quhomology (version 1.1.1)

homology: Calculation of quandle and rack homology groups of a rack / birack.

Description

This function calculates the quandle and rack homology groups of a given rack or birack.

Usage

homology(degree, k, quandle = TRUE, return_values = FALSE)

Arguments

degree

This is the degree of the Homology group, that is, if one wants to calculate $H_3$, then degree=3.

k

This describes the order of the underlying rack or birack.

quandle

If quandle=TRUE, this calculates the quandle homology group. If FALSE, the rack homology is calculated.

return_values

If return_values = TRUE, the functions returns the diagonal of the Smith Normal Form. If FALSE (the default), the function calls output_results instead which prints the homology group to the screen.

Value

NULL if return_values is FALSE, the diagonal of the Smith Normal Form if return_values is TRUE.

Details

This function is based on the algorithm described in the references below. It should be sufficient for most users to change the up/down action functions according to their requirements and then run the calculation.

References

http://www.maths.sussex.ac.uk/Staff/RAF/Maths/homo.pdf

See Also

degenerate_homology down_action up_action output_results

Examples

# NOT RUN {
homology(3,3,TRUE)
homology(3,3,FALSE)
# }