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When Henri Cohen and his coworkers set out to write PARI twenty years ago, GP was an afterthought. While GP has become the most commonly used interface to the PARI library by a large margin, both the gp interpretor and the GP language are primitive in design. Paradoxically, while gp allows to handle very high-level objects, GP itself is a low-level language coming straight from the seventies. We rewrote GP as a compiler/evaluator pair, implementing several high-level features (statically...

We describe a simple procedure to find Aurifeuillian factors of values of cyclotomic polynomials ${\Phi }_d\left(a\right)$ for integers $a$ and $d\>0$. Assuming a suitable Riemann Hypothesis, the algorithm runs in deterministic time $\tilde{O}\left(d^{2}L\right)$, using $O\left(dL\right)$ space, where $L≔log(\left|a\right|+1)$.