ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sat, 01 Dec 2012 15:59:51 +0100Square root in FunctionFieldhttps://ask.sagemath.org/question/9585/square-root-in-functionfield/Hi,
I'm working with $q$-functions and I would like to define a free algebra over the algebraic field with an extra parameter $q$ for which I can also take roots i.e. I would like to do something like this
sage: F.<q> = FunctionAlgebra(AA)
sage: A.<a,b,c,d> = FreeAlgebra(F, 4)
sage: (1+q)**(1/2)*a*b
sqrt(1+q)*a*b
The function FunctionAlgebra is not the correct function, since it only includes (integer) powers of $q$. Is it possible to extend this FunctionAlgebra to something where sums of powers of $q$ also have roots? Or is there an other function for which I can do this?
Best,
NoudThu, 29 Nov 2012 08:39:45 +0100https://ask.sagemath.org/question/9585/square-root-in-functionfield/Answer by Noud for <p>Hi,</p>
<p>I'm working with $q$-functions and I would like to define a free algebra over the algebraic field with an extra parameter $q$ for which I can also take roots i.e. I would like to do something like this</p>
<pre><code>sage: F.<q> = FunctionAlgebra(AA)
sage: A.<a,b,c,d> = FreeAlgebra(F, 4)
sage: (1+q)**(1/2)*a*b
sqrt(1+q)*a*b
</code></pre>
<p>The function FunctionAlgebra is not the correct function, since it only includes (integer) powers of $q$. Is it possible to extend this FunctionAlgebra to something where sums of powers of $q$ also have roots? Or is there an other function for which I can do this?</p>
<p>Best,
Noud</p>
https://ask.sagemath.org/question/9585/square-root-in-functionfield/?answer=14337#post-id-14337I found the answer myself. Instead of using AA you should use the SR (Symbolic Ring). An example:
sage: q = var('q')
sage: F.<a,b,c,d> = FreeAlgebra(SR, 4)
sage: (1+q)**(1/2)*b*a
(sqrt(q+1))*b*a
This SR ring is still a bit of a mystery to me, but it seems to work. Sat, 01 Dec 2012 15:59:51 +0100https://ask.sagemath.org/question/9585/square-root-in-functionfield/?answer=14337#post-id-14337