#4793 Solve: incorrect answer

[John Oliver]

Here is the following maxima system info from bug_report():
Maxima-version: "5.49.0"

Maxima build date: "2026-01-02 21:27:51"

Host type: "x86_64-w64-mingw32"

Lisp implementation type: "SBCL"

Lisp implementation version: "2.6.0"

User dir: "C:/Users/johno/maxima"

Temp dir: "C:/Users/johno/AppData/Local/Temp"

Object dir: "C:/Users/johno/maxima/binary/5_49_0/sbcl/2_6_0"

Frontend: false

Error as follows:

g:48*x^3 - 1;

solve(g,x) gives as the real root

x = (1/26)^(1/3), when the obvious answer is (1/48)^(1/3)

This result occurs with both terminal execution and wxmaxima using 5.49.0. I have inculded the .wxmx and .mac (Not familiar with proper bug reporting, as this is new to me; apologies if this is incorrect.)

[Stavros Macrakis]

In display2d:false mode, I see

x = 1/(2*6^(1/3))

I think you are interpreting the display form2 6^(1/3) as 26^(1/3).

You can also use the string function to see the linear form.

[Stavros Macrakis]

In display2d:false mode, I get

x = 1/(2*6^(1/3))

I think you are interpreting "2 6^(1/3)" as 26^(1/3).

On Sun, Jun 21, 2026, 03:30 John Oliver via Maxima-bugs maxima-bugs@lists.sourceforge.net wrote:

---

[bugs:#4793] https://sourceforge.net/p/maxima/bugs/4793/ Solve:
incorrect answer

Status: open
Group: None
Created: Sun Jun 21, 2026 07:29 AM UTC by John Oliver
Last Updated: Sun Jun 21, 2026 07:29 AM UTC
Owner: nobody
Attachments:

• Solve_Error.mac
  https://sourceforge.net/p/maxima/bugs/4793/attachment/Solve_Error.mac
  (sourceforge.net) (434 Bytes; application/octet-stream)

Here is the following maxima system info from bug_report():
Maxima-version: "5.49.0"

Maxima build date: "2026-01-02 21:27:51"

Host type: "x86_64-w64-mingw32"

Lisp implementation type: "SBCL"

Lisp implementation version: "2.6.0"

User dir: "C:/Users/johno/maxima"

Temp dir: "C:/Users/johno/AppData/Local/Temp"

Object dir: "C:/Users/johno/maxima/binary/5_49_0/sbcl/2_6_0"

Frontend: false

Error as follows:

g:48*x^3 - 1;

solve(g,x) gives as the real root

x = (1/26)^(1/3), when the obvious answer is (1/48)^(1/3)

This result occurs with both terminal execution and wxmaxima using 5.49.0.
I have inculded the .wxmx and .mac (Not familiar with proper bug reporting,
as this is new to me; apologies if this is incorrect.)

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[Stavros Macrakis]

Here's a little trick to make multiplication visible.

sols: solve(48*x^3-1,x)
    =>

      sqrt(3) %i - 1        sqrt(3) %i + 1        1
 [x = ──────────────, x = - ──────────────, x = ──────]
             1/3                   1/3             1/3
          4 6                   4 6             2 6

nary("·",120)$    /* added precedence */
subst("·","*",sols);

      1      1
[x = (─) · (────) · (sqrt(3) · %i - 1), 
      4      1/3
            6

       1      1
x = (- ─) · (────) · (sqrt(3) · %i + 1), 
       4      1/3
             6

     1      1
x = (─) · (────)]
     2      1/3
           6

That shows the internal structure of the Maxima expression (where division is multiplication by an inverse). Here is how to get a view that follows the usual Maxima external form:

nary("·",120)$
show_mult(ex):=
  if mapatom(ex) then ex
  elseif op(ex)="*" then funmake("·",maplist(show_mult,ex))
  else map('show_mult,ex)$

show_mult(sols);

     sqrt(3) · %i - 1
[x = ────────────────, 
              1/3
        4 · (6   )

      sqrt(3) · %i + 1
x = - ────────────────, 
               1/3
         4 · (6   )

        1
x = ──────────]
          1/3
    2 · (6   )