Motivation

• Provide a modular, production-style Python package implementing core algorithms in vector algebra, vector calculus, and Taylor/Maclaurin series to support numerical and symbolic workflows.
• Offer utilities for vectorized NumPy computations with optional SymPy symbolic fallback for series expressions and benchmarking comparisons.
• Ship a CLI, example scripts, visualization helpers, and a pytest suite so the package can be validated and integrated into larger projects.

Description

• Add adv_math_engine package with modules vector_algebra.py, vector_calculus.py, series_expansion.py, and utils.py implementing dot/cross/projection/angle/Gram–Schmidt/rank checks, finite-difference partials/gradient/divergence/curl/line+surface integrals, Taylor/Maclaurin series (builtin functions + numeric differentiation), and common helpers.
• Provide optional symbolic series generation via symbolic_taylor_expression when SymPy is available and a Lagrange remainder estimator via estimate_lagrange_remainder for error bounds.
• Add main.py CLI for series approximations, benchmarking scaffold benchmarks/benchmark_diff.py, visualization scripts under visualizations/, an example usage script, and README + reporting placeholders.
• Include a pytest test suite under adv_math_engine/tests/ covering vector algebra, vector calculus, series convergence, and edge cases (zero vectors, singularities, high-dimensional inputs) with type hints and docstrings throughout.

Testing

• Attempted pytest adv_math_engine/tests but test collection failed because the active interpreter lacked numpy, causing import errors during collection.
• Attempted coverage run pytest adv_math_engine/tests --cov=adv_math_engine --cov-report=term-missing but pytest-cov was not available in the active environment.
• Attempted to install dependencies (numpy, sympy, matplotlib, pytest-cov) but network/proxy restrictions prevented package installation in this environment.
• Ran static compilation check with python -m compileall adv_math_engine main.py, which completed successfully and confirmed files are syntactically valid.

Codex Task