maxima-bugs — Reports from the SF bug-tracking system

[Maxima-bugs] [maxima:bugs] #5717 limit() returns ind when the one-sided limits are different forms of the same number

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

---

**[bugs:#5717] limit\(\) returns ind when the one-sided limits are different forms of the same number**

**Status:** open
**Group:** None
**Labels:** limit 
**Created:** Mon Oct 26, 2026 08:22 AM UTC by David Scherfgen
**Last Updated:** Mon Oct 26, 2026 08:22 AM UTC
**Owner:** nobody


By Claude:

`limit()` computes a two-sided limit from both sides. When the two come out as different forms of the same number, it does not see that they are equal and returns `ind`:

```
(%i1) f : unit_step(x)*%e^(log(6)/2) + unit_step(-x)*sqrt(6)$
(%i2) [limit(f, x, 0, plus), limit(f, x, 0, minus), limit(f, x, 0)];
(%o2) [%e^(log(6)/2),sqrt(2)*sqrt(3),ind]
(%i3) g : unit_step(x)*%e^(log(x + 3)/3)/3 + unit_step(-x)/(x + 9)^(1/3)$
(%i4) [limit(g, x, 0, plus), limit(g, x, 0, minus), limit(g, x, 0)];
(%o4) [%e^(log(3)/3)/3,1/9^(1/3),ind]
```

`%e^(log(6)/2)` is `sqrt(6)` and `%e^(log(3)/3)/3` is `1/9^(1/3)`, so both limits exist. For the same reason `limit()` does not see that a numerator vanishes:

```
(%i5) limit((x^(1/3)*%e^(log(x)/3) - 9^(1/3))/(x - 3), x, 3);
(%o5) infinity
```

The numerator is `x^(2/3) - 9^(1/3)`, which is `0` at `x = 3`, so the limit is the derivative of `x^(2/3)` there, `2/3^(4/3)`.


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[Maxima-bugs] [maxima:bugs] #3047 'save' saves some built-in stuff

[Robert D. <rob...@us...>]

I bumped into another example today, in which restoring from `save(..., all)` changes the properties of MNCTIMES and therefore causes previously-acceptable `.12345` to trigger a syntax error. See comment referring to bug #3047 in tests/rtestdefstruct.mac.


---

**[bugs:#3047] 'save' saves some built-in stuff**

**Status:** open
**Group:** None
**Labels:** save 
**Created:** Thu Nov 12, 2015 08:11 PM UTC by Robert Dodier
**Last Updated:** Thu Nov 12, 2015 08:11 PM UTC
**Owner:** nobody


`save` should save only used-defined stuff, and not any built-in stuff. But `save` saves stuff related to sets and some function properties. E.g. Without any user-defined functions or variables, the saved file should be almost empty , but here's what I get at present for `save("/tmp/foo.lisp", all)`:

~~~~
;;; -*- Mode: LISP; package:maxima; syntax:common-lisp; -*- 
(in-package :maxima)
(DSKSETQ $%I1 '(($SAVE) "/tmp/foo.lisp" $ALL)) 
(ADDLABEL '$%I1) 
(MDEFPROP $NSET (NIL $VERSION 1.21) $PROPS) 
(ADD2LNC '$NSET $PROPS) 
(DEFPROP ${ %{ VERB) 
(DEFPROP ${ "{" OP) 
(SETF (GETHASH "{" *OPR-TABLE*) '${) 
(ADD2LNC '"{" $PROPS) 
(DEFINE-SYMBOL '"{") 
(SETQ *MOPL* (CONS '"{" *MOPL*)) 
(DEFPROP ${ DIMENSION-MATCH DIMENSION) 
(DEFPROP ${ ((#\{) #\}) DISSYM) 
(DEFPROP ${ MSIZE-MATCHFIX GRIND) 
(DEFPROP ${ 200. LBP) 
(DEFPROP ${ PARSE-MATCHFIX NUD) 
(DEFPROP %{ DIMENSION-MATCH DIMENSION) 
(DEFPROP %{ ((#\{) #\}) DISSYM) 
(DEFPROP ${ $} MATCH) 
(DEFPROP $} "}" OP) 
(SETF (GETHASH "}" *OPR-TABLE*) '$}) 
(ADD2LNC '"}" $PROPS) 
(DEFINE-SYMBOL '"}") 
(SETQ *MOPL* (CONS '"}" *MOPL*)) 
(DEFPROP $} 5. LBP) 
(DEFPROP $} DELIM-ERR NUD) 
(DEFPROP $} ERB-ERR LED) 
(DEFPROP %{ ${ NOUN) 
(MDEFPROP $TRYLEVEL (NIL $MAXMIN 1.) $PROPS) 
(ADD2LNC '$TRYLEVEL $PROPS) 
(MDEFPROP $MAXMIN (NIL $VERSION 1.) $PROPS) 
(ADD2LNC '$MAXMIN $PROPS) 
(MDEFPROP $NUMMOD (NIL $VERSION 3.) $PROPS) 
(ADD2LNC '$NUMMOD $PROPS) 
(DEFPROP $CONJUGATE SIMP-CONJUGATE OPERATORS) 
(ADD2LNC '$CONJUGATE $PROPS) 
(MDEFPROP $CONJUGATE (NIL $VERSION 1.) $PROPS) 
(ADD2LNC '$CONJUGATE $PROPS) 
(DEFPROP %ERF_GENERALIZED $ERF_GENERALIZED NOUN) 
(DEFPROP %ERF_GENERALIZED SIMP-ERF-GENERALIZED OPERATORS) 
(ADD2LNC '%ERF_GENERALIZED $PROPS) 
(DEFPROP %ERF_GENERALIZED T OPERS) 
(ADD2LNC '%ERF_GENERALIZED $PROPS) 
(DEFPROP %ERF_GENERALIZED T $ANTISYMMETRIC) 
(ADD2LNC '%ERF_GENERALIZED $PROPS) 
(DEFPROP $ERF_GENERALIZED %ERF_GENERALIZED VERB) 
(DEFPROP $BETA SIMPBETA OPERATORS) 
(ADD2LNC '$BETA $PROPS) 
(DEFPROP $BETA T OPERS) 
(ADD2LNC '$BETA $PROPS) 
(DEFPROP $BETA T $SYMMETRIC) 
(ADD2LNC '$BETA $PROPS) 
(SETQ $LINENUM 1.) 
(SETQ *ALPHABET* (NCONC '(#\_ #\%) *ALPHABET*)) 
(ADD2LNC '$INTEGERVALUED $FEATURES)
~~~~


