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Number field arithmetic in Pari/gp

asked 2016-02-07 17:04:39 -0600

Dianbin Bao gravatar image

updated 2016-02-08 08:02:19 -0600

Hi all,

I would like to do number field arithmetic in Pari. To be more precise, I would like let Pari do the following job as Sage does,

K.<a> = NumberField(f(x))
L.<b> = NumberField(g(x))

where f(x), g(x) are irreducible polynomials over the rational. I would like to do arithmetic with a,b. This is easily done in Sage. How can I do this by Pari?

Thanks

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answered 2016-02-08 08:04:16 -0600

You can convert the given number field into pari number field with

sage: K.<a> = NumberField(x^2 - 2)
sage: K.pari_nf()
[y^2 - 2, [2, 0], 8, 1,
[[1, -1.41421356237310; 1, 1.41421356237310],
 [1, -1.41421356237310; 1, 1.41421356237310],
 [1, -1; 1, 1], [2, 0; 0, 4], [4, 0; 0, 2], [2, 0; 0, 1], [2, [0, 2; 1, 0]], []],
 [-1.41421356237310, 1.41421356237310], [1, y], [1, 0; 0, 1], [1, 0, 0, 2; 0, 1, 1, 0]]
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Asked: 2016-02-07 17:04:39 -0600

Seen: 36 times

Last updated: Feb 08 '16