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2012-06-19 08:33:33 +0200 asked a question Generating a splitting field

Suppose I have a set of polynomials S in K[x] where K = Q(a), some number field. How could I generate a field which is the splitting field of all the polynomials in S?

2012-06-19 08:32:47 +0200 asked a question How does one tell if a number field contains a certain element?

Suppose I have a number field K, in SAGE how would can see if something like \sqrt[4]{29} is contained in this number field?