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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)
<span title="2017-01-02">2017</span> <i title="PeerJ"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/zs2czkfyybggbpvr26rbyxpsjy" style="color: black;">PeerJ Computer Science</a> </i> &nbsp;
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.  ...  In SymPy every symbolic expression is an instance of a Python Basic class, a 82 superclass of all SymPy types providing common methods to all SymPy tree-elements, 83 such as traversals.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.7717/peerj-cs.103">doi:10.7717/peerj-cs.103</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/f2mwkmqosrd5lepcej76cwalt4">fatcat:f2mwkmqosrd5lepcej76cwalt4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190222214336/http://pdfs.semanticscholar.org/3d1b/34384499f77bf317b01594c8c60af212582b.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/3d/1b/3d1b34384499f77bf317b01594c8c60af212582b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.7717/peerj-cs.103"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

miniKanren as a Tool for Symbolic Computation in Python [article]

Brandon T. Willard
<span title="2020-05-28">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this article, we give a brief overview of the current state and future potential of symbolic computation within the Python statistical modeling and machine learning community.  ...  We detail the use of miniKanren as an underlying framework for term rewriting and symbolic mathematics, as well as its ability to orchestrate the use of existing Python libraries.  ...  SYMBOLIC COMPUTATION IN PYTHON DRIVEN BY MINIKANREN In the following sections we detail our implementation of miniKanren (Willard 2020d) , operating under the PyPi name miniKanren and Python package name  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2005.11644v3">arXiv:2005.11644v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zvjqdgw2pndhvahgz2e6iyvihm">fatcat:zvjqdgw2pndhvahgz2e6iyvihm</a> </span>
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Computación neutrosófica mediante Sympy

Maikel Leyva-Vázquez, Florentin Smarandache
<span title="2018-12-10">2018</span> <i title="Figshare"> Figshare </i> &nbsp;
The Sympy library is used to perform the process of neutrosophic computation. Systems of linear neutrosóficas equations are solved by means of the symbolic computation in python.  ...  As future works are the development of new applications in different areas of engineering and science  ...  Computación neutrosófica y Sympy Para el trabajo computacional con números neutrosóficos en el lenguaje python se puede emplear SymPy .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.6084/m9.figshare.7442075">doi:10.6084/m9.figshare.7442075</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/v6vlr4fke5gs3ggrkhzayls7ka">fatcat:v6vlr4fke5gs3ggrkhzayls7ka</a> </span>
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Computing the coefficients for the power series solution of the Lane-Emden equation with the Python library SymPy [article]

Klaus Rohe
<span title="2015-01-25">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
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 solutions are compared to the numerically computed solutions using matplotlib.  ...  Here we will use SymPy (reference (4)) a Python library for symbolic computing.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1409.2008v2">arXiv:1409.2008v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hkh6upqjhbhvzpmrujwedyv5t4">fatcat:hkh6upqjhbhvzpmrujwedyv5t4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20191021035225/https://arxiv.org/pdf/1409.2008v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/33/04/3304fd3c938c03747ef72e09fcf2a1d9fddf356c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1409.2008v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

The Automation of Stochastization Algorithm with Use of SymPy Computer Algebra Library

Anastasya Demidova, Migran Gevorkyan, Dmitry Kulyabov, Anna Korolkova, Leonid Sevastianov, Gh. Adam, J. Buša, M. Hnatič, D. Podgainy
<span title="">2018</span> <i title="EDP Sciences"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/oduy4e4fvfhovftixyndrlkomi" style="color: black;">EPJ Web of Conferences</a> </i> &nbsp;
SymPy computer algebra library is used for automatic generation of ordinary and stochastic systems of differential equations from the schemes of kinetic interaction.  ...  Schemes of this type are used not only in chemical kinetics but also in biological, ecological and technical models.  ...  We carry out the implementation of the algorithm by using the Python language (version 3) and SymPy library for computer algebra.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1051/epjconf/201817305006">doi:10.1051/epjconf/201817305006</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ib6pvvlh4bfcpaa4cwub26k2lq">fatcat:ib6pvvlh4bfcpaa4cwub26k2lq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180724123137/https://www.epj-conferences.org/articles/epjconf/pdf/2018/08/epjconf_mmcp2018_05006.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/1d/c7/1dc7d3d4787bdb8fb872bf7aa3ec6cb7bb8b37c9.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1051/epjconf/201817305006"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Step-by-step analitical solutions of the Lane-Emden equation with politropic index 0, 1 and 5 using SymPy

