How do I represent roots of unity?
Adam · Mon Oct 04, 2010 5:26 am
If I want an expression that has $\zeta_3$ in it -- how would I write it?
Re: How do I represent roots of unity?
gorzel · Thu Oct 07, 2010 7:25 pm
You need to define the minimal polynomial over the ground field
of the third root of unity.
Supposed you want to compute in characteristic zero, then
of the third root of unity.
Supposed you want to compute in characteristic zero, then
Code:
> ring rQ = 0,x,dp; // Q[x]
> factorize(x3-1);
[1]:
_[1]=1
_[2]=x-1
_[3]=x2+x+1
[2]:
1,1,1
> ring rQzeta = (0,z),x,dp; // Q[z]/(z^2+z+1)[x]
> minpoly = z2+z+1; // The parameter z is now a 3rd root of unity
> z^3;
1
> z2*x4-2zx+2z+1;
(-z-1)*x4+(-2z)*x+(2z+1)
> factorize(x3-1);
[1]:
_[1]=1
_[2]=x-1
_[3]=x2+x+1
[2]:
1,1,1
> ring rQzeta = (0,z),x,dp; // Q[z]/(z^2+z+1)[x]
> minpoly = z2+z+1; // The parameter z is now a 3rd root of unity
> z^3;
1
> z2*x4-2zx+2z+1;
(-z-1)*x4+(-2z)*x+(2z+1)