diff --git a/src/Core/Dot.h b/src/Core/Dot.h
index 88b180c4c..158b852eb 100644
--- a/src/Core/Dot.h
+++ b/src/Core/Dot.h
@@ -84,7 +84,7 @@ typename NumTraits<Scalar>::Real Object<Scalar, Derived>::norm2() const
 template<typename Scalar, typename Derived>
 typename NumTraits<Scalar>::Real Object<Scalar, Derived>::norm() const
 {
-  return Sqrt(norm2());
+  return NumTraits<typename NumTraits<Scalar>::Real>::sqrt(norm2());
 }
 
 template<typename Scalar, typename Derived>
diff --git a/src/Core/Fuzzy.h b/src/Core/Fuzzy.h
index eadffcff7..0334e6d96 100644
--- a/src/Core/Fuzzy.h
+++ b/src/Core/Fuzzy.h
@@ -34,7 +34,7 @@ bool Object<Scalar, Derived>::isApprox(const OtherDerived& other) const
   {
     return((*this - other).norm2()
            <= std::min(norm2(), other.norm2())
-            * Abs2(NumTraits<Scalar>::epsilon()));
+            * NumTraits<Scalar>::epsilon2());
   }
   else
   {
@@ -50,7 +50,7 @@ bool Object<Scalar, Derived>::isNegligble(const Scalar& other) const
 {
   if(IsVector)
   {
-    return(norm2() <= Abs2(other) * Abs2(NumTraits<Scalar>::epsilon()));
+    return(norm2() <= NumTraits<Scalar>::abs2(other) * NumTraits<Scalar>::epsilon2());
   }
   else
   {
@@ -67,7 +67,7 @@ bool Object<Scalar, Derived>::isNegligble(const Object<Scalar, OtherDerived>& ot
 {
   if(IsVector)
   {
-    return(norm2() <= other.norm2() * Abs2(NumTraits<Scalar>::epsilon()));
+    return(norm2() <= other.norm2() * NumTraits<Scalar>::epsilon2());
   }
   else
   {
diff --git a/src/Core/Numeric.h b/src/Core/Numeric.h
index 1bd48044b..8437dfb2e 100644
--- a/src/Core/Numeric.h
+++ b/src/Core/Numeric.h
@@ -39,6 +39,7 @@ template<> struct NumTraits<int>
   static const bool HasFloatingPoint = false;
   
   static int epsilon() { return 0; }
+  static int epsilon2() { return 0; }
   static int real(const int& x) { return x; }
   static int imag(const int& x) { EI_UNUSED(x); return 0; }
   static int conj(const int& x) { return x; }
@@ -47,10 +48,23 @@ template<> struct NumTraits<int>
   static int abs2(const int& x) { return x*x; }
   static int rand()
   {
-    // "rand()%21" would be bad. always use the high-order bits, not the low-order bits.
-    // note: here (gcc 4.1) static_cast<int> seems to round the nearest int.
-    // I don't know if that's part of the standard.
-    return -10 + static_cast<int>(std::rand() / ((RAND_MAX + 1.0)/20.0));
+    // "rand() % n" is bad, they say, because the low-order bits are not random enough.
+    // However here, 21 is odd, so rand() % 21 uses the high-order bits
+    // as well, so there's no problem.
+    return (std::rand() % 21) - 10;
+  }
+  static bool negligible(const int& a, const int& b)
+  {
+    EI_UNUSED(b);
+    return(a == 0);
+  }
+  static bool approx(const int& a, const int& b)
+  {
+    return(a == b);
+  }
+  static bool lessThanOrApprox(const int& a, const int& b)
+  {
+    return(a <= b);
   }
 };
 
@@ -64,6 +78,7 @@ template<> struct NumTraits<float>
   static const bool HasFloatingPoint = true;
   
   static float epsilon() { return 1e-5f; }
+  static float epsilon2() { return epsilon() * epsilon(); }
   static float real(const float& x) { return x; }
   static float imag(const float& x) { EI_UNUSED(x); return 0; }
   static float conj(const float& x) { return x; }
@@ -74,6 +89,18 @@ template<> struct NumTraits<float>
   {
     return std::rand() / (RAND_MAX/20.0f) - 10.0f;
   }
+  static bool negligible(const float& a, const float& b)
+  {
+    return(abs(a) <= abs(b) * epsilon());
+  }
+  static bool approx(const float& a, const float& b)
+  {
+    return(abs(a - b) <= std::min(abs(a), abs(b)) * epsilon());
+  }
+  static bool lessThanOrApprox(const float& a, const float& b)
+  {
+    return(a <= b || approx(a, b));
+  }
 };
 
 template<> struct NumTraits<double>
@@ -86,6 +113,7 @@ template<> struct NumTraits<double>
   static const bool HasFloatingPoint = true;
   
