On 1/11/2013 9:40 AM, Raymond Toy wrote:
>>>>>> "Richard" == Richard Fateman <fateman at eecs.berkeley.edu> writes:
> Richard> Looked at it this way, a polynomial p(x) either has exact
> Richard> multiple roots or not. The test is easy. If p(x) and
> Richard> p'(x), its derivative wrt x have no common factors then
> Richard> it has no multiple roots. So compute gcd(p,p').
>
> Richard> If the gcd is 1, then you (and you can tell your
> Richard> root-finder program) that there are NO multiple
> Richard> roots. (Oh, if gcd is not 1, it tells you a polynomial
> Richard> whose roots have multiplicity >1; you can divide out by
> Richard> this ,etc.)
>
> I guess the following would be a bug in gcd?
>
> p:expand((x-sqrt(2))^2*(x^2+2*x+2));
> gcd(p,diff(p,x)) -> 1
>
> It works fine if you replace sqrt(2) with r. The gcd is then x-r.
Interesting question, but it is not a gcd bug. You seem to need to
add to the task something
involving the computation of an algebraic extension. It is possible to
do something perhaps
with tellrat. and algebraic:true....
>
> Ray
>
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