Is there a way to build subfields of finite fields that will behave as subfields?
For example, a finite field of order 3^6 will have proper subfields of order 3^1, 3^2, 3^3. The first is not too interesting and can be recovered with the .prime_subfield() method. I can easily build the set of elements for the other two, using the cyclic group structure of the nonzero elements under multiplication. But these are just lists, with no structure. For teaching purposes I'd like to get back a finite field that "checks out" as a subring or subfield. I tried building quotient rings of the ring of polynomials over Z_3, without much luck, but I was not very careful about my choices for irreducible polynomials. So maybe there is some way to make those choices and create two quotient rings that are finite fields with a subfield relationship. Any suggestions or pointers would be appreciated. Thanks, Rob -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
