Add keyword argument for 3-vector magnitude, so that they can be constructed entirely in spherical coordinates

(a feature request)

The system to construct vectors is elegant: first 2D, add an argument for 3D, add another for 4D. To quote the docs

In all, there are 12 coordinate systems [in 4-space]: {x-y vs ρ-ϕ in the azimuthal plane} × {z vs θ vs η longitudinally} × {t vs τ temporally}.

But as a consequence, there is no argument to set the magnitude of a 3-vector. Using rho (or pt) remains the radius in the azimuthal (xy) plane.

• If the user knows that pt stands for "transverse momentum" (having read the docs), this is reasonably clear. But a user who knows rho from spherical coordinates could be unaware that they need to set rho = magnitude * sin(theta).
• If a 3-vector is "close" to the z-axis, any step that involves a conversion to (rho, phi, theta) introduces rounding errors. I wouldn't call a dealbreaker for a numerical library!
• If a 3-vector is aligned with the z-axis, it however stops working entirely.

Examples:

import vector
print(vector.__version__)
# 0.8.4

# Naively using `rho` in its spherical meaning
v_spherical = vector.VectorObject3D.from_rhophitheta(1, 0, 0)
print(v_spherical.z) # showing that `rho` is from cylindrical coordinates
# 1.7976931348623157e+308

# Converting the cartesian 3-vector (0,0,1) to "spherical" coordinates
v_cartesian = vector.obj(x=0, y=0, z=1)
print(v_cartesian.mag)
# 1.0
print(v_cartesian.to_rhophitheta()) # can not be represented
# vector.obj(rho=0.0, phi=0.0, theta=0.0)
print(v_cartesian.to_rhophitheta().to_xyz()) # z-component is lost in conversion
# vector.obj(x=0.0, y=0.0, z=0.0)
print(v_cartesian.to_rhophitheta().to_xyz().mag / v_cartesian.mag) # uh-oh!
# 0.0

# Rounding errors for a vector close to the z-axis
v_close = vector.obj(x=0.01, y=0.01, z=1)
print(v_close.to_rhophitheta().mag / v_close.mag) # rounding error
# 1.000000000000742

Start by reading the 3D constructor entry point VectorObject3D.from_rhophitheta and the vector.obj factory, then compare them with to_rhophitheta(). Use the examples in this issue as behavioral checks, including a vector aligned with the z-axis and one close to it. Done means a 3-vector can be constructed from spherical coordinates with its magnitude preserved.