Ricardo Angelo Quispe Mendizábal, Martin Vuelta
<span title="2020-09-25">2020</span> <i title="Zenodo"> Zenodo </i> &nbsp;
All the calculus are performed using Sympy.  ...  Abstract: In the study of the stellar structures, some models arises to explain their interior dynamics and surface consequences (measurable in the laboratory), the Lane-Emden equation provides us with  ...  Sympy is a Python library for symbolic mathematics.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5281/zenodo.4361721">doi:10.5281/zenodo.4361721</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6mdrcfngg5d7faytqsizwujszi">fatcat:6mdrcfngg5d7faytqsizwujszi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20201222080523/https://zenodo.org/record/4361722/files/LE_Sympy.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/19/4d/194d8ace7254ee0f17ad8d7060f5a0eeaa2d2fc6.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5281/zenodo.4361721"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> zenodo.org </button> </a>

Optimised finite difference computation from symbolic equations

Michael Lange, Navjot Kukreja, Fabio Luporini, Mathias Louboutin, Charles Yount, Jan Hückelheim, Gerard Gorman
<span title="">2017</span> <i title="SciPy"> Proceedings of the 16th Python in Science Conference </i> &nbsp; <span class="release-stage">unpublished</span>
Domain-specific high-productivity environments are playing an increasingly important role in scientific computing due to the levels of abstraction and automation they provide.  ...  We highlight the generation and automated execution of highly optimized stencil code from only a few lines of high-level symbolic Python for a set of scientific equations, before exploring the use of Devito  ...  Acknowledgements This work was financially supported in part by EPSRC grant EP/L000407/1 and the Imperial College London Intel Parallel Computing Centre.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.25080/shinma-7f4c6e7-00d">doi:10.25080/shinma-7f4c6e7-00d</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3iscem4d5nhhnkafh6ibprabr4">fatcat:3iscem4d5nhhnkafh6ibprabr4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180721175856/http://conference.scipy.org/proceedings/scipy2017/pdfs/michael_lange.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c2/b9/c2b98c1e782f9c40ce1e920d25cdf098e180f1b8.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.25080/shinma-7f4c6e7-00d"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Symbolic Computing

Akinwale M. Oteniya, Matthew N. O. Sadiku, Sarhan M. Musa
<span title="2020-03-06">2020</span> <i title="International Journal of Scientific and Research Publications (IJSRP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/6ht2eimu5nflxkqur2pzauntxu" style="color: black;">International Journal of Scientific and Research Publications (IJSRP)</a> </i> &nbsp;
Symbolic computation refers to using machines or computers to manipulate mathematical equations and expressions in symbolic form, as opposed to numerical manipulation.  ...  Using symbolic computing to solve mathematical problems involves manipulations of symbolic objects, rules or programs, with the main goal of being exact.  ...  SymPy is a computer algebra system (CAS) written in the Python, which is programming language that has a focus on ease of use and readability.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.29322/ijsrp.10.03.2020.p9914">doi:10.29322/ijsrp.10.03.2020.p9914</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/j25mzj3hnfcarnktxg3daos4vq">fatcat:j25mzj3hnfcarnktxg3daos4vq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220301192049/http://www.ijsrp.org/research-paper-0320/ijsrp-p9914.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/58/b5/58b5e5fbadd7cff3345ed1c8af5499d9acf378bd.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.29322/ijsrp.10.03.2020.p9914"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Uncertainty Modeling with SymPy Stats

Matthew Rocklin
<span title="">2012</span> <i title="SciPy"> Proceedings of the 11th Python in Science Conference </i> &nbsp; <span class="release-stage">unpublished</span>
We motivate the use of symbolics and thin compilers in scientific computing.  ...  A RandomSymbol object behaves in every way like a standard sympy Symbol object.  ...  Secondarily we have motivated the use of symbolics in computation and argued for a more separable computational stack within the scientific computing domain.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.25080/majora-54c7f2c8-009">doi:10.25080/majora-54c7f2c8-009</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/m53ycuaorbb3toihjp7ejq6ffe">fatcat:m53ycuaorbb3toihjp7ejq6ffe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809021853/http://conference.scipy.org/proceedings/scipy2012/pdfs/matthew_rocklin.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/92/ef/92ef0e4eeef37fd0aad7b3a52ce922152e0f9ea9.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.25080/majora-54c7f2c8-009"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Constructing scientific programs using SymPy

Mark Dewing
<span title="">2011</span> <i > PROC. OF THE 10th PYTHON IN SCIENCE CONF </i> &nbsp; <span class="release-stage">unpublished</span>
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  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mgofzl3dpbh27hz72gjohnc2v4">fatcat:mgofzl3dpbh27hz72gjohnc2v4</a> </span>
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Computer Algebra in JULIA

D. S. Kulyabov, A. V. Korol'kova
<span title="">2021</span> <i title="Pleiades Publishing Ltd"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ooyzpvfeuvgobees33ipb3baee" style="color: black;">Programming and computer software</a> </i> &nbsp;
The aim of this paper is to combine the usage of the Julia framework for numerical computations and for symbolic computations in mathematical modeling problems.  ...  In each of these domains, generic representatives of computer algebra systems in Julia are distinguished.  ...  For calling Python libraries, Julia uses the package PyCall. The package SymPy (http://sympy.org/) is the Python library for symbolic computations.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1134/s0361768821020079">doi:10.1134/s0361768821020079</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/arppi3jm7jbybddutf6yj57vei">fatcat:arppi3jm7jbybddutf6yj57vei</a> </span>
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Python for Scientists and Engineers

