sympy

combined

Performs exact symbolic mathematics with SymPy for algebra, calculus, equation solving, symbolic linear algebra, physics, and lambdify or LaTeX code generation. Use when a task needs symbolic results, explicit assumptions, or exact arithmetic; use NumPy or SciPy for purely numerical workloads. Use this skill when working with symbolic mathematics in Python. This skill should be used for symbolic computation tasks including solving equations algebraically, performing calculus operations (derivatives, integrals, limits), manipulating algebraic expressions, working with matrices symbolically, physics calculations, number theory problems, geometry computations, and generating executable code from mathematical expressions. Apply this skill when the user needs exact symbolic results rather than numerical approximations, or when working with mathematical formulas that contain variables and parameters.

When to use

Solving equations symbolically (algebraic, differential, systems of equations)
Performing calculus operations (derivatives, integrals, limits, series)
Manipulating and simplifying algebraic expressions
Working with matrices and linear algebra symbolically
Doing physics calculations (mechanics, quantum mechanics, vector analysis)
Number theory computations (primes, factorization, modular arithmetic)
Geometric calculations (2D/3D geometry, analytic geometry)
Converting mathematical expressions to executable code (Python, C, Fortran)

When not to use

Purely numerical workloads

Skill page

Conflict

The K-Dense-AI copy is the upstream source (it carries the version, last-reviewed date, and upstream-version metadata) and contains material steps the other copies omit: an installation section with pinned SymPy 1.14.0 and mpmath constraints, a compatibility note, and a 'Best Practices' section covering exact arithmetic, evalf, lambdify, solver selection, and input-trust warnings. The other three copies are near-identical reproductions of the same core capability examples but lack those installation and best-practice steps, so crowning one of them would hide the real alternative provided by the K-Dense copy.