Kurze Polynome finden

This project concerns the number of terms of polynomials as a complexity measure.
This is an area of commutative algebra that is much less explored than degree based
complexity measures like Castelnuovo–Mumford regularity. As the finiteness results
that drive the Gröbner machinery are based on induction on the degree, they often
need to be replaced by more synergetic tools to make progress here. We envision that
combinatorial data structures like Newton polyhedra and matroids will help us to
solve the fundamental problem of this project: Is it algorithmically decidable if an
ideal in a polynomial ring contains a short polynomial?