Re: decomposition of polynomials

In article <dv9i9h$tdu$1@xxxxxxxxxxxxxxxxx>
rusin@xxxxxxxxxxxxxxxxxxxxx (Dave Rusin) writes:


More high-falutin' responses are also possible. Look for
"polynomial decomposition", "primitive Galois group", and widen
your search to the more general problem of finding g, h with
f | (g o h) instead of f = g o h .
If you'd like to try your hand at this, consider the following
interesting example proposed when this question was asked in July 2001:
x^6+235*x^5+1430*x^4+1695*x^3+270*x^2-229*x+1

If we let alpha be a root of y^3 - y^2 - 2*y + 1,
then the sextic splits over the field Q(alpha, sqrt(21)).


alias(alpha = RootOf(y^3 - y^2 - 2*y + 1, y));
alias(sqrt21 = RootOf(t^2 = 21, t));

f := x^6+235*x^5+1430*x^4+1695*x^3+270*x^2-229*x+1;
factor(f, {alpha, sqrt21}); # Six linear factors


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