composition {cubing}

Composition Operators For Cube Objects

Description

Composition operators for cubieCube objects.

Usage

aCube %v% bCube
aCube %e% bCube
aCube %c% bCube

Arguments

aCube

A cubieCube object.

bCube

A cubieCube object.

Details

Both arguments must be cubieCube objects, not stickerCube objects.

If A and B are cubes then A %v% B is the composition (or multiplication) of A and B. This means that if a and b are move sequences that produce A and B respectively from the solved cube I, then A %v% B is produced using the combined move sequence ab applied to I. Typically we just write AB for A %v% B.

Similarly to matrix multiplication, the operator %v% is associative but in general not commutative, with AI and IA both equal to A. Every 3x3x3 cube A has a unique inverse cube A' where AA' and A'A are both equal to I. The inverse cube can be calculated using the invCube function.

The %e% and %c% operators are similar to %v% but they compose only the edges and corners respectively. Use of these operators may create an unsolvable cube from two solvable cubes. They largely exist for internal reasons. See the help page on cycleEdges for details of their impact on solvability.

Value

A cubieCube object

See Also

cycleEdges, getMovesCube, invCube, is.solvable, move

Examples

aCube <- getCubieCube("Superflip")
bCube <- getCubieCube("EasyCheckerboard")
aCube %v% bCube