A41
===
For those that can't read attachments:I want to 
find the
kernel of this 80 by 96 matrix where the aijk areunspecified.
(I already know that the vector v7:= (1, 0, 0, 0, 0, 1, 0,0,
0, 0,1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0,
0, 0, 0, -1,-1,0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1,
-1, 0, 0, 0, 0, -1, 0,0,0, 0, -1, 0, 0, 0, 0, -1, -1, 0, 0, 0,
0, -1, 0, 0, 0, 0, -1, 0, 0, 0,0,-1, -1, 0, 0, 0, 0, -1, 0, 0,
0, 0, -1, 0, 0, 0, 0, -1) is in the kernelbut are there any
others?) My computerjust sits there rumbling. Is it too big
for my computer or should I notusethe 
ÔNullSpace' function?
(a1111, a1121, a1112, a1122, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0,a1111, a1211, a1121, a1221, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0,
0, 0), (a2111, a2121, a2112, a2122, 0, 0, 0, 0,0,0, 0, 0, 0,
0, 0, 0, a2111, a2211, a2121, a2221, 0, 0, 0, 0, 0, 0, 0,
0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0), (a1211, a1221,a1212,a1222, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, a1111, a1211,a1121,a1221, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0),(a2211, a2221, a2212, a2222, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, a2111, a2211, a2121,
a2221, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, a1111,
a1121, a1112, a1122, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, a1111, a1211, a1121, a1221, 0, 0, 0,0,0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0,
0, a2111, a2121,a2112, a2122, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, a2111,a2211,a2121, a2221, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0),(0,0, 0, 0, a1211, a1221, a1212, a1222, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, a1111, a1211, a1121,
a1221, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0,
0, 0, 0), (0, 0, 0, 0, a2211, a2221, a2212, a2222, 0, 0, 0,
0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, a2111,
a2211, a2121, a2221, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0,
a1111,a1121,a1112, a1122, 0, 0, 0, 0, a1112, a1212, a1122,
a1222, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0,
0,0,0, 0, 0, a2111, a2121, a2112, a2122, 0, 0, 0, 0, a2112,
a2212, a2122,a2222, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0),
(0, 0, 0, 0, 0, 0, 0, 0, a1211, a1221, a1212, a1222, 0, 0,
0,0,0, 0, 0, 0, a1112, a1212, a1122, a1222, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0,
0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0, a2211, a2221,a2212, a2222,
0, 0, 0, 0, 0, 0, 0, 0, a2112, a2212, a2122, a2222, 0, 0,0,0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0), (0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, a1111,
a1121, a1112, a1122, 0, 0, 0, 0, 0, 0, 0, 0,a1112, a1212,
a1122, a1222, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0), (0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, a2111, a2121, a2112, a2122,0,0, 0, 0, 0, 0, 0, 0,
a2112, a2212, a2122, a2222, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, a1211,a1221, a1212, a1222, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, a1112, a1212,a1122, a1222, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
(0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, a2211, a2221, a2212, a2222,
0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, a2112, a2212, a2122, a2222,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0,0,0), (a1111, a1121, a1112, a1122, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
a1111, a2111, a1211, a2211, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0,
0, 0, 0, 0, 0, 0), (a2111, a2121, a2112, a2122, 0, 0, 0, 0,
0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0,0,a1111, a2111, a1211, a2211, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0), (a1211, a1221, a1212,a1222,0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, a1111, a2111, a1211,
a2211, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),(a2211,a2221, a2212,
a2222, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
a1111,a2111, a1211, a2211, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0), (0, 0, 0, 0,
a1111, a1121, a1112, a1122, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, a1121, a2121,a1221,a2221,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0,
0, 0, 0, a2111, a2121, a2112,a2122, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0,
a1121, a2121, a1221, a2221, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0), (0, 0, 0,0,a1211, a1221, a1212, a1222, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, a1121, a2121, a1221,a2221,0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0,0,0, 0), (0, 0, 0, 0, a2211, a2221, a2212, a2222, 0, 0,
0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, a1121, a2121, a1221,
a2221, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0,
0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0, a1111,
a1121,a1112,a1122, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0,a1112,a2112, a1212, a2212, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0,0,0,
a2111, a2121, a2112, a2122, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, a1112, a2112, a1212,
a2212, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),(0, 0, 0, 0,
0, 0, 0, 0, a1211, a1221, a1212, a1222, 0, 0, 0, 0, 0, 0,0,0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
a1112,a2112, a1212, a2212, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0),
(0, 0, 0, 0, 0, 0, 0, 0, a2211, a2221,a2212,a2222, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0,
0, 0, 0, 0, 0, 0, 0, 0, a1112, a2112, a1212, a2212, 0, 0, 0,
0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0), (0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, a1111, a1121,
a1112, a1122, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0,
a1122, a2122, a1222, a2222, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0),(0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
a2111, a2121, a2112, a2122, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, a1122, a2122, a1222, a2222,0,0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0,0,0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, a1211, a1221,a1212,a1222, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, a1122, a2122,
a1222, a2222, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0,0,a2211, a2221, a2212, a2222, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, a1122, a2122, a1222, a2222, 0, 0, 0,0,0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
(a1111, a1121,a1112, a1122, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,a1111, a2111, a1112,
a2112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0,0,0, 0, 0), (a2111, a2121, a2112, a2122, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
a1111, a2111, a1112, a2112, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0,
0, 0, 0, 0, 0, 0, 0), (a1211, a1221, a1212, a1222, 0, 0, 0,
0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
a1211, a2211, a1212, a2212, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (a2211, a2221,a2212,a2222,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0,0,a1211, a2211, a1212, a2212, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),(0, 0, 0, 0, a1111,
a1121, a1112, a1122, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0,0,0, 0, 0, 0, a1121, a2121, a1122, a2122, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0), (0, 0, 0,
0, a2111, a2121, a2112, a2122, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, a1121, a2121, a1122,
a2122,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
(0, 0, 0, 0, a1211, a1221,a1212, a1222, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, a1221,a2221,a1222, a2222,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0),(0, 0, 0, 0, a2211, a2221, a2212, a2222, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, a1221,
a2221, a1222, a2222, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0,
0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0, a1111, a1121,
a1112,a1122,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, a1111, a2111,a1112, a2112, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0,
0,0,a2111, a2121, a2112, a2122, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, a1111,
a2111, a1112, a2112, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),(0,0,
0, 0, 0, 0, 0, 0, a1211, a1221, a1212, a1222, 0, 0, 0, 0, 0,
0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, a1211,
a2211, a1212, a2212, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0,
0), (0, 0, 0, 0, 0, 0, 0, 0, a2211, a2221, a2212, a2222,
0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, a1211,a2211, a1212, a2212, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, a1111,
a1121, a1112, a1122, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0,0,0, a1121, a2121, a1122, a2122, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0,0,0, 0, 0, 0, 0, 0, 0,
0, 0, a2111, a2121, a2112, a2122, 0, 0, 0, 0, 0, 0,0,0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, a1121, a2121, a1122,
a2122, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, a1211, a1221, a1212,a1222,0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, a1221, a2221, a1222,
a2222,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0,a2211,a2221, a2212, a2222, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, a1221,
a2221, a1222, a2222, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
(a1111, a1121,a1112,a1122, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, a1111, a2111, a1121, a2121, 0, 0, 0,0,0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0),(a2111, a2121, a2112, a2122, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,a1111, a2111, a1121,
a2121, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0,
0, 0, 0, 0, 0), (a1211, a1221, a1212, a1222, 0, 0, 0, 0, 0,
0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, a1211, a2211, a1221,
a2221, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0), (a2211, a2221, a2212,a2222,0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
a1211, a2211, a1221, a2221, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0,0,0, 0, a1111, a1121,
a1112, a1122, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0,0,a1111, a2111, a1121, a2121, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0), (0, 0, 0, 0,
a2111, a2121, a2112, a2122, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, a1111, a2111,
a1121, a2121, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
(0, 0, 0, 0, a1211, a1221, a1212,a1222,0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, a1211, a2211,
a1221, a2221, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0), (0, 0, 0, 0,a2211,a2221, a2212, a2222, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0,0,a1211, a2211, a1221, a2221, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0,0), (0, 0, 0, 0, 0, 0, 0, 0, a1111, a1121,
a1112, a1122, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, a1112,a2112,
a1122, a2122, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0,
a2111, a2121,a2112, a2122, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, a1112, a2112, a1122, a2122, 0, 0, 0, 0,0,0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0,0,0,
0, 0, a1211, a1221, a1212, a1222, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, a1212, a2212, a1222, a2222, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0), (0, 0, 0, 0,
0, 0, 0, 0, a2211, a2221, a2212, a2222, 0, 0, 0, 0, 0,0,0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0,0,a1212, a2212, a1222, a2222, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0), (0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, a1111,a1121,a1112, a1122, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, a1112, a2112, a1122,
a2122, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0), (0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, a2111, a2121, a2112,
a2122, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
a1112,a2112, a1122, a2122, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0),(0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, a1211,
a1221, a1212, a1222, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0,
a1212, a2212, a1222, a2222, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0,0,0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, a2211, a2221,a2212,a2222, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, a1212, a2212, a1222, a2222, 0, 0, 0,0,0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (a1111, a1121, a1112, a1122,
0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,a1111,a1211, a1112,
a1212, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), (a2111,
a2121,a2112, a2122, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0,
a2111, a2211, a2112, a2212, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0,
0), (a1211, a1221, a1212, a1222, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, a1111, a1211, a1112,a1212, 0, 0, 0,
0, 0, 0, 0, 0), (a2211, a2221, a2212, a2222, 0, 0, 0, 0,0,0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,a2111, a2211, a2112, a2212,
0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, a1111,a1121, a1112,
a1122, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, a1121, a1221, a1122, a1222, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0), (0, 0, 0, 0, a2111, a2121,
a2112, a2122, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, a2121, a2221,
a2122, a2222, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0,
a1211, a1221, a1212, a1222, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0,a1121,a1221, a1122, a1222, 0, 0, 0, 0, 0, 0, 0, 0), (0,
0, 0, 0, a2211, a2221,a2212, a2222, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0,
0, 0, 0, 0, 0, a2121, a2221, a2122, a2222, 0, 0, 0, 0, 0, 0,
0, 0),(0,0, 0, 0, 0, 0, 0, 0, a1111, a1121, a1112, a1122, 0,
0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, a1111, a1211,
a1112,a1212, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0, a2111,
a2121, a2112, a2122,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0,0,a2111, a2211, a2112, a2212, 0, 0, 0, 0), (0, 0, 0, 0, 0,
0, 0, 0, a1211,a1221, a1212, a1222, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, a1111, a1211, a1112, a1212), (0,
0,0,0, 0, 0, 0, 0, a2211, a2221, a2212, a2222, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, a2111, a2211,a2112,
a2212), (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, a1111, a1121,
a1112,a1122, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,a1121, a1221, a1122,
a1222, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, a2111,
a2121, a2112, a2122, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, a2121,
a2221, a2122, a2222, 0, 0, 0, 0), (0, 0, 0,0,0, 0, 0, 0, 0,
0, 0, 0, a1211, a1221, a1212, a1222, 0, 0, 0, 0, 0, 0, 0,0,0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, a1121, a1221,a1122,a1222), (0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, a2211, a2221, a2212, a2222,0,0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0,0,a2121, a2221, a2122,
a2222)----------------------NS Jones,
MathematicsN.S.Jones@bristol.ac.ukReply-To:
kuska@informatik.uni-leipzig.de
====
myfunc[a : {__Integer}] /;
And @@ ((# >= 0 && # <= 9) & /@ a) := blubmyfunc[_] :=
Print[incorrect input] Jens> I was wondering if there
is an easy way to do this.> I want to input a list of nine
numbers. I would like to test each element in> the list
prior to acting upon it.> This ends up being a sort of
error check on the list prior to manipulating> it, if it is
wrong, produce an error message or do nothing with the
module.> So, I would like to test each element to be a. an
integer, b. >= 0, c. <= 9.> Is there a way to test this
list at the input prior to acting upon it?>

====
>-----Original Message----->Sent: Friday, November 08,
2002 8:16 AM>To: mathgroup@smc.vnet.net>>I was wondering if
there is an easy way to do this.>>I want to input a list of
nine numbers. I would like to test >each element in>the list
prior to acting upon it.>>This ends up being a sort of error
check on the list prior to >manipulating>it, if it is wrong,
produce an error message or do nothing >with the module.>>So,
I would like to test each element to be a. an integer, b. >>=
0, c. <= 9.>>Is there a way to test this list at the input
prior to acting upon it?>>I don't understand your use of
input, and so this might be of no help. But we have pattern
matching and Condition for checking arguments, e.g.In[9]:=
Remove[f]In[10]:=f[a:{__Integer}] /; And @@ Thread[0 <= a <=
9] := a^2 In[11]:= f[Range[0, 9]]Out[11]= {0, 1, 4, 9, 16,
25, 36, 49, 64, 81}In[12]:= f[{-1, 5}]Out[12]= f[{-1,
5}]In[13]:= f[{9, 10}]Out[13]= f[{9, 10}]In[14]:=
f[3]Out[14]= f[3]In[15]:= f[{3, {3}}]Out[15]= f[{3, {3}}]You
may separate function and testing completely if you like:
In[24]:= Remove[f, test]In[25]:= f[a_] /; test[a] :=
a^2In[26]:= test[a_List /; VectorQ[a, Head[#] == Integer &]]
:= And @@ Thread[0<= a <= 9]Such you may vary the tests
whenever you like.--Hartmut Wolf
====
1. Step by StepYour
demand is a very frequent one; computer algebra does,
however, *not*act like a teacher demonstrating simplification
and final solution ofequations on the blackboard. Hence,
looking over computer algebra's shoulderis of no 
benefit for
the purpose of learning and cannot be done inMATHEMATICA.2.
