On Saturday, March 28, 2015 at 2:01:38 AM UTC+2, Jeremy Holleman wrote:
>
> I just mean that if I'm trying to write a script and I want to reduce all
> of the powers of cos or sin, I'm not sure how I would code that, because I
> can't tell if there's a pattern of which calls need to be made in which
> order to reduce an arbitrary polynomial of trig functions. For my present
> purpose, I'm doing the analysis interactively, so a little trial-and-error
> is fine. For future projects I'm trying to get a clearer understanding of
> how these functions work. So for example, why does TR7(cos(x)**7) just
> return cos(x)**7?
>
It seems that fu does not deal with higher powers of cos and sin, but if
you are writing a script, you could easily
derive a general formula to reduce the powers.
For example, if you start with Euler's formula
cos(x) = (exp(I*x) + exp(-I*x))/2
and use the binomial formula to obtain
cos(x)**n = (exp(I*n*x) + C(n, 1)*exp(I*(n-2)*x) + C(n,
2)*exp(I*(n-4)*x) + ,,, + exp(-I*n*x)) / 2**n ,
then using C(n, n-k) = C(n, k) you get
cos(x)**n = (cos(n*x) + C(n, 1)*cos((n-2)*x) + ...) / 2**(n - 1) .
(If n is even, the last term in the parentheses is C(n, n/2)/2.)
Kalevi Suominen
--
You received this message because you are subscribed to the Google Groups
"sympy" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to sympy+unsubscr...@googlegroups.com.
To post to this group, send email to sympy@googlegroups.com.
Visit this group at http://groups.google.com/group/sympy.
To view this discussion on the web visit
https://groups.google.com/d/msgid/sympy/87bd2ff5-3522-496f-8b07-a75f74002a09%40googlegroups.com.
For more options, visit https://groups.google.com/d/optout.
