How many roots of f(z) = i*z^15 + z*sin(z) + z^3*exp(2*z) are in the right half-plane and how many are in the left ?

 Follow code proposed in https://lxer.com/module/newswire/view/363645/index.html . Setup python3.14.3t on CachyOS along with aqtinstall via UV

   $ curl -LsSf https://astral.sh/uv/install.sh | sh
   $ uv python install 3.14t                                                                              $ uv python list
   $ mkdir MULTITHREAD
   $ cd MULTITHREAD
   $ python3.14t -m venv .env
   $ source .env/bin/activate
   $ pip install aqtinstall
   $ pip install --upgrade pip
   $ pip install numpy matplotlib cxroots

  

❯ cat complexSinZExpZ05.py
import os
import numpy as np
import matplotlib.pyplot as plt
from cxroots import Circle
from concurrent.futures import ThreadPoolExecutor

# Silence Qt warnings
os.environ["QT_LOGGING_RULES"] = "*.debug=false;qt.qpa.fonts.warning=false"

def count_zeros_task(f, df, contour_points):
"""Calculates zeros via the Argument Principle."""
fz, dfz = f(contour_points), df(contour_points)
integrand = dfz / fz
dz = np.diff(contour_points, append=contour_points[0])
integral = np.sum(integrand * dz)
return int(np.round((integral / (2j * np.pi)).real))

def find_roots_task(contour, f, df):
"""Calculates specific root locations using cxroots."""
return contour.roots(f, df)

# 1. Setup Data
f = lambda z: 1j*z**15 + z*np.sin(z) + z**3*np.exp(2*z)  
df = lambda z: 15j*z**14 + z*np.cos(z) + np.sin(z) +  3*z**2*np.exp(2*z) + 2*z**3*np.exp(2*z)

t = np.linspace(0, 2 * np.pi, 10000)
circle_pts = 5*np.exp(1j * t)
C = Circle(0, 5)

print("f(z) = 1j*z**15 + z*np.sin(z) + z**3*np.exp(2*z)")
print("Starting concurrent calculations...")

# 2. Parallel Execution
with ThreadPoolExecutor() as executor:
# Submit both tasks to run simultaneously
future_count = executor.submit(count_zeros_task, f, df, circle_pts)
future_roots = executor.submit(find_roots_task, C, f, df)

# Retrieve results (this waits for each to finish)
zero_count = future_count.result()
roots_result = future_roots.result()

# 3. Output and Visualization
print(f"\nVerification (Argument Principle): {zero_count} zeros found.")
print(f"Detailed Root Analysis:\n{roots_result}")

# Plotting must happen on the main thread
roots_result.show()
plt.show()

Add to the bottom of ~/.bashrc                                                        function activatevenv() {
 # Names of possible virtualenv directories
 VIRTUALENV_DIRS=("venv/" "env/" ".env/" ".venv/" "${PWD##*/}")

 for dir in "${VIRTUALENV_DIRS[@]}"; do
   if [[ -d "${dir}" ]]; then
     # Found a possible venv directory
     # Try activating the venv
     if [[ -e "./${dir}/bin/activate" ]]; then
       source ./$dir/bin/activate
       echo "Virtual environment activated automatically"
       break
     fi
   fi
 done

}
# Extension for `cd` command in order to automatically activate virtual env when changing directories.
cd() {
 builtin cd $1
 # Try activating venv
 activatevenv
}