26 Feb
2012
26 Feb
'12
11:54 a.m.
* Bill Gosper <billgosper@gmail.com> [Feb 26. 2012 18:52]:
[...]
Km(k,n)={ [ q^(n+2*k+1), q*(1-q^(2*k+n))/( (1-q^(k)) * (1-q^(k+n)) ) ; 0, 1 ]; } Nm(k,n)={ [ q^(k), q/(1-q^(k+n)); 0, 1 ]; } \\k=3; n=5; Nm(k,n)*Km(k,n+1) - Km(k,n)*Nm(k+1,n) \\ Test, OK, == zero \\ Left: Ln = prod(n=0,N, Nm(1,n) ) \\ == [0, Lam; 0, 1] Lk = prod(k=1,N, Km(k,oo) ) \\ == [0, 2; 0, 1]] L = Ln * Lk \\ == [0, Lam; 0, 1] \\ OK! \\ Right: Rk = prod(k=1,N, Km(k,oo) ) \\ == [0, 2; 0, 1] Rn = prod(n=0,N, Nm(1,n) ) \\ == [0, Lam; 0, 1] \\ BUT these are the same prods as above! R = Rk * Rn \\ [0, 2; 0, 0] \\ WRONG \\R = Rn * Rk \\ [0, Lam; 0, 0] \\ correct but useless I am giving up here.