We present an implemented algorithmic method for counting and isolating all p-adic roots of univariate polynomials f over the rational numbers. The roots of f are uniquely described by p-adic isolating balls, that can be refined to any desired precision; their p-adic distances are also computed precisely. The method is polynomial space in all input data including the prime p. We also investigate the uniformity of the method with respect to the coefficients of f and the primes p. Our method thus...

This paper provides a framework to address termination problems in term rewriting by using orderings induced by algebras over the reals. The generation of such orderings is parameterized by concrete monotonicity requirements which are connected with different classes of termination problems: termination of rewriting, termination of rewriting by using dependency pairs, termination of innermost rewriting, top-termination of infinitary rewriting, termination of context-sensitive rewriting, etc. We...

This paper provides a framework to address termination problems in term rewriting by using orderings induced by algebras over the reals. The generation of such orderings is parameterized by concrete monotonicity requirements which are connected with different classes of termination problems: termination of rewriting, termination of rewriting by using dependency pairs, termination of innermost rewriting, top-termination of infinitary rewriting, termination of context-sensitive rewriting, etc. We...

All finite simple groups of Lie type of rank $n$ over a field of size $q$, with the possible exception of the Ree groups ${}^2{G}_2\left(q\right)$, have presentations with at most 49 relations and bit-length $O(\mathrm{𝚕𝚘𝚐}n+\mathrm{𝚕𝚘𝚐}q)$. Moreover, $A_n$ and $S_n$ have presentations with 3 generators; 7 relations and bit-length $O(\mathrm{𝚕𝚘𝚐}n)$, while $\mathrm{𝚂𝙻}(n,q)$ has a presentation with 6 generators, 25 relations and bit-length $O(\mathrm{𝚕𝚘𝚐}n+\mathrm{𝚕𝚘𝚐}q)$.