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[Maxima-bugs] [maxima:bugs] #520 make_array arrays not well integrated

[Robert D. <rob...@us...>]

- **labels**: Lisp Core --> arrays, display, make\_array
- **Group**:  --> None



---

**[bugs:#520] make\_array arrays not well integrated**

**Status:** open
**Group:** None
**Labels:** arrays display make\_array 
**Created:** Tue Feb 24, 2004 01:31 AM UTC by Stavros Macrakis
**Last Updated:** Mon Jul 24, 2006 02:12 AM UTC
**Owner:** nobody


make\_array arrays are useful but ugly.

They don't print properly:

ar: make\_array\(any,3\)$
ar\[1\]: sin\(x\)$
ar => \#\(NIL \(\(%SIN SIMP\) $x\) NIL\)

and even worse:

string\(ar\) =>
?\\\#\\\(NIL\ \\\(\\\(\%SIN\ SIMP\\\)\ \$x\\\)\ NIL\\\)

There is no way to write a constant array, so you can't 
save it in Maxima form.

It's a pity that the function name "array" is taken... but 
we could define the external form of an array to be 
something like:

array\_constant\( <<type and maybe size>>,
\[ ...contents... \] \)

e.g.

array\_constant\(any,\[2,3,4\]\)

is the same as

block\(\[arr\],arr:make\_array\(any,3\),
for i:0 thru 2 do arr\[i\]:\[2,3,4\]\[i\]\)

etc.


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[Maxima-bugs] [maxima:bugs] #5693 elliptic_pi does not compute the principal value

[Raymond T. <rt...@us...>]

- **status**: open --> closed
- **assigned_to**: Raymond Toy
- **Comment**:

Fixed by commit [400842] by merging branch bug-5693-elliptic-pi-pv



---

**[bugs:#5693] elliptic\_pi does not compute the principal value**

**Status:** closed
**Group:** None
**Labels:** elliptic\_pi 
**Created:** Wed Oct 21, 2026 04:22 PM UTC by Raymond Toy
**Last Updated:** Wed Oct 21, 2026 04:22 PM UTC
**Owner:** Raymond Toy


elliptic_pi does not produce the principal value.  See the [mailing list](https://sourceforge.net/p/maxima/mailman/message/59155605/)  for further discussions, but

```
elliptic_pi(1.5, float(%pi/2), 0.5);
-0.4567203134529103
```
Wolfram says it should be `-0.45672031345 - 2.72069904635*i`.

So we have the correct real part but don't compute the imaginary part.


