[Maxima-bugs] [maxima:bugs] #5613 rectform, polarform and carg disagree with (-8)^(1/3) = -2 under domain : real

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

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

Fixed by commit [ddfef2].



---

**[bugs:#5613] rectform, polarform and carg disagree with \(-8\)^\(1/3\) = -2 under domain : real**

**Status:** closed
**Group:** None
**Labels:** rectform polarform carg domain real 
**Created:** Tue Sep 29, 2026 11:07 AM UTC by David Scherfgen
**Last Updated:** Tue Sep 29, 2026 11:08 AM UTC
**Owner:** nobody


With the default `domain : real`, the simplifier takes the real root for an odd root of a negative number, so `(-8)^(1/3)` simplifies to `-2`, and `sign` agrees. `rectform`, `realpart`, `imagpart`, `polarform` and `carg` take the principal branch instead, so substituting before or after them gives different results. `conjugate` doesn't simplify such a power at all, although it is real:

```
(%i1) display2d:false$
(%i2) rectform(x^(1/3));
(%o2) %i*sin(atan2(0,x)/3)*abs(x)^(1/3)+cos(atan2(0,x)/3)*abs(x)^(1/3)
(%i3) subst(x = -8,%);
(%o3) sqrt(3)*%i+1
(%i4) rectform(subst(x = -8,x^(1/3)));
(%o4) -2
(%i5) carg(x^(1/3));
(%o5) atan2(0,x)/3
(%i6) subst(x = -8,%);
(%o6) %pi/3
(%i7) polarform(x^(1/3));
(%o7) %e^((%i*atan2(0,x))/3)*abs(x)^(1/3)
(%i8) subst(x = -8,%);
(%o8) 2*((sqrt(3)*%i)/2+1/2)
(%i9) conjugate(x^(1/3));
(%o9) conjugate(x^(1/3))
```

For a base known to be negative, `rectform` and `polarform` contradict `sign`, and `carg` contradicts `polarform`:

```
(%i10) assume(y < 0)$
(%i11) sign(y^(1/3));
(%o11) neg
(%i12) rectform(y^(1/3));
(%o12) (sqrt(3)*%i*(-y)^(1/3))/2+(-y)^(1/3)/2
(%i13) imagpart(y^(1/3));
(%o13) (sqrt(3)*(-y)^(1/3))/2
(%i14) carg(y^(1/3));
(%o14) %pi
(%i15) polarform(y^(1/3));
(%o15) %e^((%i*%pi)/3)*(-y)^(1/3)
(%i16) conjugate(y^(1/3));
(%o16) conjugate(y^(1/3))
```

Under `domain : real`, these functions should treat an odd root of a real base as the real root, like the simplifier and `sign` do. With `domain : complex`, the principal branch is correct.


---

Sent from sourceforge.net because max...@li... is subscribed to https://sourceforge.net/p/maxima/bugs/

To unsubscribe from further messages, a project admin can change settings at https://sourceforge.net/p/maxima/admin/bugs/options.  Or, if this is a mailing list, you can unsubscribe from the mailing list.