Use "2" as a numerically-better factor in player[12]_start().

diff --git a/dunshire/games.py b/dunshire/games.py
index 0a473915716de7f4be4ce7d99cbc64d87c960795..f9877b334cfa3bcf2d60c6269ecbf4340de24eb1 100644 (file)
--- a/dunshire/games.py
+++ b/dunshire/games.py
@@ -4,8 +4,6 @@ Symmetric linear games and their solutions.
 This module contains the main :class:`SymmetricLinearGame` class that
 knows how to solve a linear game.
 """
-from math import sqrt
-
 from cvxopt import matrix, printing, solvers
 from .cones import CartesianProduct, IceCream, NonnegativeOrthant
 from .errors import GameUnsolvableException, PoorScalingException
@@ -833,9 +831,10 @@ class SymmetricLinearGame:
             # 45-45-90 triangle and the shortest distance to the
             # outside of the cone should be 1/sqrt(2) of that.
             # It works in R^2, so it works everywhere, right?
+            # We use "2" because it's better numerically than sqrt(2).
             height = self.e1()[0]
             radius = norm(self.e1()[1:])
-            dist = (height - radius) / sqrt(2)
+            dist = (height - radius) / 2
         else:
             raise NotImplementedError
 
@@ -862,9 +861,10 @@ class SymmetricLinearGame:
             # 45-45-90 triangle and the shortest distance to the
             # outside of the cone should be 1/sqrt(2) of that.
             # It works in R^2, so it works everywhere, right?
+            # We use "2" because it's better numerically than sqrt(2).
             height = self.e2()[0]
             radius = norm(self.e2()[1:])
-            dist = (height - radius) / sqrt(2)
+            dist = (height - radius) / 2
         else:
             raise NotImplementedError