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2019-06-08 09:44:49 -0600 asked a question Towered extension fields through chosen polynomial

(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.

2019-06-08 09:44:49 -0600 asked a question Towered extension fields through given irreducible polynomial

K. = GF(q)

KT. = K.extension(2)

KTT. = K.extension(6)

In this case KTT is a degree 12 extension. My question is can I obtain KTT by KTT. = K.extension(x^6 - a), where x^6 -a is some irreducible polynomial over KT ???

Documentation gives nothing about this towering of fields.