---

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[Maxima-bugs] [maxima:bugs] #5716 diff() of gamma_incomplete() and similar functions is wrong for z < 0 with domain : real

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

---

**[bugs:#5716] diff\(\) of gamma\_incomplete\(\) and similar functions is wrong for z < 0 with domain : real**

**Status:** open
**Group:** None
**Labels:** diff gamma\_incomplete domain real 
**Created:** Sun Oct 25, 2026 03:05 PM UTC by David Scherfgen
**Last Updated:** Sun Oct 25, 2026 03:05 PM UTC
**Owner:** nobody


By Claude:

With `domain : real`, the default, `(-8)^(1/3)` is the real root `-2`. `gamma_incomplete(a,z)` is on the principal branch, but its derivative `-%e^-z*z^(a-1)` is simplified with the real root, so it is wrong for `z < 0`:

```
(%i1) d : diff(gamma_incomplete(1/3, z), z);
(%o1) -%e^-z/z^(2/3)
(%i2) float(rectform(subst(z = -8, d)));
(%o2) -745.2394967604321
```

The right value is `%e^8*(1+sqrt(3)*%i)/8`, about `372.62+645.40*%i`, which a numerical derivative of `gamma_incomplete(1/3, z)` at `z = -8` confirms. The same happens for an argument that is negative for `x > 0`:

```
(%i3) diff(gamma_incomplete(1/3, -x^3), x);
(%o3) 3*%e^x^3
```

For `x > 0` this should be `3*%e^x^3*(-1/2-sqrt(3)*%i/2)`. `gamma_incomplete_lower`, `gamma_incomplete_regularized`, `gamma_incomplete_generalized`, `beta_incomplete`, `beta_incomplete_regularized`, `beta_incomplete_generalized`, `struve_h` and `struve_l` have the same problem in their derivatives.


---

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[Maxima-bugs] [maxima:bugs] #5715 elliptic_eu incorrect and inaccurate

[Raymond T. <rt...@us...>]

---

**[bugs:#5715] elliptic\_eu incorrect and inaccurate**

**Status:** open
**Group:** None
**Labels:** elliptic\_eu 
**Created:** Sun Oct 25, 2026 02:56 PM UTC by Raymond Toy
**Last Updated:** Sun Oct 25, 2026 02:56 PM UTC
**Owner:** nobody


`elliptic_eu` is inaccurate or just incorrect.  Claude found these issues:

Call | Maxima | Correct
---------- | ---------- | ------
elliptic_eu(-0.5, 0.5)	| −2.66111	| −0.48063
elliptic_eu(5.0, 0.5)	| 1.64653	| 3.75604
elliptic_eu(4.0, -2.0)	| 6.69507	| 7.82517
elliptic_eu(-0.5+0.5*%i, 0.5)	| real part −2.715	| −0.5347
elliptic_eu(0.3+5*%i, 0.5)	| imaginary part 4.72	| 2.613


---

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[Maxima-bugs] [maxima:bugs] #5714 elliptic_eu doesn't work with bigfloats

[Raymond T. <rt...@us...>]

- **status**: open --> closed
- **assigned_to**: Raymond Toy
- **Comment**:

Fixed in [6eb8e9]




---

**[bugs:#5714] elliptic\_eu doesn't work with bigfloats**

**Status:** closed
**Group:** None
**Labels:** elliptic\_eu 
**Created:** Sun Oct 25, 2026 01:50 PM UTC by Raymond Toy
**Last Updated:** Sun Oct 25, 2026 01:50 PM UTC
**Owner:** Raymond Toy


`elliptic_eu` doesn't accept bigfloat numbers.   Looking at the code shows that it's pretty obvious why.  So moving it into the bigfloat package and adding the test for bigfloat eval should fix that.


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[Maxima-bugs] [maxima:bugs] #5714 elliptic_eu doesn't work with bigfloats

[Raymond T. <rt...@us...>]

---

**[bugs:#5714] elliptic\_eu doesn't work with bigfloats**

**Status:** open
**Group:** None
**Labels:** elliptic\_eu 
**Created:** Sun Oct 25, 2026 01:50 PM UTC by Raymond Toy
**Last Updated:** Sun Oct 25, 2026 01:50 PM UTC
**Owner:** nobody


`elliptic_eu` doesn't accept bigfloat numbers.   Looking at the code shows that it's pretty obvious why.  So moving it into the bigfloat package and adding the test for bigfloat eval should fix that.


---

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[Maxima-bugs] [maxima:bugs] #5713 %i^(2/3) simplifies to -1

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

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

Fixed by commit [884d71].



---

**[bugs:#5713] %i^\(2/3\) simplifies to -1**

**Status:** closed
**Group:** None
**Labels:** simplification simpexpt 
**Created:** Sun Oct 25, 2026 09:10 AM UTC by David Scherfgen
**Last Updated:** Sun Oct 25, 2026 09:10 AM UTC
**Owner:** nobody


Under the default `domain : real`, `%i^(2/3)` incorrectly simplifies to `-1`.