Nice OutputConvert your input/output to
TraditionalForm:Cell -> Convert To ->
TraditionalForm.Matthias BodeSal. Oppenheim jr. & Cie.
KGaAKoenigsberger Strasse 29D-60487 Frankfurt am
MainGERMANYMobile: +49(0)172 6 74 95 77Internet:
http://www.oppenheim.de-----Ursprí.b9ngliche
Nachricht-----Gesendet: Freitag, 8. November 2002 08:16An:
mathgroup@smc.vnet.netBetreff: problemHow do i get
mathematica 4 to show me step-by-step how it solved my
input?iwant to see the whole process and can't 
find any option
to enable this. the other question is how can i make it show
me the solution but in a morenicer form. i mean, to be
written like i would write it for my homework.example: i
would never write 5^3 but i would write it like 5 and a small
3in the upper right corner of the number 5. i think you all
know what i mean.thanks a lot,Teo
====
I have a module which
allows a user to definea matrix.This matrix may, of course,
have an inverse or not have an inverse.As an
example,In[15]:=c = {{5, 17}, {4, 15}};In[16]:=cinv =
Inverse[c, Modulus -> 26]Out[16]={{17, 5}, {18, 23}}In[17]:=c
= {{5, 5}, {5, 5}};In[18]:=cinv = Inverse[c, Modulus ->
26]Inverse::sing: Matrix !({(({5, 5})),
(({5, 5}))}) issingular.Out[18]=Inverse[{{5, 5},
{5, 5}}, Modulus -> 26]How can I have my module fail in the
case where an inverse does not exist?I want to end the module
and give the user an error message stating to use anew
matrix: this one does not have an inverse modulo 26.How can
we in general take advantage of error messages or error
returnvalues in order to do this?
====
Flip,Here is an example
that you may be able to modify for your own use:It would be
better to use the option Modulus for inserting the modulus
touse - since this is the way that it is done in several
built-in functions.Clear[`*]RIM::usage= RIM[s,r,m],for
positive integers, s, r and non-negative integerm,
constructs an s by s square matrix of integers between -r and
r and teststo see if it is invertible modulo m. If it is not
invertable it announcesthis in a message and invites the user
to try againRIM[n___] :=Module[{s, r, m, thr, mat}, mat /;
Which[ Length[{n}] != 3, Message[RIM::argrx, RIM,
Length[{n}], 3]; False, !MatchQ[{n}, {(i__Integer)?Positive,
_Integer?NonNegative}], Message[RIM::npos]; False, {s, r, m}
= {n}; mat = Table[Random[Integer, {-r, r}], {s}, {s}];
Det[mat, Modulus -> m] == 0, Message[RIM::sing, mat, m];
False, True, True ] ];DEFINE MESSAGESI also use the built-in
message argrx which is described in the Help Browser[ Other
Information]RIM::npos= The first two arguments of RIM must be
positive integers, the last onemust be a non-negative
integer.;RIM::sing= the matrix `1` created by RIM was not
invertible Modulo `2`, please
tryagain.;TESTSRIM[3,5,-2,3] RIM::argrx: RIM called with
4 arguments; 3 arguments are expected.
RIM[3,5,-2,3]RIM[3,5,-2] RIM::npos: The first two arguments of
RIM must be positive integers, thelast  one must be a
non-negative integer. RIM[3,5,-2]RIM[3,5,0]
{{4,-5,1},{0,3,0},{5,-3,2}}RIM[3,5,5]
{{1,-2,4},{4,5,4},{-4,2,1}}RIM[3,5,5] RIM::sing: the matrix
{{-4,-4,-1},{2,5,-1},{-3,-1,2}} created by RIM wasnot 
invertible Modulo 5, please try again.
RIM[3,5,5]--Allan---------------------Allan HayesMathematica
Training and ConsultingLeicester
UKwww.haystack.demon.co.ukhay@haystack.demon.co.ukVoice: +44
(0)116 271 4198>> I have a module which allows a user to
definea matrix.>> This matrix may, of course, have an inverse
or not have an inverse.>> As an example,>> In[15]:=> c = {{5,
17}, {4, 15}};>> In[16]:=> cinv = Inverse[c, Modulus -> 26]>>
Out[16]=> {{17, 5}, {18, 23}}>> In[17]:=> c = {{5, 5}, {5,
5}};>> In[18]:=> cinv = Inverse[c, Modulus -> 26]>>
Inverse::sing: Matrix !({(({5, 5})), (({5,
5}))}) is> singular.>> Out[18]=> Inverse[{{5, 5}, {5,
5}}, Modulus -> 26]>> How can I have my module fail in the
case where an inverse does not exist?> I want to end the
module and give the user an error message stating to usea>
new matrix: this one does not have an inverse modulo 26.>>
How can we in general take advantage of error messages or
error return> values in order to do this?>
====
Adam,You
just need Select with a pure function.data = {{0.39501, 10},
{1.65689, 20}, {2.40239, 30}, {3.27252, 40}, {4.41738,
50}};Select[data, 2.0 <= First[#] < 4 &]{{2.40239, 30},
{3.27252, 40}}David
Parkdjmp@earthlink.nethttp://home.earthlink.net/~djmp/ the
final result would be{{2.40239, 30}, {3.27252, 40}}In reality
the list is several hundred pairs.Adam
====
>-----Original
Message----->Sent: Friday, November 08, 2002 8:14 AM>To:
mathgroup@smc.vnet.net>Seemingly simple gridbox question>I
think you're saying Sequence[] is always an acceptable
replacement for>an argument that otherwise would be missing,
while Null would not always>be acceptable.>>If so, that's
very useful information.>>Bobby>---snipped--Bobby,that's not
quite what I wanted to express: this was not related to
argumentsin general, but to the treatment of options.Almost
ever, options are passed by a BlankNullSequence pattern
variable.(And almost ever there exists a default for
them.)Let's first just look at the passing of 
parameters in
general:In[249]:= Remove[g]In[250]:=g[a_, b_:0, c___] :=
Print[arg 1 = , ToString[a], ; arg 2 = , ToString[b], ;
arglist 3 = , ToString[{c}]]In[251]:= g[1]In[252]:= g[1,
2]In[253]:= g[1, 2, 3]In[254]:= g[1, 2, 3, 4]In[255]:= g[, ,
,]In[256]:= g[1, Sequence[], 3, 4]In[257]:= g[1, 2,
Sequence[]]In[258]:= g[1, 2, Sequence[], 4]What I told,
applies for cases In[257] and In[258] but not for In[256]
whichwould shift a parameter (3) into a wrong slot (2). Of
course you would nevertype such things, but when we
calculate options conditionally (as I did), wehave to deal
with the case that no option results. For that Sequence[]
isan appropriate value, Null normally not. Case In[255] (or
any Null at the place of an option) is not acceptablebecause
it will early or late run into this problem:In[284]:= expr /.
{a -> 1, Null}ReplaceAll::reps: {{a -> 1, Null} is neither
a list of replacement rulesnor a valid dispatch table, and
so cannot be used for replacing.Out[284]=expr /.{a -> 1,
Null}If you program defensively, you always should protect
your options parameterby the function OptionQ:In[278]:=
Remove [f]In[279]:= f[opts___?OptionQ] :=
Print[{opts}]In[280]:= f[a -> 1, b :> 2]In[281]:=
f[]In[282]:= f[{}]In[283]:= f[, a -> 1]Out[283]= f[Null, a ->
1]Furthermore you should adapt your coding to OptionQ, as also
this...In[285]:= f[a -> 1, {{b :> 2, {{{c -> 3}, {}}}}, d ->
4}]{a -> 1, {{b :> 2, {{{c -> 3}, {}}}}, d -> 4}}...passed.
