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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 2 0 [2] F-2 1 F F-2 [3] 1 -1 -1 1 [4] F-1 -F+1 -1 1

 Splitting U(1,1)Fthe tertius Primusdoubled Quartus*(F-2)doubled Secundusdoubled Tertiusdoubled Tertiusdoubled Secundusdoubled Quartusdoubled Primus*(F-2)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 * F3-3F + -1 = -F2-F+1 * -(F2-1)*(F-2) + 1 U-4 F4-F3-3F2+2F+1 = -F * -(F2+F-1)*(F-2) + 1 = F2-2 * F2-F-1 + -1 = F2-F-1 * F2-2 + -1 = -F2-F+1 * -F*(F-2) + 1 U-3 F3-F2-2F+1 = -1 * -(F2+F-1)*(F-2) + F-1 = F * F2-F-1 + -F+1 = F-1 * F2-2 + -1 = -F-1 * -F*(F-2) + 1 U-2 F2-F-1 = -1 * -(F+1)*(F-2) + 1 = F * F-1 + -1 = F-1 * F + -1 = -F-1 * -(F-2) + 1 U-1 F-1 = 0 * -(F+1)*(F-2) + F-1 = 2 * F-1 + -F+1 = 1 * F + -1 = -1 * -(F-2) + 1 U0 1 = 0 * -(F-2) + 1 = 2 * 1 + -1 = 1 * 2 + -1 = -1 * 0 + 1 U1 1 = 1 * -(F-2) + F-1 = F * 1 + -F+1 = 1 * 2 + -1 = 1 * 0 + 1 U2 F-1 = 1 * F-2 + 1 = F * 1 + -1 = 1 * F + -1 = 1 * F-2 + 1 U3 F2-F-1 = F * F-2 + F-1 = F2-2 * 1 + -F+1 = F-1 * F + -1 = F+1 * F-2 + 1 U4 F3-F2-2F+1 = F * (F+1)*(F-2) + 1 = F2-2 * F-1 + -1 = F-1 * F2-2 + -1 = F+1 * F*(F-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 * F2-2 + -1 = F2+F-1 * F*(F-2) + 1

Note that the secundus-based split of a zero-series is neutral: what goes in comes out - in this case the tertius.
Note also that a series operating on itself - in this case the tertius - renders the secundus as its output series.