Related papers: sympy2c: from symbolic expressions to fast C/C++ f…
$\texttt{PyCosmo}$ is a Python-based framework for the fast computation of cosmological model predictions. One of its core features is the symbolic representation of the Einstein-Boltzmann system of equations. Efficient $\texttt{C/C++}$…
As wide-field surveys yield ever more precise measurements, cosmology has entered a phase of high precision requiring highly accurate and fast theoretical predictions. At the heart of most cosmological model predictions is a numerical…
SymBoltz is a new Julia package for solving the linear Einstein-Boltzmann equations in cosmology. It features a symbolic-numeric interface for specifying equations, is free of approximation switching schemes, and is compatible with…
We present SymForce, a library for fast symbolic computation, code generation, and nonlinear optimization for robotics applications like computer vision, motion planning, and controls. SymForce combines the development speed and flexibility…
Preparing problems for execution on quantum computers can require many compilation steps. Automated compilation software is useful not only for easier and faster problem execution, but also for facilitating the comparison between different…
It is shown how the Python library Sympy can be used to compute symbolically the coefficients of the power series solution of the Lane-Emden equation (LEE). Sympy is an open source Python library for symbolic mathematics. The power series…
Understanding astrophysical and cosmological processes can be challenging due to their complexity and lack of intuitive analogies. To address this, we present \texttt{AstronomyCalc}, a Python package specifically designed to aid…
PySCF is a general-purpose electronic structure platform designed from the ground up to emphasize code simplicity, both to aid new method development, as well as for flexibility in computational workflow. The package provides a wide range…
Optimization time integrators are effective at solving complex multi-physics problems including deformable solids with non-linear material models, contact with friction, strain limiting, etc. For challenging problems, Newton-type optimizers…
Despite the prevalence of symmetry in scientific linear systems, these structural properties are often underutilized by standard computational software. This paper introduces PySymmetry, an open-source Sage/Python framework that implements…
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…
We present celmech, an open-source Python package designed to facilitate a wide variety of celestial mechanics calculations. The package allows users to formulate and integrate equations of motion incorporating user-specified terms from the…
In cosmology, emulators play a crucial role by providing fast and accurate predictions of complex physical models, enabling efficient exploration of high-dimensional parameter spaces that would be computationally prohibitive with direct…
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. This enables the R user…
What mathematical functions do neural network components learn? Symbolic distillation addresses this question by expressing neural network components with interpretable, closed-form mathematical expressions that expose the functional…
The R package calculus implements C++ optimized functions for numerical and symbolic calculus, such as the Einstein summing convention, fast computation of the Levi-Civita symbol and generalized Kronecker delta, Taylor series expansion,…
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…
We present a coherent, re-usable python framework which further builds on the cosmological emulator code CosmoPower. In the current era of high-precision cosmology, we require high-accuracy calculations of cosmological observables with…
Large Language Models (LLMs) often struggle with complex mathematical reasoning, where prose-based generation leads to unverified and arithmetically unsound solutions. Current prompting strategies like Chain of Thought still operate within…
The Schrieffer-Wolff transformation (SWT) is a foundational perturbative method for deriving effective Hamiltonians in quantum systems by systematically eliminating couplings between pairs of energy distant subspaces. Despite recent…