This is done exactly because options may accumulate
throughnested calls, and also {} can now be understood as no
option specified atany place. This may be done e.g. as in
Graphics`Graphics`:ScaledPlot[funcs_List,{x_Symbol,xmin_,xmax
_},opts___?OptionQ] := Module[{scale, ..., ao, ...}, {scale,
ao} = {ScaleFunction, AxesOrigin} /. Flatten[{opts,
Options[ScaledPlot]}]; ... ]i.e. Flatten[{opts}] and combine
with default Options[...] appropriately.But, alas, not all
functions treat their option parameters in such a cleanway;
so the wary programmer moves sequence-objects to option
slots,Sequence[] is the choice for no option
specified.--Hartmut Wolf
====
I would be grateful if you
answered with some concrete arguments onthe fundamental
functional character of the Mathematica language.not very
helpful. This is a technical issue, after all.Orestis Vantzos
> Mathematica allow many programming concepts. > Because it
should be used by as many persons > as possible and all these
persons should pay for> a Mathematica license. > It is not a
good idea for a commercial product to> force the customers to
learn functional/logic> programming if these cutsomers have
10--20> years of programming experience with FORTRAN 77> (as
the most physicist have).> Deep in it's internal structure
Mathematica> is a functional/logic language and a functional>
logic language uses functions, patterns and> transformation
rules *and* it is optimzed> to do this. > If someone like
it, he can use Do[], For[] and> Goto[] as in a FORTRAN
program. This> will not make Mathematica to a
imperativ/procedural> language.> OOP is developed for
simulations and > graphical user interfaces where the
objects> *must* have its own life like a window on screen> or
a car in a traffic simulation.> This concept is very clear
realized in Objective C> or Eiffel.> Every programming
languagage has its own taste> and ßavor. The taste and ßavor
of Mathematica> is functional/logic and if someone can't
exist> without the object oriented ßavor he should> stay away
from Mathematica.> I don't like to to see that my beloved>
programming language is raped by OOP-idiots.> Jens>
> [I know what you're thinking; this guy is nuts!]>
Anyway, Jens keeps attacking the whole OOP-Mathematica idea
based on> the single premise that ÔThis is a Functional
Language'. He even does> it in a rather abrupt manner,
which I do not appreciate.> Well guess what;
Mathematica is NOT a functional language. It can> definitely
be used like one.But...> a) Wolfram in the Mathematica
Book seems to suggest that Mathematica> is primarily a
rules-based language...in A new kind of Science this>
assumption is even stronger.> b) Symbols and rules are
the fundamentals of Mathematica.> Symbols have UpValues and
DownValues (and OwnValues,etc. but let's> keep it simple).>
> It is true that an evaluation of the expression
s_Symbol[args___] can> be thought of as Ôthe function s is
applied to the subexpression> Sequence[args]'.> This
is ONLY a metaphor!!!> What really happens is that the
symbol s is called upon to apply its> transformation rules
stored under DownValues on the expression. This> is the
ONLY objective description of the process. Everything else
is> an assumption on part of the programmer.>
Moreover, UpValues completely throw the functional metaphor
out the> window:> in this case s_Symbol[x_Symbol,rest___]
is transformed not according> to the Ôfunction' 
s but
according to the UpValues of Ôargument' x !!> So 
Jens,
LISP is a functional language, since its fundamental>
structures are function-based. Mathematica is just a darn
good> simulation of a functional language. So good, that we
have learned to> ignore that it is only a facade.>
People like me are trying to build a different interpretation
of what> all these symbols and rules are doing (or can be
persuaded to do)> inside Mathematica. You look at symbols
and see functions; I look and see> objects. An OOP package
will only be a Ôsimulation', since Mathematica> 
is not
inherently OO, but I repeat that all the talk about
functional> programming in Mathematica is no better in any
way.> Rules and symbols are real; the rest is a
mindgame.> Orestis Vantzos
====
I'm trying to solve a
system of nonlinear algebraic equations.I was hoping to use
the FindRoot. However, someof the variables for which I'm
solving must satisfy someinequalities. Is there an easy way
to impose these constraintsin the
solution?George(KthielK@us.ibm.com)
====
George,You might find
the new, in Mathematica 4.2, standard
packageNumericalMath`NMinimize useful: <<
NumericalMath`NMinimize` conds = {(Sin[x] - 3/4)^2, 2*Pi < x
< 3*Pi}; NMinimize[conds, {x}] NMinimize::strong:Strong
inequality has been changed to a weakinequality.
{1.232595164407831*^-32, {x -> 7.131247386161068}}Check that
the conditions are satisfied conds /. %[[2]]
{1.232595164407831*^-32,
True}--Allan---------------------Allan HayesMathematica
Training and ConsultingLeicester
UKwww.haystack.demon.co.ukhay@haystack.demon.co.ukVoice: +44
(0)116 271 4198> I'm trying to solve a system of nonlinear
algebraic equations.> I was hoping to use the FindRoot.
However, some> of the variables for which I'm solving must
satisfy some> inequalities. Is there an easy way to impose
these constraints> in the solution?>> George>
(KthielK@us.ibm.com)>In-reply-To:
<200211080716.CAA07416@smc.vnet.net>
====
KS> How do I go about
plotting equations of the form:KS> 1. |z-2i| = 6Plot[Abs[z -
2I] - 6, {z, -3, 3}]By the way, enjoy with a remarkable shape
of Plot[Abs[z - 2I] - 6, {z, -100, 100}]Can you explain it?KS>
2. (2z-Conjugate(z))^2 = -6(z + Conjugate(z)Plot[(2z -
Conjugate[z])^2 + 6(z + Conjugate[z]), {z, -3, 3}]Plot[(2z -
Conjugate[z])^2 + 6(z + Conjugate[z]), {z, -30, 30}]Plot[(2z
- Conjugate[z])^2 + 6(z + Conjugate[z]), {z, -300, 300}]KS>
In addition, how can you solve the following in terms of
exponentials?KS> z^6 = 6 + 3iDo you mean
this?Rationalize[N[Abs[6 + 3 I]Exp[I Arg[6 + 3 I]]]]6 + 3
ISolve[z^6 == Abs[6 + 3 I]Exp[I Arg[6 + 3 I]], z]{{z ->
-(3^(1/6)*5^(1/12)*E^((I/6)*ArcTan[1/2]))},{{z -> {z ->
3^(1/6)*5^(1/12)*E^((I/6)*ArcTan[1/2])},{z ->
-((-1)^(1/3)*3^(1/6)*5^(1/12)*E^((I/6)*ArcTan[1/2]))},{z ->
{z -> (-1)^(1/3)*3^(1/6)*5^(1/12)*E^((I/6)*ArcTan[1/2])},{z
-> -((-1)^(2/3)*3^(1/6)*5^(1/12)*E^((I/6)*ArcTan[1/2]))},{z
-> {z ->
(-1)^(2/3)*3^(1/6)*5^(1/12)*E^((I/6)*ArcTan[1/2])}}Or
something else?Best wishes,Vladimir BondarenkoWeb :
http://www.CAS-testing.org/ (under development, 95% ready)
http://maple.bug-list.org/ (under development, 20%
ready)
====
1)In[1]:=<< Algebra`ReIm`In[2]:=x /: Im[x] = 0; y
/: Im[y] = 0; z = x + I*y;In[7]:=<<
Graphics`ImplicitPlot`In[11]:=ImplicitPlot[ComplexExpand[
Abs[z - 2*I], TargetFunctions -> {Re, Im}] == 6, {x, -7,
7}];2)Could be done in the same way, but is not
interesting.In fact,In[16]:=ComplexExpand[(2*z -
Conjugate[z])^2, TargetFunctions -> {Re, Im}]Out[16]=x^2 +
6*I*x*y - 9*y^2In[17]:=ComplexExpand[-6*(z + Conjugate[z]),
TargetFunctions -> {Re, Im}]Out[17]=-12*xSo x*y = 0 and
x^2-9y^2=12*x. The only point is (0;0) !3)The best is to do
it by hand :Table[Print[solution , i,  : z = , Abs[6 +
3*I]^(1/6), Simplify[ E^((Arg[6 + 3*I]/6)*I + i*2*(Pi/6))]],
{i, 0, 5}];Meilleures salutationsFlorian Jaccard-----Message
d'origine-----Envoy.8e : ven., 8. novembre 2002 
08:16è :
mathgroup@smc.vnet.netObjet : Complex Numbers: Plotting
EquationsHow do I go about plotting equations of the form:1.
|z-2i| = 62. (2z-Conjugate(z))^2 = -6(z + Conjugate(z)In
addition, how can you solve the following in terms of
exponentials?z^6 = 6 + 3iKev
====
I would like to have a latex
output for function SixJSymbolwhich in standard physics
notation should look like thisSixJSymbol[{a,b,c}, {d,e,f}]
->{ a b c }{ }{ d e f }Notice curly brackets (should be
single big { and } ).To be more accurate, here is the piece
of latex codeleft{begin{array}[c]{ccc} a & b & c  d
& e & f end{array}right}I am trying to do the following
Format[SixJSymbol[{j1_, j2_, j3_}, {l1_, l2_, l3_}], TeXForm]
:= SequenceForm[left{ begin{array}[c]{ccc}, j1,
 & , j2,  & , j3,   , l1,  & , l2,  & , l3,
end{array} right}]The problem with this
implementation: I get & (instead of simply &) in the latex
output.Is there any way to protect & or any other solution to
the problem?I am using mmka 4.1AndreiReply-To:
kuska@informatik.uni-leipzig.de
====
SixJSymbol[{j, 2, 3}, {i,
l, m}] // TraditionalForm // TeXFormdoes already what you
want. Jens> I would like to have a latex output for
function SixJSymbol> which in standard physics notation
should look like this> SixJSymbol[{a,b,c}, {d,e,f}] ->> { a b
c }> { }> { d e f }> Notice curly brackets (should be single
big { and } ).> To be more accurate, here is the piece of
latex code> left{> begin{array}[c]{ccc}> a & b & c
> d & e & f> end{array}> right}> I am trying to
do the following> Format[SixJSymbol[{j1_, j2_, j3_}, {l1_,
l2_, l3_}], TeXForm] :=> SequenceForm[left{
begin{array}[c]{ccc},> j1,  & , j2,  & , j3, 
 ,> l1,  & , l2,  & , l3,> end{array}
right}> ]> The problem with this implementation:>
I get & (instead of simply &) in the latex output.> Is
there any way to protect & or any other solution to the
problem?> I am using mmka 4.1> Andrei
====
Doris,The
problem is not at your end, it is at his end. I suspect that
he is still using OS 9, where this was a constant
aggravation. Notebooks arriving as attachments are not
recognized. (The same file inserted on a windows formatted
ßoppy will be recognized.) I wound up writing an applescript
to change the creator ßag on such files but discarded it 
when
I moved to OS 10--where it is easy to set the OS to recognize
the .nb extension.Begin forwarded message:> To:
mathgroup@smc.vnet.net> computers> I have the following
problem:>> I created notebooks with Mathematica 4 on a
Windows PC. I stored it> attachment to a Professor of mine.
