out type system (with type checking at time of compilation) than other computer mathematics systems, so writing Fricas programs (the language is called Spad, which presumably comes from Scratchpad) is nice. (Fricas can be used both interactively and as a compiled language.) This mailing list discussion may also be of interest: https://groups.google.com/forum/#!topic/fricas-devel/xVtvZ46KpGs https://groups.google.com/forum/#!topic/fricas-devel/xVtvZ46...
  • jxy 6y ago
    That's a very complete analysis. Thanks. I really wish researchers could spend their time developing on top of open sourced CAS engines.