### Who's Online

We have 101 guests and no members online

### Article Index

Splitting U(a,b)F
 U(a,b)F Primus splitvalues Secundus splitvalues Tertius splitvalues Quartus splitvalues [1] -Fa+2b a a+b -(a-b) [2] -2a+Fb b Fb-(a-b) Fb-(a+b) [3] a -a -b b [4] Fa-b -Fa+b -a a

 Splitting U(a,b)Fthe general zero series Primusdoubled U(-Fa+2b, Fb-2a)Fdoubled Secundusdoubled U(a,b)Fdoubled Tertiusdoubled U[a+b, Fb-(a-b)]Fdoubled Quartusdoubled U[-(a-b), Fb-(a+b)]Fdoubled U-4 F4a-F3b-3F2a+2Fb+a = -F * -F3a+F2b+3Fa-2b + a = F2-2 * F2a-Fb-a + -a = F2-F-1 * F2a+F(a-b)-(a+b) + -b = -F2-F+1 * -F2a+F(a+b)+(a-b) + b U-3 F3a-F2b-2Fa+b = -1 * -F3a+F2b+3Fa-2b + Fa-b = F * F2a-Fb-a + -Fa+b = F-1 * F2a+F(a-b)-(a+b) + -a = -F-1 * -F2a+F(a+b)+(a-b) + a U-2 F2a-Fb-a = -1 * -F2a+Fb+2a + a = F * Fa-b + -a = F-1 * Fa+(a-b) + -b = -F-1 * -Fa+(a+b) + b U-1 Fa-b = 0 * -F2a+Fb+2a + Fa-b = 2 * Fa-b + -Fa+b = 1 * Fa+(a-b) + -a = -1 * -Fa+(a+b) + a U0 a = 0 * -Fa+2b + a = 2 * a + -a = 1 * a+b + -b = -1 * -(a-b) + b U1 b = 1 * -Fa+2b + Fa-b = F * a + -Fa+b = 1 * a+b + -a = 1 * -(a-b) + a U2 Fb-a = 1 * Fb-2a + a = F * b + -a = 1 * Fb-(a-b) + -b = 1 * Fb-(a+b) + b U3 F2b-Fa-b = F * Fb-2a + Fa-b = F2-2 * b + -Fa+b = F-1 * Fb-(a-b) + -a = F+1 * Fb-(a+b) + a U4 F3b-F2a-2Fb+a = F * F2b-Fa-2b + a = F2-2 * Fb-a + -a = F-1 * F2b-F(a-b)-(a+b) + -b = F+1 * F2b-F(a+b)+(a-b) + b U5 F4b-F3a-3F2b+2Fa+b = F2-1 * F2b-Fa-2b + Fa-b = F3-3F * Fb-a + -Fa+b = F2-F-1 * F2b-F(a-b)-(a+b) + -a = F2+F-1 * F2b-F(a+b)+(a-b) + a

Note that the secundus-based split of a zero-series is neutral: what goes in comes out - in this case the general zero-series itself.