On Thu, Jul 30, 2009 at 10:31 AM, Jason Grout
<jason-s...@creativetrax.com>wrote:

>
> Rob Beezer wrote:
> > On Jul 30, 10:04 am, William Stein <wst...@gmail.com> wrote:
> >> What did he say?  I've only seen him speak on the History Channel
> >> (seriously).
> >
> > LOL.  Topic is now graph codes, not Bible Codes.
> >
> > I think graph7 would be worse since then we'd have 7 bits to a
> > character and more bad characters.  Maybe graph5?  But seriously, how
> > about a standard like Base-64, which would still pack 6 bits to the
> > byte while using letters, numerals and + and /?  I think this is what
> > PGP and GPG use for ASCII versions of binary objects.  First paragraph
> > at link seems to say it all:
> >
> > http://en.wikipedia.org/wiki/Base64
> >
>
> I think using the established international "standard" of Base64 is a
> good option to convert to.  It should be easy to write a function that
> gives this "sage6" format of the graph.  It would probably make sense to
> follow the other conventions of graph6/sparse6 (i.e., edge traversal
> order, etc.)


This would be trivial to implement if we just base64 encode/decode the
existing graph6 string.  Then, as illustrated below, the nauty graph6 string
":I`ASWCaG`WaJC{afP" that started this message just becomes the nice sage6
string "SXBRSlpIQEhX".

sage: h=Graph(":I`ASWCaG`WaJC{afP")
sage: h
Looped multi-graph on 10 vertices
sage: import base64
sage: base64.b64encode(h.graph6_string())
'SXBRSlpIQEhX'
sage: Graph(base64.b64decode('SXBRSlpIQEhX'))
Graph on 10 vertices

The only problem I see is that one may want to do:

Graph('SXBRSlpIQEhX')

but that could be ambiguous in some rare cases when the
string is *both* a sage6 and graph6 string.  Does that ever happen?  (Maybe
no.)

 -- William

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