Related papers: Exact $p$-adic computation in Magma
Exact representations of real numbers such as the signed digit representation or more generally linear fractional representations or the infinite Gray code represent real numbers as infinite streams of digits. In earlier work by the first…
This paper introduces a formal metalanguage called the lambda-q calculus for the specification of quantum programming languages. This metalanguage is an extension of the lambda calculus, which provides a formal setting for the specification…
We have developed a Mathematica package capable of performing gamma-matrix algebra in arbitrary (integer) dimensions. As an application we can compute Fierz transformations.
We discuss the deal of imperfectness of atomic actions in reality with the background of process algebras. And we show the applications of the imperfect actions in verification of computational systems.
We present a new algorithm to decide isomorphism between finite graded algebras. For a broad class of nilpotent Lie algebras, we demonstrate that it runs in time polynomial in the order of the input algebras. We introduce heuristics that…
We introduce a new approach for deterministic sensitivity analysis of Markov reward processes, commonly used in cost-effectiveness analyses, via reformulation into a polynomial system. Our approach leverages cylindrical algebraic…
We discuss algorithms for arithmetic properties of hypergeometric functions. Most notably, we are able to compute the p-adic valuation of a hypergeometric function on any disk of radius smaller than the p-adic radius of convergence. This we…
Approximate computing emerges as a promising approach to enhance the efficiency of compute-in-memory (CiM) systems in deep neural network processing. However, traditional approximate techniques often significantly trade off accuracy for…
We present an algorithm for the numerical evaluation of elliptic multiple polylogarithms for arbitrary arguments and to arbitrary precision. The cornerstone of our approach is a procedure to obtain a convergent $q$-series representation of…
Mathematical software systems are becoming more and more important in pure and applied mathematics in order to deal with the complexity and scalability issues inherent in mathematics. In the last decades we have seen a cambric explosion of…
We introduce our package '+Ideals' for Magma, designed to perform the basic tasks related to ideals in number fields without pre-computing integral bases. It is based on Montes algorithm and a number of local techniques that we have…
The present paper constructs three new systems of clarithmetic (arithmetic based on computability logic --- see http://www.cis.upenn.edu/~giorgi/cl.html): CLA8, CLA9 and CLA10. System CLA8 is shown to be sound and extensionally complete…
Approximate computing (AxC) has been long accepted as a design alternative for efficient system implementation at the cost of relaxed accuracy requirements. Despite the AxC research activities in various application domains, AxC thrived the…
Nowadays, the number of emerging embedded systems rapidly grows in many application domains, due to recent advances in artificial intelligence and internet of things. The main inherent specification of these application-specific systems is…
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…
The polylogarithm function is one of the constellation of important mathematical functions. It has a long history, and many connections to other special functions and series, and many applications, for instance in statistical physics.…
This article is intended to an introductory lecture in material physics, in which the modern computational group theory and the electronic structure calculation are in collaboration. The effort of mathematicians in field of the group…
Many algorithms, especially in the field of computational geometry, are based on the premise that arithmetic operations are performed exactly. Real machines are based on inexact floating-point arithmetic. Various number types have been…
This paper considers finite-automata based algorithms for handling linear arithmetic with both real and integer variables. Previous work has shown that this theory can be dealt with by using finite automata on infinite words, but this…
A constructive method for decomposing finite dimensional representations of semisimple real Lie algebras is developed. The method is illustrated by an example. We also discuss an implementation of the algorithm in the language of the…