What I want is for a calculus student to be able to say "factor(x^2+x
+1)" or "factor(x^2-x-1)" and get something useful. It would be nice
to be able to specify R or C as the relevant field. Using "solve"
instead of "factor" gives exactly what I would expect, namely the
result of applying the quadr
Oops posted too quickly. The alternative is to use the symbolic ring, though
strictly speaking that doesn't let you factor only find roots:
sage: var('x')
x
sage: (x^2-2).solve(x)
[x == -sqrt(2), x == sqrt(2)]
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You can factor it in any field that contains a square root of two. For
example, we can construct a suitable number field over QQ:
sage: z = QQ['z'].0
sage: K = NumberField(z^2 - 2,'sqrt2'); K
Number Field in sqrt2 with defining polynomial z^2 - 2
In this number field, you can (somewhat tautologi
