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Adam
 Post subject: How do I represent roots of unity?
PostPosted: Mon Oct 04, 2010 5:26 am 
If I want an expression that has $\zeta_3$ in it -- how would I write it?


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gorzel
 Post subject: Re: How do I represent roots of unity?
PostPosted: Thu Oct 07, 2010 7:25 pm 

Joined: Wed Mar 03, 2010 5:08 pm
Posts: 108
Location: Germany, Münster
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
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)


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