Solving conics over function fields
Mark van Hoeij, John Cremona (2006)
Journal de Théorie des Nombres de Bordeaux
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Let be a field whose characteristic is not and . We give a simple algorithm to find, given , a nontrivial solution in (if it exists) to the equation . The algorithm requires, in certain cases, the solution of a similar equation with coefficients in ; hence we obtain a recursive algorithm for solving diagonal conics over (using existing algorithms for such equations over ) and over .