ASKSAGE: Sage Q&A Forum - Latest question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 29 Nov 2012 01:39:45 -0600Square root in FunctionFieldhttp://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,
NoudNoudThu, 29 Nov 2012 01:39:45 -0600http://ask.sagemath.org/question/9585/Complex argument of a symbolic expressionhttp://ask.sagemath.org/question/9496/complex-argument-of-a-symbolic-expression/I was a bit surprised that simply entering a complex number and asking for its argument doesn't seem to work. Not even in the case where all numbers are known and algebraic, even integers:
(2+3*I).arg()
AttributeError: 'sage.symbolic.expression.Expression' object has no attribute 'arg'
I found out that in order to compute the argument, I'll have to manually cast my number from the symbolic ring into some complex field, e.g.
sage: CC(2+3*I).arg()
0.982793723247329
But I believe that this should work without me having to think too much about the type system. It should even work for completely symbolic expressions, as stuff like `real_part`, `imag_part` and `atan2` are all symbolic functions which may be returned in their unevaluated form if evaluation is not possible.
Is there some other way to compute the complex argument, which I missed so far, ans which works for symbolic expressions as well as elements of a complex number field?MvGFri, 02 Nov 2012 06:22:32 -0500http://ask.sagemath.org/question/9496/