Given $f(x,y)\in\mathbb Z[x,y]$ Coppersmith in https://link.springer.com/chapter/10.1007%2F3-540-68339-9_16 provides a provable method to find integer roots in polynomial time and this method was also studied in https://link.springer.com/chapter/10.1007/978-3-540-24676-3_29 and https://link.springer.com/chapter/10.1007/11426639_15.

Have these methods been implemented in Python or Mathematica?

Sage has small_roots() but that is only for the univariate situation.


An implementation in SageMath is available at https://github.com/ubuntor/coppersmith-algorithm

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  • $\begingroup$ I saw that too. Not sure if it has been tested or just an amateur post. $\endgroup$ – 1.. Oct 6 at 4:42
  • $\begingroup$ Why not give it a try? $\endgroup$ – Max Alekseyev Oct 6 at 4:52

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