Improve genus method of function fields and curves

[kwankyu]

• make genus method of function fields over number fields work.

sage: R.<T> = QQ[]
sage: N.<a> = NumberField(T^2 + 1)
sage: K.<x> = FunctionField(N)
sage: K.genus()
0
sage: S.<t> = PolynomialRing(K)
sage: L.<y> = K.extension(t^2 - x^3 + x)
sage: L.genus()  # not working without this PR
1

• allow integral curves to be defined over number fields
• make geometric genus method of integral curves defined over number fields work

sage: R.<x> = QQ[]
sage: N.<a> = NumberField(x^2 + 1)
sage: P2.<x,y,z> = ProjectiveSpace(N, 2)
sage: C = Curve(y^2*z - x^3 + x*z^2, P2)
sage: C.geometric_genus() # not working without this PR
1

• allow integral curves to be defined from one-dimensional ambient space

sage: R.<x> = QQ[]
sage: N.<a> = NumberField(x^2 + 1)
sage: P1.<x,y> = ProjectiveSpace(N, 1)
sage: C = Curve(P1)
sage: C.geometric_genus()  # not working without this PR
0

• add comments warning for nonsensical result of geometric genus method applied to geometrically-reducible curves

sage: P2.<x,y,z> = ProjectiveSpace(QQ, 2)
sage: C = Curve(x^2 + y^2, P2)
sage: C.geometric_genus()  # negative geometric genus!
-1

• remove unnecessary condition (irreducibility) on arithmetic genus of curves

sage: P.<x,y,z> = ProjectiveSpace(QQ, 2)
sage: C = Curve(x^2 - y^2, P)
sage: C.is_irreducible()
False
sage: C.arithmetic_genus()  # not working without this PR
0

📝 Checklist

• The title is concise and informative.
• The description explains in detail what this PR is about.
• I have linked a relevant issue or discussion.
• I have created tests covering the changes.
• I have updated the documentation accordingly.

⌛ Dependencies

[github-actions]

Documentation preview for this PR (built with commit 3b31b1a; changes) is ready! 🎉

[tscrim]

Thank you. LGTM.

I think these are already nailed in memory in a few places (in one of the categories; if you want to import one from there, please go ahead). I think it would be better to have just one place where such things are constructed if we decide to change this in some fashion. It also can save loading time by a few milliseconds.

[kwankyu]

Thanks!