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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 | Primus doubled | Quartus*(F-2) doubled | Secundus doubled | Tertius doubled | Tertius doubled | Secundus doubled | Quartus doubled | Primus*(F-2) doubled | |||||||||||||||||

U_{-5} | F^{5}-F^{4}-4F^{3}+3F^{2}+3F-1 | = | -F | * | -(F^{3}+F^{2}-2F-1)*(F-2) | + | F-1 | = | F^{2}-2 | * | F^{3}-F^{2}-2F+1 | + | -F+1 | = | F^{2}-F-1 | * | F^{3}-3F | + | -1 | = | -F^{2}-F+1 | * | -(F^{2}-1)*(F-2) | + | 1 |

U_{-4} | F^{4}-F^{3}-3F^{2}+2F+1 | = | -F | * | -(F^{2}+F-1)*(F-2) | + | 1 | = | F^{2}-2 | * | F^{2}-F-1 | + | -1 | = | F^{2}-F-1 | * | F^{2}-2 | + | -1 | = | -F^{2}-F+1 | * | -F*(F-2) | + | 1 |

U_{-3} | F^{3}-F^{2}-2F+1 | = | -1 | * | -(F^{2}+F-1)*(F-2) | + | F-1 | = | F | * | F^{2}-F-1 | + | -F+1 | = | F-1 | * | F^{2}-2 | + | -1 | = | -F-1 | * | -F*(F-2) | + | 1 |

U_{-2} | F^{2}-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 |

U_{0} | 1 | = | 0 | * | -(F-2) | + | 1 | = | 2 | * | 1 | + | -1 | = | 1 | * | 2 | + | -1 | = | -1 | * | 0 | + | 1 |

U_{1} | 1 | = | 1 | * | -(F-2) | + | F-1 | = | F | * | 1 | + | -F+1 | = | 1 | * | 2 | + | -1 | = | 1 | * | 0 | + | 1 |

U_{2} | F-1 | = | 1 | * | F-2 | + | 1 | = | F | * | 1 | + | -1 | = | 1 | * | F | + | -1 | = | 1 | * | F-2 | + | 1 |

U_{3} | F^{2}-F-1 | = | F | * | F-2 | + | F-1 | = | F^{2}-2 | * | 1 | + | -F+1 | = | F-1 | * | F | + | -1 | = | F+1 | * | F-2 | + | 1 |

U_{4} | F^{3}-F^{2}-2F+1 | = | F | * | (F+1)*(F-2) | + | 1 | = | F^{2}-2 | * | F-1 | + | -1 | = | F-1 | * | F^{2}-2 | + | -1 | = | F+1 | * | F*(F-2) | + | 1 |

U_{5} | F^{4}-F^{3}-3F^{2}+2F+1 | = | F^{2}-1 | * | (F+1)*(F-2) | + | F-1 | = | F^{3}-3F | * | F-1 | + | -F+1 | = | F^{2}-F-1 | * | F^{2}-2 | + | -1 | = | F^{2}+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.