On Thursday, March 21, 2019 at 9:38:03 PM UTC-7, Ai Bo wrote:
>
> Saw this in the document:
>  res/mod : only generate subset res out of subsets 0..mod-1
>

It would help if you gave some context for this. I'm guessing that most 
Sage users won't know what "geng" is. I certainly didn't. I found by 
searching the source code that you found this help message in the method 
"nauty_geng" in graph_generators.py: you should have said this at the start 
instead of just "saw this in the document". This makes it look like the 
program "geng" comes from nauty. Now look at the nauty source code (there 
is a tar file in the "upstream" directory, if you have a source code 
version of Sage, also available at 
http://files.sagemath.org/spkg/upstream/nauty/index.html). The nauty manual 
says

res/mod : only generate subset res out of subsets 0..mod-1

and

See program text for much more information.

The file geng.c says
 
            mod, res = a way to restrict the output to a subset.
                        All the graphs in G(n,mine..maxe) are divided into
                        disjoint classes C(0,mod),C(1,mod),...,C(mod-1,mod),
                        of very approximately equal size.
                        Only the class C(res,mod) is written.

                        If the -x or -X switch is used, they must have the 
                        same value for different values of res; otherwise 
                        the partitioning may not be valid.  In this case
                        (-x,-X with constant value), the usual 
relationships 
                        between modulo classes are obeyed; for example 
                        C(3,4) = C(3,8) union C(7,8).  This is not true
                        if 3/8 and 7/8 are done with -x or -X values
                        different from those used for 3/4.

 

>
> How is the output divided?
>
> I tried with : ../sage-8.6/local/bin/geng 6 -C 0/7
> and then I iterated from 0/7, 1/7, 2/7, 3/7....
> Why the output is 27, 21, 7, 1, 0, 0, ...
>
> How is the subset generated?
>
> Thank you.
>

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