Related papers: A computer algebra user interface manifesto

In recent years there has been increased use of machine learning (ML) techniques within mathematics, including symbolic computation where it may be applied safely to optimise or select algorithms. This paper explores whether using…

Algebraic effects and handlers have emerged in the programming languages community as a convenient, modular abstraction for controlling computational effects. They have found several applications including concurrent programming, meta…

When dealing with process calculi and automata which express both nondeterministic and probabilistic behavior, it is customary to introduce the notion of scheduler to solve the nondeterminism. It has been observed that for certain…

We present a generic partition refinement algorithm that quotients coalgebraic systems by behavioural equivalence, an important task in system analysis and verification. Coalgebraic generality allows us to cover not only classical…

We present a new methodology for utilising machine learning technology in symbolic computation research. We explain how a well known human-designed heuristic to make the choice of variable ordering in cylindrical algebraic decomposition may…

Despite the wide variety of input types in machine learning, this diversity is often not fully reflected in their representations or model architectures, leading to inefficiencies throughout a model's lifecycle. This paper introduces an…

We contribute results for a set of fundamental problems in the context of programmable matter by presenting algorithmic methods for evaluating and manipulating a collective of particles by a finite automaton that can neither store…

While working on a software specification, designers usually need to evaluate different architectural alternatives to be sure that quality criteria are met. Even when these quality aspects could be expressed in terms of multiple software…

In this paper we introduce the notion of Modal Software Engineering: automatically turning sequential, deterministic programs into semantically equivalent programs efficiently operating on inputs coming from multiple overlapping worlds. We…

We study the algebraic effects and handlers as a way to support decision-making abstractions in functional programs, whereas a user can ask a learning algorithm to resolve choices without implementing the underlying selection mechanism, and…

Algebraic effects offer a versatile framework that covers a wide variety of effects. However, the family of operations that delimit scopes are not algebraic and are usually modelled as handlers, thus preventing them from being used freely…

Many tools used to process programs, like compilers, analyzers, or verifiers, perform transformations on their intermediate program representation, like abstract syntax trees. Implementing such program transformations is a non-trivial task,…

This is a proposal of an algebra which aims at distributed array processing. The focus lies on re-arranging and distributing array data, which may be multi-dimensional. The context of the work is scientific processing; thus, the core…

Constructing complex computation from simpler building blocks is a defining problem of computer science. In algebraic automata theory, we represent computing devices as semigroups. Accordingly, we use mathematical tools like products and…

Algebraic effects & handlers are a modular approach for modeling side-effects in functional programming. Their syntax is defined in terms of a signature of effectful operations, encoded as a functor, that are plugged into the free monad;…

We present in this paper an evolution of a tool from a user interface for a concrete Computer Algebra system for Algebraic Topology (the Kenzo system), to a front-end allowing the interoperability among different sources for computation and…

In certain scientific domains, there is a need for tensor operations. To facilitate tensor computations,computer algebra systems are employed. In our research, we have been using Cadabra as the main computer algebra system for several…

We discuss issues of problem formulation for algorithms in real algebraic geometry, focussing on quantifier elimination by cylindrical algebraic decomposition. We recall how the variable ordering used can have a profound effect on both…

This paper presents the main features of a system that aims to transform regular expressions into shorter equivalent expressions. The system is also capable of computing other operations useful for simplification, such as checking the…

The widespread adoption of algorithmic decision-making systems has brought about the necessity to interpret the reasoning behind these decisions. The majority of these systems are complex black box models, and auxiliary models are often…