Related papers: Lectures on Reduce and Maple at UAM I - Mexico
During the last decade we have witnessed an impressive development in so-called interpreted languages and computational environments such as Maple, Mathematica, IDL, Matlab etc. Problems which until recently were typically solved on…
These are lecture notes that are based on the lectures from a class I taught on the topic of Randomized Linear Algebra (RLA) at UC Berkeley during the Fall 2013 semester.
This document contains the notes of a lecture I gave at the "Journ\'ees Nationales du Calcul Formel" (JNCF) on January 2017. The aim of the lecture was to discuss low-level algorithmics for p-adic numbers. It is divided into two main parts:…
In order to deal with the curse of dimensionality in reinforcement learning (RL), it is common practice to make parametric assumptions where values or policies are functions of some low dimensional feature space. This work focuses on the…
The diverse world of machine learning applications has given rise to a plethora of algorithms and optimization methods, finely tuned to the specific regression or classification task at hand. We reduce the complexity of algorithm design for…
This article is based on earlier papers where an approach based on Taylor expansion and the structure of its leading term as an element of a free Lie algebra was described for the setup of a system of order conditions for operator splitting…
Residuation theory concerns the study of partially ordered algebraic structures, most often monoids, equipped with a weak inverse for the monoidal operator. One of its area of application has been constraint programming, whose key…
The polynomial multiplication problem has attracted considerable attention since the early days of computer algebra, and several algorithms have been designed to achieve the best possible time complexity. More recently, efforts have been…
Reduze is a computer program for reducing Feynman integrals to master integrals employing a variant of Laporta's reduction algorithm. This article describes version 2 of the program. New features include the distributed reduction of single…
This article explains how to apply the computer algebra package GAP (www.gap-system.org) in the computation of the problems in quantum physics, in which the application of Lie algebra is necessary. The article contains several exemplary…
It is our intention here only to discuss the nature, complexity and tools concerning the design of Smart Help, an expert help facility for aiding users of Computer Algebra Systems. Although the expert help system presented here has been…
The present lectures were prepared for the Faro International Summer School on Factorization and Integrable Systems in September 2000. They were intended for participants with the background in Analysis and Operator Theory but without…
Ihe first author presented an efficient algorithm for computing involutive (and reduced Groebner) bases. In this paper, we consider a modification of this algorithm which simplifies matters to understand it and to implement. We prove…
In analyzing and assessing the condition of dynamical systems, it is necessary to account for nonlinearity. Recent advances in computation have rendered previously computationally infeasible analyses readily executable on common computer…
We propose a variant of iterated belief revision designed for settings with limited computational resources, such as mobile autonomous robots. The proposed memory architecture---called the {\em universal memory architecture}…
Computer algebra procedures to manipulate pseudo-differential operators are implemented to perform calculations with integrable models. We use lazy evaluation and streams to represent and operate with pseudo-differential operators. No order…
These notes are based on the mini-course given in June 2004 in Cetraro, Italy, in the frame of a C.I.M.E. school. Of course, they contain much more material that I could present in the 6 hours course. The main goal is to give an idea of the…
In this paper, we propose an incremental algorithm for computing cylindrical algebraic decompositions. The algorithm consists of two parts: computing a complex cylindrical tree and refining this complex tree into a cylindrical tree in real…
This article describes the authors' teaching experience in flipping the class of a basic undergraduate mathematics course Introductory Linear Algebra. We utilize a full-featured free electronic textbook, online lecture notes, an intranet…
This work studies the question of Representation Learning in RL: how can we learn a compact low-dimensional representation such that on top of the representation we can perform RL procedures such as exploration and exploitation, in a sample…