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Symbolic and numerical analysis in general relativity with open source computer algebra systems

Tolga Birkandan, Ceren Güzelgün, Elif Şirin, Mustafa Can Uslu
2018 General Relativity and Gravitation  
We study three computer algebra systems, namely SageMath (with SageManifolds package), Maxima (with ctensor package) and Python language (with GraviPy module), which allow tensor manipulation for general  ...  relativity calculations along with general algebraic calculations.  ...  We present a benchmark of these systems using simple examples.  ... 
doi:10.1007/s10714-018-2486-x fatcat:stc352hfqfhz5e5hbhivzpddme

caracas: Computer algebra in R

Mikkel Andersen, Søren Højsgaard
2021 Journal of Open Source Software  
Summary caracas is an R (R Core Team, 2018) package that enables a computer algebra system (CAS) within R via the open source Python CAS SymPy (Meurer et al., 2017) , which is made possible via reticulate  ...  However, R largely lacks the ability to perform symbolic computations.  ... 
doi:10.21105/joss.03438 fatcat:lpba4peoonh7dlqh7j6rikbabq

SymPy: symbolic computing in Python

Aaron Meurer, Christopher P. Smith, Mateusz Paprocki, Ondřej Čertík, Sergey B. Kirpichev, Matthew Rocklin, AMiT Kumar, Sergiu Ivanov, Jason K. Moore, Sartaj Singh, Thilina Rathnayake, Sean Vig (+15 others)
2017 PeerJ Computer Science  
SymPy is an open source computer algebra system written in pure Python. It is built with a focus on extensibility and ease of use, through both interactive and programmatic applications.  ...  These characteristics have led SymPy to become a popular symbolic library for the scientific Python ecosystem.  ...  SymPy is a robust computer algebra system 625 that provides a wide spectrum of features both in traditional computer algebra and 626 in a plethora of scientific disciplines.  ... 
doi:10.7717/peerj-cs.103 fatcat:f2mwkmqosrd5lepcej76cwalt4

Can we create a viable free open source alternative to magma, maple, mathematica and matlab?

William A. Stein
2008 Proceedings of the twenty-first international symposium on Symbolic and algebraic computation - ISSAC '08  
The goal of the Sage project ( is to create a truly viable free open source alternative to Magma, Maple, Mathematica and Matlab. Is this possible?  ...  Having used Magma for many years, I simply could not switch to an existing open source system.  ...  Every single copy of Sage includes all of the following software (and much much more): • Algebra and calculus: Maxima, SymPy Sage is thus the first system to combine together such a wide range of libraries  ... 
doi:10.1145/1390768.1390771 dblp:conf/issac/Stein08 fatcat:36qxjowsnngplbphyhpehzc74u

Computing the coefficients for the power series solution of the Lane-Emden equation with the Python library SymPy [article]

Klaus Rohe
2015 arXiv   pre-print
Sympy is an open source Python library for symbolic mathematics. The power series solutions are compared to the numerically computed solutions using matplotlib.  ...  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).  ...  All the tools mentioned here are available as open source.  ... 
arXiv:1409.2008v2 fatcat:hkh6upqjhbhvzpmrujwedyv5t4

Modeling and simulation optimization of the double inverted pendulum system in modelica

Zhi-hua Li, Hong-guang Yang, Guo-jin Chen, Chao Liang
2011 2011 International Conference on Electronics, Communications and Control (ICECC)  
This paper presented the modeling and simulation of a rotary quadruple pendulum (RQP) system using two open source software, i.e: scientific python stacks (SciPy stacks) and Modelica language via Anaconda  ...  In conclusion, the derivation of the governing equation using SymPy can be done in a matter of minutes without having a mistake when doing the algebraic manipulation.  ...  Modeling with Computer Algebra System There are a lot of the CAS applications that can be divided into closed and open source licenses.  ... 
doi:10.1109/icecc.2011.6067584 fatcat:ncozgp2xvrbuffn7mtrzgsvqqi

NRPyLaTeX: A LaTeX interface to computer algebra systems for general relativity [article]

Kenneth J. Sible, Zachariah B. Etienne
2022 arXiv   pre-print
While each computer algebra system (CAS) contains its own unique syntax for inputting mathematical expressions, LaTeX is perhaps the most widespread language for typesetting mathematics.  ...  Configuration commands appear as LaTeX comments, so that entire NL workflows can fit seamlessly into the LaTeX source code of scientific papers without interfering with the rendered mathematical expressions  ...  Further, computer algebra systems (CASs) like SymPy [1] , Mathematica [2] , or Maple [3] are often an essential resource in these fields, but to our knowledge there are currently no CASs or CAS add-on  ... 
arXiv:2111.05861v2 fatcat:yszfe7wdp5bhbm2ttq33msnohy

pyneqsys: Solve symbolically defined systems of non-linear equations numerically

Björn Dahlgren
2018 Journal of Open Source Software  
By relying on a computer algebra system, pyneqsys allows the user to apply e.g. variable transformations or generate representations in LaTeX, MathML etc.  ...  By default SymPy (Meurer et al. 2017 ) is used as the symbolic back-end, but other libraries are also supported.  ... 
doi:10.21105/joss.00531 fatcat:kkesm5dj4jbrfdewsg3c7lgcbi

