eq {magic} | R Documentation |
Compares two magic squares according to Frenicle's method. Mnemonic is the old Fortran ``.GT." (for ``Greater Than") comparison et seq.
To compare magic square a
with magic square b
, their
elements are compared in rowwise order: a[1,1]
is compared with
b[1,1]
, then a[1,2]
with b[1,2]
, up to
a[n,n]
. Consider the first element that is different, say
[i,j]
. Then a<b
if a[i,j]<b[i,j]
.
The generalization to hypercubes is straightforward: comparisons are carried out natural order.
eq(m1, m2) ne(m1, m2) gt(m1, m2) lt(m1, m2) ge(m1, m2) le(m1, m2) m1 %eq% m2 m1 %ne% m2 m1 %gt% m2 m1 %lt% m2 m1 %ge% m2 m1 %le% m2
m1 |
First magic square |
m2 |
Second magic square |
Rather clumsy function definition due to the degenerate case of
testing two identical matrices (min(NULL)
is undefined).
Robin K. S. Hankin
magic(4) %eq% magic.4n(1) eq(magic(4) , magic.4n(1))