new stuff about parrondo

1 files changed, 46 insertions, 0 deletions

diff --git a/buch/chapters/80-wahrscheinlichkeit/rechnungen/btilde.maxima b/buch/chapters/80-wahrscheinlichkeit/rechnungen/btilde.maxima
new file mode 100644
index 0000000..16be152
--- /dev/null
+++ b/buch/chapters/80-wahrscheinlichkeit/rechnungen/btilde.maxima
@@ -0,0 +1,46 @@
+Btilde: matrix(
+	[ -1            , 1/4 + epsilon, 3/4 - epsilon ],
+	[ 1/10 - epsilon, -1           , 1/4 + epsilon ],
+	[ 9/10 + epsilon, 3/4 - epsilon, -1            ]
+);
+
+r: expand(Btilde[1] / Btilde[1,1]);
+Btilde[1]: r;
+Btilde[2]: Btilde[2] - Btilde[2,1] * r;
+Btilde[3]: Btilde[3] - Btilde[3,1] * r;
+
+Btilde: expand(Btilde);
+
+r: Btilde[2] / Btilde[2,2];
+Btilde[2]: r;
+Btilde[3]: Btilde[3] - Btilde[3,2] * r;
+
+Btilde: ratsimp(expand(Btilde));
+
+Btilde[1]: Btilde[1] - Btilde[1,2] * Btilde[2];
+
+Btilde: ratsimp(expand(Btilde));
+
+l: 78 + 12 * epsilon + 80 * epsilon^2;
+
+D: ratsimp(expand(l*Btilde));
+n: ratsimp(expand(l -D[1,3] -D[2,3]));
+
+p: (1/n) * matrix(
+[ -Btilde[1,3]*l ],
+[ -Btilde[2,3]*l ],
+[ l ]
+);
+p: ratsimp(expand(p));
+
+taylor(p, epsilon, 0, 3);
+
+G: matrix(
+	[  0,  1, -1 ],
+	[ -1,  0,  1 ],
+	[  1, -1,  0 ]
+);
+
+e: matrix([1,1,1]);
+
+ratsimp(expand(e. (G*Btilde) . p));