Implementing a Method for Stochastization of One-Step Processes in a Computer Algebra System

M. N. Gevorkyan, A. V. Demidova, T. R. Velieva, A. V. Korol'kova, D. S. Kulyabov, L. A. Sevast'yanov
2018 Programming and computer software  
As a basis of the software implementation, we use the SymPy computer algebra system. Based on a developed algorithm, we derive stochastic di erential equations and their interaction schemes.  ...  This work is aimed at software implementation (by means of computer algebra) of a method for stochastization of one-step processes.  ...  There are not so many universal open source computer algebra systems. Let us consider several main candidates.  ... 
doi:10.1134/s0361768818020044 fatcat:6pehg6ayxzcvhp3j3er6niuuae

Rule-based integration: An extensive system of symbolic integration rules

Albert Rich, Patrick Scheibe, Nasser Abbasi
2018 Journal of Open Source Software  
open-source CAS.  ...  Rule-based integration: An extensive system of symbolic integration rules. Journal of Open Source Software, 3(32), 1073.  ... 
doi:10.21105/joss.01073 fatcat:dim5harahvghzpuqni4a6c4may

A Practical Approach to Testing Random Number Generators in Computer Algebra Systems

M. N. Gevorkyan, A. V. Demidova, A. V. Korol'kova, D. S. Kulyabov
2020 Computational Mathematics and Mathematical Physics  
Only free open source systems are considered.  ...  On addition, one can find another software implementation and build it into an open source computer algebra system.  ...  First, open source computer algebra systems often use random number generators that did not pass all available tests.  ... 
doi:10.1134/s096554252001008x fatcat:ll4oieayzrhnpb6pfztaczgrvy

Constructing scientific programs using SymPy

Mark Dewing
2011 PROC. OF THE 10th PYTHON IN SCIENCE CONF   unpublished
We present an example based on computing the partition function integrals in statistical mechanics.  ...  We describe a method for constructing scientific programs where SymPy is used to model the mathematical steps in the derivation.  ...  Conclusions We presented a snapshot of some work on some software blocks necessary for a system of scientific computing, including modeling a derivation, transforming to a source code representation, and  ... 


Rakesh Kumar
2020 International Journal of Engineering Technologies and Management Research  
Computational science (scientific computing or scientific computation) is concerned with constructing mathematical models as well as quantitative analysis techniques and using computers to analyze as well  ...  In practical use, it is basically the application of computer simulation as well as other forms of computation from numerical analysis and theoretical computer science to problems in different scientific  ...  : SymPy is an important Python library for symbolic computation that provides computer algebra system (CAS) while keeping the code as simple as possible in order to be comprehensible as well as easily  ... 
doi:10.29121/ijetmr.v2.i1.2015.28 fatcat:2y5dqj7hezgm5fwnl73mu5upf4

Component-oriented acausal modeling of the dynamical systems in Python language on the example of the model of the sucker rod string

Volodymyr B. Kopei, Oleh R. Onysko, Vitalii G. Panchuk
2019 PeerJ Computer Science  
equations, (3) the solution procedure uses a function initially created using the SymPy lambdify function and computes unknown values in the current step using known values from the previous step, (4)  ...  Python imperative constructs are used for simple events handling, (5) external solvers of differential-algebraic equations can optionally be applied via the Assimulo interface, (6) SymPy package allows  ...  Kopei conceived and designed the experiments, performed the computation work, authored or reviewed drafts of the paper, approved the final draft. Oleh R.  ... 
doi:10.7717/peerj-cs.227 pmid:33816880 pmcid:PMC7924524 fatcat:hkraobq4bnemroy4sdgi5ya4fe

Redberry: a computer algebra system designed for tensor manipulation

Stanislav Poslavsky, Dmitry Bolotin
2015 Journal of Physics, Conference Series  
In this paper we focus on the main aspects of computer-aided calculations with tensors and present a new computer algebra system Redberry which was specifically designed for algebraic tensor manipulation  ...  We touch upon distinctive features of tensor software in comparison with pure scalar systems, discuss the main approaches used to handle tensorial expressions and present the comparison of Redberry performance  ...  Here we present Redberry -a computer algebra system for algebraic manipulations with tensorial expressions.  ... 
doi:10.1088/1742-6596/608/1/012060 fatcat:ks54yrcrafhpbe7svtrsc3ebfy
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