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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)Fthe quartus Primusdoubled Tertius*(F+2)doubled Secundusdoubled Quartusdoubled Tertiusdoubled Primus*(F+2)doubled Quartusdoubled Secundusdoubled 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.