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I found a couple of interesting model examples that I would like to run in System Modeler.

https://www.wolfram.com/system-modeler/examples/life-sciences/insulin-receptor-signaling.html

Do I need to also install Mathematica to work with System Modeler or can it has work without Mathematica being installed?

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System modeler uses the modelica language for its processing and does not require mathematica. You can test this by downloading the trial. But like mentioned you won’t have any issues

System requirements

Trial download

But keep in mind there are valuable interconnections between the two softwares and Mathematica is a powerful and useful tool to learn.

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