At 01:27 PM 12/17/2008, Fred lunnon wrote:

On 12/17/08, rwg@sdf.lonestar.org <rwg@sdf.lonestar.org> wrote:

...

... Thereby reenacting one of my favorite denestings:

1/5 3/5 3/5 2/5 1/5 2/5 3/5 1/5 1/3 - 2 3 + 2 3 + 3 + 2 (3 - 2 ) = ------------------------------------- , 2/3 5

a major simplification that looks anything but.

Indeed!

u := 3^(1/5); v := 2^(1/5); w := 5^(1/3); l := (u^3 - v)^1/3;

Presumably you meant to write l := (u^3 - v)^(1/3); which would account for the difference.

r := (u + v^2 - v*u^3 + v^3*u^2)/w^2; evalf(l - r); # -.6607822845 ?!

-- Fred W. Helenius fredh@ix.netcom.com