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 2019-06-08 09:44:49 -0600 asked a question Towered extension fields through chosen polynomial (Edited, since  compiles in HTML as an underlyning tag, dan.) 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. 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.