Python How much faster is Python than Mathematica?

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The discussion centers on the use of Verlet integration for simulating a variation of a standard map in Mathematica, with the goal of generating phase space maps from approximately 25,000 initial points. Currently, the user is working with 1,000 points, with each simulation taking around 15 minutes using CompiledFunctions. There is a query about whether Python would offer a significant speed advantage over Mathematica for this type of computation. Additionally, the conversation touches on optimization strategies for improving computation times. A comparison of programming languages, particularly highlighting Julia's advantages due to its performance and MATLAB-like syntax, is also mentioned, suggesting that Julia may be a better option for numerical analysis in engineering contexts.
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I've been running some of my own simulations of a variation on a standard map using Verlet integration on Mathematica, and I would like to start generating maps of phase space using ~25,000 initial points. I'm currently at 1000 points using Mathematica, and each simulation takes about 15 minutes using CompiledFunctions. Would Python be significantly faster? Also, is there anything else I can do to optimize computation?
 
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Here's some comparative stats:

https://sciencehouse.wordpress.com/2014/06/29/julia-vs-python/

Personally I think Julia has the edge over many of these languages and it has a syntax similar to MATLAB which is the primary engineering numerical analysis language today taught at many universities and carried over to industry.
 
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