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## 2.iii. Real Solutions to Sparse Polynomial Systems

What is the maximal number of real solutions to a sparse polynomial
system (2.1) with common Newton
polytope *P*?
The situation here is far from settled.
There are constructive lower bounds, which are not optimal, which we discuss
in Section 2.iii.a.
There is a non-trivial upper bound from the theory of fewnomials, which is
almost surely not sharp, and finally there is an intriguing conjecture of
Kushnirenko, proposing better upper bounds, but that conjecture is false.

**Subsections**
- Constructive Lower Bounds
- Fewnomial Upper Bounds
- Kushnirenko's Conjecture

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