1 files changed, 81 insertions, 0 deletions
diff --git a/buch/chapters/110-elliptisch/images/unvollstaendig.m b/buch/chapters/110-elliptisch/images/unvollstaendig.m
new file mode 100644
index 0000000..25196d0
--- /dev/null
+++ b/buch/chapters/110-elliptisch/images/unvollstaendig.m
@@ -0,0 +1,81 @@
+#
+# unvollstaendig.m
+#
+# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+global N;
+N = 200;
+global n;
+n = 5;
+
+function retval = integrand_f(t, k)
+	retval = 1 / sqrt((1 - t^2) * (1 - k^2 * t^2));
+endfunction
+
+function retval = integrand_e(t, k)
+	retval = sqrt((1-k^2*t^2)/(1-t^2));
+endfunction
+
+function retval = integrand_pi(n, t, k)
+	retval = 1 / ((1-n*t^2) * sqrt((1-k^2*t^2)*(1-t^2)));
+endfunction
+
+function retval = elliptisch1(f, name, k)
+	global N;
+	global n;
+	s = 0;
+	fprintf(f, "\\def\\ell%s{ (0,0)", name);
+	delta = 1 / N;
+	for x = (0:delta:(1-delta))
+		h = delta / n;
+		for t = (x+h/2:h:x+delta)
+			s = s + integrand_f(t, k) * h;
+		endfor
+		fprintf(f, "\n    -- ({\\dx*%.4f},{\\dy*%.4f})", x + delta, s);
+	endfor
+	fprintf(f, "}\n");
+endfunction
+
+function retval = elliptisch2(f, name, k)
+	global N;
+	global n;
+	s = 0;
+	fprintf(f, "\\def\\ell%s{ (0,0)", name);
+	delta = 1 / N;
+	for x = (0:delta:(1-delta))
+		h = delta / n;
+		for t = (x+h/2:h:x+delta)
+			s = s + integrand_e(t, k) * h;
+		endfor
+		fprintf(f, "\n    -- ({\\dx*%.4f},{\\dy*%.4f})", x + delta, s);
+	endfor
+	fprintf(f, "\n}\n");
+endfunction
+
+fn = fopen("unvollpath.tex", "w");
+
+elliptisch1(fn, "Fzero", 0.0);
+elliptisch1(fn, "Fone", 0.1);
+elliptisch1(fn, "Ftwo", 0.2);
+elliptisch1(fn, "Fthree", 0.3);
+elliptisch1(fn, "Ffour", 0.4);
+elliptisch1(fn, "Ffive", 0.5);
+elliptisch1(fn, "Fsix", 0.6);
+elliptisch1(fn, "Fseven", 0.7);
+elliptisch1(fn, "Feight", 0.8);
+elliptisch1(fn, "Fnine", 0.9);
+elliptisch1(fn, "Ften", 1.0);
+
+elliptisch2(fn, "Ezero", 0.0);
+elliptisch2(fn, "Eone", 0.1);
+elliptisch2(fn, "Etwo", 0.2);
+elliptisch2(fn, "Ethree", 0.3);
+elliptisch2(fn, "Efour", 0.4);
+elliptisch2(fn, "Efive", 0.5);
+elliptisch2(fn, "Esix", 0.6);
+elliptisch2(fn, "Eseven", 0.7);
+elliptisch2(fn, "Eeight", 0.8);
+elliptisch2(fn, "Enine", 0.9);
+elliptisch2(fn, "Eten", 1.0);
+
+fclose(fn);