Groebner.jl: A package for Gr\"obner bases computations in Julia

We introduce the Julia package Groebner.jl for computing Gr\"obner bases with the F4 algorithm. Groebner.jl is an efficient, lightweight, portable, thoroughly tested, and documented open-source software. The package works over integers modulo a prime and over the rationals and supports various monomial orderings. The implementation incorporates modern symbolic computation techniques and leverages the Julia type system and tooling, which allows Groebner.jl to be on par in performance with the leading computer algebra systems. Our package is freely available at https://github.com/sumiya11/Groebner.jl .Comment: 10 page

Verified Computer Algebra in ACL2 (Gröbner Bases Computation)

In this paper, we present the formal verification of a Common Lisp implementation of Buchberger’s algorithm for computing Gröbner bases of polynomial ideals. This work is carried out in the Acl2 system and shows how verified Computer Algebra can be achieved in an executable logic

The use of data-mining for the automatic formation of tactics

This paper discusses the usse of data-mining for the automatic formation of tactics. It was presented at the Workshop on Computer-Supported Mathematical Theory Development held at IJCAR in 2004. The aim of this project is to evaluate the applicability of data-mining techniques to the automatic formation of tactics from large corpuses of proofs. We data-mine information from large proof corpuses to find commonly occurring patterns. These patterns are then evolved into tactics using genetic programming techniques

A formal quantifier elimination for algebraically closed fields

The final publication is available at www.springerlink.comInternational audienceWe prove formally that the first order theory of algebraically closed fields enjoy quantifier elimination, and hence is decidable. This proof is organized in two modular parts. We first reify the first order theory of rings and prove that quantifier elimination leads to decidability. Then we implement an algorithm which constructs a quantifier free formula from any first order formula in the theory of ring. If the underlying ring is in fact an algebraically closed field, we prove that the two formulas have the same semantic. The algorithm producing the quantifier free formula is programmed in continuation passing style, which leads to both a concise program and an elegant proof of semantic correctness

A Survey of User Interfaces for Computer Algebra Systems

AbstractThis paper surveys work within the Computer Algebra community (and elsewhere) directed towards improving user interfaces for scientific computation during the period 1963–1994. It is intended to be useful to two groups of people: those who wish to know what work has been done and those who would like to do work in the field. It contains an extensive bibliography to assist readers in exploring the field in more depth. Work related to improving human interaction with computer algebra systems is the main focus of the paper. However, the paper includes additional materials on some closely related issues such as structured document editing, graphics, and communication protocols

Residential Water Meters as Edge Computing Nodes: Disaggregating End Uses and Creating Actionable Information at the Edge

We present a new, open source, computationally capable datalogger for collecting and analyzing high temporal resolution residential water use data. Using this device, execution of water end use disaggregation algorithms or other data analytics can be performed directly on existing, analog residential water meters without disrupting their operation, effectively transforming existing water meters into smart, edge computing devices. Computation of water use summaries and classified water end use events directly on the meter minimizes data transmission requirements, reduces requirements for centralized data storage and processing, and reduces latency between data collection and generation of decision-relevant information. The datalogger couples an Arduino microcontroller board for data acquisition with a Raspberry Pi computer that serves as a computational resource. The computational node was developed and calibrated at the Utah Water Research Laboratory (UWRL) and was deployed for testing on the water meter for a single-family residential home in Providence City, UT, USA. Results from field deployments are presented to demonstrate the data collection accuracy, computational functionality, power requirements, communication capabilities, and applicability of the system. The computational node’s hardware design and software are open source, available for potential reuse, and can be adapted to specific research needs