From efd0b14ae2c6515239aa08a627da98d206264e6d Mon Sep 17 00:00:00 2001
From: Christoph Ruegg <git@cdrnet.ch>
Date: Mon, 10 Feb 2014 20:41:58 +0100
Subject: [PATCH] Constants: sqrt(3) #194

---
 src/Numerics/Constants.cs                        |  3 +++
 src/Numerics/RootFinding/Cubic.cs                |  2 +-
 src/UnitTests/ComplexTests/Complex32Test.cs      |  2 +-
 .../RootFindingTests/RobustNewtonRaphsonTest.cs  | 16 ++++++++--------
 4 files changed, 13 insertions(+), 10 deletions(-)

diff --git a/src/Numerics/Constants.cs b/src/Numerics/Constants.cs
index ef7734d1..386694aa 100644
--- a/src/Numerics/Constants.cs
+++ b/src/Numerics/Constants.cs
@@ -67,6 +67,9 @@ namespace MathNet.Numerics
         /// <summary>The number sqrt(2)</summary>
         public const double Sqrt2 = 1.4142135623730950488016887242096980785696718753769d;
 
+        /// <summary>The number sqrt(3)</summary>
+        public const double Sqrt3 = 1.7320508075688772935274463415058723669428052538104d;
+
         /// <summary>The number sqrt(1/2) = 1/sqrt(2) = sqrt(2)/2</summary>
         public const double Sqrt1Over2 = 0.70710678118654752440084436210484903928483593768845d;
 
diff --git a/src/Numerics/RootFinding/Cubic.cs b/src/Numerics/RootFinding/Cubic.cs
index 7fbd9541..7921ca21 100644
--- a/src/Numerics/RootFinding/Cubic.cs
+++ b/src/Numerics/RootFinding/Cubic.cs
@@ -82,7 +82,7 @@ namespace MathNet.Numerics.RootFinding
             var S = Complex.Pow(R + rootD, 1d / 3d);
             var T = Complex.Pow(R - rootD, 1d / 3d);
             var shift = -a2 / 3d;
-            var sharedI = 0.5 * Complex.ImaginaryOne * Math.Sqrt(3) * (S - T);
+            var sharedI = 0.5 * Complex.ImaginaryOne * Constants.Sqrt3 * (S - T);
 
             var x1 = shift + (S + T);
             var x2 = shift - 0.5 * (S + T);
diff --git a/src/UnitTests/ComplexTests/Complex32Test.cs b/src/UnitTests/ComplexTests/Complex32Test.cs
index 0acccf26..ec28709c 100644
--- a/src/UnitTests/ComplexTests/Complex32Test.cs
+++ b/src/UnitTests/ComplexTests/Complex32Test.cs
@@ -290,7 +290,7 @@ namespace MathNet.Numerics.UnitTests.ComplexTests
         public void CanCreateComplexNumberWithModulusArgument()
         {
             var complex = Complex32.FromPolarCoordinates(2, (float)-Math.PI / 6);
-            Assert.AreEqual((float)Math.Sqrt(3), complex.Real, 1e-7f, "Real part is Sqrt(3).");
+            Assert.AreEqual((float)Constants.Sqrt3, complex.Real, 1e-7f, "Real part is Sqrt(3).");
             Assert.AreEqual(-1.0f, complex.Imaginary, 1e-7f, "Imaginary part is -1.");
         }
 
diff --git a/src/UnitTests/RootFindingTests/RobustNewtonRaphsonTest.cs b/src/UnitTests/RootFindingTests/RobustNewtonRaphsonTest.cs
index 6c341c42..4986898f 100644
--- a/src/UnitTests/RootFindingTests/RobustNewtonRaphsonTest.cs
+++ b/src/UnitTests/RootFindingTests/RobustNewtonRaphsonTest.cs
@@ -86,17 +86,17 @@ namespace MathNet.Numerics.UnitTests.RootFindingTests
 
             Func<double, double> f3 = x => 1/(x - 2) + x + 2;
             Func<double, double> df3 = x => -1/(x*x - 4*x + 4) + 1;
-            Assert.AreEqual(-Math.Sqrt(3), RobustNewtonRaphson.FindRoot(f3, df3, -2, -1, 1e-14, 100, 20), 1e-14);
-            Assert.AreEqual(Math.Sqrt(3), RobustNewtonRaphson.FindRoot(f3, df3, 1, 1.99, 1e-14, 100, 20));
-            Assert.AreEqual(Math.Sqrt(3), RobustNewtonRaphson.FindRoot(f3, df3, -1.5, 1.99, 1e-14, 100, 20));
-            Assert.AreEqual(Math.Sqrt(3), RobustNewtonRaphson.FindRoot(f3, df3, 1, 6, 1e-14, 100, 20));
+            Assert.AreEqual(-Constants.Sqrt3, RobustNewtonRaphson.FindRoot(f3, df3, -2, -1, 1e-14, 100, 20), 1e-14);
+            Assert.AreEqual(Constants.Sqrt3, RobustNewtonRaphson.FindRoot(f3, df3, 1, 1.99, 1e-14, 100, 20));
+            Assert.AreEqual(Constants.Sqrt3, RobustNewtonRaphson.FindRoot(f3, df3, -1.5, 1.99, 1e-14, 100, 20));
+            Assert.AreEqual(Constants.Sqrt3, RobustNewtonRaphson.FindRoot(f3, df3, 1, 6, 1e-14, 100, 20));
 
             Func<double, double> f4 = x => 1/(2 - x) - x + 6;
             Func<double, double> df4 = x => 1/(x*x - 4*x + 4) - 1;
-            Assert.AreEqual(4 + Math.Sqrt(3), RobustNewtonRaphson.FindRoot(f4, df4, 5, 6, 1e-14, 100, 20), 1e-14);
-            Assert.AreEqual(4 - Math.Sqrt(3), RobustNewtonRaphson.FindRoot(f4, df4, 2.01, 3, 1e-14, 100, 20));
-            Assert.AreEqual(4 - Math.Sqrt(3), RobustNewtonRaphson.FindRoot(f4, df4, 2.01, 5, 1e-14, 100, 20));
-            Assert.AreEqual(4 - Math.Sqrt(3), RobustNewtonRaphson.FindRoot(f4, df4, -2, 4, 1e-14, 100, 20));
+            Assert.AreEqual(4 + Constants.Sqrt3, RobustNewtonRaphson.FindRoot(f4, df4, 5, 6, 1e-14, 100, 20), 1e-14);
+            Assert.AreEqual(4 - Constants.Sqrt3, RobustNewtonRaphson.FindRoot(f4, df4, 2.01, 3, 1e-14, 100, 20));
+            Assert.AreEqual(4 - Constants.Sqrt3, RobustNewtonRaphson.FindRoot(f4, df4, 2.01, 5, 1e-14, 100, 20));
+            Assert.AreEqual(4 - Constants.Sqrt3, RobustNewtonRaphson.FindRoot(f4, df4, -2, 4, 1e-14, 100, 20));
         }
 
         [Test]