# real roots of algebraic equation

Let we have algebraic equation on one variable. Which methods (exept Sturm's theorem and Descartes' rule) exist to find real roots of equation (or real positive)?

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This is what "root systems" mean: en.wikipedia.org/wiki/Root_system . Retagged as polynomials for now. –  Willie Wong Nov 6 '10 at 15:04
Also, without further motivation ad clarification, your question is overbroad: please read the FAQ and note the part where it says MO is not an encyclopaedia. –  Willie Wong Nov 6 '10 at 15:05
I'm personally fond of using Sturm sequences to generate the (symmetric!) tridiagonal matrix whose characteristic polynomial is the original polynomial. If there is no such matrix, you know at once that the polynomial has complex roots. –  J. M. Nov 6 '10 at 15:41
I tend to agree with Willie here. –  Nikita Sidorov Nov 6 '10 at 16:08
I would agree with the encyclopaedia criticism, except that in this case, once you ruled out Sturm's theorem and Descartes' rule, there shouldn't be much left. –  Thierry Zell Nov 6 '10 at 16:13