cayleypy.MatrixGroups

class cayleypy.MatrixGroups[source]

Pre-defined Cayley graphs for matrix groups.

Methods

`__init__`()
`heisenberg`([modulo])	Returns Cayley graph for the Heisenberg group.

static heisenberg(modulo: int = 0) → CayleyGraphDef[source]

Returns Cayley graph for the Heisenberg group.

This is a group of upper triangular 3x3 integer matrices with 1s on main diagonal. See https://en.wikipedia.org/wiki/Heisenberg_group.

Generated by 4 matrices: x=(110,010,001), y=(100,011,001), and their inverses. Central element is identity matrix.

Parameters:: modulo – multiplication modulo (or 0 if multiplication is not modular).
Returns:: requested graph as CayleyGraphDef.