how to use NTL library for huge polynomial gcd’s over finite fields very quickly).

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If you are working in Sage, hopefully Sage will call NTL when appropriate. If you notice a case when Sage is not calling NTL, but could be made faster by calling NTL, please report.

If you want to work with NTL directly...

• The NTL home page has a link to the NTL documentation, which includes a page of examples, including about extension rings and fields over finite fields, and polynomial arithmetic over such extensions.

• See also the NTL discussion forum.