As far as I know both sage and magma utilize Brendan McKay's program nauty in
order to check 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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