#2818 Problem with trigreduce

[Nils Bruin]

I observe the following on both Maxima 5.33.0 on ECL and 5.34.1 on SBCL:

Maxima AM_INIT_AUTOMAKE([-Wno-portability] http://maxima.sourceforge.net
using Lisp SBCL 1.1.8-2.fc19
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) trigreduce(sin(1/8*%pi)*sin(3/8*%pi)*sin(5/8*%pi)*sin(7/8*%pi));

Maxima encountered a Lisp error:

Unrecognised output from sp1sintcos.

On Maxima 5.30.0 the expression simplifies without problem, so I suspect it's an error in maxima that was relatively recently introduced. Hopefully this provides enough information to solve the issue

(this came up in http://trac.sagemath.org/ticket/17065 )

[Aleksas]

With "trigrat":
(%i1) trigrat(sin(1/8%pi)sin(3/8%pi)sin(5/8%pi)sin(7/8*%pi));
(%o1) 1/8

or with "trigeval":
(%i2) load(trigtools)$
(%i3) trigeval(sin(%pi/8)sin((3%pi)/8)sin((5%pi)/8)sin((7%pi)/8));
(%o3) ((2-sqrt(2))*(sqrt(2)+2))/16
(%i4) ratsimp(%);
(%o4) 1/8

(%i5) trigeval([sin(%pi/8),sin((3%pi)/8),sin((5%pi)/8),sin((7*%pi)/8)]);
(%o5) [sqrt(2-sqrt(2))/2,sqrt(sqrt(2)+2)/2,sqrt(sqrt(2)+2)/2,sqrt(2-sqrt(2))/2]

best
Aleksas D

[Aleksas]

Other examples of "trigeval":
(%i1) load(trigtools)$
(%i2) trigeval(sin(%pi/16)sin((3%pi)/16)sin((5%pi)/16)sin((7%pi)/16));
(%o2) (sqrt(2-sqrt(2-sqrt(2)))sqrt(sqrt(2-sqrt(2))+2)sqrt(2-sqrt(sqrt(2)+2))*sqrt(sqrt(sqrt(2)+2)+2))/16
(%i3) rootscontract(%);
(%o3) 1/2^(7/2)

(%i4) trigeval(sin(%pi/10)sin((3%pi)/10)sin((5%pi)/10)sin((7%pi)/10));
(%o4) ((sqrt(5)-1)*(sqrt(5)+1)^2)/64
(%i5) radcan(%);
(%o5) (sqrt(5)+1)/16

In this case "trigrat" will not help.

best
Aleksas D

[Robert Dodier]

SP1SINTCOS caller (SP1TPLUS) wasn't handling all possible return values. Fixed by commit [4f5ff9c]. Closing this report.