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Are there any know (preferably implemented) algorithms to find solutions to quadratic forms over number fields (or global fields)?

I am especially interested in the quaternary case. There exist some algorithms for ternary quadratic forms, some of which are implemented in Magma.

The only algorithm for quaternary forms over the rationals I know of is described in Algorithms for solving rational quadratics (Schicho, Pílniková). It works by dividing the equation up into two appropriate ternary forms. However I see no easy way to make it work over number fields.

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