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Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
This paper narrows the gap between previous literature on quantum linear algebra and practical data analysis on a quantum computer, formalizing quantum procedures that speed-up the solution of eigenproblems for data representations in…
The braid group appears in many scientific fields and its representations are instrumental in understanding topological quantum algorithms, topological entropy, classification of manifolds and so on. In this work, we study planer diagrams…
This a book is for those who would like to learn something about special and general relativity beyond the usual textbooks, about quantum field theory, the elegant Fock-Schwinger-Stueckelberg proper time formalism, the elegant description…
In this research, a new numerical method is proposed for solving fractional Bratu type boundary value problems. Fractional derivatives are taken in Caputo sense. This method is predicated on iterative approach of reproducing kernel Hilbert…
We use homological perturbation machinery specific for the algebra category [P. Real. Homological Perturbation Theory and Associativity. Homology, Homotopy and Applications vol. 2, n. 5 (2000) 51-88] to give an algorithm for computing the…
Many computer algebra systems have more than 1000 built-in functions, making expertise difficult. Using mock dialog boxes, this article describes a proposed interactive general-purpose wizard for organizing optional transformations and…
Recent advances in artificial intelligence have demonstrated the learnability of symbolic computation through end-to-end deep learning. Given a sufficient number of examples of symbolic expressions before and after the target computation,…
An effective algorithm is presented for solving the Beltrami equation df/dz = mu (df/dzbar) in a planar disk. The disk is triangulated in a simple way and f is approximated by piecewise linear mappings; the images of the vertices of the…
I apply the algebraic framework introduced in arXiv:1101.4542v3[math.MG] to Minkowski (pseudo-Euclidean) spaces in 2, 3, and 4 dimensions. The exposition follows the template established in arXiv:1307.2917[math.MG] for Euclidean spaces. The…
The Python package ComCH is a lightweight specialized computer algebra system that provides models for well known objects, the surjection and Barratt-Eccles operads, parameterizing the product structure of algebras that are commutative in a…
A general formalism is developed that allows the construction of field theory on quantum spaces which are deformations of ordinary spacetime. The symmetry group of spacetime is replaced by a quantum group. This formalism is demonstrated for…
This is a set of lecture notes on the operator algebraic approach to 2-dimensional conformal field theory. Representation theoretic aspects and connections to vertex operator algebras are emphasized. No knowledge on operator algebras or…
We develop algebraic models of simple type theories, laying out a framework that extends universal algebra to incorporate both algebraic sorting and variable binding. Examples of simple type theories include the unityped and simply-typed…
Solving time-dependent parametric partial differential equations (PDEs) is challenging for data-driven methods, as these models must adapt to variations in parameters such as coefficients, forcing terms, and initial conditions.…
We present a computer algebra package based on Magma for performing computations in rational Cherednik algebras at arbitrary parameters and in Verma modules for restricted rational Cherednik algebras. Part of this package is a new general…
Tensor contraction operations in computational chemistry consume significant fractions of computing time on large-scale computing platforms. The widespread use of tensor contractions between large multi-dimensional tensors in describing…
There are a wide range of applications that involve multi-modal data, such as cross-modal retrieval, visual question-answering, and image captioning. Such applications are primarily dependent on aligned distributions of the different…
An alternative, pedagogically simpler derivation of the allowed physical wave fronts of a propagating electromagnetic signal is presented using geometric algebra. Maxwell's equations can be expressed in a single multivector equation using…
I present the tensor computer algebra package FieldsX, which extends the xAct suite of tensor algebra packages to perform computations in field theory with fermions and gauge fields. This includes the standard tools of curved-space $\gamma$…