Tarski-Seidenberg theorem

Tarski-Seidenberg theorem

States that a set of equalities and inequalities f(x1,x2,x3,....xn)>=0 can be reduced down to a set of equalities and inequalities f(x1,x2,x3,....xn-1)>=0 with one less variable.

Thus all equations can be reduced to a set of equalities and inequalities on their coefficients.

See also: cylindrical algebraic decomposition

 See: Elimination

These algorithms aren't very simple.

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