Relax, but Don’t be Too Lazy

Relaxed algorithms for p-adic numbers

“…The relaxed computational model was first introduced in [Hoe97] for formal power series, and further improved in [Hoe02,Hoe07b]. In this article, we extend the model to more general completions R p .…”

“…The relaxed computational model. For the description of our relaxed algorithms, we will follow [Hoe02] and use a C++-style pseudo-code, which is very similar to the actual C++ implementation in Mathemagix. As in [Hoe02], we will not discuss memory management related issues, which have to be treated with care in real implementations, especially when it comes to recursive expansions (see Section 5 below).…”

“…Subsequently [Hoe02], this compromise between the zealous and the naive lazy approaches has been called the relaxed model. The main aim of this paper is the design of relaxed algorithms for computing in the completion R p .…”

“…We will show that the known complexity results for power series extend to this setting. For more details on the power series setting, we refer the reader to the introduction of [Hoe02].…”

Code Generation for Polynomial Multiplication

“…The algorithms we consider will be called "divide-and-conquer", following the terminology of [19]. The most well-known representatives of this class are due to Karatsuba and Toom, though many more exist.…”