On Apr 15, 2009, at 3:34 AM, Diravan wrote:
>
> I need to solve a very simple equation x^2 + 1 = 0 and I don't want
> any complex solutions.
> I tried this
> x = var('x')
> assume(x,'real')
> solve(x^2 + 1 == 0)
> but the output is [x == -1*I, x == I]
> Does exist any solution in order to avoid this ?
I think the assume commands are mostly used for simplification.
A quadratic equation has at most two roots (ignoring multiplicity)
and since you have two non-real roots, that means there are no real
roots. If you are interested in finding the real roots of a
polynomial you can do
sage: R.<t> = QQ[]
sage: (t^2 + 1).roots(RR)
[]
I.e. there are no roots over RRl. Here's a more interesting example:
sage: (t^7 - 10*t^4 + 1).roots(RR)
[(-0.559900456639459, 1), (0.564904614143836, 1), (2.15107524883421, 1)]
sage: (t^7 - 10*t^4 + 1).roots(RIF)
[(-0.559900456639458794479977438451?, 1),
(0.56490461414383587778472669435284?, 1),
(2.151075248834206453076?, 1)]
- Robert
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