Integral Calculator

by beckthompson • 2 years ago

96 24 2 years ago

blobcode• 2 years ago

I think the really neat piece of software behind this is maxima (https://maxima.sourceforge.io/), a rather influential computer algebra system of ancient lineage still in use today in more places than you might think.

kristopolous2• 2 years ago

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

anthk4• 2 years ago

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

lupire• 2 years ago

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.

nsajko2• 2 years ago

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

cjk22• 2 years ago

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

enriquto• 2 years ago

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.

constantcrying2• 2 years ago

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.

nsajko2• 2 years ago

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...

iillexial• 2 years ago

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

anthk4• 2 years ago

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

mochito_bottle• 2 years ago

I love this site. Without it I wouldn't be able to self learn calc 2

beckthompson• 2 years ago

Right? Its such a useful site that is regularly updated and just made by some guy (David Scherfgen) and not a big company trying to make money (E.g symbolab).

fragebogen• 2 years ago

Shout out to another project by the same creator: https://www.derivative-calculator.net/ Both of these helped me through my undergrad physics degree, especially because of the step-by-step solutions. Without it I wouldn't have learned nearly as much about calculus.

CamperBob2• 2 years ago

I really like the interactive function graph. Feels lightweight and snappy compared to the usual framework-driven solutions. I wish the author had gone into a bit more detail on how that works.

abhinavstarts• 2 years ago

Wow. Thanks for sharing

ekiauhce• 2 years ago

Integrating is a part of wolfram alpha, e.g https://www.wolframalpha.com/input?i=integrate+%28sin%28sqrt...

Integral Calculator

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