Finite fields

**Mike12** · January 29th 2011, 03:28 PM

can any one help me to know how to do this question please:
if I have theta is a root of the polynomial p(x) ,where p(x)=x^3-2x-2 is irreducible in Q[x] how can I compute (1+theta)(1+theta+theta^2) and (1+theta)/1+theta+theta^2 in Q(theta)

**tonio** · January 30th 2011, 12:54 AM

Originally Posted by Mike12

can any one help me to know how to do this question please:
if I have theta is a root of the polynomial p(x) ,where p(x)=x^3-2x-2 is irreducible in Q[x] how can I compute (1+theta)(1+theta+theta^2) and (1+theta)/1+theta+theta^2 in Q(theta)

$\displaystyle{p(\theta)=\theta^3-2\theta-2=0\Longrightarrow \theta^3=2\theta+2}$ , so for example

$\displaystye{(1+\theta)(1+\theta+\theta^2)=1+2\the ta+2\theta^2+\theta^3=1+2\theta+2\theta^2+2\theta+ 2=3+4\theta+2\theta^2}$

Tonio

Math Help - Finite fields

LinkBack

Thread Tools

Display

Finite fields

Similar Math Help Forum Discussions

Distinct Bases for Finite Vector Spaces over Finite Fields

finite fields

Finite fields....

about finite fields

Finite Fields

Search Tags