Ask Your Question

Towered extension fields through chosen polynomial

asked 2019-06-08 14:23:35 +0200

pch gravatar image

updated 2019-06-13 15:54:25 +0200

dan_fulea gravatar image

(Edited, since <u> compiles in HTML as an underlyning tag, dan.)

K.<u> = GF(q)
KT.<u> = K.extension(2)
KTT.<u> = K.extension(6)

In this case KTT is a degree 12 extension. My question is:

Can I obtain KTT by KTT.<u> = K.extension(x^6 - a), where x^6 -a is some irreducible polynomial over KT ???

Documentation gives nothing about this towering of fields.

edit retag flag offensive close merge delete


The above was edited to see the real question. Note that "displayed code" can be marked as such with an indent of 4 spaces, or hit Control+K after marking it, or press the button in the edit mask with 101 and 010 after marking it. In-line the marking is done by ticks.

dan_fulea gravatar imagedan_fulea ( 2019-06-13 15:56:29 +0200 )edit

1 Answer

Sort by ยป oldest newest most voted

answered 2019-06-13 16:01:03 +0200

dan_fulea gravatar image

The following worked for me:

sage: q = 27
sage: K.<u> = GF(q)
sage: K.extension(2)
Finite Field in z6 of size 3^6
sage: KT.<a> = K.extension(2)
sage: KT
Finite Field in a of size 3^6
sage: RT.<Z> = PolynomialRing(KT)
sage: KTT.<b> = KT.extension(Z^6-a)
sage: KTT
Univariate Quotient Polynomial Ring in b over Finite Field in a of size 3^6 with modulus b^6 + 2*a
sage: b.minpoly()
x^6 + 2*a
edit flag offensive delete link more

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

Question Tools

1 follower


Asked: 2019-06-08 14:23:35 +0200

Seen: 257 times

Last updated: Jun 13 '19