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.

Usage

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

Arguments

m1

First magic square

m2

Second magic square

Author

Robin K. S. Hankin

Note

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.

See also

as.standard

Examples

magic(4) %eq% magic.4n(1)
#> [1] FALSE
eq(magic(4) , magic.4n(1))
#> [1] FALSE