Segmentation fault when calculating the taylor series of a specific function

[frcl]

The following code evaluated in Sage 9.2 leads to a segmentation fault

sin(4*arctan(1/(sqrt(3) + 2))-x).taylor(x, 0, 1)

The error message is

;;;
;;; Detected access to protected memory, also known as 'bus or segmentation fault'.
;;; Jumping to the outermost toplevel prompt
;;;

Changing the constant slightly gives the desired result, e.g.

sin(4*arctan(1/(sqrt(3) + 1))-x).taylor(x, 0, 1)

evaluates to

-x*cos(4*arctan(1/2*sqrt(3) - 1/2)) + sin(4*arctan(1/2*sqrt(3) - 1/2))

Upstream report:

• Maxima bug 3716

Upstream: Reported upstream. No feedback yet.

Component: calculus

Keywords: maxima, taylor series

Issue created by migration from https://trac.sagemath.org/ticket/31401

[DaveWitteMorris]

comment:1

This is a maxima bug:

(%i1) taylor(sin(atan(1/(sqrt(3) + 2)) - x), x, 0, 1);

      Message from maxima's stderr stream: INFO: Control stack guard page unprotected
      Control stack guard page temporarily disabled: proceed with caution
      Control stack guard page temporarily disabled: proceed with caution
      Maxima encountered a Lisp error:
       Control stack exhausted (no more space for function call frames).
      This is probably due to heavily nested or infinitely recursive function
      calls, or a tail call that SBCL cannot or has not optimized away.

I tested with some other nonzero integers a and b in the place of 3 and 2. It seems that the crash happens whenever a < b^2 (including all cases where a < 0).

[DaveWitteMorris]

Changed keywords from none to maxima, taylor series

[frcl]

comment:2

Replying to @DaveWitteMorris:

I tested with some other nonzero integers a and b in the place of 3 and 2. It seems that the crash happens whenever a < b^2 (including all cases where a < 0).

This seems to be the case, except if a is a square number. I guess the sqrt is evaluated first in that case. This implies that the sqrt is somehow involved in triggering the bug.

I will file a bug report on the maxima bug tracker. Should I close the ticket here?

[DaveWitteMorris]

comment:3

Thanks for volunteering to report the bug to maxima (and for clarifying that a should not be a square).

Please keep this ticket open. The "Report Upstream" field of this ticket should be set to "Reported upstream. No feedback yet", and that field can be updated as the situation progresses. It would also be helpful if you can add a comment here with a link to the maxima bug report, so it is easy for sage trac followers to check on the status in maxima.

[DaveWitteMorris]

comment:4

PS If you need a workaround for the bug, you can replace 2 with a variable, and then substitute at the end:

sage: var('a');
sage: sin(4*arctan(1/(sqrt(3) + a))-x).taylor(x, 0, 1).subs(a=2)
-x*cos(4*arctan(1/(sqrt(3) + 2))) + sin(4*arctan(1/(sqrt(3) + 2)))

[slel]

Upstream: Reported upstream. No feedback yet.

[slel]

comment:5

Upstream ticket in the Maxima bug tracker:

• https://sourceforge.net/p/maxima/bugs/3716/

[slel]

Description changed:

--- 
+++ 
@@ -24,3 +24,7 @@
 ```
 -x*cos(4*arctan(1/2*sqrt(3) - 1/2)) + sin(4*arctan(1/2*sqrt(3) - 1/2))
 ```
+
+Upstream report:
+
+- [Maxima bug 3716](https://sourceforge.net/p/maxima/bugs/3716/)

[mkoeppe]

comment:6

Moving to 9.4, as 9.3 has been released.