homology: Calculation of quandle and rack homology groups of a rack /...
In quhomology: Calculation of Homology of Quandles, Racks, Biquandles and Biracks

Description Usage Arguments Details Value Note References See Also Examples

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

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

`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.

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.

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

Note that the rack/birack is determined by not only $k$, but also by the up and down actions in up_action and down_action

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

degenerate_homology down_action up_action output_results