As described in Appendix 1.2 of "Modal Color Theory," information about the
defining hyperplane arrangements is stored as a matrix containing the
hyperplanes' normal vectors as rows. (Because these are matrices
and they correspond ultimately to the intervallic inequalities
that define MCT geometry, this package refers to them as ineqmats, and
sometimes to the individual hyperplanes as ineqs.) These have already been computed and
are stored as data in this package (ineqmats) for cardinalities up to 53,
but they can be recreated from scratch with makeineqmat. This might be
useful if for some reason you need to deal with a huge scale and therefore
want to use an arrangement whose matrix isn't already saved. Note that a
call like makeineqmat(60) may take a dozen or more seconds to run (and
at sizes that large, the arrangement is terribly complex, with ~17K
distinct hyperplanes).
getineqmat tests whether the matrix already exists for the desired
cardinality. If so, it is retrieved; if not, it is created using makeineqmat.
Examples
makeineqmat(2) # Cute: is step 1 > step 2?
#> [1] -2 2 -1
makeineqmat(3) # Cute: step 1 > step 2? step 1 > step 3? step 2 > step 3?
#> [,1] [,2] [,3] [,4]
#> [1,] -1 2 -1 0
#> [2,] -2 1 1 -1
#> [3,] -1 -1 2 -1
makeineqmat(7) # Okay...
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#> [1,] -1 2 -1 0 0 0 0 0
#> [2,] -1 1 1 -1 0 0 0 0
#> [3,] 0 -1 2 -1 0 0 0 0
#> [4,] -1 1 0 1 -1 0 0 0
#> [5,] 0 -1 1 1 -1 0 0 0
#> [6,] 0 0 -1 2 -1 0 0 0
#> [7,] -1 1 0 0 1 -1 0 0
#> [8,] 0 -1 1 0 1 -1 0 0
#> [9,] 0 0 -1 1 1 -1 0 0
#> [10,] 0 0 0 -1 2 -1 0 0
#> [11,] -1 1 0 0 0 1 -1 0
#> [12,] 0 -1 1 0 0 1 -1 0
#> [13,] 0 0 -1 1 0 1 -1 0
#> [14,] 0 0 0 -1 1 1 -1 0
#> [15,] 0 0 0 0 -1 2 -1 0
#> [16,] -2 1 0 0 0 0 1 -1
#> [17,] -1 -1 1 0 0 0 1 -1
#> [18,] -1 0 -1 1 0 0 1 -1
#> [19,] -1 0 0 -1 1 0 1 -1
#> [20,] -1 0 0 0 -1 1 1 -1
#> [21,] -1 0 0 0 0 -1 2 -1
#> [22,] -1 0 2 0 -1 0 0 0
#> [23,] -1 0 1 1 0 -1 0 0
#> [24,] 0 -1 0 2 0 -1 0 0
#> [25,] -1 0 1 0 1 0 -1 0
#> [26,] 0 -1 0 1 1 0 -1 0
#> [27,] 0 0 -1 0 2 0 -1 0
#> [28,] -2 0 1 0 0 1 0 -1
#> [29,] -1 -1 0 1 0 1 0 -1
#> [30,] -1 0 -1 0 1 1 0 -1
#> [31,] -1 0 0 -1 0 2 0 -1
#> [32,] 0 -2 0 1 0 0 1 -1
#> [33,] 0 -1 -1 0 1 0 1 -1
#> [34,] 0 -1 0 -1 0 1 1 -1
#> [35,] 0 -1 0 0 -1 0 2 -1
#> [36,] -1 0 0 2 0 0 -1 0
#> [37,] -2 0 0 1 1 0 0 -1
#> [38,] -1 -1 0 0 2 0 0 -1
#> [39,] 0 -2 0 0 1 1 0 -1
#> [40,] 0 -1 -1 0 0 2 0 -1
#> [41,] 0 0 -2 0 0 1 1 -1
#> [42,] 0 0 -1 -1 0 0 2 -1
ineqmat20 <- makeineqmat(20)
dim(ineqmat20) # Yikes!
#> [1] 1000 21