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Matrices
| Matrix of the output-series of splits of the fabfour and U(0,0,1)F | ||||
| Primus based | Secundus based | Tertius based | Quartus based | |
| Primus | secundus | primus | quartus | tertius |
| Secundus | primus*(F+2)(F-2) | secundus | tertius*(F+2) | quartus*(F-2) |
| Tertius | quartus*(F-2) | tertius | secundus | primus*(F-2) |
| Quartus | tertius*(F+2) | quartus | primus*(F+2) | secundus |
| U(0,0,1)F | quartus | tertius/(F-2) | secundus/(F-2) | primus |
The outputseries in the blue area have an index-shift of two with regard to the corresponding outputseries in the yellow area (and with the rest of the matrix for that matter).
| Matrix of the output-series of splits of the general series U(a,b)F and U(a,b,c)F | ||||
| Primus based | Secundus based | Tertius based | Quartus based | |
| U(a,b)F | U(-Fa+2b, Fb-2a)F | U(a,b)F | U[a+b, Fb-(a-b)]F | U[-(a-b), Fb-(a+b)]F |
| U(a,b,c)F | U(-Fa+2b-c, Fb-2a+c)F | U[a+ c/(F-2), b+ c/(F-2)]F | U[a+b+ 2c/(F-2), Fb-(a-b)+Fc/(F-2)]F | U[-(a-b), Fb-(a+b)+c]F |
Note how the secundus only acts as 'unity operator' if c=0.