Use this worksheet to test the program SSHY. SSHY calculates the Surface Spherical Harmonics Y(n,d,x). n = order, d = dimension, x = vector of dimension d with point coordinates. Written with Maple 12. thomas.wieder@t-online.de Last date changed: 29 May 2009. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Initialisation: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjpGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTA== QyQtSSV3aXRoRzYiNiNJKWNvbWJpbmF0RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlISIi QyRBUUpjOi9Vc2Vycy9UaG9tYXMvRG9jdW1lbnRzL0FyYmVpdC9TU0hZLm1wbDYiISIi LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Example: Use a dummy vector x and cartesian coordinates to get the Y(n,d,x) in symobolic form: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= QyQ+SSJkRzYiIiIkISIi QyQ+SSJuRzYiIiIjISIi QyQ+SSJ4RzYiLUkmYXJyYXlHJSpwcm90ZWN0ZWRHNiM7IiIiSSJkR0YlISIi QyQtSSVTU0hZRzYiNiZJIm5HRiVJImRHRiVJInhHRiVRKmNhcnRlc2lhbkYlIiIi NihRMVNTSFk6fm9yZGVyfm5+PX42IiIiI1EwfmRpbWVuc2lvbn5kfj1+RiQiIiRRNH5wb2ludH5jb29yZGluYXRlczpGJEkieEdGJA== NiZRP1NTSFl+LS0+fmksfmQtdHVwZWwsfllOWFtpXX46fjYiIiIiNyUiIiEiIiNGJywqKiQmSSJ4R0YkNiNGKCIiJSEiIiomRitGKCZGLDYjIiIkRighIiMqJEYxRi5GLyokRitGKEYo USJ+NiI= NiZRP1NTSFl+LS0+fmksfmQtdHVwZWwsfllOWFtpXX46fjYiIiIjNyVGJSIiIUYnKiYsKCokJkkieEdGJDYjIiIiRiUiIiQqJCZGLDYjRiVGJSEiIiokJkYsNiNGL0YlRjNGLiwoRipGLkYwRi5GNEYuRi4= USJ+NiI= NiZRP1NTSFl+LS0+fmksfmQtdHVwZWwsfllOWFtpXX46fjYiIiIkNyUiIiJGJyIiISwkKigmSSJ4R0YkNiMiIiNGJywoKiQmRiw2I0YnRi5GJyokRitGLkYnKiQmRiw2I0YlRi5GJyNGJ0YuRjFGJyIiJQ== USJ+NiI= NiZRP1NTSFl+LS0+fmksfmQtdHVwZWwsfllOWFtpXX46fjYiIiIlNyUiIiEiIiJGKCwkKiYmSSJ4R0YkNiMiIiNGKCZGLDYjIiIkRihGLg== USJ+NiI= NiZRP1NTSFl+LS0+fmksfmQtdHVwZWwsfllOWFtpXX46fjYiIiImNyUiIiIiIiFGJywkKigmSSJ4R0YkNiMiIiRGJywoKiQmRiw2I0YnIiIjRicqJCZGLDYjRjNGM0YnKiRGK0YzRicjRidGM0YxRiciIiU= USJ+NiI= NihRM1NTSFl+LS0+fmQtdHVwZWxzOjYiNyUiIiEiIiNGJjclRidGJkYmNyUiIiJGKkYmNyVGJkYqRio3JUYqRiZGKg== NiRRU1NTSFl+LS0+fk51bWJlcn5vZn5wb2x5bm9taWFsc35zaG91bGR+YmV+ZXF1YWx+dG9+NiIiIiY= UTVTU0hZfi0tPn5FbmR+b2Z+cnVuITYi NicsKiokJkkieEc2IjYjIiIjIiIlISIiKiZGJUYpJkYmNiMiIiRGKSEiIyokRi1GKkYrKiRGJUYpRikqJiwoKiQmRiY2IyIiIkYpRi9GMkYrKiRGLUYpRitGOCwoRjVGOEYyRjhGOUY4RjgsJCooRiVGOEY6I0Y4RilGNkY4RiosJComRiVGOEYtRjhGKSwkKihGLUY4RjpGPUY2RjhGKg== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Check whether any two functions are orthogonal: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= QyQtSSV3aXRoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJL1ZlY3RvckNhbGN1bHVzR0YlISIi QyQtSS9TZXRDb29yZGluYXRlc0c2IjYjJi5JKmNhcnRlc2lhbkdGJTYlSSJ4R0YlSSJ5R0YlSSJ6R0YlISIi QygvSSJ4RzYiLkYkISIiL0kieUdGJS5GKUYnPkkiekdGJS5GLEYn Qy4+SSN4bEc2Ii1JIi1HNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lR0YlSS9WZWN0b3JDYWxjdWx1c0c2JEYpSShfc3lzbGliR0YlNiMiIiIhIiI+SSN4aEdGJUYwRjE+SSN5bEdGJUYmRjE+SSN5aEdGJUYwRjE+SSN6bEdGJUYmRjE+SSN6aEdGJUYwRjE= JSFH