He is using a Macintosh> (Mathematica 4 / 4.1). When he saves
the attachment on his hard disk> (as Name.nb) Mathematica
doesn«t recognize this file and 
doesn«t open> it. Changing
the name of the stored file to Name.txt and then again to>
Name.nb solves this problem, the notebook can be opened.>>
How do I have to save the notebook or send the attachment
that the> notebook can be opened at once without renaming the
extension?> I appreciate any help!> TIA>> Doris S.>>Garry
HelzerDepartment of MathematicsUniversity of Maryland1303
Math BldgCollege Park, MD 20742-4015
====
> Aaaargh.> What
is with Mathematica (4.2 here) and infinite sums?! (The>
following has annoyed me for years. I'm finally 
indignant
enough to> pose this query.)> A nominally infinite sum for
which only a finite number of terms> contribute FAILS to
evaluate for an uppper index limit of Infinity,> but evaluates
PROPERLY for an (arbitrary) finite upper index limit.>
Example:> cn = If[n == 0, 1, 0] - 1/2 If[n == 1, 1, 0];>
Sum[x^(n-1) cn,{n,0,Infinity}]> gives> If[n == 0, 1, 0] -
1/2 If[n == 1, 1, 0]/((1 - x) x)> while> Sum[x^(n-1)
cn,{n,0,731}]> gives> -1/2 + 1/x> (which is, of course,
what I want). I've Google-searched to no avail,> nested
Evaluate every which way, but only a finite upper limit works>
properly--inconvenient for formal results.> Can anybody
explain what's going on, or how to coerce Mathematica into
not> choking on an infinite number of non-contributing
terms?> David M. Wood, Department of Physics, Colorado
School of Mines,>
http://www.mines.edu/Academic/physics/people/pages/wood.html>
> --> David M. Wood, Dept. of Physics, Colorado School of
Mines, Golden, CO 80401You get the desired result for
concrete upper bounds because the sum isevaluated
procedurally, that is, it is explicitly summed. I
shouldmention that this is a bit of a design controversy in
that proceduraland functional summation are not separated.You
do not get a sum using a symbolic or infinite upper bound
becausethe symbolic summation code is not able to handle If.
You can get whatyou want if you rewrite your function in
terms of, say, KroneckerDelta.For example:In[1]:= cn[r_] :=
KroneckerDelta[r] + KroneckerDelta[r-1]/2In[2]:=
InputForm[Sum[x^(n-1) cn[n],{n,0,Infinity}]]Out[2]//InputForm=
1/2 + x^(-1)In[3]:=
InputForm[Sum[x^(n-1)*cn[n],{n,0,t}]]Out[3]//InputForm=
UnitStep[-1 + t]/2 + UnitStep[t]/xDaniel LichtblauWolfram
Research
====
Here is one way that works:In[3]:=cn =
KroneckerDelta[n, 0] - (1/2)*KroneckerDelta[n,
1];Sum[Evaluate[x^(n - 1)*cn], {n, 0, Infinity}]Out[4]=-(1/2)
+ 1/xHowever, I really do think you ought to use;In[5]:=c[n_]
:= KroneckerDelta[n, 0] - (1/2)*KroneckerDelta[n,
1]In[6]:=Sum[x^(n - 1)*c[n], {n, 0, Infinity}]Out[6]=-(1/2) +
1/xNote that this way you do not even need Evaluate.And, by
the way, the reason why your approach does not work is simply
that Mathematica does not expect having to deal with an
If[...] in an infinite sum. After all, in the case of 
infinite
sums (unlike in the finite one) no actual summation takes
place: Mathematica has to work out the answer by means of
various transofrmation and the rules it knows about. In the
finite case it just counts ...Andrzej KozlowskiYokohama,
Japanhttp://www.mimuw.edu.pl/~akoz/http://
platon.c.u-tokyo.ac.jp/andrzej/> Aaaargh.>> What is with
Mathematica (4.2 here) and infinite sums?! (The> following has
annoyed me for years. I'm finally indignant 
enough to> pose
this query.)>> A nominally infinite sum for which only a 
finite
number of terms> contribute FAILS to evaluate for an uppper
index limit of Infinity,> but evaluates PROPERLY for an
(arbitrary) finite upper index limit.>> Example:>> cn = If[n
== 0, 1, 0] - 1/2 If[n == 1, 1, 0];> Sum[x^(n-1)
cn,{n,0,Infinity}]>> gives>> If[n == 0, 1, 0] - 1/2 If[n == 1,
1, 0]/((1 - x) x)>> while>> Sum[x^(n-1) cn,{n,0,731}]>>
gives>> -1/2 + 1/x>> (which is, of course, what I want). 
I've
Google-searched to no avail,> nested Evaluate every which way,
but only a finite upper limit works> properly--inconvenient 
for
formal results.>> Can anybody explain what's going on, or 
how
to coerce Mathematica into > not> choking on an infinite
number of non-contributing terms?> David M. Wood,
Department of Physics, Colorado School of Mines,>
http://www.mines.edu/Academic/physics/people/pages/wood.html>
> -- > David M. Wood, Dept. of Physics, Colorado School of
Mines, Golden, CO > 80401>
====
> A nominally infinite sum for
which only a finite number of terms> contribute FAILS to
evaluate for an uppper index limit of Infinity,> but evaluates
PROPERLY for an (arbitrary) finite upper index limit.>
Example:> cn = If[n == 0, 1, 0] - 1/2 If[n == 1, 1, 0];>
Sum[x^(n-1) cn,{n,0,Infinity}]> gives> If[n == 0, 1, 0] - 1/2
If[n == 1, 1, 0]/((1 - x) x)> while> Sum[x^(n-1)
cn,{n,0,731}]> gives> -1/2 + 1/xBoth Andrzej Kozlowski and
Daniel Lichtblau were kind enough to respond but maps my
original query into a new one:How can I persuade Mathematica
to convert its conditionals (which weregenerated by RSolve
from a set of recursion relations) into KronckerDeltaswithout
carefuly human intervention?-- David M. Wood, Dept. of
Physics, Colorado School of Mines, Golden, CO 80401Reply-To:
kuska@informatik.uni-leipzig.de
====
in a finite sum the index is
replaced by the numericalvalue and all results of the
evaluation of the sum-argumentwith arg /. n->i are added.In a
infinite sum the index is handled symbolical andso Sum[] can
not find out that some of your If[] testswould give True
because mathematica can't insert a 
infinitenumber of n's in a
finite time to find all cases where a 
If[Mod[n,2]==0,__] would
give True. Jens> Aaaargh.> What is with Mathematica (4.2
here) and infinite sums?! (The> following has annoyed me for
years. I'm finally indignant enough to> pose 
this query.)> A
nominally infinite sum for which only a finite 
number of terms>
contribute FAILS to evaluate for an uppper index limit of
Infinity,> but evaluates PROPERLY for an (arbitrary) 
finite
upper index limit.> Example:> cn = If[n == 0, 1, 0] - 1/2
If[n == 1, 1, 0];> Sum[x^(n-1) cn,{n,0,Infinity}]> gives>
If[n == 0, 1, 0] - 1/2 If[n == 1, 1, 0]/((1 - x) x)> while>
> Sum[x^(n-1) cn,{n,0,731}]> gives> -1/2 + 1/x> (which
is, of course, what I want). I've Google-searched to no
avail,> nested Evaluate every which way, but only a finite
upper limit works> properly--inconvenient for formal
results.> Can anybody explain what's going on, or how to
coerce Mathematica into not> choking on an infinite number of
non-contributing terms?> David M. Wood, Department of
Physics, Colorado School of Mines,>
http://www.mines.edu/Academic/physics/people/pages/wood.html>
> --> David M. Wood, Dept. of Physics, Colorado School of
Mines, Golden, CO 80401
====
Teo,One of the features of
Mathematica is that it does a lot of elementaryevaluation and
doesn't show you the steps. In some cases it uses
internalmethods and you wouldn't even what to see the
steps.Still, it is possible to do calculations in a more
controlled manner. Thereare a couple of notebooks and a
package at my web site that may help you.The
StepByStepEquations notebook shows how to solve equations
step by stepusing pure functions and map. The
ExpressionManipulation package and theaccompanying
EvaluationTutorial notebook has routines for
evaluatingexpressions in a controlled manner. There are many
examples from addition offractions to integration by
parts.David
Parkdjmp@earthlink.nethttp://home.earthlink.net/~djmp/
====

Daniel,There are a number of ways.1) Use
ImplicitPlotNeeds[Graphics`ImplicitPlot`]ImplicitPlot[x^2 +
(y - 1)^2 == 1, {x, -1, 1}];2) Parametrize the circle and use
ParametricPlotcirclecurve[center : {_, _}][t_] := {Cos[t],
Sin[t]} + centerParametricPlot[Evaluate[circlecurve[{0,
1}][t]], {t, 0, 2Pi}, AspectRatio -> Automatic];3) Use the
Circle graphics primitiveShow[Graphics[{Circle[{0, 1}, 1]}],
Axes -> True, AspectRatio -> Automatic];David
Parkdjmp@earthlink.nethttp://home.earthlink.net/~djmp/
Sender: steve@smc.vnet.netApproved: Steven M. Christensen
<steve@smc.vnet.net>, Moderator
====
This is an elementary
problem. You'd do well to get acquainted with the verybasics
of Mathematica, which requires little more than a couple of
weeksreading The Book or some textbook on the subject.
Anyway, I propose thefirst three approaches which come to my
mind, to deal with a list of 10,000pairs. In[1]:=data =
Transpose[{Table[Random[Real, {0, 5}], {10000}],
Range[10000]}];In[2]:=Timing[Select[data, 2<= #[[1]]< 4 & ];
]Out[2]={0.047Second,Null}In[3]:=Timing[Cases[data, {x_, y_}
/; 2<= x< 4]; ]Out[3]={0.062
Second,Null}In[4]:=Timing[data[[Flatten[Position[Transpose[
data][[1]], x_ /; 2<= x< 4]]]]; ]Out[4]={0.063
Second,Null}Tomas GarzaMexico City----- Original Message
-----> {{0.39501, 10}, {1.65689, 20}, {2.40239, 30},
{3.27252, 40}, {4.41738,> 50}}>> I want to select only the
pairs for which the first element of each> pair is greater
than or equal to 2.0 and less than 4.0 In this case> the final
result would be>> {{2.40239, 30}, {3.27252, 40}}>> In reality
the list is several hundred pairs.> Adam>>
====
Use
this:Cases[data, {_?(# >= 2 && # <= 4 &), _}]Steve Luttrell>
I know that this has been covered before, but I could not find
it.>> I have a list of data and I want to select a subset
based on a> condition.>> A simple example:>> data =>
{{0.39501, 10}, {1.65689, 20}, {2.40239, 30}, {3.27252, 40},
{4.41738,> 50}}>> I want to select only the pairs for which
the first element of each> pair is greater than or equal to
2.0 and less than 4.0 In this case> the final result would
be>> {{2.40239, 30}, {3.27252, 40}}>> In reality the list is
several hundred pairs.> Adam>Reply-To:
kuska@informatik.uni-leipzig.de
====
Select[data, First[#] >= 2
&& First[#] <= 4 &] Jens> I know that this has been covered
before, but I could not find it.> I have a list of data and
I want to select a subset based on a> condition.> A simple
example:> data => {{0.39501, 10}, {1.65689, 20}, {2.40239,
30}, {3.27252, 40}, {4.41738,> 50}}> I want to select only
the pairs for which the first element of each> pair is greater
than or equal to 2.0 and less than 4.0 In this case> the final
result would be> {{2.40239, 30}, {3.27252, 40}}> In
reality the list is several hundred pairs.> Adam
====
Try
these:In[1]:=data={1,3.23,-12,9.5,8.9,2,5,8,-4};In[2]:=If[
Union[IntegerQ /@ data] != {True},
Print[ouch!]]ouch!In[3]:=If[Union[(#1 >= 0 & ) /@ data] !=
{True}, Print[ouch!]]ouch!In[4]:=If[Union[(#1 <= 9 & ) /@
data] != {True}, Print[ouch!]]ouch!Tomas GarzaMexico
City----- Original Message -----> This ends up being a sort
of error check on the list prior to manipulating> it, if it
is wrong, produce an error message or do nothing with
themodule.>> So, I would like to test each element to be a.
