The custom solver is really neat too

> In order to show the steps, the calculator applies the same integration techniques that a human would apply. The program that does this has been developed over several years and is written in Maxima's own programming language. It consists of more than 17000 lines of code. When the integrand matches a known form, it applies fixed rules to solve the integral (e. g. partial fraction decomposition for rational functions, trigonometric substitution for integrands involving the square roots of a quadratic polynomial or integration by parts for products of certain functions). Otherwise, it tries different substitutions and transformations until either the integral is solved, time runs out or there is nothing left to try. The calculator lacks the mathematical intuition that is very useful for finding an antiderivative, but on the other hand it can try a large number of possibilities within a short amount of time. The step by step antiderivatives are often much shorter and more elegant than those found by Maxima.

This is known as rule-based integration. Here's a powerful system of such rules: https://rulebasedintegration.org/integrationRules.html

Does one know if mathematica uses that too ? I rememebr an HN post where one could see that sympy, maxima and the likes where way behind for a lot of more peculiar integrals..

ah the comparison is here : https://www.12000.org/my_notes/CAS_integration_tests/index.h...

(and posted by other on this very thread...)

There is a go implementation of a CAS which syntax similar to Mathematica which uses this rules based integration library.

https://github.com/corywalker/expreduce

Apparently that lineage goes back to 1968 https://en.m.wikipedia.org/wiki/Macsyma

I wonder what those early versions were like. It's on lisp so it's feasibly still runnable without too much fussing around

Compile ITS and just run :macsyma at the DDT prompt (shell/debugger) from ITS:

https://github.com/pdp-10/its

The syntax it's the same, I even made a plot and 'printed' into the host from an ARDS output from the plot command, by converting the file into PPM->PNG or PPM->PDF.

This is a plot from Macsyma converted into PDF:

http://0x0.st/X-67.pdf

that y2k bug is delightful

And it has been fixed =)

    :date
      MONDAY, APRIL 15, 2024  07:37:33 PM

Maxima ist absolutely great. It can be somewhat confusing, but it is actually quite advanced.

Calculating integrals is extremely hard (unlike calculating derivatives, which is very easy to do) and maxima comes with some of the more advanced and comprehensive strategies to solve integrals.

It's integration functionalities are less advanced and comprehensive than those of Fricas. Interestingly, the latter is, like Maxima, implemented using Lisp and stems from an ancient software lineage. Both systems are free and open-source.

Fricas home page: http://fricas.github.io

Fricas Archlinux package page: https://archlinux.org/packages/extra/x86_64/fricas/

Some independent integration benchmarks, comparing multiple computer algebra systems: https://www.12000.org/my_notes/CAS_integration_tests/index.h...

Both Fricas and Maxima use Common Lisp, most people will just use SBCL for both.

But, the magic of Lisp is that you might call Common Lisp functions from one suite into another and viceversa without too much trouble.

Fascinating, thank you!

I use it in the university and I hate it. The interface is ugly and very unintuitive, as well as the language.

Interface? You can use wxmaxima, maxima.el from Emacs (and with Gnuplot/LaTex support to render inline equations), or KDE's Cantor too.

I still use this daily. It's ugly and cranky but it works and it's the right price.

Ugly and cranky is quite subjective... As much as I like Mathematica the language, the user interfaces that they propose are so wonky and ugly (in my eyes) that Maxima feels like a breath of fresh air and elegance.

I don't disagree there.