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Computer Languages and Systems
Published in Daniel Zwillinger, Vladimir Dobrushkin, Handbook of Differential Equations, 2021
Daniel Zwillinger, Vladimir Dobrushkin
SageMath (previously “Sage”) is an open-source mathematics software system built on top of other open-source languages including: NumPy, SciPy, Sympy, Maxima, and R. SageMath uses a Python-based language that can call the capabilities of other languages. As such, it has both numeric and symbolic capabilities. Some of the differential equation routines [1069][1070] are: desolve() – Symbolically solve first and second order ODEs (using Maxima)desolve_system() – Symbolically solve a system of first order ODEs (using Maxima)desolve_rk4() – Numerically solve an ODE using a fourth order Runge–Kutta method.
Introduction
Published in Vladimir A. Dobrushkin, Applied Differential Equations, 2022
SageMath is a free open-source mathematics software system licensed under the GPL. It builds on top of many existing open-source packages Python, R, Julia (computational geometry), GAP (discrete algebra), Octave, including computer algebra systems Maxima and SymPy, and much more. Sage comes with two options: one can download it6 (for free) or use it interactively through cloud version. SageMath is available for every platform, and is ubiquitous throughout industry. SageMathCloud supports authoring documents written in LaTeX, Markdown, or HTML. SageMathCloud also allows you to publish documents online.
Introduction
Published in Vladimir A. Dobrushkin, Applied Differential Equations with Boundary Value Problems, 2017
SageMath is a free open-source mathematics software system licensed under the GPL. It builds on top of many existing open-source packages Python, R, Julia (computational geometry), GAP (discrete algebra), Octave, including computer algebra systems Maxima and SymPy, and much more. Sage comes with two options: one can download it6 (for free) or use it interactively through cloud version. SageMath is available for every platform, and is ubiquitous throughout industry. SageMathCloud supports authoring documents written in LATEX, Markdown, or HTML. SageMathCloud also allows you to publish documents online.
Combinatorial diversity metrics for declarative processes: an application to policy process analysis
Published in International Journal of General Systems, 2021
Our modelling code (written in the SageMath computer algebra system) used a combination of reduction techniques in being able to compute the valid traces of a given declarative process. A discussion of these would be somewhat out of place in the current paper, but one overarching fact is that there is a combinatorial explosion with every extra activity introduced into a declarative process. The main reason for this is that once there is one more degree of freedom in when activities may occur for the first time with respect to one another, this will allow for a significant increase in the number of traces that will satisfy the constraint(s).
Imaging phase plane models
Published in International Journal of Mathematical Education in Science and Technology, 2023
Richard F. Melka, Hashim A. Yousif
The use of computational packages to aid in the study of planar systems of differential equations is not new, extensive relevant resources are in the literature, as shown in the reference section of this paper. Some of the computational packages are open-source, such as SageMath, Maxima, Magma, Cadabra, Octave and Scilab. Commercial options include Mathematica, MATLAB and Maple. We chose SageMath to write a computer code for the calculations of this paper for reasons that we discuss below.