Related papers: A Symbolic Transformation Language and its Applica…
Declarative modeling uses symbolic expressions to represent models. With such expressions one can formalize high-level mathematical computations on models that would be difficult or impossible to perform directly on a lower-level simulation…
Rascal is a high-level transformation language that aims to simplify software language engineering tasks like defining program syntax, analyzing and transforming programs, and performing code generation. The language provides several…
This paper is an example-based demonstration of our initial results on the formal specification of programs written in the computer algebra language MiniMaple (a substantial subset of Maple with slight extensions). The main goal of this…
A numerical framework is developed to solve various types of PDEs on complicated domains, including steady and time-dependent, non-linear and non-local PDEs, with different boundary conditions that can also include non-linear and non-local…
DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the…
Computer Algebra Systems (e.g. Maple) are used in research, education, and industrial settings. One of their key functionalities is symbolic integration, where there are many sub-algorithms to choose from that can affect the form of the…
The possibility of interaction between Maple and numeric compiled languages in performing extensive numeric calculations is exemplified by the Ndynamics package, a tool for studying the (chaotic) behavior of dynamical systems. Programming…
Domain specific languages (DSLs) allow domain experts to model parts of the system under development in a problem-oriented notation that is well-known in the respective domain. The introduction of a DSL is often accompanied the desire to…
Optimizing parallel programs for distributed systems is a complex task, often requiring significant code modifications. Task-based programming systems improve modularity by separating performance decisions from application logic, but their…
This paper comprises a SysML-based approach to support the model-driven engineering (MDE) of Manufacturing Automation Software Projects (MASP). The Systems Modeling Language (SysML) is adapted to define the SysML-AT (SysML for automation),…
We have developed a symbolic algebra approach to automatically produce, verify, and optimize computer code for the Fast Multipole Method (FMM) operators. This approach allows for flexibility in choosing a basis set and kernel, and can…
It is the aim of this work to identify and illustrate the potential and weaknesses of the computer algebra system Maple in the area of the Calculus of Variations: a classical area of mathematics that studies the methods for finding maximum…
The use of Domain-Specific Languages (DSLs) is a promising field for the development of tools tailored to specific problem spaces, effectively diminishing the complexity of hand-made software. With the goal of making models as precise,…
Motivated by the surge of large language models, there has been a push to formally characterize the symbolic abilities intrinsic to the transformer architecture. A programming language, called RASP, has been proposed, which can be directly…
Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the…
We investigate the following question for machine translation (MT): can we develop a single universal MT model to serve as the common seed and obtain derivative and improved models on arbitrary language pairs? We propose mRASP, an approach…
Symbolic encoding has been used in multi-operator learning as a way to embed additional information for distinct time-series data. For spatiotemporal systems described by time-dependent partial differential equations, the equation itself…
Algebraic specification has a long tradition in bridging the gap between specification and programming by making specifications executable. Building on extensive experience in designing, implementing and using specification formalisms that…
This study investigates the use of symbolic computation in Matrix Structural Analysis (MSA) for continuous beams, leveraging the MATLAB Symbolic Math Toolbox. By employing symbolic MSA, analytical expressions for displacements, support…
In this paper, we present our ongoing work and initial results on the formal specification and verification of MiniMaple (a substantial subset of Maple with slight extensions) programs. The main goal of our work is to find behavioral errors…