p. orders the roots by decreasing magnitude, and within that (for roots with equal magnitude) the ordering used by \: . For example:
p. p. < 3 1 4 1 5 9 ┌─┬───────────┐ │1│9 5 4 3 1 1│ └─┴───────────┘ p. p. <3 1 4 1 5 9 3j4 3j_4 _3j4 _3j_4 ┌─┬───────────────────────────────┐ │1│9 5 3j4 3j_4 _3j4 _3j_4 4 3 1 1│ └─┴───────────────────────────────┘ If I may be permitted to show off a bit: p. p. <1+i.20x ┌─┬──────────────────────────────────────────────────┐ │1│20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1│ └─┴──────────────────────────────────────────────────┘ https://en.wikipedia.org/wiki/Wilkinson%27s_polynomial On Mon, Aug 10, 2015 at 6:54 AM, Don Guinn <[email protected]> wrote: > Thanks. I was being a little dense in forgetting that it is solving for x, > not for all values. My thinking gets a little muddled with grandkids > around. I was just surprised at the neatness of the solution. > > I played with products of consecutive numbers greater than 3 (are those > still special products?) and p. still works until p. becomes unstable due > to the order of the polynomial. I'm curious as to why the desired value for > x is always the last root. Just the luck of the draw or is there some > reason as to why it is always last. Do real values always come last? For > the products of even consecutive numbers the number of real roots found by > p. must be even. But the last one still seems to be the correct one. > > Take of two different product of 4 sequential numbers. Their gcd many cases > is s special product. Those that aren't are a multiple of a special > product. This seems to be the case that the gcd for the products of n > consecutive integers is the a product or a multiple of n-1 and n-2 ... > consecutive integers. The multiples seem to be in one consecutive group. > > Now that the grandkids are gone maybe I can play with this more with a > clearer mind. > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
