# Structure of zero-divisors of the 64-ions # that are sums or differences of two units. # # In the 64 x 64 matrix below # a one corresponds to a pair of indices A and B # such that (A+B) is a zero-divisor. # For each such pair all of (+-A +-B) are zero divisors. # If (A + B) is a zero-divisor the trivially also # (B + A) is a zero-divisor, hence the symmetry. # The upper left 32 x 32 square gives the structure for # the 32-ions, the upper left 16 x 16 square for the sedenions. # The upper left 8x8 square contains no ones: # there are no zero-divisors for the octonions, # quaternions, complex, and real numbers. # #. # Generated by Joerg Arndt, 2009-September-14 # ................................................................ ..........111111..11111111111111..111111111111111111111111111111 .........1.11111.1.1111111111111.1.11111111111111111111111111111 .........11.1111.11.111111111111.11.1111111111111111111111111111 .........111.111.111.11111111111.111.111111111111111111111111111 .........1111.11.1111.1111111111.1111.11111111111111111111111111 .........11111.1.11111.111111111.11111.1111111111111111111111111 .........111111..111111.11111111.111111.111111111111111111111111 .................1111111.1111111.1111111.11111111111111111111111 ..111111.........11111111.111111.11111111.1111111111111111111111 .1.11111.........111111111.11111.111111111.111111111111111111111 .11.1111.........1111111111.1111.1111111111.11111111111111111111 .111.111.........11111111111.111.11111111111.1111111111111111111 .1111.11.........111111111111.11.111111111111.111111111111111111 .11111.1.........1111111111111.1.1111111111111.11111111111111111 .111111..........11111111111111..11111111111111.1111111111111111 .................................111111111111111.111111111111111 ..11111111111111..........111111.1111111111111111.11111111111111 .1.1111111111111.........1.11111.11111111111111111.1111111111111 .11.111111111111.........11.1111.111111111111111111.111111111111 .111.11111111111.........111.111.1111111111111111111.11111111111 .1111.1111111111.........1111.11.11111111111111111111.1111111111 .11111.111111111.........11111.1.111111111111111111111.111111111 .111111.11111111.........111111..1111111111111111111111.11111111 .1111111.1111111.................11111111111111111111111.1111111 .11111111.111111..111111.........111111111111111111111111.111111 .111111111.11111.1.11111.........1111111111111111111111111.11111 .1111111111.1111.11.1111.........11111111111111111111111111.1111 .11111111111.111.111.111.........111111111111111111111111111.111 .111111111111.11.1111.11.........1111111111111111111111111111.11 .1111111111111.1.11111.1.........11111111111111111111111111111.1 .11111111111111..111111..........111111111111111111111111111111. ................................................................ ..111111111111111111111111111111..........111111..11111111111111 .1.11111111111111111111111111111.........1.11111.1.1111111111111 .11.1111111111111111111111111111.........11.1111.11.111111111111 .111.111111111111111111111111111.........111.111.111.11111111111 .1111.11111111111111111111111111.........1111.11.1111.1111111111 .11111.1111111111111111111111111.........11111.1.11111.111111111 .111111.111111111111111111111111.........111111..111111.11111111 .1111111.11111111111111111111111.................1111111.1111111 .11111111.1111111111111111111111..111111.........11111111.111111 .111111111.111111111111111111111.1.11111.........111111111.11111 .1111111111.11111111111111111111.11.1111.........1111111111.1111 .11111111111.1111111111111111111.111.111.........11111111111.111 .111111111111.111111111111111111.1111.11.........111111111111.11 .1111111111111.11111111111111111.11111.1.........1111111111111.1 .11111111111111.1111111111111111.111111..........11111111111111. .111111111111111.111111111111111................................ .1111111111111111.11111111111111..11111111111111..........111111 .11111111111111111.1111111111111.1.1111111111111.........1.11111 .111111111111111111.111111111111.11.111111111111.........11.1111 .1111111111111111111.11111111111.111.11111111111.........111.111 .11111111111111111111.1111111111.1111.1111111111.........1111.11 .111111111111111111111.111111111.11111.111111111.........11111.1 .1111111111111111111111.11111111.111111.11111111.........111111. .11111111111111111111111.1111111.1111111.1111111................ .111111111111111111111111.111111.11111111.111111..111111........ .1111111111111111111111111.11111.111111111.11111.1.11111........ .11111111111111111111111111.1111.1111111111.1111.11.1111........ .111111111111111111111111111.111.11111111111.111.111.111........ .1111111111111111111111111111.11.111111111111.11.1111.11........ .11111111111111111111111111111.1.1111111111111.1.11111.1........ .111111111111111111111111111111..11111111111111..111111.........