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Splitting U(a,b,c)F
 U(a,b,c)F Primus splitvalues Secundus splitvalues Tertius splitvalues Quartus splitvalues [1] -Fa+2b-c a+ c/(F-2) (a+b)+ 2c/(F-2) -(a-b) [2] Fb-2a+c b+ c/(F-2) Fb-(a-b)+ Fc/(F-2) Fb-(a+b)+c [3] a -a- 2c/(F-2) -b- 2c/(F-2) b [4] Fa-b+c -Fa+b- Fc/(F-2) -a- 2c/(F-2) a

 Splitting U(a,b,c)Fthe general series Primusdoubled U(-Fa+2b-c, Fb-2a+c)Fdoubled Secundusdoubled U[a+ c/(F-2), b+ c/(F-2)]Fdoubled Tertiusdoubled U[a+b+ 2c/(F-2), Fb-(a-b)+ Fc/(F-2)]Fdoubled Quartusdoubled U[-(a-b), Fb-(a+b)+c]Fdoubled U-4 F4a-F3(b-c)-F2(3a-c)+F(2b-c)+a = -F * -F3a+F2(b-c)+F(3a-c)-2b+c + a = F2-2 * F2a-Fb-a+ c(F2-F-1)/(F-2) + -a- 2c/(F-2) = F2-F-1 * F2a+F(a-b)-(a+b) +c(F2-2)/(F-2) + -b -2c/(F-2) = -F2-F+1 * -F2a+F(a+b-c)+(a-b) + b U-3 F3a-F2(b-c)-F(2a-c)+b = -1 * -F3a+F2(b-c)+F(3a-c)-2b+c + Fa-b+c = F * F2a-Fb-a+ c(F2-F-1)/(F-2) + -Fa+b -Fc/(F-2) = F-1 * F2a+F(a-b)-(a+b) +c(F2-2)/(F-2) + -a -2c/(F-2) = -F-1 * -F2a+F(a+b-c)+(a-b) + a U-2 F2a-F(b-c)-(a-c) = -1 * -F2a+F(b-c)+2a-c + a = F * Fa-b+ c(F-1)/(F-2) + -a- 2c/(F-2) = F-1 * Fa+(a-b) +Fc/(F-2) + -b -2c/(F-2) = -F-1 * -Fa+(a+b)-c + b U-1 Fa-(b-c) = 0 * -F2a+F(b-c)+2a-c + Fa-b+c = 2 * Fa-b+ c(F-1)/(F-2) + -Fa+b -Fc/(F-2) = 1 * Fa+(a-b) +Fc/(F-2) + -a -2c/(F-2) = -1 * -Fa+(a+b)-c + a U0 a = 0 * -Fa+2b-c + a = 2 * a+ c/(F-2) + -a- 2c/(F-2) = 1 * (a+b)+ 2c/(F-2) + -b -2c/(F-2) = -1 * -(a-b) + b U1 b = 1 * -Fa+2b-c + Fa-b+c = F * a+ c/(F-2) + -Fa+b -Fc/(F-2) = 1 * (a+b)+ 2c/(F-2) + -a -2c/(F-2) = 1 * -(a-b) + a U2 Fb-(a-c) = 1 * Fb-2a+c + a = F * b+ c/(F-2) + -a- 2c/(F-2) = 1 * Fb-(a-b)+ Fc/(F-2) + -b -2c/(F-2) = 1 * Fb-(a+b)+c + b U3 F2b-F(a-c)-(b-c) = F * Fb-2a+c + Fa-b+c = F2-2 * b+ c/(F-2) + -Fa+b -Fc/(F-2) = F-1 * Fb-(a-b)+ Fc/(F-2) + -a -2c/(F-2) = F+1 * Fb-(a+b)+c + a U4 F3b-F2(a-c)-F(2b-c)+a = F * F2b-F(a-c)-2b+c + a = F2-2 * Fb-a+ c(F-1)/(F-2) + -a- 2c/(F-2) = F-1 * F2b-F(a-b)-(a+b)+ c(F2-2)/(F-2) + -b -2c/(F-2) = F+1 * F2b-F(a+b-c)+(a-b) + b U5 F4b-F3(a-c)-F2(3b-c)+F(2a-c)+b = F2-1 * F2b-F(a-c)-2b+c + Fa-b+c = F3-3F * Fb-a+ c(F-1)/(F-2) + -Fa+b -Fc/(F-2) = F2-F-1 * F2b-F(a-b)-(a+b)+ c(F2-2)/(F-2) + -a -2c/(F-2) = F2+F-1 * F2b-F(a+b-c)+(a-b) + a

This is the alpha and omega of splitting in the U(a,b,c)F domain: the split of the general series.
Secundus- and tertius-based splits go clearly into the realm of rational numbers. Clearly too, the secundus loses the 'unity role' it has for zero series.