In Sage 9.7.beta1, we have

sage: S.<theta, phi> = manifolds.Sphere(2, coordinates='spherical')
sage: F = S.scalar_field(function('f')(theta, phi) + function('g')(theta))
sage: F.display()
S^2 → ℝ
on A: (theta, phi) ↦ f(theta, phi) + g(theta)

So far, so good, but

sage: S.options.omit_function_arguments = True
sage: F.display()
S^2 → ℝ
on A: (theta, phi) ↦ f(theta, phi) + g

The r.h.s. should be f + g.

This bug is actually triggered by the following feature/bug of symbolic expressions:

sage: function('f')(theta, phi).arguments()
(phi, theta)

i.e. arguments() returns the arguments sorted according to the alphabetical order, as reported in https://groups.google.com/g/sage-devel/c/Gt6GWZU-cI4/. See also #32227.

Component: manifolds

Keywords: omit_function_arguments

Author: Utkarsh Sharma

Branch/Commit: 6dc5953

Reviewer: Eric Gourgoulhon

Issue created by migration from https://trac.sagemath.org/ticket/33957