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Effective Hasse principle for the intersection of two quadrics
Published online by Cambridge University Press: 26 August 2016
Abstract
We consider a smooth system of two homogeneous quadratic equations over $\mathbb{Q}$ in $n\geqslant 13$ variables. In this case, the Hasse principle is known to hold, thanks to the work of Mordell in 1959. The only local obstruction is over $\mathbb{R}$. In this paper, we give an explicit algorithm to decide whether a nonzero rational solution exists and, if so, compute one.
MSC classification
- Type
- Research Article
- Information
- LMS Journal of Computation and Mathematics , Volume 19 , Special Issue A: Algorithmic Number Theory Symposium XII , 2016 , pp. 73 - 82
- Copyright
- © The Author 2016
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