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