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### Translating a polygon into a fundamental domain

Hello.

I have a polygon (defined, say, via polygon()) that I'm thinking of as filled in with some color. I'd like to understand its image on the quotient of $\mathbb{R}^2$ mod $\mathbb{Z}^2$ by seeing this image in a fundamental domain like the unit square with corners (0,0), (1,0), (0,1), (1,1).

Put differently, I want to translate (by a lattice point) each point in and on the polygon into this square and see what the result looks like.

Is there a reasonable way to do this in SAGE?