# zbMATH — the first resource for mathematics

The author considers indefinite quadratic forms with integer coefficients and gives a polynomial time algorithm (based on LLL) to reduce it to a diagonal form. Further, an algorithm is given for the minimization of a ternary quadratic form: if a quadratic equation $$q(x,y,z)=0$$ is solvable over the rationals, a solution can be deduced from another quadratic form equation of determinant $$\pm 1$$. Combining these methods we obtain a polynomial time algorithm to solve any ternary quadratic equation over the rationals. The paper is illustrated with interesting examples.