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author | Andreas Müller <andreas.mueller@ost.ch> | 2022-06-25 14:36:04 +0200 |
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committer | Andreas Müller <andreas.mueller@ost.ch> | 2022-06-25 14:36:04 +0200 |
commit | 7cc8f34f003ecb25ade7f1ff2287fe12b5a22c40 (patch) | |
tree | 4a234cf09ee14df548f9937fd1f08baa5e564900 /buch/chapters/110-elliptisch/experiments | |
parent | more improvements (diff) | |
download | SeminarSpezielleFunktionen-7cc8f34f003ecb25ade7f1ff2287fe12b5a22c40.tar.gz SeminarSpezielleFunktionen-7cc8f34f003ecb25ade7f1ff2287fe12b5a22c40.zip |
arithmetic-geometric-mean
Diffstat (limited to '')
-rw-r--r-- | buch/chapters/110-elliptisch/experiments/agm.maxima | 26 |
1 files changed, 26 insertions, 0 deletions
diff --git a/buch/chapters/110-elliptisch/experiments/agm.maxima b/buch/chapters/110-elliptisch/experiments/agm.maxima new file mode 100644 index 0000000..c7facd4 --- /dev/null +++ b/buch/chapters/110-elliptisch/experiments/agm.maxima @@ -0,0 +1,26 @@ +/* + * agm.maxima + * + * (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule + */ + +S: 2*a*sin(theta1) / (a+b+(a-b)*sin(theta1)^2); + +C2: ratsimp(diff(S, theta1)^2 / (1 - S^2)); +C2: ratsimp(subst(sqrt(1-sin(theta1)^2), cos(theta1), C2)); +C2: ratsimp(subst(S, sin(theta), C2)); +C2: ratsimp(subst(sqrt(1-S^2), cos(theta), C2)); + +D2: (a^2 * cos(theta)^2 + b^2 * sin(theta)^2) + / + (a1^2 * cos(theta1)^2 + b1^2 * sin(theta1)^2); +D2: subst((a+b)/2, a1, D2); +D2: subst(sqrt(a*b), b1, D2); +D2: ratsimp(subst(1-S^2, cos(theta)^2, D2)); +D2: ratsimp(subst(S, sin(theta), D2)); +D2: ratsimp(subst(1-sin(theta1)^2, cos(theta1)^2, D2)); + +Q: D2/C2; +Q: ratsimp(subst(x, sin(theta1), Q)); + +Q: ratsimp(expand(ratsimp(Q))); |