On Fri, Feb 28, 2014 at 4:18 PM, Aleksandr Kodess <amkod...@gmail.com> wrote:
> As far as I know both sage and magma utilize Brendan McKay's program nauty in
> order to check
That is completely false. Robert Miller implemented from scratch a
number of graph-theory
algorithms independently of the code in nauty.
I don't know the answer to your question below but want to correct you on this
one statement.
> whether two given graphs (directed or undirected) are isomorphic. As is
> demonstrated
> by the following example, sage and magma greatly differ in the efficiency in
> which this
> program is utilized.
>
> # sage code
> q = 19
> n1 = 7
> n2 = 13
> F = FiniteField(q, 'xi')
> V = [(x,y) for x in F for y in F]
> G1 = DiGraph([V, lambda x,y: x[1] + y[1] == x[0]*(y[0]**n1)])
> G2 = DiGraph([V, lambda x,y: x[1] + y[1] == x[0]*(y[0]**n2)])
> G1.is_isomorphic(G2)
>
> // magma code for the same operation
> q := 19;
> n1 := 7;
> n2 := 13;
> F := FiniteField(q);
> V := {[x,y] : x,y in F};
> G1 := Digraph< V|{ [x,y] : x,y in V | x[2] + y[2] eq ((x[1])^1)*((y[1])^n1)}>;
> G2 := Digraph< V|{ [x,y] : x,y in V | x[2] + y[2] eq ((x[1])^1)*((y[1])^n2)}>;
> IsIsomorphic(G1,G2);
>
>
> It takes sage forever to test whether these two directed graphs of order 19^2
> are
> isomorphic (they are in fact not), while it takes magma only a second. The
> same
> problem occurs for other values of q, n1 and n2. The version of sage I'm
> running
> is 5.12, and the version of magma I'm running is 2.19.10.
>
> Is this a known issue? Is this going to be fixed any time soon?
>
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