9 ms·

Fricas (a fork of Axiom, which is a rename of Scratchpad 2) is another very old CAS implemented with Lisp, also now open sourced. I think Fricas is more powerfu

by nsajko 6y ago

Fricas (a fork of Axiom, which is a rename of Scratchpad 2) is another very old CAS implemented with Lisp, also now open sourced. I think Fricas is more powerful than Maxima (maybe much more) regarding symbolic integration and its type system, but it sadly has very few developers maintaining it. Fricas links: https://en.wikipedia.org/wiki/FriCAS https://en.wikipedia.org/wiki/FriCAS https://fricas.github.io https://fricas.github.io https://fricas.github.io/book.pdf https://fricas.github.io/book.pdf Axiom links: https://en.wikipedia.org/wiki/Axiom_(computer_algebra_system) https://en.wikipedia.org/wiki/Axiom_(computer_algebra_system... https://github.com/daly/axiom https://github.com/daly/axiom

kzrdude 6y ago
There must be a reason that maxima is more widely used. Is Maxima easier to use? Or did maxima just have better distribution channels?
- blihp 6y ago
  At least a couple of non-technical reasons: I believe Maxima was open sourced a few years earlier (1998 vs 2001) which helped it get established. Maxima was also supported by a rather prolific open source developer which probably helped a community coalesce around it. Axiom, on the other hand, looks like it was more of a 'throw it over the wall' open source project which only happened after it failed commercially.
  - lokedhs 6y ago
    Axiom is also not a normal Lisp program. Maxima can be loaded using ASDF and you can hack on it like any other Lisp project. Axiom in the other hand generates Lisp code from some other format and is rather incomprehensible to someone just coming into the project. Not that Maxima is all that easy to understand either. The nature of the software makes it complicated, but there is code in there from the 60's, which carries with it some more the classic issues with Lisp code from that era, short symbol names, use of dynamic variables, etc.
    - jart 6y ago
      Axiom is sort of like Scratchpad source code converted to Literate Programming, and since TeX is near impossible to build these days, that makes Axiom score low on the hackability scale. Fricas on the other hand is much easier to build. However a lot of the equations that are programmed into the system, are sort of like ASCII art mathematics that the system is trained to decipher. A lot of those certainly got handed down over the decades of people figuring things out at IBM.
SiempreViernes 6y ago
Does it come with proper equation printing? A big problem for me getting into Maxima is that the frontends I've found are pretty unstable and the terminal version only does equations as ascii art, which I just cant' stand reading.
- forgotpwd16 6y ago
  >pretty unstable What do you mean? wxMaxima has worked fine for me.
  - jgalt212 6y ago
    I've had good success with wxMaxima as well, but none of the equations I've worked with can fill a blackboard. SymPy is very nice as well, but for obvious reasons, it feels a bit more forced when interacting with it.
    - lokedhs 6y ago
      Do you accept the output from Climaxima? Granted, the project isn't near finished (currently held back due to some dependency issues). I included some example videos in this reply: https://news.ycombinator.com/item?id=24467593 https://news.ycombinator.com/item?id=24467593
    - ogogmad 6y ago
      I use Sympy interactively, and I don't know what you mean by "forced". It doesn't feel that way to me.
      - jgalt212 6y ago
        this is a bit rush, but an example setting up the quadratic equation. f(x) := a*x^2 + b*x + c solve( f(x),x ); from sympy import symbols, solve a, b, c, x = sympy.symbols(('a', 'b', 'c', 'x')) y = sympy.Eq(a*x**2+b*x+c, 0) solve(y, x)
        6y ago
jxy 6y ago
> 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...
  - 6y ago

by nsajko 6y ago

kzrdude 6y ago

There must be a reason that maxima is more widely used. Is Maxima easier to use? Or did maxima just have better distribution channels?

blihp 6y ago
At least a couple of non-technical reasons: I believe Maxima was open sourced a few years earlier (1998 vs 2001) which helped it get established. Maxima was also supported by a rather prolific open source developer which probably helped a community coalesce around it. Axiom, on the other hand, looks like it was more of a 'throw it over the wall' open source project which only happened after it failed commercially.
- lokedhs 6y ago
  Axiom is also not a normal Lisp program. Maxima can be loaded using ASDF and you can hack on it like any other Lisp project. Axiom in the other hand generates Lisp code from some other format and is rather incomprehensible to someone just coming into the project. Not that Maxima is all that easy to understand either. The nature of the software makes it complicated, but there is code in there from the 60's, which carries with it some more the classic issues with Lisp code from that era, short symbol names, use of dynamic variables, etc.
  - jart 6y ago
    Axiom is sort of like Scratchpad source code converted to Literate Programming, and since TeX is near impossible to build these days, that makes Axiom score low on the hackability scale. Fricas on the other hand is much easier to build. However a lot of the equations that are programmed into the system, are sort of like ASCII art mathematics that the system is trained to decipher. A lot of those certainly got handed down over the decades of people figuring things out at IBM.

SiempreViernes 6y ago

Does it come with proper equation printing? A big problem for me getting into Maxima is that the frontends I've found are pretty unstable and the terminal version only does equations as ascii art, which I just cant' stand reading.

forgotpwd16 6y ago
>pretty unstable What do you mean? wxMaxima has worked fine for me.
- jgalt212 6y ago
  I've had good success with wxMaxima as well, but none of the equations I've worked with can fill a blackboard. SymPy is very nice as well, but for obvious reasons, it feels a bit more forced when interacting with it.
  - lokedhs 6y ago
    Do you accept the output from Climaxima? Granted, the project isn't near finished (currently held back due to some dependency issues). I included some example videos in this reply: https://news.ycombinator.com/item?id=24467593 https://news.ycombinator.com/item?id=24467593
  - ogogmad 6y ago
    I use Sympy interactively, and I don't know what you mean by "forced". It doesn't feel that way to me.
    - jgalt212 6y ago
      this is a bit rush, but an example setting up the quadratic equation. f(x) := a*x^2 + b*x + c solve( f(x),x ); from sympy import symbols, solve a, b, c, x = sympy.symbols(('a', 'b', 'c', 'x')) y = sympy.Eq(a*x**2+b*x+c, 0) solve(y, x)
      - 6y ago

jxy 6y ago

> 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...
- 6y ago