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authorAndreas Müller <andreas.mueller@ost.ch>2021-01-29 20:59:05 +0100
committerAndreas Müller <andreas.mueller@ost.ch>2021-01-29 20:59:05 +0100
commit474af74b757abcc54670c8de170c7458543a801a (patch)
treeabb0fd44390ab8969ff07c2bec7550b4046a31d5 /buch/chapters/80-wahrscheinlichkeit/rechnungen
parentMerge pull request #2 from Ayexor/master (diff)
downloadSeminarMatrizen-474af74b757abcc54670c8de170c7458543a801a.tar.gz
SeminarMatrizen-474af74b757abcc54670c8de170c7458543a801a.zip
new stuff about parrondo
Diffstat (limited to '')
-rw-r--r--buch/chapters/80-wahrscheinlichkeit/rechnungen/btilde.maxima46
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
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+++ b/buch/chapters/80-wahrscheinlichkeit/rechnungen/btilde.maxima
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+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));