as.standard {magic}R Documentation

Standard form for magic squares

Description

Transforms a magic square or magic hypercube into Frenicle's standard form

Usage

as.standard(a)
is.standard(a)

Arguments

a Magic square or hypercube (array) to be tested or transformed

Details

For a square, as.standard() transforms a magic square into Frenicle's standard form. The four numbers at each of the four corners are determined. First, the square is rotated so the smallest of the four is at the upper left. Then, element [1,2] is compared with element[2,1] and, if it is larger, the transpose is taken.

Thus all eight rotated and transposed versions of a magic square have the same standard form.

The square returned by magic() is in standard form.

For hypercubes, the algorithm is generalized. Firstly, the hypercube is reflected so that a[1,1,...,1,1] is the smallest of the 2^d corner elements (eg a[1,n,1,...,1,1]).

Next, aperm() is called so that

a[1,1,...,1,2] < a[1,1,...,2,1] < ... < a[2,1,...,1,1].

Note that the inequalities are strict as hypercubes are assumed to be normal. As of version 1.3-1, as.standard() will accept arrays of any dimension (ie arrays a with minmax(dim(a))==FALSE will be handled sensibly).

An array with any dimension of extent zero is in standard form by definition; dimensions of length one have the relevant dimensions dropped.

is.standard() returns TRUE if the magic square or hypercube is in standard form. is.standard() and as.standard() check for neither magicness nor normality (use is.magic and is.normal for this).

Note

There does not appear to be a way to make the third letter of “Frenicle” have an acute accent, as it should do.

Author(s)

Robin K. S. Hankin

See Also

magic, eq

Examples

is.standard(magic.2np1(4))
as.standard(magic.4n(3))

as.standard(magichypercube.4n(1,5))

##non-square arrays:
as.standard(magic(7)[1:3,])


[Package magic version 1.4-4 Index]