pythonica is a Python package for the sane interface between Mathematica and python via mathlink. The mathlink api provided with Mathematica has a comprehensive and universal way of communicating with the Mathematica Kernel that doesn't make quick and dirty communication all that easy. This wraps around the mathlink module in a way to make things easier.

Getting started is easy:

>>> import pythonica
>>> m = pythonica.Pythonica()
>>> result = m.eval('D[Log[x],x]')
>>> print(result)
x^(-1)
>>> X = [1,2,3,4]
>>> m.push(X)
>>> m.eval('sX = Mean[X];')
>>> sX = m.pull('sX')
>>> print(sX)
2.5

The workhorse of the module is the Pythonica class, this makes a link to the Mathematica kernel, and takes care of all the token, packet communication that goes on between mathlink and python. It can take several arguments.

• name - The name provided to mathlink to start the Kernel
• mode - The mode to launch the mathlink Kernel. In combination with name you can start remote kernels, but I don't understand howthis works, so best to leave it be.
• timeout - Provides the time to wait after starting the Kernel before it's usable. 1 second seems to overkill, adjust at will.
• debug - For debugging use, will printout tons of information if you use it.
• plot_dir - Where to store plots created by Mathematica. If set to None, no plots will be produces.
• plot_size - Tuple indicating the size in pixels for plots
• plot_format - string indicating file extension. If Mathematica can use it, it should work.
• input_prompt - boolean indicating whether to print input prompts from Mathematica
• output_prompt - boolean indicating whether to print output prompts from Mathematica

All of the values from debug on can be set interactively, for example:

>>> m.debug = False

The eval function takes string to be processes as Mathematica input and returns the result. It takes several options

• expression - The expression to be evaluated. If it is malformed it will throw a PythonicaException.
• make_plots - A boolean indicating whether to make any plots occuring from the function call.
• output_type - A string indicating the type of output to produce. If the output type is 'string' it will produce a string. If the output type is 'python' will attempt to convert the output to python for storage. For conversion to work the str_format must be 'input' See Pythonica.pull for more info.
• str_format - A string indicating the type of string to produce if output_type is 'string'. If 'input' will produce a string which is valid Mathematica Code, and can be fed back into eval, if 'tex' will produce tex code, or if 'plain' will produce whatever mathematica would have produced. If you use print this usually looks ok.

>>> m.eval('Series[Exp[x],{x,0,3}]')
'SeriesData[x, 0, {1, 1, 1/2, 1/6}, 0, 4, 1]'
>>> m.eval('Series[Exp[x],{x,0,3}]', str_format='tex')
'1+x+\\\\frac{x^2}{2}+\\\\frac{x^3}{6}+O\\\\left(x^4\\\\right)'
>>> result = m.eval('Series[Exp[x],{x,0,3}]',str_format='plain')
>>> print(result)
         2    3
        x    x        4
1 + x + -- + -- + O[x]
        2    6
>>> m.eval('Mean[{1,2,3,4}]',output_type='python')
2.5

This function attempts to push a python value to the Mathematica Kernel. It attempts to convert the value first then sends it.

• name - The name the value will have in the Mathematica Kernel
• value - The python value to be passed.

This currently works by just calling the Mathematica function Set. Mathematica's type system is not as extensive as Python's here are how things are set.

• Python type -> Mathematica type
• bool -> Booleans
• None -> Null
• float -> Real
• int -> Integer
• long -> Integer
• complex -> Complex
• iter -> List
• list -> List
• set -> List
• xrange -> List
• str-> String
• tuple -> List
• frozenset -> List

Note that there is currently no support for numpy arrays. This could be possible in the future given the current interface, but for large arrays would be slow. Note that since we are essentially converting everything to strings, this can be exceptionally slow and memory intensive for large amounts of data. Consider reading and writing to and from files.

There is no simple type in Mathematica that corresponds to dict, or at least not that I can find, patches welcome!

The conversion happens recursively so a list of lists will be appropriately converted.

>>> m.push('x',5)
>>> m.eval('x')
'5'
>>> m.push('l',4L)
>>> m.eval('l')
'4'
>>> m.push('y',.5)
>>> m.eval('y')
'0.5'
>>> m.push('z',complex(3,4))
>>> m.eval('z')
'3. + 4.*I'
>>> m.push('t',True)
>>> m.eval('t')
'True'
>>> m.push('f',False)
>>> m.eval('f')
'False')
>>> m.push('n',None)
>>> m.eval('n')
'None'
>>> m.push('r',range(3))
>>> m.eval('r')
'{0, 1, 2}'
>>> m.push('L',[1,2,3])
>>> m.eval('L')
'{1, 2, 3}'
>>> m.push('s',set([1,2,3])
>>> m.eval('s')
'{1, 2, 3}'
>>> m.push('xr',xrange(2))
>>> m.eval('xr')
'{0, 1}'
>>> m.push('st','spam')
>>> m.eval('st')
'"spam"'
>>> m.push('fs',frozenset([1,2,3])
>>> m.eval('fs')
'{1, 2, 3}'
>>> m.push('ll', [1,2,'hello',[2,2.5,4],complex(3,4)]
>>> m.eval('ll')
'{1, 2, "hello", {2, 2.5, 4}, 3. + 4*I}'

This command pulls variables out of the Mathematica kernel into python and attempts to convert them into python types. The return value is the same as the return from eval when output_type is 'python'. Since Mathematica returns expressions which are based on function calls we take those function calls and try to convert them. First the basics.

• Mathematica Type -> Python Type
• Integer -> int or long depending on size
• Rational or anything with '' -> Attempts to go to float
• Complex or anything with 'I' -> Attempts to go to complex
• String -> str
• symbols -> str
• functions -> dict...

Let me explain the functions -> dict. If we can't convert the part of the expression into a python type, we make a dictionary with a single key, the function name, the value of which is a list of arguments to that function. If there are nested function calls the produces dicts of lists of dicts. If all else fails it just returns the original string. Still with me? If not here are some...

>>> m.eval('X = Unevaluated[D[Log[x],x]];')
>>> m.pull('X')
{'Hold': [{'D': [{'Log': ['q']}, 'q']}]}
>>> m.eval('Y = Integrate[D[Log[q],q],{q,1.1,10.1}];'
>>> m.pull('Y')
2.2172252349699813

In the future we could convert different function types. IE if Mathematica returns Log[10], we could evaluate math.log(10).

Mathematica has a rich graphics system. If any of your output produces the words 'Graphics', 'Graphics3D', 'Image', or 'Grid', pythonica will use the Export function of Mathematica to produce the image. The images will be called 'pythonica_plot_x.ext' where 'x' is an increasing number as you produce more plots, and 'ext' is the extension provided by Pythonica.plot_format.

>>> m.plot_dir = '.'
>>> res = m.eval('Plot[Sin[q],{q,0,10}]')

Produces a plot called 'pythonica_plot_0.png' in the current directory.

Copyright (C) 2012 Benjamin Edwards <[email protected]>

Distributed with a BSD license; see LICENSE