What is the command to find function invariant?

<http://demonstrations.wolfram.com/AFunctionInvariantUnderAGroupOfTransformations/>

what is algorithm it use to calculate this?

**Edit**

[there is a book do it in this way](http://books.google.com.ar/books?id=MNKmHgDZBK8C&pg=PA108&lpg=PA108&dq=symmetry%2banalysis%2bof%2bdifferential%2bequations%2b%2bmathematica%2binvariant%2bfunctions&source=bl&ots=h7IyVMW1Il&sig=2piZfJn3wiaYNZvQKOB_-pNEe8U&hl=en)

Hope this book give you an idea on how to do multivariate case