SymPy
Symbolic mathematics library for Python — performs exact algebraic computation, calculus, and equation solving. SymPy features: Symbol declarations (x = symbols('x')), simplify(), expand(), factor(), solve() for equations, diff() derivatives, integrate() integrals, limit(), series() Taylor expansion, Matrix operations, ODE solving (dsolve), LaTeX output (latex()), code generation (lambdify(), ccode(), fcode()), number theory, combinatorics, and Diophantine equations. Fully Python-based CAS (Computer Algebra System). Used by agents for symbolic equation solving, formula derivation, mathematical proof verification, and code generation from symbolic expressions.
Score Breakdown
⚙ Agent Friendliness
🔒 Security
Pure Python computation — no network calls, no code execution from expressions. lambdify() generates Python lambda functions from symbolic expressions — safe as no eval() of untrusted strings. No security concerns for local use.
⚡ Reliability
Best When
Exact algebraic manipulation, symbolic calculus, equation solving, ODE solving, or generating LaTeX/code from mathematical expressions — SymPy provides a full CAS in pure Python without external dependencies.
Avoid When
You need fast numerical computation (use NumPy), ML training (use PyTorch/JAX), or statistical analysis (use scipy).
Use Cases
- • Agent symbolic equation solving — from sympy import symbols, solve; x = symbols('x'); solutions = solve(x**2 - 5*x + 6, x) — returns [2, 3] as exact values; agent math tutor solves equations symbolically without floating-point error; solve() handles systems of equations with multiple variables simultaneously
- • Agent calculus computation — x = symbols('x'); f = x**3 + 2*x**2; deriv = diff(f, x); antideriv = integrate(f, x) — symbolic differentiation and integration; agent physics/engineering simulator derives equations analytically; no numerical approximation error
- • Agent LaTeX generation — expr = integrate(sin(x)*exp(x), x); latex_str = latex(expr) — produces LaTeX: 'e^{x}(\sin(x) - \cos(x))/2'; agent math documentation generator formats equations for reports/papers; renders correctly in Jupyter, Markdown, and LaTeX documents
- • Agent code generation from formula — f = x**2 + 2*x + 1; f_numpy = lambdify(x, f, 'numpy'); results = f_numpy(np.array([1, 2, 3])) — convert symbolic expression to fast NumPy function; agent derives formula symbolically then generates efficient numerical code for execution on arrays
- • Agent ODE solving — t, C1 = symbols('t C1'); y = Function('y'); ode = Eq(y(t).diff(t), -2*y(t)); solution = dsolve(ode, y(t)) — solve ordinary differential equations symbolically; agent models exponential decay, population dynamics, or electrical circuits analytically
Not For
- • Numerical computation — SymPy is symbolic (exact) not numerical; for fast numerical arrays use NumPy; symbolic computation is 100-1000x slower than numerical for same expression
- • Machine learning — SymPy has no autograd or tensor operations; for ML use PyTorch or JAX with numerical gradients
- • Statistical computation — SymPy has limited statistics; use scipy.stats or statsmodels for statistical modeling
Interface
Authentication
No auth — local computation library.
Pricing
SymPy is BSD licensed. Free for all use including commercial.
Agent Metadata
Known Gotchas
- ⚠ Python division is numeric not symbolic — x = symbols('x'); 1/x in Python returns 0 for integer x; agent code must write Integer(1)/x or sympy.Rational(1,1)/x or use S.One/x for symbolic rational; mixing Python integers with sympy symbols causes unexpected numeric evaluation
- ⚠ solve() returns list or dict not single value — solve(x**2 - 4, x) returns [-2, 2]; solve([x+y-1, x-y], [x,y]) returns {x: 1/2, y: 1/2}; agent code doing solution = solve(eq, x)[0] fails when no solution exists (empty list); always check: sols = solve(eq, x); if sols: use(sols[0])
- ⚠ simplify() may not produce expected form — simplify(expr) applies heuristics that may not simplify toward agent's expected form; use specific functions: expand(), factor(), trigsimp(), radsimp(), cancel(); agent code relying on simplify() for pattern matching must use explicit simplification
- ⚠ lambdify() for numerical evaluation not lambdify for display — lambdify(x, sin(x), 'numpy') creates fast NumPy function; lambdify(x, sin(x)) without module creates slow SymPy evaluation; agent code doing numerical evaluation after symbolic derivation MUST specify module='numpy' or module='scipy'
- ⚠ Symbolic equality is not Python == — sin(x)**2 + cos(x)**2 == 1 returns False (structural not mathematical equality); agent code testing symbolic equivalence must use: sympy.simplify(expr1 - expr2) == 0 or sympy.Eq(expr1, expr2).simplify()
- ⚠ Large expression trees are slow — simplify/solve on expressions with 100+ terms can take minutes; agent code building expressions in loops (sum of symbolic terms) can create exponentially large trees; use Add(*terms) for efficient sum construction; consider numerical approach for large-scale problems
Alternatives
Full Evaluation Report
Detailed scoring breakdown, competitive positioning, security analysis, and improvement recommendations for SymPy.
Scores are editorial opinions as of 2026-03-06.