Allow for multiple intermediate fields in number field search

[rvisser7]

In the number field search page, we currently allow for the user to specify a single intermediate field as part of the search query. Perhaps we could also allow for multiple intermediate subfields to be given in the search box? i.e. allow the user to give a comma-separated list of polynomials and/or field ids: "x^2-2, x^2-3, x^2-5" or "2.2.8.1, 2.2.12.1, 2.2.5.1".

Of course, this is just equivalent to searching for fields that contain the compositum of the listed subfields. Though I think allowing for users to specify multiple subfields directly would be a very nice convenience feature, as otherwise one needs to manually compute a defining polynomial or field id for the compositum field. 🙂

One nice consequence of this is that it would allow users to very quickly and easily search for fields with multiple generators, e.g. $Q(\sqrt{2}, \sqrt{3}, \sqrt{5})$, or $Q(\sqrt[4]{2}, \sqrt[3]{5})$, as I'm not sure if there's actually any easy way to search for such fields at the moment? (again, other than loading up Sage/Magma/Pari, manually constructing the compositum field, and then computing an absolute defining polynomial).