Random free algebra objects — rfalg • freealg

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

What you see is what you get, basically. A term such as 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
#> + 9a + 11ba + 4bbaa + 4cb
rfalg(include.negative=TRUE)^2
#> free algebra element algebraically equal to
#> + 16CBCB + 24CBCAAA + 28CBBCbC + 4CBBB + 8CBBaaB + 20CBA + 12CBAcAB + 24CAAACB
#> + 36CAAACAAA + 42CAAABCbC + 6CAAABB + 12CAAABaaB + 30CAAAA + 18CAAAAcAB +
#> 28BCbCCB + 42BCbCCAAA + 49BCbCBCbC + 7BCbCBB + 14BCbCBaaB + 35BCbCA +
#> 21BCbCAcAB + 4BBCB + 6BBCAAA + 7BBBCbC + BBBB + 2BBBaaB + 5BBA + 3BBAcAB +
#> 8BaaBCB + 12BaaBCAAA + 14BaaBBCbC + 2BaaBBB + 4BaaBBaaB + 10BaaBA + 6BaaBAcAB +
#> 20ACB + 30ACAAA + 35ABCbC + 5ABB + 10ABaaB + 25AA + 15AAcAB + 12AcABCB +
#> 18AcABCAAA + 21AcABBCbC + 3AcABBB + 6AcABBaaB + 15AcABA + 9AcABAcAB


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