# Create and Investigate Magic Squares

## Documentation for package ‘magic’ version 1.6-0

- DESCRIPTION file.
- User guides, package vignettes and other documentation.

## Help Pages

A B C D E F G H I L M N O P R S T U misc

magic-package | Create and Investigate Magic Squares

## -- A --

adiag | Binds arrays corner-to-corner
allsubhypercubes | Subhypercubes of magic hypercubes
allsums | Row, column, and two diagonal sums of arrays
another_incidence | Random latin squares
another_latin | Random latin squares
apad | Pad arrays
apl | Replacements for APL functions take and drop
apldrop | Replacements for APL functions take and drop
apldrop<- | Replacements for APL functions take and drop
apltake | Replacements for APL functions take and drop
apltake<- | Replacements for APL functions take and drop
aplus | Generalized array addition
arev | Reverses some dimensions; a generalization of rev
arot | Rotates an array about two specified dimensions
arow | Generalized row and col
as.standard | Standard form for magic squares
ashift | Shift origin of arrays and vectors

## -- B --

bernhardsson | N queens problem
bernhardssonA | N queens problem
bernhardssonB | N queens problem

## -- C --

cilleruelo | A class of multiplicative magic squares due to Cilleruelo and Luca
circulant | Circulant matrices of any order
cube2 | A pantriagonal magic cube

## -- D --

diag.off | Extracts broken diagonals
do.index | Apply a function to array element indices

## -- E --

eq | Comparison of two magic squares

## -- F --

fnsd | First non-singleton dimension
force.integer | Integerize array elements
Frankenstein | A perfect magic cube due to Frankenstein

## -- G --

ge | Comparison of two magic squares
gt | Comparison of two magic squares

## -- H --

hadamard | Hadamard matrices
hendricks | A perfect magic cube due to Hendricks
hudson | Pandiagonal magic squares due to Hudson

## -- I --

incidence | Random latin squares
inc_to_inc | Random latin squares
is.2x2.correct | Various tests for the magicness of a square
is.alicehypercube | magic hypercubes
is.antimagic | Various tests for the magicness of a square
is.associative | Various tests for the magicness of a square
is.bree.correct | Various tests for the magicness of a square
is.centrosymmetric | Is a square matrix square palindromic?
is.circulant | Circulant matrices of any order
is.diagonally.correct | magic hypercubes
is.hadamard | Hadamard matrices
is.heterosquare | Various tests for the magicness of a square
is.incidence | Random latin squares
is.incidence.improper | Random latin squares
is.latin | Various tests for the magicness of a square
is.latinhypercube | magic hypercubes
is.magic | Various tests for the magicness of a square
is.magichypercube | magic hypercubes
is.mostperfect | Various tests for the magicness of a square
is.nasik | magic hypercubes
is.normal | Various tests for the magicness of a square
is.ok | does a vector have the sum required to be a row or column of a magic square?
is.pandiagonal | Various tests for the magicness of a square
is.panmagic | Various tests for the magicness of a square
is.perfect | magic hypercubes
is.persymmetric | Is a square matrix square palindromic?
is.regular | Various tests for the magicness of a square
is.sam | Various tests for the magicness of a square
is.semimagic | Various tests for the magicness of a square
is.semimagic.default | Various tests for the magicness of a square
is.semimagichypercube | magic hypercubes
is.sparse | Various tests for the magicness of a square
is.square.palindromic | Is a square matrix square palindromic?
is.stam | Various tests for the magicness of a square
is.standard | Standard form for magic squares
is.standard.toroidal | Standard form for magic squares
is.totally.antimagic | Various tests for the magicness of a square
is.totally.heterosquare | Various tests for the magicness of a square
is.ultramagic | Various tests for the magicness of a square

## -- L --

latin | Random latin squares
le | Comparison of two magic squares
lozenge | Conway's lozenge algorithm for magic squares
lt | Comparison of two magic squares

## -- M --

magic | Creates magic squares
magic.2np1 | Magic squares of odd order
magic.4n | Magic squares of order 4n
magic.4np2 | Magic squares of order 4n+2
magic.8 | Regular magic squares of order 8
magic.constant | Magic constant of a magic square or hypercube
magic.prime | Magic squares prime order
magic.product | Product of two magic squares
magic.product.fast | Product of two magic squares
magiccube.2np1 | Magic cubes of order 2n+1
magiccubes | Magic cubes of order 3
magichypercube.4n | Magic hypercubes of order 4n
magicplot | Joins consecutive numbers of a magic square.
minmax | are all elements of a vector identical?

## -- N --

ne | Comparison of two magic squares
notmagic.2n | An unmagic square
nqueens | N queens problem

## -- O --

Ollerenshaw | A most perfect square due to Ollerenshaw

## -- P --

panmagic.4 | Panmagic squares of order 4
panmagic.4n | Panmagic squares of order 4n, 6n+1 and 6n-1
panmagic.6nm1 | Panmagic squares of order 4n, 6n+1 and 6n-1
panmagic.6np1 | Panmagic squares of order 4n, 6n+1 and 6n-1
panmagic.6npm1 | Panmagic squares of order 4n, 6n+1 and 6n-1
panmagic.8 | Panmagic squares of order 8
perfectcube5 | A perfect magic cube of order 5
perfectcube6 | A perfect cube of order 6
process | Force index arrays into range

## -- R --

recurse | Recursively apply a permutation
rlatin | Random latin squares

## -- S --

sam | Sparse antimagic squares
shift | Shift origin of arrays and vectors
strachey | Strachey's algorithm for magic squares
subsums | Sums of submatrices
sylvester | Hadamard matrices

## -- T --

take | Replacements for APL functions take and drop
transf | Frenicle's equivalent magic squares

## -- U --

unincidence | Random latin squares

## -- misc --

%eq% | Comparison of two magic squares
%ge% | Comparison of two magic squares
%gt% | Comparison of two magic squares
%le% | Comparison of two magic squares
%lt% | Comparison of two magic squares
%ne% | Comparison of two magic squares