The mmapy Package Documentation

The mmapy package is designed to bring interoperability between Python (IPython/Jupyter) and Wolfram Mathematica.

Introduction

Features

Demonstration

Importing mmapy

As long as mmapy is properly deployed, import can be done with the following line.

import mmapy

To further simplify the workflow, map mmapy to single-character variables, e.g.

import mmapy as M

Using mmapy to call Mathematica evaluations

M.[Variation]( 'Some Mathematica Command' )

As of the current stage of development, 5 variations of mmapy functions can be called to launch a Mathematica kernel to evaluate a given (set of) expression(s). While all functions trigger similar evaluation sequences, different output processing procedures are incurred. The following table demonstrates the usage scenario and output format of each variation.

Variation	Scenario	Output
n	When expecting raw Mathematica output in plain text	String (Plain/Mathematica)
t	When expecting TeX-form output in plain text	String (TeX)
td	When expecting TeX-form output compiled and displayed	IPython.core.display.Math object
p	When expecting Python/numpy/sympy expressions as output	Python expression
g	When expecting graphics output	IPython.core.display.Image object

mmapy.n() -- Producing unconverted Mathematica output in plain text

When the expression returned from Mathematica is originally a string, or when sympy.parsing is not able to guarantee correct conversions, the n variation should be chosen to produce a raw Mathematica output, which can be picked up and recycled by a custom parser. e.g.

M.n( 'StringTake["The Ultimate Answer", {5, 12}]' )

'Ultimate'

mmapy.t() -- Producing TeX-form output in plain text

Mathematica provides the option to format an expression in TeX while converting it into a string. Only use this option when the output's content and structure can be well represented by TeX expressions (e.g. math/symbolic expressions, tables, matrices). Further string operations can then be called to manipulate the output.

M.t( 'Integrate[1/(x^3 + 1), x]' )

'-\frac{1}{6} \log \left(x^2-x+1\right)+\frac{1}{3} \log (x+1)+\frac{\tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)}{\sqrt{3}}'

mmapy.td() -- Displaying TeX-form output

The td variation puts a wrapper outside t and utilizes the IPython.display module to compile and render reader-friendly output. This option is more preferable in interactive and exploratory contexts than in automated pipelines.

M.td( 'Integrate[1/(x^3 + 1), x]' )

mmapy.p() -- Producing Python-compatible expressions as output

It is sometimes a preferable option to integrate mmapy into a Python scientific computing workflow. The p variation converts Mathematica output into Python expressions by calling mathematica in the sympy.parsing module to complete the parsing and conversion process.

A standalone example:

M.p( 'M.p( '{a, b, c}.{x, y, z}' )' )

a*x + b*y + c*z

As integrated:

# Determine how many 15-USD-Bagels you can buy with a 100-EUR note.

def currency(list):
	return "".join(['QuantityMagnitude@CurrencyConvert[Quantity[', str(list[0]), ',', '"', list[1], '"', '],', '"', list[2], '"',']'])

inboundData = ('100', 'Euros', 'USDollars')

cmd = currency(inboundData)
conv = M.p(cmd)

print('You can buy', int(conv) // 15, "bagels!")

You can buy 7 bagels!

mmapy.g() -- Producing graphics output

In compliance with the need for data visualization and graphical operations, the g variation is developed to channel graphics output from the Mathematica kernel to the IPython/Jupyter frontend. Take special note that Mathematica is designed to have its frontend handle all rendering operations, thus a working display must be available on the remote machine. A few examples are given below to illustrate the use of mmapy.g in various scenarios.

2-D and 3-D plotting:

# Create a 2-D stream plot and a 3-D region plot
D2Plot = 'StreamPlot[{Cos[x], Tan[x]}, {x, -3, 3}, {y, -3, 3}]'
D3Plot = 'RegionPlot3D[x^2 - y^2*z^2 > 0, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}]'

M.g( 'GraphicsRow[{' + D2Plot + ',' + D3Plot + '}, ImageSize -> {Automatic, 300}]' )

Image processing/preparation:

imgPath = 'documentation-images/landsat.jpg'

cmdImport = 'img = Rasterize[Import[' + imgPath + '], ImageSize -> 1000];'
cmdMesh = 'mesh = ImageMesh[img];'
cmdComp = 'GraphicsRow[{img, HighlightImage[img, mesh]}, ImageSize -> {Automatic, 300}, Spacings -> 0, Background -> None];'

M.g(cmdImport + cmdMesh + cmdComp)

Using Mathematica's Print function

mmapy is designed to channel Mathematica Print

Methodology

Limitation

Notes on Further Development

License