Stephen M. Watt
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Structuring Definitions in Mathematical Libraries Open
Codifying mathematical theories in a proof assistant or computer algebra system is a challenging task, of which the most difficult part is, counterintuitively, structuring definitions. This results in a steep learning curve for new users a…
Well-Conditioned Polynomial Representations for Mathematical Handwriting Recognition Open
Previous work has made use of a parameterized plane curve polynomial representation for mathematical handwriting, with the polynomials represented in a Legendre or Legendre-Sobolev graded basis. This provides a compact geometric representa…
Generative AI for Multiple Choice STEM Assessments Open
Artificial intelligence (AI) technology enables a range of enhancements in computer-aided instruction, from accelerating the creation of teaching materials to customizing learning paths based on learner outcomes. However, ensuring the math…
Software Portability for Computer Algebra Open
We have been involved in the creation of multiple software systems for computer algebra, including Reduce, Maple, Axiom and Aldor as well as a number of smaller specialised programs. We relate observations on how the meaning of software po…
Semi-Centennial REDUCE Open
We present a version of the REDUCE computer algebra system as it was in the early 1970s. We show how this historical version of REDUCE may be built and run in very modest present-day environments and outline some of its capabilities.
Disrupting Civil Engineering Open
This chapter uses the author's experiences with a Disrupting interview to describe the connections among decolonization, teaching, and the land in the author's home discipline of civil engineering and in their personal relationship with wa…
Symbolic Mathematical Computation 1965--1975: The View from a Half-Century Perspective Open
The 2025 ISSAC conference in Guanajuato, Mexico, marks the 50th event in this significant series, making it an ideal moment to reflect on the field's history. This paper reviews the formative years of symbolic computation up to 1975, fifty…
A First Look at Chebyshev-Sobolev Series for Digital Ink Open
Considering digital ink as plane curves provides a valuable framework for various applications, including signature verification, note-taking, and mathematical handwriting recognition. These plane curves can be obtained as parameterized pa…
An Abstraction-Preserving Block Matrix Implementation in Maple Open
A Maple implementation of partitioned matrices is described. A recursive block data structure is used, with all operations preserving the block abstraction. These include constructor functions, ring operations such as addition and product,…
Algorithms for Recursive Block Matrices Open
We study certain linear algebra algorithms for recursive block matrices. This representation has useful practical and theoretical properties. We summarize some previous results for block matrix inversion and present some results on triangu…
Computing Clipped Products Open
Sometimes only some digits of a numerical product or some terms of a polynomial or series product are required. Frequently these constitute the most significant or least significant part of the value, for example when computing initial val…
A Symbolic Computing Perspective on Software Systems Open
Symbolic mathematical computing systems have served as a canary in the coal mine of software systems for more than sixty years. They have introduced or have been early adopters of programming language ideas such ideas as dynamic memory man…
Using General Large Language Models to Classify Mathematical Documents Open
In this article we report on an initial exploration to assess the viability of using the general large language models (LLMs), recently made public, to classify mathematical documents. Automated classification would be useful from the appl…
GPU Implementations for Midsize Integer Addition and Multiplication Open
This paper explores practical aspects of using a high-level functional language for GPU-based arithmetic on ``midsize'' integers. By this we mean integers of up to about a quarter million bits, which is sufficient for most practical purpos…
The Inverse of the Complex Gamma Function Open
We consider the functional inverse of the Gamma function in the complex plane, where it is multi-valued, and define a set of suitable branches by proposing a natural extension from the real case.
Hybrid Intervals and Symbolic Block Matrices Open
Structured matrices with symbolic sizes appear frequently in the literature, especially in the description of algorithms for linear algebra. Recent work has treated these symbolic structured matrices themselves as computational objects, sh…
Efficient Quotients of Non-Commutative Polynomials Open
It is shown how to compute quotients efficiently in non-commutative univariate polynomial rings. This extends earlier work where efficient generic quotients were studied with a primary focus on commutative domains. Fast algorithms are give…
Efficient Generic Quotients Using Exact Arithmetic Open
The usual formulation of efficient division uses Newton iteration to compute an inverse in a related domain where multiplicative inverses exist. On one hand, Newton iteration allows quotients to be calculated using an efficient multiplicat…
Health Provider and Sexual and Gender Minority Service User Perspectives on Provision of Mental Health Services During the Early Phase of the COVID-19 Pandemic in British Columbia, Canada Open
While the COVID-19 pandemic impacted everyone, social determinants of health and structural inequities have had compounding effects that shaped the experiences of some sub-populations during the pandemic. Stigmatization, discrimination, an…
Telescopers for differential forms with one parameter Open
Telescopers for a function are linear differential (resp. difference) operators annihilated by the definite integral (resp. definite sum) of this function. They play a key role in Wilf-Zeilberger theory and algorithms for computing them ha…
Genetic associations at regulatory phenotypes improve fine-mapping of causal variants for twelve immune-mediated diseases Open
The identification of causal genetic variants for common diseases improves understanding of disease biology. Here we use data from the BLUEPRINT project to identify regulatory quantitative trait loci (QTL) for three primary human immune ce…
Variation in PU.1 binding and chromatin looping at neutrophil enhancers influences autoimmune disease susceptibility Open
Neutrophils play fundamental roles in innate inflammatory response, shape adaptive immunity 1 , and have been identified as a potentially causal cell type underpinning genetic associations with immune system traits and diseases 2,3 The maj…
Origami folds in higher-dimension Open
We present a generalization of mathematical origami to higher dimensions. We briefly explain Huzita- Justin’s axiomatic treatment of mathematical origami. Then, for concreteness, we apply it to origami on 3-dimensional Euclidean space in w…