```python
import numpy as np
from sympy import Symbol, Eq, simplify
from sympy import sqrt, cosh, exp
from sympy.solvers import solve
from sympy import init_printing
init_printing()
```


```python
# Relevant variables
eta = Symbol(r'\eta')
x = Symbol('x')

# Kinematics
Q = Symbol('Q', positive=True)
qT = Symbol(r'|\mathbf{q}_T|', positive=True)
y = Symbol('y')
M = Symbol('M') #sqrt(Q**2+qT**2)

# Cut parameters
etamax = Symbol(r'\eta_{\rm max}', positive=True)
pTmin = Symbol(r'p_{T,\rm min}', positive=True)

# Definitions
ch = Symbol('\cosh(\eta-y)') #cosh(eta - y)
pTo = Q**2 / 2 / ( M * ch - qT * x)
```


```python
# xpTmin1
f = Eq(pTo, pTmin)
solve(f, x)
```


```python
# xpTmin2
f = Eq(qT**2 + pTo * ( pTo - 2 * qT * x), pTmin**2)
solve(f, x)
```


```python
f = Eq( ( M * exp(y) - pTo * exp(eta) ) / ( M * exp(-y) - pTo * exp(-eta) ) , exp(2*etamax))
solve(f, x)
```


```python
che = Symbol('\cosh(\eta)')
she = sqrt(che**2 - 1)
f = Eq(( che * ( Q**2 - 2 * pTmin**2 ) - Q * sqrt( Q**2 * she**2 + pTmin**2) ) / ( Q**2 - pTmin**2 ), 0)
solve(f, Q)
```


```python

```

b54c1b7fb77711bd3307b617a4bac9e3812f1ecc
ipynb
Jupyter Notebook
doc/src/plots/Solutions.ipynb
intrepid42/apfelxx
34b0bb4f134ddf42aa7eccceaa6c3b91b5414cd6
MIT
2019-10-07T14:01:59.000Z
2021-04-13T19:54:47.000Z
doc/src/plots/Solutions.ipynb
intrepid42/apfelxx
34b0bb4f134ddf42aa7eccceaa6c3b91b5414cd6
MIT
2017-05-30T10:43:40.000Z
2018-09-11T14:29:53.000Z
doc/src/plots/Solutions.ipynb
intrepid42/apfelxx
34b0bb4f134ddf42aa7eccceaa6c3b91b5414cd6
MIT
2019-06-23T08:42:00.000Z
2022-03-18T15:25:46.000Z
Qwen/Qwen-72B
1. YES
2. YES