Bonjour Grimbert,

Alas my french is to bad to write this in french.

It took some time to find the old files and the mathematical derivation 
with
pow 16.
Because in the past it was not possible to test a poly 16, I never had 
made
a file for it.
It took me the whole day to build a poly 16 file with 969 factors in it 
and
put
this in an old file that uses a poly 8 object (only 165 factors). 
Luckily
this should produce the same
result, but I expect the poly 16 to be without the central line and be
completely stable.

To keep the maxpower under 15 I invented a tric to avoid one squaring in 
the
derivation so
the result was a poly 8 object. This I could test in 1997 (version 3.0 
or
3.1 ?), but I got
system crashes in those days and there is a line along the y-axis. I 
always
suspected the mathematical
tric to cause this behaviour although subtraction of two equations is
mathematically
perfectly alright.

You find in the pakket a poly 8 file that works. It produces a spiral 
for
which you can alter
the parameters in the beginging of the file.
Further there is a parallel file that uses the poly 16 object. The rest 
is
identical.
If everything is alright, then this should work too if you change Pov 
3.7.

Further you find a file called TestPolyC. When I was playing with my
derivations I was
curious about the way Pov solves a poly with high powers. So I 
downloaded
the source files and
studied the math in poly.cpp. Because I have programmed in pascal for my 
own
fun, I can, with some
difficulty, read the code. Of course I found the code for the binomial
calculation and because I
didn't quit understood the jump with goto l1:, I translated it in SDL 
and
put it in this file.
In my opinion there is a bug in the code. The jump goes to the wrong 
place
so stack2 is not used
correctly and only the first entry is processed. I've put two examples
(bottom of file) that shows
that it goes wrong. Take a look at around the middle of the file, where 
the
cpp code is present too.
I've suggested an improvement in binomial(int n, int  r) too.

You asked if I could go to stil higher powers. I don't think this will
happen, because the power 16
took about two weeks every night and parts of the weekends to solve. I 
don't
think I will do this again.

By the way, can you explain how the solving of the equations goes. There 
are
three loops and a lot of
operations mixed with this, so I can't figure out how this works. 
Searching
on the internet points to math
I can't figure out too. The only thing I could follow is that the ray is
substituted in the equations
somehow. From there on I loose track.

Hope this helps,

Jaap Frank