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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)Fthe secundus Primusdoubled Primus*(F2-4)doubled Secundusdoubled Secundusdoubled Tertiusdoubled Tertius*(F+2)doubled Quartusdoubled 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.