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Splitting U(1,1)F
| U(1,1)F | Primus splitvalues | Secundus splitvalues | Tertius splitvalues | Quartus splitvalues |
| [1] | -F+2 | 1 | 2 | 0 |
| [2] | F-2 | 1 | F | F-2 |
| [3] | 1 | -1 | -1 | 1 |
| [4] | F-1 | -F+1 | -1 | 1 |
| Splitting U(1,1)F the tertius | Primus doubled | Quartus*(F-2) doubled | Secundus doubled | Tertius doubled | Tertius doubled | Secundus doubled | Quartus doubled | Primus*(F-2) doubled | |||||||||||||||||
| U-5 | F5-F4-4F3+3F2+3F-1 | = | -F | * | -(F3+F2-2F-1)*(F-2) | + | F-1 | = | F2-2 | * | F3-F2-2F+1 | + | -F+1 | = | F2-F-1 | * | F3-3F | + | -1 | = | -F2-F+1 | * | -(F2-1)*(F-2) | + | 1 |
| U-4 | F4-F3-3F2+2F+1 | = | -F | * | -(F2+F-1)*(F-2) | + | 1 | = | F2-2 | * | F2-F-1 | + | -1 | = | F2-F-1 | * | F2-2 | + | -1 | = | -F2-F+1 | * | -F*(F-2) | + | 1 |
| U-3 | F3-F2-2F+1 | = | -1 | * | -(F2+F-1)*(F-2) | + | F-1 | = | F | * | F2-F-1 | + | -F+1 | = | F-1 | * | F2-2 | + | -1 | = | -F-1 | * | -F*(F-2) | + | 1 |
| U-2 | F2-F-1 | = | -1 | * | -(F+1)*(F-2) | + | 1 | = | F | * | F-1 | + | -1 | = | F-1 | * | F | + | -1 | = | -F-1 | * | -(F-2) | + | 1 |
| U-1 | F-1 | = | 0 | * | -(F+1)*(F-2) | + | F-1 | = | 2 | * | F-1 | + | -F+1 | = | 1 | * | F | + | -1 | = | -1 | * | -(F-2) | + | 1 |
| U0 | 1 | = | 0 | * | -(F-2) | + | 1 | = | 2 | * | 1 | + | -1 | = | 1 | * | 2 | + | -1 | = | -1 | * | 0 | + | 1 |
| U1 | 1 | = | 1 | * | -(F-2) | + | F-1 | = | F | * | 1 | + | -F+1 | = | 1 | * | 2 | + | -1 | = | 1 | * | 0 | + | 1 |
| U2 | F-1 | = | 1 | * | F-2 | + | 1 | = | F | * | 1 | + | -1 | = | 1 | * | F | + | -1 | = | 1 | * | F-2 | + | 1 |
| U3 | F2-F-1 | = | F | * | F-2 | + | F-1 | = | F2-2 | * | 1 | + | -F+1 | = | F-1 | * | F | + | -1 | = | F+1 | * | F-2 | + | 1 |
| U4 | F3-F2-2F+1 | = | F | * | (F+1)*(F-2) | + | 1 | = | F2-2 | * | F-1 | + | -1 | = | F-1 | * | F2-2 | + | -1 | = | F+1 | * | F*(F-2) | + | 1 |
| U5 | F4-F3-3F2+2F+1 | = | F2-1 | * | (F+1)*(F-2) | + | F-1 | = | F3-3F | * | F-1 | + | -F+1 | = | F2-F-1 | * | F2-2 | + | -1 | = | F2+F-1 | * | F*(F-2) | + | 1 |
Note that the secundus-based split of a zero-series is neutral: what goes in comes out - in this case the tertius.
Note also that a series operating on itself - in this case the tertius - renders the secundus as its output series.