Related papers: Introducing Geometric Algebra to Geometric Computi…
We report about significant enhancements of the complex algebraic geometry theorem proving subsystem in GeoGebra for automated proofs in Euclidean geometry, concerning the extension of numerous GeoGebra tools with proof capabilities. As a…
An effective, accessible abstraction hierarchy has made using and programming computers possible for people across all disciplines. Establishing such a hierarchy for quantum programming is an outstanding challenge, especially due to a…
These lectures given to graduate students in theoretical particle physics, provide an introduction to the ``inner workings'' of computer algebra systems. Computer algebra has become an indispensable tool for precision calculations in…
In existing computing systems, such as edge computing and cloud computing, several emerging applications and practical scenarios are mostly unavailable or only partially implemented. To overcome the limitations that restrict such…
A short survey on applications of algebraic geometry in topological data analysis.
Scientists often infer abstract procedures from specific instances of problems and use the abstractions to generate new, related instances. For example, programs encoding the formal rules and properties of a system have been useful in…
The field of geometric automated theorem provers has a long and rich history, from the early AI approaches of the 1960s, synthetic provers, to today algebraic and synthetic provers. The geometry automated deduction area differs from other…
The field of numerical algebraic geometry consists of algorithms for numerically solving systems of polynomial equations. When the system is exact, such as having rational coefficients, the solution set is well-defined. However, for a…
Isogeometric analysis (IGA) represents a recently developed technology in computational mechanics that offers the possibility of integrating methods for analysis and Computer Aided Design (CAD) into a single, unified process. The…
Generic programming is an effective methodology for developing reusable software libraries. Many programming languages provide generics and have features for describing interfaces, but none completely support the idioms used in generic…
Implementing an application on a FPGA remains a difficult, non-intuitive task that often requires hardware design expertise in a hardware description language (HDL). High-level synthesis (HLS) raises the design abstraction from HDL to…
Implementing large software, as software analyzers which aim to be used in industrial settings, requires a well-engineered software architecture in order to ease its daily development and its maintenance process during its lifecycle. If the…
The main objective of this work is to describe a general and original approach for computing an off-line solution for a set of parameters describing the geometry of the domain. That is, a solution able to include information for different…
We describe our ongoing project of formalization of algebraic methods for geometry theorem proving (Wu's method and the Groebner bases method), their implementation and integration in educational tools. The project includes formal…
Novel user interfaces based on artificial intelligence, such as natural-language agents, present new categories of engineering challenges. These systems need to cope with uncertainty and ambiguity, interface with machine learning…
So far, the scope of computer algebra has been needlessly restricted to exact algebraic methods. Its possible extension to approximate analytical methods is discussed. The entangled roles of functional analysis and symbolic programming,…
Computer algebra systems are complex software systems that cover a wide range of scientific and practical problems. However, the absolute coverage cannot be achieved. Often, it is required to create a user extension for an existing computer…
We revisit the topic of two-state quantum systems using Geometric Algebra (GA) in three dimensions $\mathcal G_3$. In this description, both the quantum states and Hermitian operators are written as elements of $\mathcal G_3$. By writing…
Much of the success of deep learning is drawn from building architectures that properly respect underlying symmetry and structure in the data on which they operate - a set of considerations that have been united under the banner of…
We demonstrate how methods in Functional Programming can be used to implement a computer algebra system. As a proof-of-concept, we present the computational-algebra package. It is a computer algebra system implemented as an embedded…