---

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[Maxima-bugs] [maxima:bugs] #5713 %i^(2/3) simplifies to -1

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

---

**[bugs:#5713] %i^\(2/3\) simplifies to -1**

**Status:** open
**Group:** None
**Labels:** simplification simpexpt 
**Created:** Sun Oct 25, 2026 09:10 AM UTC by David Scherfgen
**Last Updated:** Sun Oct 25, 2026 09:10 AM UTC
**Owner:** nobody


Under the default `domain : real`, `%i^(2/3)` incorrectly simplifies to `-1`.


---

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[Maxima-bugs] [maxima:bugs] #5294 diff(struve_h(v, t), t) and diff(struve_l(v, t), t) contain x^v instead of t^v

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

- Description has changed:

Diff:

~~~~



~~~~

- **status**: open --> closed
- **Priority**:  --> 5
- **Comment**:

Fixed by commit [30638c].



---

**[bugs:#5294] diff\(struve\_h\(v,t\),t\) and diff\(struve\_l\(v,t\),t\) contain x^v instead of t^v**

**Status:** closed
**Group:** Includes\_proposed\_fix
**Labels:** Claude trivial bug bessel.lisp 
**Created:** Sun Sep 27, 2026 08:34 AM UTC by David Scherfgen
**Last Updated:** Sun Sep 27, 2026 12:31 PM UTC
**Owner:** nobody


This bug was discovered by Claude Opus 5.5 and reproduced on Maxima Git commit c62924c (2026-09-26) with SBCL 2.2.9.

**Where:** `src/bessel.lisp`, DEFGRAD %STRUVE\_H, DEFGRAD %STRUVE\_L

The derivative templates use x^v, but the DEFGRAD placeholders are $v and $z, so x is a literal free symbol instead of the argument. The result is only right when the variable happens to be named x; struve\_l has the same error.

### Steps

1. Verify that the existing behavior is incorrect: run the reproducer below; it gives the result under "Before the fix". Judge for yourself that this is wrong instead of relying on the ticket: where the bug allows it, try some related inputs of your own, or check the result another way, for example numerically or against the documentation.
2. Edit the file `src/bessel.lisp` as described under "Fix".
3. Rebuild Maxima.
4. Verify that the behavior is now correct: the reproducer gives the result under "Correct result". Judge for yourself that this is right, not only that it matches: where the bug allows it, try some related inputs of your own, including some that the fix should leave unchanged.
5. Add the test case(s) under "Test cases" to `tests/rtest16.mac`, just before the block "Leave this at the end of the file!" at its end.
6. Run the complete test suite, share tests included (`make check`, or `run_testsuite(share_tests=true);` in `./maxima-local`), and check that the change breaks no test. Failures that also occur without the change (a run on the unchanged build shows which) are pre-existing and can be ignored.
7. Add the line `* \#5294 diff(struve_h(v,t),t) and diff(struve_l(v,t),t) contain x^v instead of t^v` to `ChangeLog`, under "Bug fixes for numbered bugs:".
8. Commit the fix; a proposed Git commit message is under "Commit message".
9. Push the commit. Then set this ticket's status to "closed" and add a comment naming the commit, for example `Fixed by commit [1a2b3c].`, with the first six characters of the commit's SHA in the brackets (`git rev-parse HEAD | cut -c1-6` prints them). SourceForge links this to the commit.

### Reproducer

```
diff(struve_h(v,t),t);
```

Before the fix:

```
(x^v/(2^v*sqrt(%pi)*gamma(v+3/2))-struve_h(v+1,t)+struve_h(v-1,t))/2
```

Correct result:

```
(t^v/(2^v*sqrt(%pi)*gamma(v+3/2))-struve_h(v+1,t)+struve_h(v-1,t))/2
```

### Fix

In `src/bessel.lisp` (DEFGRAD %STRUVE\_H, search for "-struve\_h(v+1,z)+struve\_h(v-1,z))/2$"), replace

```
  #$$ (x^v/(2^v*sqrt(%pi)*gamma(v+3/2))-struve_h(v+1,z)+struve_h(v-1,z))/2$
```

with

```
  #$$ (z^v/(2^v*sqrt(%pi)*gamma(v+3/2))-struve_h(v+1,z)+struve_h(v-1,z))/2$
```

In `src/bessel.lisp` (DEFGRAD %STRUVE\_L, search for "+struve\_l(v+1,z)+struve\_l(v-1,z))/2$"), replace

```
  #$$ (x^v/(2^v*sqrt(%pi)*gamma(v+3/2))+struve_l(v+1,z)+struve_l(v-1,z))/2$
```

with

```
  #$$ (z^v/(2^v*sqrt(%pi)*gamma(v+3/2))+struve_l(v+1,z)+struve_l(v-1,z))/2$
```

