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Bennett Kanuka

Using math and software to solve real world problems

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Convert Mathematica Equation to Python

I recently used Mathematica to solve a Lagrangian differential equation. I wish I could have used Sage but I was unable to find a simple way to program the Euler-Lagrange equation into a function. See this bug report. Mathematica on the other hand, came with a reference notebook with the Lagrangian and E-L equations built-in.

I solved the equations in Mathematica, but needed to use the resulting equations in Python code. I saved the notebook as a text file (using Save As) and tirmmed the resulting text file to just the parts I wanted to convert to Python. A single line of output was something like this (trimmed):

{x[t]->1/(-1+Subscript[r, 1])^3 E^(-t-t Subscript[r, 1]) (-E^t s+E^(t+t Subscript[r, 1]) s-E^(t Subscript[r, 1]) t v-E^(t Subscript[r, 1]) y-E^(t Subscript[r, 1]) t y+E^t s Subscript[r, 1]+2 E^(t Subscript[r, 1]) s Subscript[r, 1]-3 E^(t+t Subscript[r, 1]) s Subscript[r, 1]+E^(t Subscript[r, 1]) s t Subscript[r, 1]+3 E^(t Subscript[r, 1]) t v Subscript[r, 1]+…

To convert this long equation to Python code, I wrote a Perl script with a bunch of substitution commands.

It can be run by feeding a document on stdin:

./ < notebook.txt

Considering that the variables used in Mathematica will change for every notebook, this script will have to be adapted for every use. However, the comments should make this fairly straight-forward.

An example output [trimmed]:

1/(-1 \
+ MIX_RATE)**3 * np.exp(-t - t * MIX_RATE) * (-np.exp(t) * SCALE \
+ np.exp(t + t * MIX_RATE) * SCALE \
- np.exp(t * MIX_RATE) * t * v_old \
- np.exp(t * MIX_RATE) * ss_old \
- np.exp(t * MIX_RATE) * t * ss_old \
+ np.exp(t) * SCALE * MIX_RATE \

It may be worth nothing this is the first time I’ve used Perl. There may be far better ways to do this, but I wanted an excuse to learn some Perl.