Related papers: sympy2c: from symbolic expressions to fast C/C++ f…
This paper tackles the challenge of teaching code semantics to Large Language Models (LLMs) for program analysis by incorporating code symmetries into the model architecture. We introduce a group-theoretic framework that defines code…
We present pyBoLaNO, a Python symbolic package based on SymPy to quickly normal-order (Wick-order) any polynomial in bosonic ladder operators. By extension, this package offers the normal ordering of commutators of any two polynomials in…
Symbolic regression plays a crucial role in modern scientific research thanks to its capability of discovering concise and interpretable mathematical expressions from data. A key challenge lies in the search for parsimonious and…
Symbolic regression (SR) is an emerging branch of machine learning focused on discovering simple and interpretable mathematical expressions from data. Although a wide-variety of SR methods have been developed, they often face challenges…
Algorithms are presented for the tanh- and sech-methods, which lead to closed-form solutions of nonlinear ordinary and partial differential equations (ODEs and PDEs). New algorithms are given to find exact polynomial solutions of ODEs and…
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…
Pattern matching is a powerful tool for symbolic computations. Applications include term rewriting systems, as well as the manipulation of symbolic expressions, abstract syntax trees, and XML and JSON data. It also allows for an intuitive…
Symbolic execution is a key technology in software testing, which generates test cases by collecting symbolic path constraints and then solving constraints with SMT solvers. Symbolic execution has been proven helpful in generating…
The cost of combustion simulations is often dominated by the evaluation of net production rates of chemical species and mixture thermodynamics (thermochemistry). Execution on computing accelerators (XPUs) like graphic processing units…
CP2K is a versatile open-source software package for simulations across a wide range of atomistic systems, from isolated molecules in the gas phase to low-dimensional functional materials and interfaces, as well as highly symmetric…
We introduce, a large-scale synthetic benchmark of 15,045 university-level physics problems (90/10% train/test split). Each problem is fully parameterized, supporting an effectively infinite range of input configurations, and is accompanied…
The capability of R to do symbolic mathematics is enhanced by the caracas package. This package uses the Python computer algebra library SymPy as a back-end but caracas is tightly integrated in the R environment, thereby enabling the R user…
Probabilistic software analysis aims at quantifying the probability of a target event occurring during the execution of a program processing uncertain incoming data or written itself using probabilistic programming constructs. Recent…
Symbolic execution is a powerful technique for bug finding and program testing. It is successful in finding bugs in real-world code. The core reasoning techniques use constraint solving, path exploration, and search, which are also the same…
The traditional split-up into a low level language and a high level language in the design of computer algebra systems may become obsolete with the advent of more versatile computer languages. We describe GiNaC, a special-purpose system…
Current and upcoming cosmological experiments open a new era of precision cosmology, thus demanding accurate theoretical predictions for cosmological observables. Because of the complexity of the codes delivering such predictions, reaching…
Structural Equation Modeling (SEM) is an umbrella term that includes numerous multivariate statistical techniques that are employed throughout a plethora of research areas, ranging from social to natural sciences. Until recently, SEM…
Non-convex optimization problems are pervasive across mathematical programming, engineering design, and scientific computing, often posing intractable challenges for traditional solvers due to their complex objective functions and…
Ordinary Differential Equations (ODE) are used throughout science where the capture of rates of change in states is sought. While both pieces of commercial and open software exist to study such systems, their efficient and accurate usage…
This paper presents an experimental performance study of implementations of three symbolic algorithms for solving band matrix systems of linear algebraic equations with heptadiagonal, pentadiagonal, and tridiagonal coefficient matrices. The…