### Test cases

Add these lines to `tests/rtest16.mac`, separated from the tests before them by two empty lines:

```
/* Bug #5294: "diff(struve_h(v,t),t) and diff(struve_l(v,t),t) contain x^v instead of t^v" */

diff(struve_h(v,t),t);
(t^v/(2^v*sqrt(%pi)*gamma(v+3/2))-struve_h(v+1,t)+struve_h(v-1,t))/2$

diff(struve_l(v,t),t);
(t^v/(2^v*sqrt(%pi)*gamma(v+3/2))+struve_l(v+1,t)+struve_l(v-1,t))/2$
```

### Commit message

```
bessel.lisp: fix derivatives of struve_h and struve_l

The derivative templates of struve_h and struve_l wrote the power term
as x^v, but the DEFGRAD placeholders are v and z, so x was a free symbol
instead of the argument. They now use z^v.

This fixes bug #5294.

Found and fixed by Claude Opus 5.5.
```


---

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[Maxima-bugs] [maxima:bugs] #5711 integrate() reads c^3 as c+3 in (c-c*x)^3/((1-x)^3*sqrt(1-x^2))

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

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

Fixed by commit [8f787d].



---

**[bugs:#5711] integrate\(\) reads c^3 as c+3 in \(c-c\*x\)^3/\(\(1-x\)^3\*sqrt\(1-x^2\)\)**

**Status:** closed
**Group:** None
**Labels:** integrate 
**Created:** Sat Oct 24, 2026 10:42 AM UTC by David Scherfgen
**Last Updated:** Sat Oct 24, 2026 10:42 AM UTC
**Owner:** nobody


By Claude:

`integrate` gives a wrong result for a product of a polynomial and a square root:

```
(%i1) integrate((c-c*x)^3/((1-x)^3*sqrt(1-x^2)), x);
(%o1) c*asin(x)+3*asin(x)
```

The integrand is `c^3/sqrt(1-x^2)`, so the result should be `c^3*asin(x)`. It is as if `c^3` were read as `c+3`. A similar integrand ends in a Lisp error:

```
(%i2) integrate(sqrt(1+x)/sqrt(1-x)*(c-c*x), x);
Maxima encountered a Lisp error:
 The value
   $C
 is not of type
   LIST
```

Here the integrand is `c*sqrt(1-x^2)`, and the result should be `c*asin(x)/2+c*x*sqrt(1-x^2)/2`.


---

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[Maxima-bugs] [maxima:bugs] #5710 ((-2)^(1/6))^2 simplifies to the real root (-2)^(1/3) with radexpand : false

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

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

Fixed by commit [965d32].



---

**[bugs:#5710] \(\(-2\)^\(1/6\)\)^2 simplifies to the real root \(-2\)^\(1/3\) with radexpand : false**

**Status:** closed
**Group:** None
**Labels:** simplification simpexpt radexpand 
**Created:** Sat Oct 24, 2026 10:31 AM UTC by David Scherfgen
**Last Updated:** Sat Oct 24, 2026 10:31 AM UTC
**Owner:** nobody


By Claude:

With the default `domain : real`, `(-2)^(1/3)` is the real root `-2^(1/3)`, while `(-2)^(1/6)` is the principal value `2^(1/6)*(-1)^(1/6)`. With `radexpand : false`, squaring `(-2)^(1/6)` gives `(-2)^(1/3)`, so the principal value becomes the real root, and a real root times a principal value is simplified as if both were principal values:

```
(%i1) radexpand : false$
(%i2) ((-2)^(1/6))^2;
(%o2) (-2)^(1/3)
(%i3) csign(%);
(%o3) neg
(%i4) (-2)^(1/3)*(-2)^(1/6);
(%o4) sqrt(-2)
```

With `radexpand : true`, both are right:

```
(%i5) radexpand : true$
(%i6) ((-2)^(1/6))^2;
(%o6) 2^(1/3)*((sqrt(3)*%i)/2+1/2)
(%i7) (-2)^(1/3)*(-2)^(1/6);
(%o7) -(-1)^(1/6)*sqrt(2)
```

The same happened for `(-1)^(1/6)` in bug #5705.


---

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[Maxima-bugs] [maxima:bugs] #5217 rectform(sqrt(x*y)) under domain : complex

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

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

Fixed by commit [b52022].



---

**[bugs:#5217] rectform\(sqrt\(x\*y\)\) under domain : complex**

**Status:** closed
**Group:** None
**Labels:** rectform domain complex sqrt 
**Created:** Wed Sep 02, 2026 08:05 PM UTC by David Scherfgen
**Last Updated:** Wed Sep 02, 2026 08:05 PM UTC
**Owner:** nobody


Isn't `rectform` supposed to always take the principal branch?
Here's an example where depending on whether we substitute concrete values before or after applying `rectform`, we get a different result:

~~~
(%i1) domain : complex$

(%i2) f : sqrt(x * y)$

(%i3) subst([x = -1, y = -1], rectform(f));
(%o3) -1

(%i4) rectform(subst([x = -1, y = -1], f));
(%o4) 1
~~~


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[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.


