Re: question on converting general cubic equations to Weierstrass format

[American Citizen <website.reader3@gmail.com>]

Bill et al:

The problem was that I was using the kill(variable) inside my code, when 
I should have been using the ticked 'variable instead as a temporary.

After carefully removing all the killed variables and replacing them 
with the 'variable, the code worked as it was supposed to.

I have both the forward and reverse maps done now, which goes from 
certain Pythagorean ratios in the body/edge/face cuboids and the points 
on the elliptic curves derived from these ratios.

Example:

Bpy=[11/2, 6/5, 8/5] (body cuboid Pythagorean generators)

? [e,p]=b2w(11/2)
%260 = [[0, 15625, 0, 26501904, 0], [[-13068, 300564]]]

And taking the point [-13068,300654] on the curve yields

? w2bt(p,11/2)
%264 = [11/2, 6/5, 8/5]

which is the body cuboid triad again.

If I find a pool of 25 low height points on e [0, 15625, 0, 26501904, 0] 
and run them through the w2bt() function I get

W = [[11/2, 6/5, 8/5], [11/2, 13/3, 11], [11/2, 5859/3901, 2573/987]] 
and we find the following sets of body cuboids

> ? PY_to_BEF(W[1])
> %309 = [[44, 117, 240, 270.60118255469616480151251659073179262], [429, 
> 880, 2340, 2536.5411488875949240489465244824297348]]
> ? PY_to_BEF(W[2])
> %310 = [[429, 880, 2340, 2536.5411488875949240489465244824297348], 
> [44, 117, 240, 270.60118255469616480151251659073179262]]
> ? PY_to_BEF(W[3])
> %311 = [[9555040, 22855959, 25407720, 
> 35485854.742554546504823379268483905437], [111740244, 124215520, 
> 297127467, 340881371.13061198346174879379986397024]]
Randall

P.S.: the space diagonal is the 4th term for the body cuboid, it is 
irrational and in a quadratic field. We also notice that body cuboids 
are related in pairs.

All the rational points on the curve will create body cuboids containing 
the 11/2 ratio, which is why we searched for points on this particular 
elliptic curve.