diff options
Diffstat (limited to '')
-rw-r--r-- | buch/chapters/110-elliptisch/agm/agm.m | 20 | ||||
-rw-r--r-- | buch/chapters/110-elliptisch/agm/agm.maxima | 26 |
2 files changed, 46 insertions, 0 deletions
diff --git a/buch/chapters/110-elliptisch/agm/agm.m b/buch/chapters/110-elliptisch/agm/agm.m new file mode 100644 index 0000000..dcb3ad8 --- /dev/null +++ b/buch/chapters/110-elliptisch/agm/agm.m @@ -0,0 +1,20 @@ +# +# agm.m +# +# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +format long + +n = 10; +a = 1; +b = sqrt(0.5); + +for i = (1:n) + printf("%20.16f %20.16f\n", a, b); + A = (a+b)/2; + b = sqrt(a*b); + a = A; +end + +K = pi / (2 * a) + diff --git a/buch/chapters/110-elliptisch/agm/agm.maxima b/buch/chapters/110-elliptisch/agm/agm.maxima new file mode 100644 index 0000000..c7facd4 --- /dev/null +++ b/buch/chapters/110-elliptisch/agm/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))); |