Solving Polynomial Systems in the Cloud with Polynomial Homotopy Continuation

Bliss, Nathan; Sommars, Jeff; Verschelde, Jan; Yu, Xiangcheng

doi:10.1007/978-3-319-24021-3_7

Cited by 7 publications

(4 citation statements)

References 27 publications

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“…Installing Macaulay2 on a Windows machine is an especially arduous task, creating an enormous barrier to entry for potential Windows users of the package. These are common challenges for specialized mathematical software, and like others before us we concluded that a cloud version of our software was a worthwhile venture (Bliss et al, 2015;Kastner et al, 2015). Amazon Web Services (AWS, available at https://aws.amazon.com/) is a subsidiary of Amazon, Inc. that sells cloud computing solutions.…”

Section: Macaulay2 In the Cloudsupporting

confidence: 74%

A computer algebra system for R: Macaulay2 and the m2r package

Kahle¹,

O’Neill²,

Sommars³

2017

Preprint

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Algebraic methods have a long history in statistics. The most prominent manifestation of modern algebra in statistics can be seen in the field of algebraic statistics, which brings tools from commutative algebra and algebraic geometry to bear on statistical problems. Now over two decades old, algebraic statistics has applications in a wide range of theoretical and applied statistical domains. Nevertheless, algebraic statistical methods are still not mainstream, mostly due to a lack of easy off-the-shelf implementations. In this article we debut m2r, an R package that connects R to Macaulay2 through a persistent back-end socket connection running locally or on a cloud server. Topics range from basic use of m2r to applications and design philosophy.

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Section: Macaulay2 In the Cloudsupporting

confidence: 74%

A computer algebra system for R: Macaulay2 and the m2r package

Kahle¹,

O’Neill²,

Sommars³

2017

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Installing Macaulay2 on a Windows machine is an especially arduous task, creating an enormous barrier to entry for potential Windows users of the package. These are common challenges for specialized mathematical software, and like others before us we concluded that a cloud version of our software was a worthwhile venture (Bliss, Sommars, Verschelde, and Yu 2015;Kastner, Hinkelmann, and Stillman 2015).…”

Section: Macaulay2 In the Cloudsupporting

confidence: 72%

A Computer Algebra System for R: Macaulay2 and the m2r Package

Kahle¹,

O’Neill²,

Sommars³

2020

J. Stat. Soft.

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Algebraic methods have a long history in statistics. Apart from the ubiquitous applications of linear algebra, the most visible manifestations of modern algebra in statistics are found in the young field of algebraic statistics, which brings tools from commutative algebra and algebraic geometry to bear on statistical problems. Now over two decades old, algebraic statistics has applications in a wide range of theoretical and applied statistical domains. Nevertheless, algebraic statistical methods are still not mainstream, mostly due to a lack of easy off-the-shelf implementations. In this article we debut m2r, an R package that connects R to Macaulay2 through a persistent back-end socket connection running locally or on a cloud server. Topics range from basic use of m2r to applications and design philosophy.

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“…The focus of this paper is on the application of new technology to solve polynomial systems, in particular, cloud computing [BSVY15] and multicore shared memory parallelism accelerated with graphics processing units [VY15]. Our web interface offers phcpy in a SageMath [Sage], [SJ05] kernel or in a Python kernel of a Jupyter notebook [Klu16].…”

Section: Introductionmentioning

confidence: 99%

Solving Polynomial Systems with phcpy

Otto¹,

Forbes²,

Verschelde³

2019

Proceedings of the Python in Science Conference

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The solutions of a system of polynomials in several variables are often needed, e.g.: in the design of mechanical systems, and in phase-space analyses of nonlinear biological dynamics. Reliable, accurate, and comprehensive numerical solutions are available through PHCpack, a FOSS package for solving polynomial systems with homotopy continuation.This paper explores new developments in phcpy, a scripting interface for PHCpack, over the past five years. For instance, phcpy is now available online through a JupyterHub server featuring Python2, Python3, and SageMath kernels. As small systems are solved in real-time by phcpy, they are suitable for interactive exploration through the notebook interface. Meanwhile, phcpy supports GPU parallelization, improving the speed and quality of solutions to much larger polynomial systems. From various model design and analysis problems in STEM, certain classes of polynomial system frequently arise, to which phcpy is well-suited.

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Solving Polynomial Systems in the Cloud with Polynomial Homotopy Continuation

Cited by 7 publications

References 27 publications

A computer algebra system for R: Macaulay2 and the m2r package

A computer algebra system for R: Macaulay2 and the m2r package

A Computer Algebra System for R: Macaulay2 and the m2r Package

Solving Polynomial Systems with phcpy

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