josdejong/mathjs

simplify("(x^2)^0.5") should be "abs(x)"

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#3,329 opened on Nov 29, 2024

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 (5 comments) (0 reactions) (0 assignees)JavaScript (13,832 stars) (1,298 forks)batch import
bughelp wanted

Description

While there are genuine use cases when returning "x" would be better (that's what most humans would expect), strictly speaking it is incorrect.

To reproduce in the mathnotepad:

derivative("(x^2)^0.5", "x").evaluate({x:-3})
    1

derivative("(x^2)^0.5", "x", {simplify:false}).evaluate({x:-3})
    -1

Here I evaluate the same derivative at the same point x=-3 but get two different results. Same problem for x^4 and I assume all other even powers.

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Tech stack
javascript
Domain
backendapi
Issue type
bug
DifficultyEstimated implementation difficulty for a new contributor, from 1 for very small changes to 5 for expert-level work.
3
Estimated timeA rough time range for an experienced contributor to investigate, implement, test, and prepare a pull request.
1-3 hours
Activity statusHow available the issue appears right now: fresh, active, stale, blocked, or waiting on maintainer input.
fresh
ClarityHow clearly the issue explains the expected change, acceptance criteria, and next step.
clear
Prerequisites
JavaScriptbasic algebra
Newbie friendlinessA 1-100 score estimating how approachable this issue is for first-time contributors.
70
Research direction
Look at the simplify function in mathjs, particularly the rules for exponent simplification. The issue is that (x^2)^0.5 currently simplifies to x, but should be abs(x) to ensure correctness for negative x. Given that the derivative evaluation gives different results, this is a bug. Check simplify.js and the combsimp logic. Consider adding a rule that converts (x^n)^(1/m) to abs(x)^(n/m) when n is even and m is odd. There are 5 comments that may contain additional context or proposed approaches.
simplify("(x^2)^0.5") should be "abs(x)" · josdejong/mathjs#3329 | Good First Issue