[seqfan] Re: Overview of sequence arising from binary quadratic forms

[Peter Luschny]

Dear Neil,

since my only intention (besides from learning something)
was to support your Wiki page, I have no problem to delete
the x != 0 condition from the definition on my blog to ensure
that no confusion can arise -- although the significance
of the x != 0 condition is exactly the point I've learned.

The significance as I see it is twofold: the theoretical
which is explained by Sutherland in his lecture and the
practical which I think the users of the database could
benefit from: if the crucial condition is dropped the user
will always see (0,a,b,c,..) and know -- nothing about
the kind of representation of 0. In the other case he will
see (0,a,b,c,..) or (a,b,c,..) with a != 0 and know
immediately if 0 is represented in a nontrivial way or not.
He gets more information!

Finally a word to the Sage program. I did not implement
'my' definition but the standard definition. I just do not
prepend in a final step the '0' to the computed list.
Doing so I leave it to the user if he is willing to
include 0 in all cases or only under some conditions.
It is precisely in this sense that I meant that it does
not matter what definition you prefer when you use the
program: it remains to the user to extend it in the way he
prefers. This is clearly indicated in the title of my blog:
"Positive numbers represented by a binary quadratic form".

This said , may I apologize for remaining linguistic inaccuracies.
Errors in the program I deny, however, and ask the community
to help me to confirm this by diligent testing.

Peter