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Splitting U(a,b)F
| U(a,b)F | Primus splitvalues | Secundus splitvalues | Tertius splitvalues | Quartus splitvalues |
| [1] | -Fa+2b | a | a+b | -(a-b) |
| [2] | -2a+Fb | b | Fb-(a-b) | Fb-(a+b) |
| [3] | a | -a | -b | b |
| [4] | Fa-b | -Fa+b | -a | a |
| Splitting U(a,b)F the general zero series | Primus doubled | U(-Fa+2b, Fb-2a)F doubled | Secundus doubled | U(a,b)F doubled | Tertius doubled | U[a+b, Fb-(a-b)]F doubled | Quartus doubled | U[-(a-b), Fb-(a+b)]F doubled | |||||||||||||||||
| U-4 | F4a-F3b-3F2a+2Fb+a | = | -F | * | -F3a+F2b+3Fa-2b | + | a | = | F2-2 | * | F2a-Fb-a | + | -a | = | F2-F-1 | * | F2a+F(a-b)-(a+b) | + | -b | = | -F2-F+1 | * | -F2a+F(a+b)+(a-b) | + | b |
| U-3 | F3a-F2b-2Fa+b | = | -1 | * | -F3a+F2b+3Fa-2b | + | Fa-b | = | F | * | F2a-Fb-a | + | -Fa+b | = | F-1 | * | F2a+F(a-b)-(a+b) | + | -a | = | -F-1 | * | -F2a+F(a+b)+(a-b) | + | a |
| U-2 | F2a-Fb-a | = | -1 | * | -F2a+Fb+2a | + | a | = | F | * | Fa-b | + | -a | = | F-1 | * | Fa+(a-b) | + | -b | = | -F-1 | * | -Fa+(a+b) | + | b |
| U-1 | Fa-b | = | 0 | * | -F2a+Fb+2a | + | Fa-b | = | 2 | * | Fa-b | + | -Fa+b | = | 1 | * | Fa+(a-b) | + | -a | = | -1 | * | -Fa+(a+b) | + | a |
| U0 | a | = | 0 | * | -Fa+2b | + | a | = | 2 | * | a | + | -a | = | 1 | * | a+b | + | -b | = | -1 | * | -(a-b) | + | b |
| U1 | b | = | 1 | * | -Fa+2b | + | Fa-b | = | F | * | a | + | -Fa+b | = | 1 | * | a+b | + | -a | = | 1 | * | -(a-b) | + | a |
| U2 | Fb-a | = | 1 | * | Fb-2a | + | a | = | F | * | b | + | -a | = | 1 | * | Fb-(a-b) | + | -b | = | 1 | * | Fb-(a+b) | + | b |
| U3 | F2b-Fa-b | = | F | * | Fb-2a | + | Fa-b | = | F2-2 | * | b | + | -Fa+b | = | F-1 | * | Fb-(a-b) | + | -a | = | F+1 | * | Fb-(a+b) | + | a |
| U4 | F3b-F2a-2Fb+a | = | F | * | F2b-Fa-2b | + | a | = | F2-2 | * | Fb-a | + | -a | = | F-1 | * | F2b-F(a-b)-(a+b) | + | -b | = | F+1 | * | F2b-F(a+b)+(a-b) | + | b |
| U5 | F4b-F3a-3F2b+2Fa+b | = | F2-1 | * | F2b-Fa-2b | + | Fa-b | = | F3-3F | * | Fb-a | + | -Fa+b | = | F2-F-1 | * | F2b-F(a-b)-(a+b) | + | -a | = | F2+F-1 | * | F2b-F(a+b)+(a-b) | + | a |
Note that the secundus-based split of a zero-series is neutral: what goes in comes out - in this case the general zero-series itself.