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