an integer, b. >= 0, c. <=9.>> Is there a way to test this
list at the input prior to acting upon
it?>
====
Flip,Something like this.ßiptest = Head[#] ===
Integer && 0 <= # <= 9 &;list1 = {1.0, 3, 7, 14, 2.5};list2 =
{2, 7, 3, 6, 5};ßiptest /@ list1And @@ %{False, True, True,
False, False}FalseAnd @@ ßiptest /@ list2TrueDavid
Parkdjmp@earthlink.nethttp://home.earthlink.net/~djmp/
====
Try
this:In[1]:=<<Graphics`ImplicitPlot`In[2]:=ImplicitPlot[x^2 +
(y-1)^2 == 1,{x,-2,2},{y,-2,2}];Tomas GarzaMexico City-----
Original Message ----- > Dan> 
====
Dan,To obtain the graph
you have several alternatives. Two of them are:1) Use
parametric equations and the Mathematica function
ParametricPlot:ParametricPlot[{Cos[t], Sin[t]}, {t, 0, 2*Pi},
AspectRatio -> Automatic];2) Load the standard add-on package
Graphics`ImplicitPlot ` and use thefunction
ImplicitPlot:<<Graphics`ImplicitPlot`ImplicitPlot[x^2 + y^2
== 1, {x, -1, 1}];German Buitrago----- Original Message
-----> Dan>>Reply-To:
kuska@informatik.uni-leipzig.de
====
Needs[Graphics`
ImplicitPlot`]ImplicitPlot[x^2 + (y - 1)^2 == 1, {x, -2, 2}]
Jens> I want to plot the function x^2 + (y-1)^2 == 1>
How do I do this.> DanIn-reply-To:
<200211080715.CAA07383@smc.vnet.net>
====
DS> I want to plot
the function x^2 + (y-1)^2 == 1DS> How do I do this.<<
Graphics`ImplicitPlot`ImplicitPlot[x^2 + (y - 1)^2 == 1, {x,
-1, 1}]Reading Help might add your life by way of ornament
;-)Why don't come and try, at the cursor at 
Ôplot', hitting
F1?The total Bible's sweep considered, the biggest thrill
available,enjoy :)Best wishes,Vladimir BondarenkoMathematical
and Production DirectorSymbolic Testing GroupWeb :
http://www.CAS-testing.org/ (under development, 95% ready)
http://maple.bug-list.org/ (under development, 20% ready)Mail
: 76 Zalesskaya Str, Simferopol, Crimea,
Ukraine
====
In[1]:=<<Graphics`ImplicitPlot`In[5]:=ImplicitPlot
[x^2+(y-1)^2==1,{x,-1,1},AxesLabel->{x,y}];Meilleures
salutationsFlorian Jaccard-----Message
d'origine-----Envoy.8e : ven., 8. novembre 2002 
08:16è :
mathgroup@smc.vnet.netObjet : Plotting a circle...I want to
plot the function x^2 + (y-1)^2 == 1How do I do
this.Dan
====
Teo,Steps:We would have to set up some code to go
through the kind of steps that wewould use steps and show them
because the methods that Mathematica uses willoften not be
the ones a person would use.FormatOutput:You can get the
output to look like traditional math by selecting the
outputcell and using the menu item Cell>Convert To >
Traditional Form.(or you can make all output appear in this
form by using Cell>Default OutputFormat Type>Traditional
FormInput:You can convert your input into traditional math
form by selecting the celland and using the menu item
Cell>Convert To > Traditional Form.Or you might like to learn
to type such forms in directly or by usingpalettes. Help may
be found at Help>Help Browser>Other Information >2DExpression
Input--Allan---------------------Allan HayesMathematica
Training and ConsultingLeicester
UKwww.haystack.demon.co.ukhay@haystack.demon.co.ukVoice: +44
(0)116 271 4198> How do i get mathematica 4 to show me
step-by-step how it solved myinput?i> want to see the whole
process and can't find any option to enable 
this.> the other
question is how can i make it show me the solution but in
amore> nicer form. i mean, to be written like i would write
it for my homework.> example: i would never write 5^3 but i
would write it like 5 and a small 3> in the upper right
corner of the number 5. i think you all know what imean.>
thanks a lot,> Teo>
====
Teo,For built-in functions, you are
out of luck. If you program an algorithmand use that in
mathematica, then do Trace[fcn[inputs],_=_], and you willsee
most of what is going on. For your last question, set the
defaultoutput to TraditionalForm.Matt Herman> How do i get
mathematica 4 to show me step-by-step how it solved my
input?i> want to see the whole process and can't 
find any
option to enable this.> the other question is how can i make
it show me the solution but in a more> nicer form. i mean,
to be written like i would write it for my homework.>
example: i would never write 5^3 but i would write it like 5
and a small 3> in the upper right corner of the number 5. i
think you all know what i mean.> thanks a lot,>
Teo>>In-reply-To:
<200211080716.CAA07443@smc.vnet.net>
====
T> How do i get
mathematica 4 to show me step-by-step how it solved my
input?iT> want to see the whole process and can't 
find any
option to enable this.What you are asking for is an age-long
dream of many lazy-bonesincluding me and you ;-)Actually, the
algorithms and heuristics behind the scene of
symboliccomputations yield human unreadable intermediate data
roughly equivalentthe omnibus edition of Balzac... or even far
much bulkier! There is evena special tech term, intermediate
expression swell, to denote this biggestproblem in Computer
Algebra.Usually, even for many seemingly innocuous inputs
there should be doneformidable, massive, large scale
calculations... which are hidden so notto confuse us the
users.To see the whole process? The pot of gold at the end of
the rainbow?Sure not. However, to produce such the expert
system you want wouldrequire a quite sizable investment...
That will run to a pretty penny,and up to now, AFAIK, the
entrepreneurs seems to be reluctant enoughto tread this
thorny path...However, not all is so pitch-dark!Below comes a
quotation from the Calculus Derivative and Integral siteat
http://www.calc101.com/ Day or night, from anywhere, you can
get calculus problems solved in seconds, automatically. You
get all the steps including the final answer. Each step is
explained in plain English, just like the examples in your
textbook. You see it all in standard math notation, just like
your teacher at the blackboard.But I am prepared to admit I
find it difficult to name the second URLof that 
ilk 8-(T> the
other question is how can i make it show me the solution but
in a moreT> nicer form. i mean, to be written like i would
write it for my homework.T> example: i would never write 5^3
but i would write it like 5 and a small 3T> in the upper
right corner of the number 5. i think you all know what i
mean.Use TraditionalForm.{5^3, D[f[z], z], Integrate[f[z],
z]} // TraditionalFormBest wishes,Vladimir BondarenkoWeb :
http://www.CAS-testing.org/ (under development, 95% ready)
http://maple.bug-list.org/ (under development, 20%
ready)
====
I am looking for Mathematica code computing
representation of _large_ suitableintegers as sums of three
squares. I would like to try the approach of EmilGrosswald
in chapter 4 of his book `Representation of integers as sums
ofsquares', Û1 to 7.
====
>> I am looking for Mathematica code
computing representation of _large_ > suitable> integers as
sums of three squares. I would like to try the approach > of
Emil> Grosswald in chapter 4 of his book `Representation of
integers as sums > of> squares', ¤1 to 7.>>How 
large? If
not too large the following will
do:In[1]:=<<NumberTheory`NumberTheoryFunctions`In[2]:=
SumOfSquaresRepresentations[3,10^6+1]//TimingOut[2]={19.35
Second,{{0,1,1000},{0,199,980},{1,280,960},{1,352,936},{
1,600,800},{
2,194,981},{2,454,891},{7,444,896},{8,44,999},{8,
89,996},{12,401,916},{12,544,839},{14,357,934},{
14,533,846},{20,40,999},{20,660,751},{21,286,958},{21,
346,938},{22,299,954},{22,614,789},{27,106,994},{28,476,879},
{30,485,874},{36,121,992},{36,692,721},{40,600,799},{
42,101,994},{43,446,894},{4
4,327,944},{44,559,828},{44,593,804},{46,154,987},{
46,469,882},{47,76,996},{
52,441,896},{54,181,982},{54,677,734},{56,104,993},{
56,679,732},{57,464,884},{58,219,974},{62,251,966},{
64,377,924},{64,513,856},{68,524,849},{71,224,972},{
71,404,912},{72,601,796},{75,370,926},{76,324,943},{
76,560,825},{78,226,971},{78,506,859},{82,334,939},{
82,426,901},{84,196,977},{84,664,743},{85,210,974},{
89,604,792},{90,299,950},{91,242,966},{91,386,918},{
96,121,988},{96,236,967},{96,496,863},{96,632,769},{
98,309,946},{100,624,775},{101,238,966},{101,630,770},{103,
456,884},{104,551,828},{106,618,779},{107,306,
946},{107,474,874},{111,404,908},{111,484,868},{112,444,889},
{ 117,194,974},{118,154,981},{118,539,834},{120,124,985},{
121,516,848},{121,624,772},{124,391,912},{124,495,860},{
124,687,716},{126,230,965},{126,395,910},{126,491,862},{
126,634,763},{127,656,744},{128,636,761},{132,551,824},{
133,666,734},{134,198,971},{134,334,933},{134,546,827},{
134,658,741},{138,554,821},{139,218,966},{139,642,754},{
140,615,776},{142,474,869},{145,460,876},{146,149,978},{
146,693,706},{149,414,898},{149,470,870},{150,574,805},{
154,629,762},{154,683,714},{155,670,726},{160,455,876},{
161,288,944},{161,336,928},{162,341,926},{167,344,924},{
175,340,924},{181,546,818},{190,390,901},{194,587,786},{
194,678,709},{196,519,832},{197,226,954},{197,586,786},{
198,386,901},{199,588,784},{202,534,821},{202,686,699},{
203,294,934},{204,224,953},{204,628,751},{212,281,936},{
212,484,849},{216,359,908},{216,511,832},{217,504,836},{
218,266,939},{
219,538,814},{222,526,821},{223,384,896},{224,640,735},{
225,520,824},{226,645,730},{229,366,902},{229,502,834},{
230,426,875},{231,328,916},{231,536,812},{232,644,729},{
236,657,
716},{240,376,895},{245,274,930},{246,299,922},{246,314,
917},{250,670,699},{251,282,926},{251,330,910},{251,530,
810},{257,576,776},{260,460,849},{260,576,775},{261,286,
922},{261,566,782},{266,389,882},{267,406,874},{268,401,
876},{272,351,896},{273,476,836},{274,362,891},{274,597,
754},{278,629,726},{281,364,888},{281,392,876},{281,492,
824},{286,558,779},{286,581,762},{288,356,889},{292,601,
744},{293,666,686},{294,398,869},{299,498,814},{299,590,
750},{299,642,706},{302,331,894},{303,356,884},{303,524,
796},{306,482,821},{308,364,879},{309,646,698},{313,624,
716},{314,586,747},{315,370,874},{315,526,790},{320,351,
880},{324,337,884},{324,505,800},{328,504,799},{331,418,
846},{331,426,842},{331,534,778},{334,629,702},{334,666,667},
{336,428,
839},{341,426,838},{344,639,688},{345,376,860},{346,546,
763},{351,512,784},{357,634,686},{358,366,859},{359,372,
856},{363,574,734},{373,646,666},{376,481,792},{376,572,
729},{380,540,751},{384,583,
716},{385,624,680},{386,478,789},{386,602,699},{389,546,742},
{391,448, 804},{392,456,799},{401,540,740},{404,456,793},{
404,604,687},{406,539,738},{408,481,776},{412,516,751},{
414,629,658},{420,601,680},{426,475,770},{426,562,709},{
432,484,761},{438,581,686},{441,496,748},{443,526,726},{
444,532,721},{444,623,644},{446,502,741},{448,456,769},{
453,506,734},{454,533,714},{455,524,720},{464,576,673},{
469,566,678},{474,610,635},{476,505,720},{484,552,679},{
491,614,618},{511,536,672},{513,544,664},{519,548,656},{
532,559,636},{545,560,624},{551,580,600},{554,574,603}}}This
is on a 400 mghz PowerBook G4.Andrzej KozlowskiYokohama,
Japanhttp://www.mimuw.edu.pl/~akoz/http://
platon.c.u-tokyo.ac.jp/andrzej/
====
On Sun, 10 Nov 2002
10:38:31 +0000 (UTC), Andrzej Kozlowski|>
SumOfSquaresRepresentationsSorry, ways off what I need. I
already have faster routines for such toyexamples. Perhaps
should I have written `really large' instead of
`_large_'.
