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LM Project Setup Instructions

Project Structure

E:\engGit\Gem\WN\LM\              # Lemaire Project (Delta Detector)
├── venv/                          # Python virtual environment
├── delta_detector/                # Main package
│   ├── core/                      # Core algorithms
│   │   ├── detector.py           # Main DeltaDetector class
│   │   ├── chebyshev.py         # Chebyshev computations
│   │   ├── weights.py           # Weight functions (Fejér kernel)
│   │   ├── primes.py            # Prime number utilities
│   │   └── params.py            # Default parameters
│   ├── analysis/                  # Analytical tools
│   │   ├── lehmer.py            # Lehmer hypothesis testing
│   │   └── sign_map.py          # Sign map analysis
│   ├── data/                      # Data loading
│   │   ├── loader.py            # Eigenvalue loader
│   │   └── sato_tate.py         # Sato-Tate distribution
│   ├── visualize/                 # Visualization
│   │   └── plots.py             # Plots and diagrams
│   └── cli.py                    # Command line interface
├── data/                          # Eigenvalue data
│   ├── lmfdb/                    # Raw LMFDB data
│   └── processed/                # Processed tables
├── scripts/                       # Demonstration scripts
│   ├── demo_bsplines.py         # B-splines demo
│   ├── demo_improvements.py      # Method improvements demo
│   ├── parse_lmfdb.py           # LMFDB data parser
│   ├── test_detector_real.py     # Tests on real data
│   └── test_extended_data.py     # Extended tests
├── results/                       # Computation results
├── cache/                         # Intermediate computation cache
├── tests/                         # Unit tests
├── setup.py                       # Setup script
├── requirements.txt               # Python dependencies
└── README.md                      # Documentation

Environment Setup

1. Open Terminal/PowerShell

cd E:\engGit\Gem\WN\LM

2. Create Virtual Environment (if not already created)

python -m venv venv

3. Activate Environment

  • Windows (PowerShell): .\venv\Scripts\Activate.ps1
  • Windows (CMD): .\venv\Scripts\activate.bat
  • Linux/macOS: source venv/bin/activate

4. Install Package in Development Mode

pip install -e .

This will install:

  • Core dependencies from requirements.txt:
    • numpy (arrays and computations)
    • scipy (scientific computing)
    • matplotlib (plotting)
    • click (CLI framework)
  • delta_detector package in development mode

5. Install Additional Dependencies (optional)

pip install -r requirements-extras.txt

Usage

Command Line Interface (CLI)

After installation, the delta-detect command is available:

1. Compute Single Eigenvalue

# Compute λ(p) for prime p
delta-detect prime 29 --sigma 1.3

# With additional parameters
delta-detect prime 29 --sigma 1.3 --T-factor 20 --M 2

2. Scan Range of Primes

# Scan primes from 1000 to 10000
delta-detect scan --start 1000 --end 10000 --output results/scan.csv

3. Test Lehmer Hypothesis

# Test hypothesis up to limit
delta-detect lehmer --limit 1000000 --output results/lehmer_test.csv

Python API

Basic Example

from delta_detector import DeltaDetector
from delta_detector.data import load_lambda_from_csv

# Load known eigenvalues
lambdas = load_lambda_from_csv('data/processed/ramanujan_lambda.csv')

# Create detector
detector = DeltaDetector(p0=29, sigma=1.3)
detector.set_lambda_values(lambdas)

# Compute λ(29)
result = detector.estimate_lambda()
print(f"λ(29) = {result.lambda_estimate:.6f}")
print(f"Error: {result.error:.2e}")

Demonstration Scripts

1. Main Demonstration

cd scripts
python test_detector_real.py

2. Improvements Demo

python demo_improvements.py

3. Parse LMFDB Data

python parse_lmfdb.py --input ../data/lmfdb/raw_data.txt --output ../data/processed/

Method Parameters

Core Parameters

  • σ (sigma): Real part of s = σ + it (default: 1.3)
  • T: Window size, T = T_factor × p0^(aσ) (default: T_factor = 20)
  • M: Maximum power in sum over p^m (default: 2)
  • P: Prime cutoff (default: 10^6)

Integration Parameters

  • quad_limit: Limit of subintervals for quad (default: 1000)
  • quad_epsabs: Absolute accuracy (default: 1e-12)
  • quad_epsrel: Relative accuracy (default: 1e-10)

Data Structure

Input Data

CSV files with eigenvalues in format:

n,lambda_n
2,-24
3,252
5,-4830
...

Output Data

  • results/: Computation results
  • cache/: Cached intermediate computations
  • logs/: Execution logs (if enabled)

Quick Start for New Session

# 1. Navigate to project directory
cd E:\engGit\Gem\WN\LM

# 2. Activate environment
.\venv\Scripts\Activate.ps1  # PowerShell
# or
.\venv\Scripts\activate.bat   # CMD

# 3. Quick test
delta-detect prime 29 --sigma 1.3

# 4. Run demo
cd scripts
python test_detector_real.py

Installation Verification

# Check environment is activated
where python
# Should show: E:\engGit\Gem\WN\LM\venv\Scripts\python.exe

# Check installed packages
pip list | findstr "delta"
# Should show: delta-detector ... (editable)

# Check CLI
delta-detect --help

Troubleshooting

  1. "delta-detect: command not found"

    • Ensure package is installed: pip install -e .
    • Check venv activation

  2. "ModuleNotFoundError: No module named 'delta_detector'"

    • Install package in development mode: pip install -e .

  3. numpy/scipy errors

    • Update dependencies: pip install -U numpy scipy

  4. PowerShell execution policy

    Set-ExecutionPolicy -ExecutionPolicy RemoteSigned -Scope CurrentUser

Performance

  • Single eigenvalue computation: ~0.1 sec
  • Scan 1000 primes: ~2 min
  • Memory usage: < 500 MB for standard tasks

Related Projects

  • RH Project: E:\engGit\Gem\WN\RH - Riemann Hypothesis computations
  • LMFDB: https://www.lmfdb.org - Source of eigenvalue data