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Sunday, October 17, 2010

Galois Theory (2)

The polynomial F(x) = x^8 - 40x^6 + 352x^4 +960x^2 - 576 has 8 ( real ) roots : +/- Sqrt(2) +/- Sqrt(3) +/- Sqrt(5). ( See image above. ) The symmetry group of the roots is abelian and has order 8, all elements have order 2, so the group is isomorphic to C2 X C2 X C2.

I have found another introductory book on Galois Theory for undergraduates ( to support my study of Weintraub's Galois Theory I think, for the moment anyway. )

It comes with AlgFields ( download here ), a system of Maple and Mathematica routines for calculating with low-dimensional number fields and finite fields.

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