Depending on what you need, there are several libraries in C and C++ that should be wrap-able. For instance, [CoCoA](http://cocoa.dima.unige.it/), [Singular](https://www.singular.uni-kl.de/), [LinBox](http://linalg.org/), [Pari](http://pari.math.u-bordeaux.fr/), ... . Each of these is _very_ likely to be the best at some aspect of what it does, because they are all developed by leading researchers in the field.
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