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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...
We give an effective characterization theorem for integral monic irreducible polynomials of degree whose Galois groups over are Frobenius groups with kernel of order and complement of prime order.
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