I'm in the process of developing simple functions that generate constants for various filters of various orders, such as Butterworth. For example, the result of Butterworth(2) would be:
s^2 + sqrt(2)*s + 1
(Darn the administrators for not choosing to support MathJax!)
I'm trying to simplify the generated coefficients. The example I'm having trouble with is a little more complicated than the example I'll present here. But the example here will get the point across.
Suppose I have the expression:
sqrt(2) * sqrt( sqrt(2) + 2 ) + 2 * sqrt( sqrt(2) + 2) )
Then using:
simplify( sqrt(2) * sqrt( sqrt(2) + 2 ) + 2 * sqrt( sqrt(2) + 2) ) )
Produces:
(sqrt(2) + 2)**(3/2)
Which is perfect for me.
But when I try something like:
simplify( 1 + sqrt(2) * sqrt( sqrt(2) + 2 ) + 2 * sqrt( sqrt(2) + 2) ) )
Then I get:
1 + sqrt(2) * sqrt( sqrt(2) + 2 ) + 2 * sqrt( sqrt(2) + 2) )
When I'd rather get:
1 + (sqrt(2) + 2)**(3/2)
Other than muddling through, using simplify() on all of the various combinations of 2 or more terms in an Add-instance to see what I get, and then prioritizing the better of them using some algorithm (as yet not well-conceived) I develop over time, my question is this:
Is there an existing function call that will recognize that:
1+sqrt(2)*sqrt(sqrt(2)+2)+2*sqrt(sqrt(2)+2)) = 1+(sqrt(2)+2)**(3/2)
I have other interests with simplification of constants that include radicals as well as rational values. But getting this far would be a big help.
[Since I'm only working with constants here (I use Poly() to gain access to the coefficients), this may be more of a Sage issue than sympy. But I'm not well-versed enough into these tools to know better. If an answer requires some explanation about the conceptual differences, feel free to inform me about it. Just FYI.]
Thanks in advance.