Better support for surds: conversion between powers and roots

[sangwinc]

From the Zulip chat: persuade Maxima to display 2^(1/2) as sqrt(2).

[georgeionutionita]

When displaying mathematical expressions, positive rational powers such as $2^{5/2}$ or $3^{3/4}$ are often more naturally expressed using surds. Although Maxima supports noun forms such as sqrt and root, it does not currently provide a general mechanism for rewriting arbitrary positive rational powers into these forms.

The reroot function rewrites positive rational powers as equivalent noun root expressions while preserving the surrounding expression. The current implementation works for arbitrary positive rational exponents and leaves other cases (such as negative exponents or integer powers) unchanged.

If this simplification could be controlled, it would make displaying surds in a more natural form much easier.

Test examples

• reroot(x^2) → $x^2$
• reroot(2*3^(3/4)) → $2 \cdot \sqrt[4]{3^3}$
• reroot(2^(5/2)) → $2^2 \cdot \sqrt{2}$
• reroot(3*7^(-1/2)) → $3 \cdot 7^{-\frac{1}{2}}$ (negative exponents are left unchanged)

One can modify the function reroot such that reroot(2^(5/2)) → $4 \cdot \sqrt{2}$.

[sangwinc]

Thanks @georgeionutionita we now have a branch (https://github.com/maths/moodle-qtype_stack/tree/iss1816) which we can use to add and test this, and consolidate the topic of surds in STACK more generally.

[sangwinc]

@georgeionutionita just to warn you that I've moved the surds.mac file, and changed branches: #iss1816b

The surds.mac file is now here: https://github.com/maths/moodle-qtype_stack/blob/iss1816b/stack/maximasrc/surds/surds.mac

We still have some decisions to make, but I think most of the changes from now will be in this file. You'll notice this auto-builds the docs for any functions we add, which is part of the motivation for the re-factoring.

[bgailer]

Hello,

me and my colleague developed some helper functions for changing the display of surds over the time as we often did not want Maxima to output rational exponents. The reroot function now helps with a lot of cases of surd display for us :)

@sangwinc We have also developed some code for dealing with the display of surds. Some of it is now already done by reroot but we also cover moving surds out of the denominator. If you like we can send you our code together with some testcases, maybe parts of it could also be added to the surds.mac file.

[sangwinc]

@bgailer thanks so much for picking this up. I've been talking with Prof. Meike Akveld during the STACK conference last week in Nairobi about what to do about this issue. We want to write a short account of the actual mathematical issue so we can make sure we are clear about the choices (and there are choices!) to be made. It this this is a good way to proceed, and I hope @georgeionutionita will help write this. It won't be long or complicated, and these things always turn out to be interesting.

If you have some code, then I would be very grateful if you're willing to include this in the core of STACK @bgailer. We haven't released this yet, and if you already have questions I hope we can include your code without breaking your existing questions!