# Computing relations in Jacobi algebras

Sometimes I am given a superpotential, for which I want to compute the relations in the associated Jacobi algebra, e.g. when I'm working with graded 3-Calabi–Yau algebras. This is a straightforward procedure using the *cyclic partial derivative*, but I am known to make a computational mistake or two from time to time.

So I quickly implemented a small script for this in Sage. I thought **superpotentiator** was a good name, and so this is how you can find it on GitHub.

I discovered that using Sage Cell Server it is possible to include Sage-scripts on your website, so below you can find an interactive version of the code. The quiver is defined on line 25, the superpotential on line 30. There are no checks on whether the input actually makes sense (such as the path being cyclic).