I wanted to verify if n-th roots of unity are actually the n-th roots of unity?
i.e. if (root)^n = 1
I was trying to use sagemath to do this.
For e.g. for regular expressions sage seems to evaluate stuff
For e.g.
sage: x = var('x')
sage: f(x) = (x+2)^3
sage: f(5)
343
But I am unable to do this
sage: a = var('a')
sage: b = var('b')
sage: f(a, b) = (a + i*b)^3
sage: f(cos((2*pi)/3) , sin((2*pi)/3))
(1/2*I*sqrt(3) - 1/2)^3
How do I make sage raise it to power 3 & evaluate?
>Solution :
A sage expression has several methods to manipulate it, including expanding, factoring and simplifying:
e = f(cos((2*pi)/3) , sin((2*pi)/3))
e.expand()
e.simplify()
e.full_simplify()
e.factor()
You can see the list of all available methods by typing the name of the variable, followed by a dot, followed by a tabulation: e.<tab>.
In your case, it would appear e.full_simplify() should do the trick.
Relevant documentation: