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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 math
import pytest
import vector
sympy = pytest.importorskip("sympy")
pytestmark = pytest.mark.sympy
x, y, rho, phi, z, t = sympy.symbols("x y rho phi z t", real=True, positive=True)
values = {x: 3, y: 4, rho: 5, phi: 0, z: 10, t: 20}
def test_xy_z_t():
vec = vector.MomentumSympy4D(
vector.backends.sympy.AzimuthalSympyXY(x, y),
vector.backends.sympy.LongitudinalSympyZ(z),
vector.backends.sympy.TemporalSympyT(t),
)
assert vec.Et == t * sympy.sqrt(x**2 + y**2) / sympy.sqrt(x**2 + y**2 + z**2)
assert vec.Et.subs(values).evalf() == pytest.approx(math.sqrt(80))
def test_xy_z_tau():
vec = vector.MomentumSympy4D(
vector.backends.sympy.AzimuthalSympyXY(x, y),
vector.backends.sympy.LongitudinalSympyZ(z),
vector.backends.sympy.TemporalSympyTau(
sympy.sqrt(sympy.Abs(-(t**2) + x**2 + y**2 + z**2))
),
)
# TODO: the expression blows up on simplifying?
assert vec.Et == sympy.sqrt(x**2 + y**2) * sympy.sqrt(
x**2 + y**2 + z**2 + sympy.Abs(-(t**2) + x**2 + y**2 + z**2)
) / sympy.sqrt(x**2 + y**2 + z**2)
assert vec.Et.subs(values).evalf() == pytest.approx(math.sqrt(80))
def test_xy_theta_t():
vec = vector.MomentumSympy4D(
vector.backends.sympy.AzimuthalSympyXY(x, y),
vector.backends.sympy.LongitudinalSympyTheta(
sympy.acos(z / sympy.sqrt(x**2 + y**2 + z**2))
),
vector.backends.sympy.TemporalSympyT(t),
)
assert vec.Et.simplify() == t * sympy.sqrt(x**2 + y**2) / sympy.sqrt(
x**2 + y**2 + z**2
)
assert vec.Et.subs(values).evalf() == pytest.approx(math.sqrt(80))
def test_xy_theta_tau():
vec = vector.MomentumSympy4D(
vector.backends.sympy.AzimuthalSympyXY(x, y),
vector.backends.sympy.LongitudinalSympyTheta(
sympy.acos(z / sympy.sqrt(x**2 + y**2 + z**2))
),
vector.backends.sympy.TemporalSympyTau(
sympy.sqrt(sympy.Abs(-(t**2) + x**2 + y**2 + z**2))
),
)
assert vec.Et.simplify() == sympy.sqrt(x**2 + y**2) * sympy.sqrt(
x**2 + y**2 + z**2 + sympy.Abs(-(t**2) + x**2 + y**2 + z**2)
) / sympy.sqrt(x**2 + y**2 + z**2)
assert vec.Et.subs(values).evalf() == pytest.approx(math.sqrt(80))
def test_xy_eta_t():
vec = vector.MomentumSympy4D(
vector.backends.sympy.AzimuthalSympyXY(x, y),
vector.backends.sympy.LongitudinalSympyEta(
sympy.asinh(z / sympy.sqrt(x**2 + y**2))
),
vector.backends.sympy.TemporalSympyT(t),
)
assert vec.Et.simplify() == t / sympy.sqrt(z**2 / (x**2 + y**2) + 1)
assert vec.Et.subs(values).evalf() == pytest.approx(math.sqrt(80))
def test_xy_eta_tau():
vec = vector.MomentumSympy4D(
vector.backends.sympy.AzimuthalSympyXY(x, y),
vector.backends.sympy.LongitudinalSympyEta(
sympy.asinh(z / sympy.sqrt(x**2 + y**2))
),
vector.backends.sympy.TemporalSympyTau(
sympy.sqrt(sympy.Abs(-(t**2) + x**2 + y**2 + z**2))
),
)
assert (
sympy.simplify(
vec.Et.simplify()
- 2
* sympy.sqrt(
0.25
* (x**2 + y**2)
* (sympy.exp(2 * sympy.asinh(z / sympy.sqrt(x**2 + y**2))) + 1) ** 2
+ sympy.exp(2 * sympy.asinh(z / sympy.sqrt(x**2 + y**2)))
* sympy.Abs(-(t**2) + x**2 + y**2 + z**2)
)
/ (sympy.exp(2 * sympy.asinh(z / sympy.sqrt(x**2 + y**2))) + 1)
)
== 0
)
assert vec.Et.subs(values).evalf() == pytest.approx(math.sqrt(80))
def test_rhophi_z_t():
vec = vector.MomentumSympy4D(
vector.backends.sympy.AzimuthalSympyRhoPhi(rho, phi),
vector.backends.sympy.LongitudinalSympyZ(z),
vector.backends.sympy.TemporalSympyT(t),
)
assert vec.Et.simplify() == rho * t / sympy.sqrt(rho**2 + z**2)
assert vec.Et.subs(values).evalf() == pytest.approx(math.sqrt(80))
def test_rhophi_z_tau():
vec = vector.MomentumSympy4D(
vector.backends.sympy.AzimuthalSympyRhoPhi(rho, phi),
vector.backends.sympy.LongitudinalSympyZ(z),
vector.backends.sympy.TemporalSympyTau(
sympy.sqrt(sympy.Abs(rho**2 - t**2 + z**2))
),
)
assert vec.Et.simplify() == rho * sympy.sqrt(
rho**2 + z**2 + sympy.Abs(rho**2 - t**2 + z**2)
) / sympy.sqrt(rho**2 + z**2)
assert vec.Et.subs(values).evalf() == pytest.approx(math.sqrt(80))
def test_rhophi_theta_t():
vec = vector.MomentumSympy4D(
vector.backends.sympy.AzimuthalSympyRhoPhi(rho, phi),
vector.backends.sympy.LongitudinalSympyTheta(
sympy.acos(z / sympy.sqrt(rho**2 + z**2))
),
vector.backends.sympy.TemporalSympyT(t),
)
assert vec.Et.simplify() == rho * t / sympy.sqrt(rho**2 + z**2)
assert vec.Et.subs(values).evalf() == pytest.approx(math.sqrt(80))
def test_rhophi_theta_tau():
vec = vector.MomentumSympy4D(
vector.backends.sympy.AzimuthalSympyRhoPhi(rho, phi),
vector.backends.sympy.LongitudinalSympyTheta(
sympy.acos(z / sympy.sqrt(rho**2 + z**2))
),
vector.backends.sympy.TemporalSympyTau(
sympy.sqrt(sympy.Abs(rho**2 - t**2 + z**2))
),
)
assert vec.Et.simplify() == rho * sympy.sqrt(
rho**2 + z**2 + sympy.Abs(rho**2 - t**2 + z**2)
) / sympy.sqrt(rho**2 + z**2)
assert vec.Et.subs(values).evalf() == pytest.approx(math.sqrt(80))
def test_rhophi_eta_t():
vec = vector.MomentumSympy4D(
vector.backends.sympy.AzimuthalSympyRhoPhi(rho, phi),
vector.backends.sympy.LongitudinalSympyEta(sympy.asinh(z / rho)),
vector.backends.sympy.TemporalSympyT(t),
)
assert vec.Et.simplify() == t / sympy.sqrt(1 + z**2 / rho**2)
assert vec.Et.subs(values).evalf() == pytest.approx(math.sqrt(80))
def test_rhophi_eta_tau():
vec = vector.MomentumSympy4D(
vector.backends.sympy.AzimuthalSympyRhoPhi(rho, phi),
vector.backends.sympy.LongitudinalSympyEta(sympy.asinh(z / rho)),
vector.backends.sympy.TemporalSympyTau(
sympy.sqrt(sympy.Abs(rho**2 - t**2 + z**2))
),
)
assert vec.Et.simplify() == 2 * sympy.sqrt(
0.25 * rho**2 * (sympy.exp(2 * sympy.asinh(z / rho)) + 1) ** 2
+ sympy.exp(2 * sympy.asinh(z / rho)) * sympy.Abs(rho**2 - t**2 + z**2)
) / (sympy.exp(2 * sympy.asinh(z / rho)) + 1)
assert vec.Et.subs(values).evalf() == pytest.approx(math.sqrt(80))
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