rtoy
commented
4 months ago Imported from SourceForge on 2024-07-05 21:35:10 Created by macrakis on 2020-05-10 19:58:39 Original: https://sourceforge.net/p/maxima/bugs/2263/#74e7
Verified that this is still a problem in 5.43 on SBCL.
Note that the result is doubly bad: not only does it make something simple into something complicated, but the imaginary part can actually be simplified by trigrat to zero:
e1: trigrat(sin(%pi/5))$
e2: imagpart(e1) => -(cos((3*%pi)/5)-cos((2*%pi)/5)+2*cos(%pi/5)-1)/2
trigrat(e2) => 0
float(e2) => -5e-17 << sanity checkI ran into a similar problem with sin(%pi/7). In fact, it gives stuff like this for all
sin(%pi*m/n)with n>4.
A side-effect of this non-simplification is that trying scanmap(trigrat,e1) gets into an infinite loop, since a subexpression gets expanded....
Interestingly, if you load(spangl) (range reduction for trig), some of these problems go away:
(fresh Maxima)
load(spangl)$
trigrat(sin(%pi/5)) => sin(%pi/5)but sometimes trigrat loops:
(fresh Maxima)
load(spangl)$
e1: trigrat(sin(%pi/7)) => (%i*(2*sin((3*%pi)/14)-2*cos(%pi/7)-2*sin(%pi/14)+1)+2*sin(%pi/7))/2
trigrat(e1) => sin(%pi/7)That is, it's not idempotent.
Imported from SourceForge on 2024-07-05 21:35:09 Created by antonvoropaev on 2011-08-25 15:53:26 Original: https://sourceforge.net/p/maxima/bugs/2263
See also bug reports ID: 742909 and ID: 2999635
INPUT
build_info(); display2d : false; trigrat(sin(%pi/5));
INPUT AND OUTPUT
(%i1) build_info(); Maxima version: 5.25.0 Maxima build date: 12:0 8/2/2011 Host type: i686-pc-mingw32 Lisp implementation type: Clozure Common Lisp Lisp implementation version: Version 1.7-r14925M (WindowsX8632) (%o1) (%i2) display2d : false; (%o2) false (%i3) trigrat(sin(%pi/5)); (%o3) -(-sin(3*%pi/5)+%i*(cos(3*%pi/5)-cos(2*%pi/5)+2*cos(%pi/5)-1) +sin(2*%pi/5)-2*sin(%pi/5)) /2