====
You may be able to, but it will require some
though and a trial an error, for there is no built in option
or anything like that to do this. But the basic idea is
simple. L t me illustrate it on a toy problem. Suppose I want
to find the solutions of Sin[x]==3/4 lying somewhere between
2Pi and 3Pi. Of course the obvious way would be to use
FindRoot with a starting value 2Pi, but I want to start at 0.
I simply define a suitable function as follows:In[1]:=g[x_] :=
(Sin[x] - 3/4)^2 + If[2*Pi < x < 3*Pi, 0, 1]and then use
FindRoot in the usual way:In[2]:=FindRoot[Evaluate[g[x] ==
0], {x, 0}, WorkingPrecision -> 50, MaxIterations ->
100]Out[2]={x ->
7.1312473861610674849663965707576817827292718868836790
013303355880347`50}There are of course lots of different
variants of this approach and some will work better than
others. In some cases it may be better to use only smooth
functions (created by means of Interpolation) but usually
its not needed.Andrzej KozlowskiToyama International
UniversityJAPANhttp://sigma.tuins.ac.jp/~andrzej/> I'm 
trying
to solve a system of nonlinear algebraic equations.> I was
hoping to use the FindRoot. However, some> of the variables
for which I'm solving must satisfy some> inequalities. Is
there an easy way to impose these constraints> in the
solution?>> George> (KthielK@us.ibm.com)>
====
One
possibility:inv[M_, p_] := Block[{$Messages = {}},
Check[Inverse[M, Modulus -> p], Your matrix has no inverse
modulo  <> ToString[p] <> . Use another one.]]In[2]:=a =
{{5, 17}, {4, 15}};In[3]:=b= {{5, 5}, {5, 5}};In[4]:=inv[a,
26]Out[4]={{17,5},{18,23}}In[5]:=inv[b,26]Out[5]=Your matrix
has no inverse modulo 26. Use another one.Andrzej
KozlowskiYokohama,
Japanhttp://www.mimuw.edu.pl/~akoz/http://
platon.c.u-tokyo.ac.jp/andrzej/>> I have a module which
allows a user to definea matrix.>> This matrix may, of course,
have an inverse or not have an inverse.>> As an example,>>
In[15]:=> c = {{5, 17}, {4, 15}};>> In[16]:=> cinv =
Inverse[c, Modulus -> 26]>> Out[16]=> {{17, 5}, {18, 23}}>>
In[17]:=> c = {{5, 5}, {5, 5}};>> In[18]:=> cinv = Inverse[c,
Modulus -> 26]>> Inverse::sing: Matrix !({(({5,
5})), (({5, 5}))}) is> singular.>> Out[18]=>
Inverse[{{5, 5}, {5, 5}}, Modulus -> 26]>> How can I have my
module fail in the case where an inverse does not > exist?> I
want to end the module and give the user an error message
stating to > use a> new matrix: this one does not have an
inverse modulo 26.>> How can we in general take advantage of
error messages or error return> values in order to do
this?>
====
>One possibility:>>inv[M_, p_] :=
Block[{$Messages = {}}, Check[Inverse[M, Modulus -> p],
>Your> matrix has no inverse modulo  <> ToString[p] <> .
Use another >one.]]Hmmm...This Check function does not
halt the computation...In[]:=Check[ Inverse[{{5, 5}, {5,
5}}, Modulus -> 26]; Print[123], $Failed]-->Inverse::modp:
Value of option Modulus -> 26 should be a prime
number.123Out[]=$FailedSome more
test:Unprotect[Message];Message[Inverse::modp,__]:=Throw[$
Failed];Protect[Message];Catch[ Inverse[{{5, 5}, {5, 5}},
Modulus -> 26]; 123]--> 123So Throw doesn't work
either.Likewise for Return as well.DH
====
Excuse me, that I
state some simple thoughts, being in contrast to the thorough
insight of Orestis:If you look at the statements of Jens-Peer
in a general way, you may state,Jens Peer proposes
subroutines as the way to structure programs. That
thesubroutines are called functions in this case is rather
irrelevant.This leads to the conclusion:Oh what revelation:
This is always the starting point of OOP, because theOOP fans
think that using objects leads to better programs than
usingsubroutines. Hermann Schmitt> ----- Original Message
-----> To: <mathgroup@smc.vnet.net>> Sent: Saturday, November
09, 2002 6:29 AM>> I would be grateful if you answered
with some concrete arguments on> the fundamental functional
character of the Mathematica language.> not very helpful.
This is a technical issue, after all.> Orestis Vantzos>>
>> Mathematica allow many programming concepts.>
Because it should be used by as many persons> as possible
and all these persons should pay for> a Mathematica
license.>> It is not a good idea for a commercial
product to> force the customers to learn
functional/logic> programming if these cutsomers have
10--20> years of programming experience with FORTRAN 77>
> (as the most physicist have).>> Deep in it's
internal structure Mathematica> is a functional/logic
language and a functional> logic language uses functions,
patterns and> transformation rules *and* it is optimzed>
> to do this.>> If someone like it, he can use Do[],
For[] and> Goto[] as in a FORTRAN program. This> will
not make Mathematica to a imperativ/procedural> language.>
>> OOP is developed for simulations and> graphical
user interfaces where the objects> *must* have its own
life like a window on screen> or a car in a traffic
simulation.> This concept is very clear realized in
Objective C> or Eiffel.>> Every programming
languagage has its own taste> and ßavor. The taste and
ßavor of Mathematica> is functional/logic and if someone
can't exist> without the object oriented ßavor he 
should>
> stay away from Mathematica.> Jens>
> [I know what you're thinking; this
guy is nuts!]> Anyway, Jens keeps attacking the whole
OOP-Mathematica idea based on> the single premise that
ÔThis is a Functional Language'. He evendoes> it 
in a
rather abrupt manner, which I do not appreciate.>>
> Well guess what; Mathematica is NOT a functional language.
It can> definitely be used like one.But...>>
a) Wolfram in the Mathematica Book seems to suggest that
Mathematica> is primarily a rules-based language...in
A new kind of Science this> assumption is even
stronger.>> b) Symbols and rules are the
fundamentals of Mathematica.> Symbols have UpValues and
DownValues (and OwnValues,etc. but let's> keep it
simple).> It is true that an evaluation of the
expression s_Symbol[args___]can> be thought of as Ôthe
function s is applied to the subexpression>
Sequence[args]'.>> This is ONLY a metaphor!!!>
>> What really happens is that the symbol s is called
upon to apply its> transformation rules stored under
DownValues on the expression. This> is the ONLY
objective description of the process. Everything else is>
> an assumption on part of the programmer.>>
Moreover, UpValues completely throw the functional metaphor
out the> window:> in this case
s_Symbol[x_Symbol,rest___] is transformed not according>
> to the Ôfunction' s but according to the 
UpValues of
Ôargument' x !!>> So Jens, LISP is a functional
language, since its fundamental> structures are
function-based. Mathematica is just a darn good>
simulation of a functional language. So good, that we have
learnedto> ignore that it is only a facade.>>
> People like me are trying to build a different
interpretation ofwhat> all these symbols and rules are
doing (or can be persuaded to do)> inside Mathematica.
You look at symbols and see functions; I lookand> see>
objects. An OOP package will only be a 
Ôsimulation',
sinceMathematica> is not inherently OO, but I repeat
that all the talk aboutfunctional> programming in
Mathematica is no better in any way.>> Rules and
symbols are real; the rest is a mindgame.>>
Orestis Vantzos>>
====
I am using Mathematica 4.0. It might
not support Import function, since the expression you
proposed to me cannot work.