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[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].



---

**[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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[Maxima-bugs] [maxima:bugs] #5706 (-2*%i)^(1/3) simplifies to the wrong cube root

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

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

Fixed by commit [e5f42a].



---

**[bugs:#5706] \(-2\*%i\)^\(1/3\) simplifies to the wrong cube root**

**Status:** closed
**Group:** None
**Labels:** simplification simpexpt 
**Created:** Fri Oct 23, 2026 08:20 AM UTC by David Scherfgen
**Last Updated:** Fri Oct 23, 2026 08:20 AM UTC
**Owner:** nobody


By Claude:

With the default `domain : real` and `radexpand : true`, an odd root of a product is split into odd roots of its factors, and a negative factor gets its real root. That is only right when all factors are real. If a factor is complex, the root of the product is the principal one, and splitting gives a different cube root:

```
(%i1) (-2*%i)^(1/3);
(%o1) -(-1)^(1/6)*2^(1/3)
(%i2) float(rectform(%));
(%o2) -0.6299605249474366*%i-1.0911236359717214
(%i3) float(rectform(exp(log(-2*%i)/3)));
(%o3) 1.0911236359717214-0.6299605249474366*%i
```

The same happens with other complex factors, such as `(-1)^(1/4)`, a symbol declared imaginary, or the square root of a negative symbol:

```
(%i4) (-2*(-1)^(1/4))^(1/3);
(%o4) -(-1)^(1/12)*2^(1/3)
(%i5) declare(j, imaginary)$
(%i6) (-2*j)^(1/3);
(%o6) -2^(1/3)*j^(1/3)
(%i7) assume(xn < 0)$
(%i8) (-2*sqrt(xn))^(1/3);
(%o8) -2^(1/3)*xn^(1/6)
```


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[Maxima-bugs] [maxima:bugs] #5705 ((-1)^(1/6))^2 simplifies to -1

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

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

Fixed by commit [d96bc5].



---

**[bugs:#5705] \(\(-1\)^\(1/6\)\)^2 simplifies to -1**

**Status:** closed
**Group:** None
**Labels:** simplification simpexpt 
**Created:** Fri Oct 23, 2026 08:19 AM UTC by David Scherfgen
**Last Updated:** Fri Oct 23, 2026 08:19 AM UTC
**Owner:** nobody


By Claude:

With the default `domain : real`, Maxima reads `(-1)^(p/q)` with odd `q` as the real root, so `(-1)^(1/3)` simplifies to `-1`. `(-1)^(1/6)` has no real value and is the principal root `exp(%i*%pi/6)`, which is also how `rectform` and `float` evaluate it. But a power or a product of such roots is folded into `(-1)^(1/3)`, which is then read as the real root:

```
(%i1) ((-1)^(1/6))^2;
(%o1) -1
(%i2) (-1)^(1/6)*(-1)^(1/6);
(%o2) -1
(%i3) ((-8)^(1/6))^2;
(%o3) -2
```

The correct value of the first two is `exp(%i*%pi/3)`, that is `1/2+sqrt(3)*%i/2`:

```
(%i4) expand(float(rectform((-1)^(1/6)))^2);
(%o4) 0.8660254037844386*%i+0.4999999999999999
```

As `ratsimp` multiplies such powers out, it often returns wrong values for expressions with `(-1)^(1/6)` or `(-1)^(1/10)`. Here the difference should be `0`:

```
(%i5) r : ratsimp(1/(1+(-1)^(1/6))), algebraic : true;
(%o5) -((%i+(-1)^(5/6)+(-1)^(1/6)-1)/2)
(%i6) float(rectform(r - 1/(1+(-1)^(1/6))));
(%o6) 5.551115123125783e-17-0.8660254037844386*%i
```

With `domain : complex`, all of these are correct.


