S_test: Testing of possible quandle/biquandle actions
In quhomology: Calculation of Homology of Quandles, Racks, Biquandles and Biracks

Description Usage Arguments Details Value References See Also Examples

This functions tests if a given set with given operations is a biquandle (or quandle), or not.

1	S_test(k, return_result = FALSE)

`k`	Order of set, a positive integer.
`return_result`	This variable specifies if the results of the tests should be returned (as a list, if TRUE) or if the result of the tests should be printed to the screen (if FALSE, the default).

The test requires the user to define their own up and down actions. The different tests confirm two facts, namely, the bijectivity of the two functions f, g is considered, as well as the bijectivity of the switch map S, via their permutations. Furthermore, via the Yang-Baxter Check, it confirm whether the Yang-Baxter equation holds for the given up and down functions or not.

A vector with 4 boolean entries for the permutation tests for S, f and g, respectively as well as a check that Yang-Baxter holds.

add in thesis.

up_action, down_action

###Using the provided up/down action functions.
S_test(3)
##Output:
"The permutation checks hold that S is TRUE, f is TRUE
and g is TRUE and that the Yang-Baxter check holds TRUE."