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## 2.ii. The Polyhedral Homotopy Algorithm

The polyhedral homotopy algorithm of Huber and
Sturmfels [HS] deforms
the sparse system (2.1)
into a system where the number of solutions is evident.
The deformed system is a disjunction of systems whose Newton polytope is a
simplex, an important example treated in Section 2.ii.a.
The deformation relies on the combinatorial structure of a regular
triangulation, discussed in Section 2.ii.b.
Finally, we give the polyhedral homotopy algorithm in Section 2.ii.c.

**Subsections**
- A Simplex System
- Regular Triangulations
- Polyhedral Homotopy Algorithm

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