In[2]:=Import[data.csv]Import::guess: Could not guess
format from channel
data.csv.Out[2]=Import[data.csv]In[3]:=Import[data.csv,
CSV]Import::format: CSV is not a recognized Import
format.Out[3]=Import[data.csv, CSV]Fortunately, Sseziwa's
method works fine to
me.{ToExpression[#[[1]]],#[[2]],Sequence@@Table[ToExpression[
#[[i]]],{i,3,8 }]}&/
@ReadList[strm,Word,WordSeparators[Rule]{,},RecordLists
[Rule]True]Wen-Feng Hsiao----------> Import[data.css,
CSV]> ??> Jens>
====
I am trying to help a friend at a
University create some plots of his data. I have a trial
version of Mathematica and it looks like it will do the job,
but I need help with a simple problem.I have written some
code to massage the data and put it in forms for reading into
Mathematica.I will be doing a surface plot and want to provide
can provide my own triangulation data.I will have data of the
form n n n n n n n n n n n n n n n n nI can read this into
lists and end up with
{n,n,n,n},{n,n,n,n,n,n},{n,n,n,n,n},{n,n}I need to turn this
into {n,{n,n,n}},{n,{n,n,n,n,n}},{n,{n,n,n,n}},{n,{n}}to use
as the triangulation data.Can some kind soul provide me with
some Mathematica code to transfrom my data into the proper
format. There are so many features, there must be some simple
transformation code.-- Terrell MitchellReply-To:
kuska@informatik.uni-leipzig.de
====
{First[#], Rest[#]} & /@
{{n, n, n, n}, {n, n, n, n, n, n}, {n, n, n, n, n}, {n, n}}
Jens> I am trying to help a friend at a University create
some plots of his> data. I have a trial version of
Mathematica and it looks like it will> do the job, but I need
help with a simple problem.> I have written some code to
massage the data and put it in forms for> reading into
Mathematica.> I will be doing a surface plot and want to
provide can provide my own> triangulation data.> I will
have data of the form> n n n n> n n n n n n> n n n n n> n n>
I can read this into lists and end up with>
{n,n,n,n},{n,n,n,n,n,n},{n,n,n,n,n},{n,n}> I need to turn
this into> {n,{n,n,n}},{n,{n,n,n,n,n}},{n,{n,n,n,n}},{n,{n}}>
to use as the triangulation data.> Can some kind soul
provide me with some Mathematica code to transfrom my> data
into the proper format. There are so many features, there
must be> some simple transformation code.> --> Terrell
Mitchell
====
> I can read this into lists and end up with>
{n,n,n,n},{n,n,n,n,n,n},{n,n,n,n,n},{n,n}> I need to turn
this into> {n,{n,n,n}},{n,{n,n,n,n,n}},{n,{n,n,n,n}},{n,{n}}>
to use as the triangulation data.How about...In[1]:= tmp =
{{n,n,n,n},{n,n,n,n,n,n},{n,n,n,n,n},{n,n}};In[2]:=
Map[{First[#], Rest[#]}&, tmp]Out[2]= {{n, {n, n, n}}, {n,
{n, n, n, n, n}}, {n, {n, n, n, n}}, {n,
{n}}}--Bhuvanesh,Wolfram Research.
====
Here's one approach.
Define f[{x_, y___}] := {x, {y}}Then map f through a list
containing your lists:In: f /@ {{n, n, n, n}, {n, n, n, n, n,
n}, {n, n, n, n, n}}Out: {{n, {n,n,n}}, {n, {n, n, n , n, n}},
{n, {n, n, n, n}}}----Selwyn Hollis> I am trying to help a
friend at a University create some plots of his > data. I
have a trial version of Mathematica and it looks like it will
> do the job, but I need help with a simple problem.> I have
written some code to massage the data and put it in forms for
> reading into Mathematica.> I will be doing a surface plot
and want to provide can provide my own > triangulation data.>
> I will have data of the form> n n n n > n n n n n n> n n n
n n> n n> I can read this into lists and end up with>
{n,n,n,n},{n,n,n,n,n,n},{n,n,n,n,n},{n,n}> I need to turn
this into> {n,{n,n,n}},{n,{n,n,n,n,n}},{n,{n,n,n,n}},{n,{n}}>
to use as the triangulation data.> Can some kind soul
provide me with some Mathematica code to transfrom my > data
into the proper format. There are so many features, there
must be > some simple transformation code.> 
====
Terrell,
dat={{n,n,n,n},{n,n,n,n,n,n},{n,n,n,n,n},{n,n}};
{First[#],Rest[#]}&/@dat
{{n,{n,n,n}},{n,{n,n,n,n,n}},{n,{n,n,n,n}},{n,{n}}}--Allan---
------------------Allan HayesMathematica Training and
ConsultingLeicester
UKwww.haystack.demon.co.ukhay@haystack.demon.co.ukVoice: +44
(0)116 271 4198>> I am trying to help a friend at a
University create some plots of his> data. I have a trial
version of Mathematica and it looks like it will> do the job,
but I need help with a simple problem.>> I have written some
code to massage the data and put it in forms for> reading
into Mathematica.>> I will be doing a surface plot and want
to provide can provide my own> triangulation data.>> I will
have data of the form> n n n n> n n n n n n> n n n n n> n n>
I can read this into lists and end up with>
{n,n,n,n},{n,n,n,n,n,n},{n,n,n,n,n},{n,n}> I need to turn
this into> {n,{n,n,n}},{n,{n,n,n,n,n}},{n,{n,n,n,n}},{n,{n}}>
to use as the triangulation data.>> Can some kind soul provide
me with some Mathematica code to transfrom my> data into the
proper format. There are so many features, there must be>
some simple transformation code.>> -->> Terrell
Mitchell>
====
please excuse my basic Mathematica coding skills
as I am only a casual user and wishI could write thing like
Stan Wagon, David Wagner or Roam Maeder (maybe
someday).Anyway, I have the following snippet from some RSA
code I have and waswondering if it could be made cleaner.
Sometimes, an e cannot be foundfor the p and q, but I just
rerun it. Maybe this should be automatic also,but I am
concerned that it may run forever.Any hints as to how to make
this more efficient are appreciated. The nrepresents the
number of digits in n = pq. I like all of the printouts
asthis code is meant to help teach the method (RSA).(*RSA
Code Snippet Follows
*)Needs[NumberTheory`NumberTheoryFunctions`]RandomPrime[d_]
:= NextPrime[Random[Integer, {10^(d - 1), 10^d}]]findE[p_, q_]
:= Module[{res, n = p q, phi = EulerPhi[n]}, res =
Random[Integer, {p, n}]; While[GCD[res, phi] != 1, res =
Random[Integer, {p, n}]]; res]PubPrivKey[nDigits_] :=
Module[{l, p, q, n, d, e, publicKey, privateKey}, Clear[l, p,
q, n, d, e, publicKey, privateKey]; l = Floor[N[nDigits/2]]; p
= RandomPrime[l]; Print[p = , p]; q = RandomPrime[l];
Print[q = , q]; n = p q; Print[n = pq = , n]; phi =
EulerPhi[n]; Print[phi = , phi]; e = findE[p, q];
Print[Coprime to phi = e = , e]; d = PowerMod[e, -1, phi];
Print[Modular inverse d = , d]; publicKey = {d, n};
Print[Public Key = {d,n} = , {d, n}]; privateKey = {e, n};
Print[Private Key = {e,n} = , {e, n}]; {publicKey,
privateKey}]{$PublicKey, $PrivateKey} =
PubPrivKey[10]
====
hi!Has anybody found a final solution to
this problem?> If you follow this link, you will see what I
have found out about this:>
http://forums.wolfram.com/student-support/topics/5709>
Brian> Deleting the browserindex.nb does not correct the
online help e.g the> online mathematica book is not fully
accessable etc.Why are some of> the *.nb files corrupted in
the first place?It seems to occur only on> win2k.>
>Try deleting ...>
>Mathematica4.2DocumentationEnglishMainBook
BrowserIndex.nb>>
====
you
write below, that you have never written a function with more
tha ca. 30statements and a function has typical 5-10
statements.But in the next section you write about packages.
That is, there issomething to be designed beyond the single
function!You do not see the forest because of the many
trees!Hermann Schmitt----- Original Message ----->> It seems
that larger packages work perfectly right> without any object
oriented extension -- how can this> happen ?>> And yes I mean
functional programming when I say> functional programming.
Every> real functional/logic programming language> has an
assigment. The assigment is not needed> but it save some
computation time. Mathematica> has also functions like
While[] only for> efficiency.>> Jens> you must
differentiate between instructions and the structuring
ofprograms.> If you write a small program the structure of
the program is no issue.But I> think, that Mathematica is
one of the best programming languages, youcan> also program
larger programs/applications with Mathematica. Then the>
structuring of the program/the applications is an issue. You
ignore the> problems of structuring.> Additionally, your
usage of the notion functional programming iswrong. If>
you read in the literature, you will see, that functional
programming is> programming only with functions and
expressions and without variablesand> without the
assignement of values to variables. I think, you canprogram
in> this way in Mathematica, but I do not think, that you
mean this.> Hermann>
====
As you write below:Mathematica
contains all that is necessary to program in an OO style,
butperhaps lacks tools to make such an endeavor
easy.Therefore I created an OO system for Mathematica as a
package. I think, thatit contains all the features, which
are considered necessary for an OOsystem.You may find a small
example program for my system in my contribution ofNov. 4,
10.38.I shall make my package available, soon, on my web
site:www.schmitther.deHermann Schmitt----- Original Message
----->> (unfortunately due to the change in subject lines
this thread seems to>> have split into 4 separate ones) you
can inherit structure and methods>> etc. I know Orestis used
downvalues but I think upvalues would be>> more>>
efficient. I'd also change his method to use a 
symbol without
a>> definition rather than overloading Dot. If you are using
Mathematica>> you already have to condition yourself to use
Map, Fold et al. rather>> than Do, For, While etc. What's
wrong with using pattern matching for>> structures instead
of tuples?>> The whole idea is going beyond a simple
Ôrecord', all the way to a> full ßedged 
object, complete
with methods. I used DownValues, because> I think that the
message passing mechanism is best pictured in> Mathematica
as obj@method[args] rather than as method[obj,args]. What>
I mean to say is that the object obj receives the message
method[args]> rather than method is applied on {obj,args},
which would be more> functional in style.> There is a
major implementation issue related with my use of>
DownValues, instead of UpValues. Although the identity of the
object> is obvious, the identity of the method is not, given
that inheritance> and polymorphism can identify several
pieces of code with the same> Ômethod'. It is 
therefore
wise to enclose the Ôunstable' part of the> 
expression
(method[args]) with the definite one (obj), incase some>
form of processing is needed before the message is actualy
evaluated> (in which case you would
SetAttributes[onj,HoldAll] ).> The UpValues versus
DownValues issue is a matter of taste as you seem> to agree
(as is the use of Dot). I was just suggesting the my
personal> preference is to use the UpValues. The post to
which you are replying> was a response to a question about
porting code which used C struct> types to Mathematica, OO
issues were not mentioned. I was merely> suggesting that if
you wanted to mechanically port (by which I mean>
substituting a roughly equivalent Mathematica expression for
each line> of C code) C code containing structs then changing
the structs to> expressions with heads sorted by type may be a
better idea than> maintaining them as lists.>> That said, I
have never had occasion to do this myself and am merely> it
seems you have had experience in just such a project and I
will> defer to your wisdom on the subject.>> Finally to make
my own position perfectly clear. I believe that> Mathematica
contains all that is necessary to program in an OO style> but
perhaps lacks tools to make such an endeavor easy. I'm not
even> sure what those tools should be since they would almost
necessarily> enforce some sort of OO policy decisions (ie.