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[Maxima-bugs] [maxima:bugs] #5712 integrate(%e^atanh(x), x) returns a noun form

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

---

**[bugs:#5712] integrate\(%e^atanh\(x\), x\) returns a noun form**

**Status:** open
**Group:** None
**Labels:** integrate 
**Created:** Sat Oct 24, 2026 10:44 AM UTC by David Scherfgen
**Last Updated:** Sat Oct 24, 2026 10:44 AM UTC
**Owner:** nobody


By Claude:

`integrate` cannot integrate `%e^atanh(x)`:

```
(%i1) integrate(%e^atanh(x), x);
(%o1) 'integrate(%e^atanh(x),x)
```

But `%e^atanh(x) = sqrt(1+x)/sqrt(1-x)`, since `atanh(x) = (log(1+x)-log(1-x))/2`, as `logarc` writes it, and `integrate` finds the integral of that form:

```
(%i2) integrate(sqrt(1+x)/sqrt(1-x), x);
(%o2) asin(x)-sqrt(1-x^2)
```

The same holds for other powers of `%e^atanh(u)` and `%e^acoth(u)` times algebraic functions, such as `x^4*%e^atanh(a*x)`.


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[Maxima-bugs] [maxima:bugs] #5711 integrate() reads c^3 as c+3 in (c-c*x)^3/((1-x)^3*sqrt(1-x^2))

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

---

**[bugs:#5711] integrate\(\) reads c^3 as c+3 in \(c-c\*x\)^3/\(\(1-x\)^3\*sqrt\(1-x^2\)\)**

**Status:** open
**Group:** None
**Labels:** integrate 
**Created:** Sat Oct 24, 2026 10:42 AM UTC by David Scherfgen
**Last Updated:** Sat Oct 24, 2026 10:42 AM UTC
**Owner:** nobody


By Claude:

`integrate` gives a wrong result for a product of a polynomial and a square root:

```
(%i1) integrate((c-c*x)^3/((1-x)^3*sqrt(1-x^2)), x);
(%o1) c*asin(x)+3*asin(x)
```

The integrand is `c^3/sqrt(1-x^2)`, so the result should be `c^3*asin(x)`. It is as if `c^3` were read as `c+3`. A similar integrand ends in a Lisp error:

```
(%i2) integrate(sqrt(1+x)/sqrt(1-x)*(c-c*x), x);
Maxima encountered a Lisp error:
 The value
   $C
 is not of type
   LIST
```

Here the integrand is `c*sqrt(1-x^2)`, and the result should be `c*asin(x)/2+c*x*sqrt(1-x^2)/2`.


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[Maxima-bugs] [maxima:bugs] #5710 ((-2)^(1/6))^2 simplifies to the real root (-2)^(1/3) with radexpand : false

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

---

**[bugs:#5710] \(\(-2\)^\(1/6\)\)^2 simplifies to the real root \(-2\)^\(1/3\) with radexpand : false**

**Status:** open
**Group:** None
**Labels:** simplification simpexpt radexpand 
**Created:** Sat Oct 24, 2026 10:31 AM UTC by David Scherfgen
**Last Updated:** Sat Oct 24, 2026 10:31 AM UTC
**Owner:** nobody


By Claude:

With the default `domain : real`, `(-2)^(1/3)` is the real root `-2^(1/3)`, while `(-2)^(1/6)` is the principal value `2^(1/6)*(-1)^(1/6)`. With `radexpand : false`, squaring `(-2)^(1/6)` gives `(-2)^(1/3)`, so the principal value becomes the real root, and a real root times a principal value is simplified as if both were principal values:

```
(%i1) radexpand : false$
(%i2) ((-2)^(1/6))^2;
(%o2) (-2)^(1/3)
(%i3) csign(%);
(%o3) neg
(%i4) (-2)^(1/3)*(-2)^(1/6);
(%o4) sqrt(-2)
```

With `radexpand : true`, both are right:

```
(%i5) radexpand : true$
(%i6) ((-2)^(1/6))^2;
(%o6) 2^(1/3)*((sqrt(3)*%i)/2+1/2)
(%i7) (-2)^(1/3)*(-2)^(1/6);
(%o7) -(-1)^(1/6)*sqrt(2)
```

The same happened for `(-1)^(1/6)` in bug #5705.


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[Maxima-bugs] [maxima:bugs] Re: #5695 fullratsimp(rat(sqrt(c-1)/(c-f(a))^(3/2)-1/(sqrt(c-1)*sqrt(c-f(a))))) loops forever

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

Intuition about "fast" and "slow" in Maxima is often misleading, we'd have to measure. In the normal case, the new expression is not `alike1` any previous, and I guess that `alike1` aborts very quickly in the average case. I'll do some experiments soon.


---

**[bugs:#5695] fullratsimp\(rat\(sqrt\(c-1\)/\(c-f\(a\)\)^\(3/2\)-1/\(sqrt\(c-1\)\*sqrt\(c-f\(a\)\)\)\)\) loops forever**

**Status:** closed
**Group:** None
**Labels:** fullratsimp 
**Created:** Thu Oct 22, 2026 03:06 AM UTC by David Scherfgen
**Last Updated:** Fri Oct 23, 2026 01:42 PM UTC
**Owner:** nobody


Discovered by Claude:

~~~
fullratsimp(rat(sqrt(c-1)/(c-f(a))^(3/2)-1/(sqrt(c-1)*sqrt(c-f(a)))));
~~~

This loops forever, cycling over two representations.