   static double epsilon() { return 1e-11; }
+  static double epsilon2() { return epsilon() * epsilon(); }
   static double real(const double& x) { return x; }
   static double imag(const double& x) { EI_UNUSED(x); return 0; }
   static double conj(const double& x) { return x; }
@@ -96,6 +124,18 @@ template<> struct NumTraits<double>
   {
     return std::rand() / (RAND_MAX/20.0) - 10.0;
   }
+  static bool negligible(const double& a, const double& b)
+  {
+    return(abs(a) <= abs(b) * epsilon());
+  }
+  static bool approx(const double& a, const double& b)
+  {
+    return(abs(a - b) <= std::min(abs(a), abs(b)) * epsilon());
+  }
+  static bool lessThanOrApprox(const double& a, const double& b)
+  {
+    return(a <= b || approx(a, b));
+  }
 };
 
 template<typename _Real> struct NumTraits<std::complex<_Real> >
@@ -109,6 +149,7 @@ template<typename _Real> struct NumTraits<std::complex<_Real> >
   static const bool HasFloatingPoint = NumTraits<Real>::HasFloatingPoint;
   
   static Real epsilon() { return NumTraits<Real>::epsilon(); }
+  static Real epsilon2() { return epsilon() * epsilon(); }
   static Real real(const Complex& x) { return std::real(x); }
   static Real imag(const Complex& x) { return std::imag(x); }
   static Complex conj(const Complex& x) { return std::conj(x); }
@@ -122,48 +163,16 @@ template<typename _Real> struct NumTraits<std::complex<_Real> >
   {
     return Complex(NumTraits<Real>::rand(), NumTraits<Real>::rand());
   }
+  static bool negligible(const Complex& a, const Complex& b)
+  {
+    return(abs2(a) <= abs2(b) * epsilon2());
+  }
+  static bool approx(const Complex& a, const Complex& b)
+  {
+    return(NumTraits<Real>::approx(std::real(a), std::real(b))
+        && NumTraits<Real>::approx(std::imag(a), std::imag(b)));
+  }
+  // lessThanOrApprox wouldn't make sense for complex numbers
 };
 
-template<typename T> typename NumTraits<T>::Real Real(const T& x)
-{ return NumTraits<T>::real(x); }
-
-template<typename T> typename NumTraits<T>::Real Imag(const T& x)
-{ return NumTraits<T>::imag(x); }
-
-template<typename T> T Conj(const T& x)
-{ return NumTraits<T>::conj(x); }
-
-template<typename T> typename NumTraits<T>::FloatingPoint Sqrt(const T& x)
-{ return NumTraits<T>::sqrt(x); }
-
-template<typename T> typename NumTraits<T>::RealFloatingPoint Abs(const T& x)
-{ return NumTraits<T>::abs(x); }
-
-template<typename T> typename NumTraits<T>::Real Abs2(const T& x)
-{ return NumTraits<T>::abs2(x); }
-
-template<typename T> T Rand()
-{ return NumTraits<T>::rand(); }
-
-template<typename T> bool Negligible(const T& a, const T& b)
-{
-  return(Abs(a) <= Abs(b) * NumTraits<T>::epsilon());
-}
-
-template<typename T> bool Approx(const T& a, const T& b)
-{
-  if(NumTraits<T>::IsFloat)
-    return(Abs(a - b) <= std::min(Abs(a), Abs(b)) * NumTraits<T>::epsilon());
-  else
-    return(a == b);
-}
-
-template<typename T> bool LessThanOrApprox(const T& a, const T& b)
-{
-  if(NumTraits<T>::IsFloat)
-    return(a < b || Approx(a, b));
-  else
-    return(a <= b);
-}
-
 #endif // EI_NUMERIC_H
diff --git a/src/Core/Random.h b/src/Core/Random.h
index 9827f5585..a90d69d5b 100644
--- a/src/Core/Random.h
+++ b/src/Core/Random.h
@@ -51,7 +51,7 @@ template<typename MatrixType> class Random
     {
       EI_UNUSED(row);
       EI_UNUSED(col);
-      return Rand<Scalar>();
+      return NumTraits<Scalar>::rand();
     }
     
   protected:
diff --git a/test/main.cpp b/test/main.cpp
index 8610cf363..f5c758961 100644
--- a/test/main.cpp
+++ b/test/main.cpp
@@ -25,7 +25,7 @@
 
 #include "main.h"
 
-genTest::genTest()
+EigenTest::EigenTest()
 {
     unsigned int t = (unsigned int) time( NULL );
     qDebug() << "Initializing random number generator with seed"
diff --git a/test/main.h b/test/main.h
index 47ea1b928..85968134c 100644
--- a/test/main.h
+++ b/test/main.h
@@ -29,7 +29,7 @@
 #include <QtTest/QtTest>
 #include "../src/Core.h"
 
-USING_EIGEN_DATA_TYPES
+using namespace Eigen;
 
 #include <cstdlib>
 #include <ctime>
@@ -62,6 +62,9 @@ template<typename T> bool TestNegligible(const T& a, const T& b)
   return(Abs(a) <= Abs(b) * TestEpsilon<T>());
 }
 
+//template<typename Scalar, typename Derived, typename OtherDerived>
+//bool TestNegligible
+
 template<typename T> bool TestApprox(const T& a, const T& b)
 {
   if(Eigen::NumTraits<T>::IsFloat)