Restrict search space for enumpoly to be strictly interior.

This shrinks the search space for searching for equilibria on a
given support to be in the interior of the simplex (rather than
including the boundaries as before).

This solves the behaviour noted in #756, in which degenerate situations
which required a solution to be on
the boundary would be very slow as it tried
to approach the solution on the boundary.

Author: tturocy

src/solvers/enumpoly/efgpoly.cc

@@ -161,8 +161,8 @@ std::list<MixedBehaviorProfile<double>> SolveSupport(const BehaviorSupportProfil
 
   // set up the rectangle of search
   Vector<double> bottoms(data.space->GetDimension()), tops(data.space->GetDimension());
-  bottoms = 0;
-  tops = 1;
+  bottoms = 1e-12;
+  tops = 1 - 1e-12;
 
   PolynomialSystemSolver solver(equations);
   std::list<Vector<double>> roots;

src/solvers/enumpoly/nfgpoly.cc

@@ -111,8 +111,8 @@ EnumPolyStrategySupportSolve(const StrategySupportProfile &support, bool &is_sin
   const PolynomialSystem<double> equations = ConstructEquations(space, support, strategy_poly);
 
   Vector<double> bottoms(space->GetDimension()), tops(space->GetDimension());
-  bottoms = 0;
-  tops = 1;
+  bottoms = 1e-12;
+  tops = 1 - 1e-12;
   PolynomialSystemSolver solver(equations);
   is_singular = false;
   std::list<Vector<double>> roots;

src/solvers/enumpoly/poly.h

@@ -375,7 +375,11 @@ template <class T> class Polynomial {
     });
   }
   [[nodiscard]] const std::vector<Monomial<T>> &GetTerms() const noexcept { return m_terms; }
-  bool IsZero() const noexcept { return m_terms.empty(); }
+  bool IsZero() const noexcept
+  {
+    return m_terms.empty() || std::all_of(m_terms.begin(), m_terms.end(),
+                                          [](const auto &mono) { return mono.IsZero(); });
+  }
   bool IsConstant() const noexcept
   {
     return m_terms.size() == 1 && m_terms.front().TotalDegree() == 0;