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| How do I represent roots of unity? https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=1866 |
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| Author: | Adam [ Mon Oct 04, 2010 5:26 am ] |
| Post subject: | How do I represent roots of unity? |
If I want an expression that has $\zeta_3$ in it -- how would I write it? |
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| Author: | gorzel [ Thu Oct 07, 2010 7:25 pm ] |
| Post subject: | Re: How do I represent roots of unity? |
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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