QyQ+SSJmRzYiKiYsKCokJkkieEdGJTYjIiIiIiIjIiIkKiQmRio2I0YtRi0hIiIqJCZGKjYjRi5GLUYyRiwsKEYoRixGL0YsRjNGLEYsRiw= KiYsKCokJkkieEc2IjYjIiIiIiIjIiIkKiQmRiY2I0YqRiohIiIqJCZGJjYjRitGKkYvRiksKEYkRilGLEYpRjBGKUYp Qyo+SSNmeEc2Ii1JJXN1YnNHJSpwcm90ZWN0ZWRHNiQvJkkieEdGJTYjIiIiRixJImZHRiUhIiI+SSNmeUdGJS1GJzYkLyZGLDYjIiIjSSJ5R0YlRiRGMD5JI2Z6R0YlLUYnNiQvJkYsNiMiIiRJInpHRiVGMkYwPkYvRjtGLg== KiYsKCokSSJ4RzYiIiIjIiIkKiRJInlHRiZGJyEiIiokSSJ6R0YmRidGKyIiIiwoRiRGLkYpRi5GLEYuRi4= JSFH QyQ+SSJnRzYiLUkiKkc2JCUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHRiVJL1ZlY3RvckNhbGN1bHVzRzYkRilJKF9zeXNsaWJHRiU2JC1GJzYkLUYnNiQiIiUmSSJ4R0YlNiMiIiQtSSVzcXJ0R0YtNiMtSSIrR0YoNiQtRj02JCokJkY2NiMiIiIiIiMqJCZGNjYjRkVGRSokRjVGRUZCRkQ= LCQqKCZJInhHNiI2IyIiJCIiIiwoKiQmRiU2I0YpIiIjRikqJCZGJTYjRi5GLkYpKiRGJEYuRikjRilGLkYsRikiIiU= Qyo+SSNneEc2Ii1JJXN1YnNHJSpwcm90ZWN0ZWRHNiQvJkkieEdGJTYjIiIiRixJImdHRiUhIiI+SSNneUdGJS1GJzYkLyZGLDYjIiIjSSJ5R0YlRiRGMD5JI2d6R0YlLUYnNiQvJkYsNiMiIiRJInpHRiVGMkYwPkYvRjtGLg== LCQqKEkiekc2IiIiIiwoKiRJInhHRiUiIiNGJiokSSJ5R0YlRipGJiokRiRGKkYmI0YmRipGKUYmIiIl QyQ+SSJ3RzYiIiIiRiY= IiIi QyQtSSRpbnRHNiI2JC1JIipHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lR0YlSS9WZWN0b3JDYWxjdWx1c0c2JEYqSShfc3lzbGliR0YlNiQtRig2JEkiZkdGJUkiZ0dGJUkid0dGJS83JUkieEdGJUkieUdGJUkiekdGJS1JL1BhcmFsbGVsZXBpcGVkR0YlNiU7SSN4bEdGJUkjeGhHRiU7SSN5bEdGJUkjeWhHRiU7SSN6bEdGJUkjemhHRiUiIiI= IiIh LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEiI0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUkjbWlHRiQ2JVFib35UaGV+YWJvdmV+aW50ZWdyYWx+aXN+ZXF1YWx+dG9+MC5+VGhlfmZ1bmN0aW9uc35zZWVtfnRvfmJlfm9ydGhvZ29uYWwuRicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdGNEYv LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Example: Use a vector x provided with explicit coordinates to get the Y(n,d,x) in numeric form: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= QyQ+SSJkRzYiIiIkISIi QyQ+SSJuRzYiIiIjISIi QyQ+SSJ4RzYiLUkmYXJyYXlHJSpwcm90ZWN0ZWRHNiM7IiIiSSJkR0YlISIi Qyg+JkkieEc2IjYjIiIiRihGKD4mRiU2IyIiI0YoRig+JkYlNiMiIiRGKEYo IiIi IiIi IiIi QyQtSSVTU0hZRzYiNiZJIm5HRiVJImRHRiVJInhHRiVRKmNhcnRlc2lhbkYlIiIi NihRMVNTSFk6fm9yZGVyfm5+PX42IiIiI1EwfmRpbWVuc2lvbn5kfj1+RiQiIiRRNH5wb2ludH5jb29yZGluYXRlczpGJEkieEdGJA== NiZRP1NTSFl+LS0+fmksfmQtdHVwZWwsfllOWFtpXX46fjYiIiIiNyUiIiEiIiNGJyEiIw== NiZRP1NTSFl+LS0+fmksfmQtdHVwZWwsfllOWFtpXX46fjYiIiIjNyVGJSIiIUYnIiIk NiZRP1NTSFl+LS0+fmksfmQtdHVwZWwsfllOWFtpXX46fjYiIiIkNyUiIiJGJyIiISwkKiRGJSNGJyIiIyIiJQ== NiZRP1NTSFl+LS0+fmksfmQtdHVwZWwsfllOWFtpXX46fjYiIiIlNyUiIiEiIiJGKCIiIw== NiZRP1NTSFl+LS0+fmksfmQtdHVwZWwsfllOWFtpXX46fjYiIiImNyUiIiIiIiFGJywkKiQiIiQjRiciIiMiIiU= NihRM1NTSFl+LS0+fmQtdHVwZWxzOjYiNyUiIiEiIiNGJjclRidGJkYmNyUiIiJGKkYmNyVGJkYqRio3JUYqRiZGKg== NiRRU1NTSFl+LS0+fk51bWJlcn5vZn5wb2x5bm9taWFsc35zaG91bGR+YmV+ZXF1YWx+dG9+NiIiIiY= UTVTU0hZfi0tPn5FbmR+b2Z+cnVuITYi NichIiMiIiQsJCokRiQjIiIiIiIjIiIlRilGJQ== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=