Function classify

benchmarks/audit/gen_solve.py:193–232

Return (cardinality, roots[]) for the real solution set of expr = 0. Cardinality comes from `solveset` (the only API that distinguishes a finite set from a periodic ImageSet); reference roots come from `solve` (more capable for transcendental closed forms) or mpmath for the frontier.

(expr, seeds)

def classify(expr, seeds):
    """Return (cardinality, roots[]) for the real solution set of expr = 0.

    Cardinality comes from `solveset` (the only API that distinguishes a finite
    set from a periodic ImageSet); reference roots come from `solve` (more
    capable for transcendental closed forms) or mpmath for the frontier.
    """
    # Frontier: mpmath-recovered numeric roots (solve has no closed form).
    if seeds is not None:
        roots = []
        for s0 in seeds:
            try:
                r = mpmath.findroot(lambda v: complex(expr.subs(x, v)), s0)
                if abs(r.imag) < 1e-18:
                    roots.append(mpmath.nstr(r.real, 24))
            except Exception:
                pass
        return ("finite", sorted(set(roots), key=float))

    try:
        sol = solveset(expr, x, domain=S.Reals)
    except Exception:
        sol = None

    if sol is S.EmptySet:
        return ("empty", [])
    # Periodic infinite real solution set (trig): completeness is N/A.
    if sol is not None and (sol.has(sp.ImageSet) or "ImageSet" in type(sol).__name__):
        return ("infinite", [])

    # Finite set, or a ConditionSet solveset couldn't close — reference roots
    # from the capable solver.
    roots = solve_real_roots(expr)
    if isinstance(sol, FiniteSet):
        if not roots:
            roots = real_numeric_roots(list(sol))
        return ("finite", roots)
    if roots:  # ConditionSet but solve() found a finite real closed form
        return ("finite", roots)
    return ("unknown", [])


def sympy_solve(expr):