[Maxima-bugs] [maxima:bugs] #5707 ratsimp treats sqrt(x) and x^(1/4) as unrelated

[David S. <tom...@us...>]

- **status**: open --> closed
- **Comment**:

Fixed by commit [2d498e].



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**[bugs:#5707] ratsimp treats sqrt\(x\) and x^\(1/4\) as unrelated**

**Status:** closed
**Group:** None
**Labels:** ratsimp CRE 
**Created:** Fri Oct 23, 2026 08:21 AM UTC by David Scherfgen
**Last Updated:** Fri Oct 23, 2026 08:21 AM UTC
**Owner:** nobody


By Claude:

`ratsimp` represents `sqrt(x)` and `x^(1/4)` by two independent variables. It knows that `sqrt(x)^2 = x` and `(x^(1/4))^4 = x`, but not that `(x^(1/4))^2 = sqrt(x)`. So it misses simplifications, and calling it again gives a different result:

```
(%i1) ratsimp((7^(1/4)+1)*(7^(1/4)-1)*sqrt(7));
(%o1) (sqrt(7)-1)*sqrt(7)
(%i2) ratsimp(%);
(%o2) 7-sqrt(7)
```

`fullratsimp` repeats `ratsimp` until nothing changes, but it can stop too early. This expression equals `sqrt(x)`:

```
(%i3) fullratsimp(sqrt(x)*(x^(1/4)*y+1) - x^(3/4)*y);
(%o3) sqrt(x)*(x^(1/4)*y+1)-x^(3/4)*y
```

`expand` and `radcan` simplify both examples fully.


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