Thanks Maarten for a quick reply. I tried to hack this functionality but as you pointed out sage does not treat L(below) as a field.
sage: n=2 sage: m=3 sage: q=2; sage: k=GF(q); sage: K=GF(q^n,'w');K Finite Field in w of size 2^2 sage: P1.<t> = PolynomialRing(K,'t'); P1 Univariate Polynomial Ring in t over Finite Field in w of size 2^2 sage: r1 = P1.random_element(m); sage: while (len(r1.coeffs()) != m+1): ....: r1= P1.random_element(m) ....: sage: while (r1.is_primitive() == False): ....: r1 = P1.random_element(m); ....: while ( len(r1.coeffs()) != m+1 ): ....: r1 = P1.random_element(m); ....: sage: r1 w*t^3 + w*t^2 + w*t + 1 sage: L.<t> = K.extension(r1, 't'); L Univariate Quotient Polynomial Ring in t over Finite Field in w of size 2^2 with modulus t^3 + t^2 + t + w + 1 sage: L.is_field() True Though L above is field and k -> K -> L is a tower. I am not able to treat L as a field. May be I will look at towers of number field and try to write my own code. Thanks, Shashank On Tuesday, September 4, 2012 2:10:24 PM UTC+5:L is30, sha2nk wrote: > > k=GF(2^11); > K=GF(2^33) > > How to see K as a vector space over filed k ? How to form its basis ? > How to construct tower of field extensions ? > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support?hl=en.
