SymPy: Symbolic computing in Python

Meurer, Aaron; Smith, Christopher P.; Paprocki, Mateusz; Čertı́k, Ondřej; Rocklin, Matthew; Kumar, Amit; Ivanov, Sergiu; Moore, Jason K.; Singh, Sartaj; Rathnayake, Thilina; Vig, Sean; Granger, Brian; Muller, Richard P.; Bonazzi, Francesco; Gupta, Harsh; Vats, Shivam; Johansson, Fredrik; Pedregosa, Fabián; Curry, Matthew; Saboo, Ashutosh; Fernando, Isuru; Kulal, Sumith; Cimrman, Robert; Scopatz, Anthony

doi:10.7287/peerj.preprints.2083v1

Cited by 72 publications

(82 citation statements)

References 17 publications

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“…and Y are object nodes representing the domain of the ith operand x i and the result of the operation y, respectively, and f is a function that implements the operation and can be finished by a series of symbolic execution [1,9,17] process using a symbolic execution library (e.g. SymPy [26], Mathematica [16]) even if some operands are uncertain instances.…”

Section: An Operation Nodementioning

confidence: 99%

“…Now the constraint set includes and formalizes all the constraints in the exercise. So we can apply methods of a symbolic execution library [16,26] or some approximation algorithms [12,29] to solve these equations and/or inequalities. Finally, we will get the value (or range of value) of every instance in S I .…”

Section: Organizing and Solving Constraintsmentioning

confidence: 99%

“…All algorithms are implemented in Python 3.7. Sympy [25] is used to do the work of symbolic execution. All the experiments are conducted in a machine with 2.40 GHz Intel Xeon CPU E52630, 48 GB RAM, running Ubuntu 14.04.…”

Section: Datasets and Experiments Settingmentioning

confidence: 99%

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Towards Automatic Mathematical Exercise Solving

et al. 2019

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Knowledge graphs are widely applied in many applications. Automatically solving mathematical exercises is also an interesting task which can be enhanced by knowledge reasoning. In this paper, we design MathGraph, a knowledge graph aiming to solve high school mathematical exercises. Since it requires fine-grained mathematical derivation and calculation of different mathematical objects, we design a crowdsourcing-based method to help build MathGraph. MathGraph supports massive kinds of mathematical objects, operations and constraints which may be involved in exercises. Furthermore, we propose an algorithm to align a semantically parsed exercise to MathGraph and figure out the answer automatically. Extensive experiments on real-world datasets verify the effectiveness of MathGraph.

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Section: An Operation Nodementioning

confidence: 99%

Section: Organizing and Solving Constraintsmentioning

confidence: 99%

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Towards Automatic Mathematical Exercise Solving

et al. 2019

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“…Using the constants defined above, the following integrals are solved: With the help of the symbolic mathematics tool SymPy [38], the solutions of the above integrals can be found:…”

Section: Ac K N O W L E D G M E N T Smentioning

confidence: 99%

Discontinuous Boundary Elements for Fluid Flow Problems in Discrete Fracture Networks

Wang¹,

Feng²,

Zhou³

et al. 2019

Preprint

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Modeling fluid flow in three-dimensional (3D) Discrete Fracture Networks (DFNs) is of relevance in many engineering applications, such as hydraulic fracturing, oil/gas production, geothermal energy extraction, nuclear waste disposal and CO2 sequestration. A new Boundary Element Method (BEM) technique with discontinuous quadratic elements and a parallel Domain Decomposition Method (DDM) is presented herein for the simulation of the steady-state fluid flow in 3D DFN systems with wellbores, consisting of planar fractures having arbitrary properties and wellbore trajectories. Numerical examples characterized by DFNs of increasing complexity are investigated to evaluate the accuracy and efficiency of the presented technique. The results show that accurate solutions can be obtained with less nodes than with mesh-based methods (e.g. Finite Element Method). In addition, the DDM algorithm used provides a quite fast convergence. The simulation results of the fluid flow around intersections among traces (linear intersections between fractures), intersections between traces and a fracture boundaries, and wellbore intersections is accurate. Source code is available at : https://github.com/BinWang0213/PyDFN3D.

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“…The method was implemented by the authors in the context of a recent study conducted in four tropical mountain rivers, in Costa Rica where a clear need to estimate bed load transport rates and evaluate input‐variable sensitivity and uncertainty of bed load transport relations with no data available for validation existed. Selection of the MVFOSM method was based on the following aspects: (i) it is quick and easy to implement for any transport relation, especially with the aid of symbolic math packages such as the Symbolic Math toolbox and MuPad [ The Mathworks, Inc ., , b], or open source libraries as SymPy [ Meurer et al , ] which are widely available; (ii) allows assessing sensitivity for a single input only or multiple input variables at the same time; (iii) requires only two values for each input variable, namely a mean and a variance which can be estimated from basic knowledge of the river in question and a one day visit to the site; (iv) as a local sensitivity analysis, it allows evaluating the effect of variations (perturbations) about a base state, i.e., the river's current conditions (slope and grain size distribution), on the variability of the transport estimates; and (v) in places where there is sufficient information for one or more variables, but there is still need to better constrain others, the method is able to point out which of the remaining variables will introduce the largest variability in the transport estimates thus helping with the design of field campaigns in such a way as to better invest the available resources. The methodology, developed to assess input‐variable sensitivity and to better inform field measurement campaigns to complement the transport estimates and associated uncertainty is presented next.…”

Section: Introductionmentioning

confidence: 99%

Input‐variable sensitivity assessment for sediment transport relations

Fernández

García

2017

Water Resources Research

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A methodology to assess input‐variable sensitivity for sediment transport relations is presented. The Mean Value First Order Second Moment Method (MVFOSM) is applied to two bed load transport equations showing that it may be used to rank all input variables in terms of how their specific variance affects the overall variance of the sediment transport estimation. In sites where data are scarce or nonexistent, the results obtained may be used to (i) determine what variables would have the largest impact when estimating sediment loads in the absence of field observations and (ii) design field campaigns to specifically measure those variables for which a given transport equation is most sensitive; in sites where data are readily available, the results would allow quantifying the effect that the variance associated with each input variable has on the variance of the sediment transport estimates. An application of the method to two transport relations using data from a tropical mountain river in Costa Rica is implemented to exemplify the potential of the method in places where input data are limited. Results are compared against Monte Carlo simulations to assess the reliability of the method and validate its results. For both of the sediment transport relations used in the sensitivity analysis, accurate knowledge of sediment size was found to have more impact on sediment transport predictions than precise knowledge of other input variables such as channel slope and flow discharge.

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SymPy: Symbolic computing in Python

Cited by 72 publications

References 17 publications

Towards Automatic Mathematical Exercise Solving

Towards Automatic Mathematical Exercise Solving

Discontinuous Boundary Elements for Fluid Flow Problems in Discrete Fracture Networks

Input‐variable sensitivity assessment for sediment transport relations

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