delegates as Orestis uses> or the more static hierarchy using
lists of rules presented earlier)> which would make someone
unhappy. In fact it seems that similarly to> the way X
Windows allows the creation of a GUI without specifying the>
rules of the GUI (focus follows mouse, menubar on window or
desktop> etc.) Mathematica allows OO without making decisions
about the specific> form either. To use OO in Mathematica then
it would probably be better> to understand the more general
object model of a system such as CLOS> than a more rigid
model such as Java or C++. Anyway, I've already said> more
than I ever intended to on this subject. It seems the best
way to> make any productive contributions to this subject is
for people to> actually implement projects using OO
techniques in Mathematica and> present them. If there is any
interest then I'm sure Mathematica users> will be able to
generalize whatever features are necessary to make OO>
programming easy in Mathematica and maybe even get them
included as a> standard package.> Ssezi>>
====
> I will have
data of the form> n n n n > n n n n n n> n n n n n> n n> I
can read this into lists and end up with>
{n,n,n,n},{n,n,n,n,n,n},{n,n,n,n,n},{n,n}> I need to turn
this into>
{n,{n,n,n}},{n,{n,n,n,n,n}},{n,{n,n,n,n}},{n,{n}}Lett = {{a,
b, c, d, e}, {f, g, h}, {i, j}, {k}};Then a suitable
transformation isr = {(a_)?AtomQ, b__} :> {a, {b}}so thatt /.
rgives you what you want. If you choose to process the members
of list t oneat a time (or if you give t some Head other than
List), then the simplerpattern {a_, b__} will do. The more
complicated pattern avoids a match withthe entire list as a
unit (i.e., at level 0).Tom Burton
====
Terrell,If you start
withdata = {{n, n, n, n}, {n, n, n, n, n, n}, {n, n, n, n,
n}, {n, n}};Map the following pure function onto the data
items{First[#], Rest[#]} & /@ data{{n, {n, n, n}}, {n, {n, n,
n, n, n}}, {n, {n, n, n, n}}, {n, {n}}}/@ is the shortcut for
Map and everything through & is the pure function.David
Parkdjmp@earthlink.nethttp://home.earthlink.net/~djmp/ n n n
n n n n n n n n n nI can read this into lists and end up with
{n,n,n,n},{n,n,n,n,n,n},{n,n,n,n,n},{n,n}I need to turn this
into {n,{n,n,n}},{n,{n,n,n,n,n}},{n,{n,n,n,n}},{n,{n}}to use
as the triangulation data.Can some kind soul provide me with
some Mathematica code to transfrom my data into the proper
format. There are so many features, there must be some simple
transformation code.-- Terrell Mitchell
====
I have, what I
believe, a system of two linear, first-order, inhomogeneous
differential equations describing a real biological system.
When I tried to solve this system for a numerical solution by
NDSolve, it gave a solution that was different from that of
the symbolic solution (in which I used the same boundary
conditions).NDSolve[{y1'[t] == a y1[t] + b y2[t], 
y2'[t] == d
+ c y1[t] - b y2[t], y1[0] == 0.0018, y2[0] == 0.03}, {y1[t],
y2[t]}, {t, 0, 18000}, MaxSteps -> 1000000, AccuracyGoal ->
10, PrecisionGoal -> 10, WorkingPrecision ->
20]DSolve[{y1'[t] == a y1[t] + b y2[t] , 
y2'[t] == d + c
y1[t] - b y2[t] }, {y1[t], y2[t]}, t]I am puzzled by these
results, and would very much like to arrive at an analytical
solution. I would very much appreciate ideas and suggestions
to help me get there.Many thanks in advance.Loling
SongCornell UniversityDepartment of Physics,117 Clark
Hall,Ithaca, NY 14853
====
Is there any standard, immediately
available way in the Mathematica front end to obtain an
Outline type of behavior, in which one can close and/or
then re-open cells in a Mathematica notebook level by level,
globally, preferably using a keyboard shortcut, in a
hierarchical fashion which follows the numbered Styles in the
Format menu?I' m sure there's some complex way 
to do this, but
is there anything immediately built in?)-----Power tends to
corrupt. Absolute power corrupts absolutely. Lord Acton
(1834-1902) (slightly modified)Dependence on advertising
tends to corrupt. Total dependence on advertising corrupts
totally. -- Modern equivalent. 
====
I'm quite new in
operating with Mathematica. Solving a problem
concerningnetwork reliability I have to implement an
algorithm which uses idempotence(e.g.: a*a=a, a^2*b^3=ab).As
a result of this fact, the following lists should be the
same:list1={b+a c-a b c,c,1}list2={2 b+2 a c-a b c-a c (b+a
c-a b c)-b (b+2 a c-a b c-a c (b+a c-a bc)),c,1}The result of
list1===list2 should be true.Does anybody have a hint or an
idea how to solve it with Mathematica? Icouldn't 
find anything
about it even on Wolfram's webpage.Tilo.
====
Just a
remark:Writing package code with a simple text editor can
give you more control, fewer headaches, and cleaner code
faster.---Selwyn Hollis
====
> I can write a simple package
with a single line of code written in> StandardForm, so the
1/10 term is written 1 on top of 10...> test := Module[(x =
1/10, (* now is the time *) y = 2}, x]> Using StandardForm
and 2D mathematical typesetting, it works fine in> the
notebook. Save it as a package and load it in, and I get a
slew of> error messages...>
!(InputForm`Syntax::sntxb :> Expression cannot begin
with etc....> This is KILLING me!Same goes for highlighting
changes with color, font changes, etc. A seriousnuisance!
Problems may lie dormant until you port to another platform.
Arelated issue is that when you process the code through the
kernel (e.g.,menu Cell, Convert To, StandardForm), this local
formatting is strippedaway. This loss cannot be undone.Wolfram
Support has discouraged me from using all such
fragileconstructions. Comments are the least of it really,
because alternatives arebetter for other reasons: (1) Divide
code into small chunks interspersedwith explanatory material.
(2) Use longer, self-descriptive names forsymbols.The related
issue above suggests a cure: Process the code through
thekernel, stripping out all local formatting, on the way to
the m-file. Thischange would kill folks who still look at m
files. Still, if thecorrection were that easy, WRI would have
done by now :-) Perhaps theinstability is in the notebook.
That would present a more difficult problem. Tom
Burton
====
Mike,I set your code (in 2D form)and put it into a
.m file (1) by copying andp[asting into a the file 
(2) by
making the containing cell initializing andusing Edit>Copy
Selection As>Package Format.I then loaded the file using <<.In
both cases test evaluated with no problem.Maybe I am missing
something/I am using Mathematica
m.2--Allan---------------------Allan HayesMathematica
Training and ConsultingLeicester
UKwww.haystack.demon.co.ukhay@haystack.demon.co.ukVoice: +44
(0)116 271 4198> I can write a simple package with a single
line of code written in> StandardForm, so the 1/10 term is
written 1 on top of 10...>> test := Module[(x = 1/10, (* now
is the time *) y = 2}, x]>> Using StandardForm and 2D
mathematical typesetting, it works fine in> the notebook. Save
it as a package and load it in, and I get a slew of> error
messages...>> !(InputForm`Syntax::sntxb :>
Expression cannot begin with etc....>> This is KILLING me!
If the Front End has a bug in it, then make> to) use text,
mathematical typesetting, and comments to provide a best>
product to my customer. While text is great, there is
certainly a time> and a place for comments within the code.>>
Does anyone have some sort of add-in such that the
autopackage> function converts all cells to input form first?
Or reconverts to> StandardForm? I don't need to carry any of
the comments or formatting> into the *.m file, and prefer that
none of it did. Wolfram, do you> guys have anything like
this?>> Why hasn't this been fixed?>> Mike>
====
I've been
bitten by problems with comments, (legal) white space,
andMathematica's autoformatting in the past. I gave up using
all of them and theneventually gave up using Mathematica for
large coding projects. Luckily Imostly do numerical work so
other solutions will work for me. Sadly,Mathematica remains a
difficult environment to code and debug in. Sorry, Ihave no
solution for you only my own story.-- Lou Pecora - My views
are my own.
====
zeno:Look at the code and you'll see 9
instances where the author uses Round[thing + .5]. Replace
each of those with Ceiling[thing]. That fixed it for
me.---Selwyn Hollis> The Menger Sponge code in the mathsource
archives does not work in> version 3 or 4. The notebook is
called fractals.nb> It is claimed to be for version 3
however...but does not work right in> version 3...> It
gives an output that is the opposite of what it should
be...(where> there are holes in the menger sponge there are
blocks and vice-versa).> Also, under iteration of 0 it
works, but with iterations of 1 and 2 it> gives a postscrip
error..> I ahd tech Support run the notebook in version 4
and it came out the> same..> is there code for version 3 or
4 that makes a correct Menger Sponge?> 
====
The Menger Sponge
code in the mathsource archives does not work inversion 3 or
4. The notebook is called fractals.nbIt is claimed to be for
version 3 however...but does not work right inversion 3...It
gives an output that is the opposite of what it should
be...(wherethere are holes in the menger sponge there are
blocks and vice-versa).Also, under iteration of 0 it works,
but with iterations of 1 and 2 itgives a postscrip error..I
ahd tech Support run the notebook in version 4 and it came
out thesame..is there code for version 3 or 4 that makes a
correct Menger Sponge?
====
How can one solve multiple linear
and quadratic inequalities (in my case, atmost 3) in
multiple variables (in my case, at most 3)?I am using
Mathematica 4.0.Matt Herman
====
If you have Mathematica 4.2
and time constraints are not too severe (i.e. the system
contains not too many equations and variables), simply
reformulate the root finding problem as a maximization problem
and use NMinimize. The reformulation is simple: just minimize
the constant function 1 subject to your equality and
inequality constraints. Johannes> I'm trying to solve a
system of nonlinear algebraic equations.> I was hoping to use
the FindRoot. However, some> of the variables for which I'm
solving must satisfy some> inequalities. Is there an easy way
to impose these constraints> in the solution?> George>
(KthielK@us.ibm.com)>
<><><><><><><><><><><><><><><><><><>Johannes LudsteckInstitut
fuer VolkswirtschaftslehreLehrstuhl Prof. Dr.
MoellerUniversitaet RegensburgUniversitaetsstrasse 3193053
Regensburg
====
I have to find many complex roots of complex
function likef[z]=0 where z is complex.I try first the
graphical approch:ImplicitPlot[{Re[f[a+ Ib]]==0,Im[f[a+I
b]]==0},{a,amin,amax},{b,bmin,bmax}]or somethink else, and it
works good and I visualize the solution in thespecificated
region.Now I'd like to compute the finding 
automaticaly.I'
seen other posts which illustrates how find many roots of real
functionof real varible but I'm unable to genaralize in 2D
case.Some one can help me?P.S. sorry for my english
====
The
use of n is a handy way to get line breaks in text
strings, as in Epilog->{Text[purengainnguiding, {4, 5},
{-1,-1}]to get pure gain guidingIs there a way to change the
alignment of the text box from Left justify to Center or
Right justify?-----Power tends to corrupt. Absolute power
corrupts absolutely. Lord Acton (1834-1902) (slightly
modified)Dependence on advertising tends to corrupt. Total
dependence on advertising corrupts totally. -- Modern
equivalent.