From 7cc8f34f003ecb25ade7f1ff2287fe12b5a22c40 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Sat, 25 Jun 2022 14:36:04 +0200 Subject: arithmetic-geometric-mean --- .../chapters/110-elliptisch/experiments/agm.maxima | 26 ++++++++++++++++++++++ 1 file changed, 26 insertions(+) create mode 100644 buch/chapters/110-elliptisch/experiments/agm.maxima (limited to 'buch/chapters/110-elliptisch/experiments/agm.maxima') 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))); -- cgit v1.2.1