---

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[Maxima-bugs] [maxima:bugs] #5695 fullratsimp(rat(sqrt(c-1)/(c-f(a))^(3/2)-1/(sqrt(c-1)*sqrt(c-f(a))))) loops forever

[Barton W. <wil...@us...>]

Most likely no.  The iteration limit check is fast, but the cycle detection is slow.  If we got rid of one check, maybe it should be the cycle detection?


---

**[bugs:#5695] fullratsimp\(rat\(sqrt\(c-1\)/\(c-f\(a\)\)^\(3/2\)-1/\(sqrt\(c-1\)\*sqrt\(c-f\(a\)\)\)\)\) loops forever**

**Status:** closed
**Group:** None
**Labels:** fullratsimp 
**Created:** Thu Oct 22, 2026 03:06 AM UTC by David Scherfgen
**Last Updated:** Fri Oct 23, 2026 12:32 PM UTC
**Owner:** nobody


Discovered by Claude:

~~~
fullratsimp(rat(sqrt(c-1)/(c-f(a))^(3/2)-1/(sqrt(c-1)*sqrt(c-f(a)))));
~~~

This loops forever, cycling over two representations.


---

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[Maxima-bugs] [maxima:bugs] Re: #5695 fullratsimp(rat(sqrt(c-1)/(c-f(a))^(3/2)-1/(sqrt(c-1)*sqrt(c-f(a))))) loops forever

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

Do we need an iteration limit if we detect cycles and abort then? I'd say no, intuitively.


---

**[bugs:#5695] fullratsimp\(rat\(sqrt\(c-1\)/\(c-f\(a\)\)^\(3/2\)-1/\(sqrt\(c-1\)\*sqrt\(c-f\(a\)\)\)\)\) loops forever**

**Status:** closed
**Group:** None
**Labels:** fullratsimp 
**Created:** Thu Oct 22, 2026 03:06 AM UTC by David Scherfgen
**Last Updated:** Fri Oct 23, 2026 12:07 PM UTC
**Owner:** nobody


Discovered by Claude:

~~~
fullratsimp(rat(sqrt(c-1)/(c-f(a))^(3/2)-1/(sqrt(c-1)*sqrt(c-f(a)))));
~~~

This loops forever, cycling over two representations.


---

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[Maxima-bugs] [maxima:bugs] #5695 fullratsimp(rat(sqrt(c-1)/(c-f(a))^(3/2)-1/(sqrt(c-1)*sqrt(c-f(a))))) loops forever

[Barton W. <wil...@us...>]

A better version:

~~~
(defmvar *max-fullratsimp-iterations* 32
  "Maximum number of iterations allowed for fullratsimp before falling back.")

(defmfun ($fullratsimp :properties ((evfun t))) (exp &rest argl)
  "Repeatedly applies `ratsimp` to `exp` until either (a) a fixpoint is reached,
   (b) a cycle is detected, or (c) the number of iterations exceeds 
   *max-fullratsimp-iterations*."
  (labels ((local-ratsimp (e)
             (simplify (apply #'$ratsimp e argl))))
    (let* ((k *max-fullratsimp-iterations*)
           (seen (list exp))
           (current exp)
           (next (local-ratsimp exp))
           (best exp)
           (min-size (conssize exp)))
      (loop
        ;; Track the minimum size on the fly
        (let ((sz (conssize next)))
          (when (< sz min-size)
            (setf min-size sz
                  best next)))

        ;; (a) Fixpoint reached
        (when (alike1 current next)
          (return next)) ; or current, they are alike

        ;; (b) Cycle detected or (c) Max iterations exceeded
        (when (or (member next seen :test #'alike1) (< k 0))
          (return best))

        (push next seen)
        (decf k)
        (setf current next
              next (local-ratsimp next))))))
~~~


---

**[bugs:#5695] fullratsimp\(rat\(sqrt\(c-1\)/\(c-f\(a\)\)^\(3/2\)-1/\(sqrt\(c-1\)\*sqrt\(c-f\(a\)\)\)\)\) loops forever**

**Status:** closed
**Group:** None
**Labels:** fullratsimp 
**Created:** Thu Oct 22, 2026 03:06 AM UTC by David Scherfgen
**Last Updated:** Thu Oct 22, 2026 08:11 PM UTC
**Owner:** nobody


Discovered by Claude:

~~~
fullratsimp(rat(sqrt(c-1)/(c-f(a))^(3/2)-1/(sqrt(c-1)*sqrt(c-f(a)))));
~~~

This loops forever, cycling over two representations.


---

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