For those who do not know, the split-complex numbers are an analogue to the complex numbers where J is defined such that $J^2=1$ but $J\ne\pm1$, so they are all of the form $a+bJ$.
By using TagSetDelayed, I tried to define the split-complex numbers as so:
J /: J^2 := 1
If I then type
J^2, I get the output
However, if I type
J^3, I just get the output
J^3. I would like to instead get the output $J$, since $J^3=J^2J=1J=J$.
Is there a better way to implement this number system?