Bill Hale on Sun, 15 Jun 2003 07:02:04 -0500

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Re: Finding an integral basis of a relative extension of nf's

At 10:23 PM -0400 6/14/03, Mak Trifkovic wrote:
>I need help with the following:
>I have a number field K=bnfinit(P(y)), and an extension L given by a
>polynomial Q(x) in K[x].  Assuming K has class number one,how do I get
>gp to find an integral basis for O_L over O_K, expressed as a set of
>polynomials in x with coefficients in Q[y]?

I am new to Pari myself. I am not sure if the following is
totally correct. Look at the following and refer to the
manual for details. You may wish to try your own polynomials
to test.


The output that I get for last three statements is:

? %5 = [1, y]
? %6 = [Mod(1, y^2 + y + 1), Mod(1, y^2 + y + 1)*x, Mod(1, y^2 + y +
1)*x^2, Mod(1, y^2 + y + 1)*x^3, Mod(1, y^2 + y + 1)*x^4, Mod(1, y^2 + y +
? %7 = [1, x, x^2, x^3, x^4, x^5]

-- Bill Hale