quhomology (version 1.1.1)

S_test: Testing of possible quandle/biquandle actions

Description

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

Usage

S_test(k, return_result = FALSE)

Arguments

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).

Value

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.

Details

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.

References

add in thesis.

See Also

up_action, down_action

Examples

# NOT RUN {
###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."
# }