On Tuesday, May 13, 2014 12:50:41 PM UTC-7, David Joyner wrote: > > On Tue, May 13, 2014 at 2:19 PM, <[email protected] <javascript:>> > wrote: > > It is known that a polynomial x^2 +x +1= 0 has a solution in Zp if and > only > > if -3 is a square root > > in Zp, which is if and only if p=1.mod 6. the splitting field Zp(y1) > where > > y1 is a solution of the polynomial x^2 +x +1= 0 . > > > > So, > > * Zp(y1) is not a complex field and > * you mistakenly put CC when you meant a finite field and > * you mistakenly wrote y1=-0.5000 + 0.8660*i when you meant y1 is a > 3rd root of unity in a field GF(p), where p is 1 (mod 6)? > > Is that correct? > > If so, > > * figure out what p you want to use, > * compute what y1 is in that case, > * replace CC by GF(p) i your Sage code. >
So something like this might work: sage: K = GF(5) sage: R.<x> = K[] sage: F = K.extension(x^2+x+1, 'a') sage: F Finite Field in a of size 5^2 > > > > > -- > > You received this message because you are subscribed to the Google > Groups > > "sage-support" group. > > To unsubscribe from this group and stop receiving emails from it, send > an > > email to [email protected] <javascript:>. > > To post to this group, send email to > > [email protected]<javascript:>. > > > Visit this group at http://groups.google.com/group/sage-support. > > > > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
