How would you compute the fractional chromatic index of an edge-weighted graph using SAGE?

The built-in function fractional_chromatic_index seems to compute the fractional chromatic index for only unweighted graphs. For instance, if $G$ is the 5-cycle graph, its fractional chromatic index is $2.5$. But if one of the edges can be ignored, say by giving it a zero weight, then the fractional chromatic index becomes $2$. The following code and output shows that SAGE ignores the edge-weights and computes only for unweighted graphs:

```
sage: G = graphs.EmptyGraph()
sage: G.add_edges([(1,2,1),(2,3,1),(3,4,1),(4,5,1),(5,1,0)])
sage: G.fractional_chromatic_index()
5/2
sage:
```

Is there some way to get the built-in function to take edge weights into account?