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# Copyright (c) 2019-2025, Saransh Chopra, Henry Schreiner, Eduardo Rodrigues, Jonas Eschle, and Jim Pivarski.
#
# Distributed under the 3-clause BSD license, see accompanying file LICENSE
# or https://github.com/scikit-hep/vector for details.
from __future__ import annotations
import pytest
import vector
sympy = pytest.importorskip("sympy")
pytestmark = pytest.mark.sympy
x, y, z, t, nx, ny, nz, nt = sympy.symbols("x y z t nx ny nz nt", real=True)
values = {x: 1.0, y: 1.0, z: 1.0, t: 1.0, nx: -1.0, ny: -1.0, nz: -1.0, nt: 1.0}
def test_lorentz_sympy():
v1 = vector.MomentumSympy4D(
vector.backends.sympy.AzimuthalSympyXY(x, y),
vector.backends.sympy.LongitudinalSympyZ(z),
vector.backends.sympy.TemporalSympyTau(t),
)
v2 = vector.MomentumSympy4D(
vector.backends.sympy.AzimuthalSympyXY(nx, ny),
vector.backends.sympy.LongitudinalSympyZ(nz),
vector.backends.sympy.TemporalSympyTau(nt),
)
assert (
v1.deltaRapidityPhi2(v2).simplify()
== 0.25
* (
sympy.log(
(-nz - sympy.sqrt(nt**2 + nx**2 + ny**2 + nz**2))
/ (nz - sympy.sqrt(nt**2 + nx**2 + ny**2 + nz**2))
)
- sympy.log(
(-z - sympy.sqrt(t**2 + x**2 + y**2 + z**2))
/ (z - sympy.sqrt(t**2 + x**2 + y**2 + z**2))
)
)
** 2
+ (
sympy.Mod(-sympy.atan2(ny, nx) + sympy.atan2(y, x) + sympy.pi, 2 * sympy.pi)
- sympy.pi
)
** 2
)
expected_result = (
# phi
sympy.pi**2
# rapidity
+ ((0.5 * sympy.log(3 / 1) - 0.5 * sympy.log(1 / 3)) ** 2)
)
for t1 in (
"xyzt",
"xythetat",
"xyetat",
"rhophizt",
"rhophithetat",
"rhophietat",
"xyztau",
"xythetatau",
"xyetatau",
"rhophiztau",
"rhophithetatau",
"rhophietatau",
):
for t2 in (
"xyzt",
"xythetat",
"xyetat",
"rhophizt",
"rhophithetat",
"rhophietat",
"xyztau",
"xythetatau",
"xyetatau",
"rhophiztau",
"rhophithetatau",
"rhophietatau",
):
tr1, tr2 = getattr(v1, "to_" + t1)(), getattr(v2, "to_" + t2)()
assert tr1.deltaRapidityPhi2(tr2).subs(values).evalf() == pytest.approx(
expected_result.evalf()
)
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