Random free algebra objects — rfalg • freealg

Generate random elements of the free algebra, intended as quick “get you going” examples of freealg objects

rfalg(n=7, distinct=3, maxsize=4, include.negative=FALSE)
rfalgg(n=30, distinct=8, maxsize=7, include.negative=FALSE)
rfalggg(n=100, distinct=26, maxsize=30, include.negative=FALSE)

Arguments

n: Number of terms to generate
distinct: Number of distinct symbols to use
maxsize: Maximum number of symbols in any word
include.negative: Boolean, with default FALSE meaning to use only positive symbols (lower-case letters) and TRUE meaning to use upper-case letters as well, corresponding to the inverse of the lower-case symbols

Details

Terms are automatically simplified; for example, aaBaAbaC will be simplified to aaaC.

Functions rfalgg() and rfalggg() return successively more complicated freealg objects.

Author

Robin K. S. Hankin

Examples

rfalg()
#> free algebra element algebraically equal to
#> + 5acab + 6bb + bbaa + 2bca + 4bcab + 3cbcb + 7ccb
rfalg(include.negative = TRUE)^2
#> free algebra element algebraically equal to
#> + 9 + 24CbA + 16CbACbA + 20CbABAbC + 4CbAA + 28CbAbc + 24CbAc + 8CbcAA + 30BAb
#> + 30BAbC + 20BAbCCbA + 25BAbCBAbC + 5BAbCA + 10BAbCacAA + 35BAbCbc + 6A + 4ACbA
#> + 5ABAbC + AA + 7Abc + 6Ac + 12acAA + 8acAACbA + 10acAABAbC + 2acAAA + 14acAAbc
#> + 12acAAc + 4acAcAA + 24bA + 28bbA + 42bc + 35bcBAbC + 7bcA + 14bcacAA + 49bcbc
#> + 42bcc + 36c + 30cBAbC + 6cA + 2cAA + 12cacAA + 42cbc + 36cc

constant(rfalg())
#> [1] 0