K. Jarrod Millman, Michael Aivazis
<span title="">2011</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4hwwgwyqabardl76zzbexzcmhu" style="color: black;">Computing in science &amp; engineering (Print)</a> </i> &nbsp;
SymPy is a computer algebra system written in pure Python. Figure 1 shows a simple SymPy session to give you an idea of what SymPy provides.  ...  Python for Mathematicians Although Python has been used for serious numerical computing since the mid '90s, Python has only in the last few years become popular for symbolic computing.  ...  Paul Dubois, "Python: Batteries Included," Computing in Science and Eng., vol. 9, no. 3, 2007 , pp. 7 -9. K. Jarrod Millman  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/mcse.2011.36">doi:10.1109/mcse.2011.36</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/b23hrx4o3zho7oazoumontv6tu">fatcat:b23hrx4o3zho7oazoumontv6tu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180724081557/https://ieeexplore.ieee.org/ielx5/5992/5725228/05725235.pdf?tp=&amp;arnumber=5725235&amp;isnumber=5725228" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ca/be/cabe056aae591821fb3608728a139616f759a746.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/mcse.2011.36"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Devito: Towards a Generic Finite Difference DSL Using Symbolic Python

Michael Lange, Navjot Kukreja, Mathias Louboutin, Fabio Luporini, Felippe Vieira, Vincenzo Pandolfo, Paulius Velesko, Paulius Kazakas, Gerard Gorman
<span title="">2016</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/zigbcra6rjdivda6lkzknwuo5q" style="color: black;">2016 6th Workshop on Python for High-Performance and Scientific Computing (PyHPC)</a> </i> &nbsp;
In this paper we present Devito, a new finite difference DSL that provides optimized stencil computation from high-level problem specifications based on symbolic Python expressions.  ...  We demonstrate Devito's symbolic API and performance advantages over traditional Python acceleration methods before highlighting its use in the scientific context of seismic inversion problems.  ...  The Symbolic Python package SymPy used in Devito also provides JIT compilation via the lambdify utility function that compiles a symbolic expression into either a Python function that supports NumPy vectorization  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/pyhpc.2016.013">doi:10.1109/pyhpc.2016.013</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/sc/LangeKLLVPVKG16.html">dblp:conf/sc/LangeKLLVPVKG16</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/543upzuglzhwvgfgdg2oiqrklq">fatcat:543upzuglzhwvgfgdg2oiqrklq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180719203655/http://spiral.imperial.ac.uk/bitstream/10044/1/51691/7/1609.03361.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/82/6c/826c0d51ac9c4e81ed4d950672182fa05940606b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/pyhpc.2016.013"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Performance Analysis of Effective Symbolic Methods for Solving Band Matrix SLAEs [article]

Milena Veneva, Alexander Ayriyan
<span title="2019-03-04">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
These algorithms are implemented using the GiNaC library of C++ and the SymPy library of Python, considering five different data storing classes.  ...  The only assumption on the coefficient matrix in order for the algorithms to be stable is nonsingularity.  ...  All the figures in this paper have been generated using Matplotlib (2.1.0) [15] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1903.02423v1">arXiv:1903.02423v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/g2jjkb5rrrempjv2ld3ny66mwm">fatcat:g2jjkb5rrrempjv2ld3ny66mwm</a> </span>
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Performance Analysis of Effective Symbolic Methods for Solving Band Matrix SLAEs

Milena Veneva, Alexander Ayriyan, A. Forti, L. Betev, M. Litmaath, O. Smirnova, P. Hristov
<span title="">2019</span> <i title="EDP Sciences"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/oduy4e4fvfhovftixyndrlkomi" style="color: black;">EPJ Web of Conferences</a> </i> &nbsp;
These algorithms are implemented using the GiNaC library of C++ and the SymPy library of Python, considering five different data storing classes.  ...  The only assumption on the coefficient matrix in order for the algorithms to be stable is nonsingularity.  ...  One possible approach to this problem is the symbolic algorithms. An overview of some of the symbolic algorithms which exist in the literature is done by us in [1] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1051/epjconf/201921405004">doi:10.1051/epjconf/201921405004</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/itleods7wbadvdf56aemzxa3su">fatcat:itleods7wbadvdf56aemzxa3su</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200212025839/https://www.epj-conferences.org/articles/epjconf/pdf/2019/19/epjconf_chep2018_05004.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/1f/c6/1fc6b23ece099e19699ba6d6a179d45a7712043f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1051/epjconf/201921405004"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>
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