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**Splitting U(0,1)F**

U(0,1)F | Primus splitvalues | Secundus splitvalues | Tertius splitvalues | Quartus splitvalues |

[1] | 2 | 0 | 1 | 1 |

[2] | F | 1 | F+1 | F-1 |

[3] | 0 | 0 | -1 | 1 |

[4] | -1 | 1 | 0 | 0 |

Splitting U(0,1)Fthe primus | Primus doubled | Secundus doubled | Secundus doubled | Primus doubled | Tertius doubled | Quartus doubled | Quartus doubled | Tertius doubled | |||||||||||||||||

U_{-5} | -F^{4}+3F^{2}-1 | = | -F | * | F^{3}-3F | + | -1 | = | F^{2}-2 | * | -F^{2}+1 | + | 1 | = | F^{2}-F-1 | * | -F^{2}-F+1 | + | 0 | = | -F^{2}-F+1 | * | F^{2}-F-1 | + | 0 |

U_{-4} | -F^{3}+2F | = | -F | * | F^{2}-2 | + | 0 | = | F^{2}-2 | * | -F | + | 0 | = | F^{2}-F-1 | * | -F-1 | + | -1 | = | -F^{2}-F+1 | * | F-1 | + | 1 |

U_{-3} | -F^{2}+1 | = | -1 | * | F^{2}-2 | + | -1 | = | F | * | -F | + | 1 | = | F-1 | * | -F-1 | + | 0 | = | -F-1 | * | F-1 | + | 0 |

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

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

U_{0} | 0 | = | 0 | * | 2 | + | 0 | = | 2 | * | 0 | + | 0 | = | 1 | * | 1 | + | -1 | = | -1 | * | 1 | + | 1 |

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

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

U_{3} | F^{2}-1 | = | F | * | F | + | -1 | = | F^{2}-2 | * | 1 | + | 1 | = | F-1 | * | F+1 | + | 0 | = | F+1 | * | F-1 | + | 0 |

U_{4} | F^{3}-2F | = | F | * | F^{2}-2 | + | 0 | = | F^{2}-2 | * | F | + | 0 | = | F-1 | * | F^{2}+F-1 | + | -1 | = | F+1 | * | F^{2}-F-1 | + | 1 |

U_{5} | F^{4}-3F^{2}+1 | = | F^{2}-1 | * | F^{2}-2 | + | -1 | = | F^{3}-3F | * | F | + | 1 | = | F^{2}-F-1 | * | F^{2}+F-1 | + | 0 | = | F^{2}+F-1 | * | F^{2}-F-1 | + | 0 |

Note that the secundus-based split of a zero-series is

*neutral*: what goes in comes out - in this case the primus.

Note also that a series operating on itself - in this case the primus-based split - renders the secundus as its output series.