Comparison of two magic squares
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).
The two arguments are assumed to be matrices of the same size. If not, an error is given.
Robin K. S. Hankin
magic(4) %eq% magic.4n(1) eq(magic(4) , magic.4n(1))
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