nerdamer/solve

Solves an equation or finds the zeros of an expression in one variable. The solver normalizes the input to `expression = 0`, tries direct symbolic transformations, factors numerator and denominator, and then applies symbolic, polynomial-numeric, and bounded function-numeric strategies to the factors. Zeros of denominator factors are excluded from the result.

Solves a system of expressions or equations for an ordered set of variables. Expressions are interpreted as equal to zero. The solver first tries exact linear reduction, then a lexicographic Groebner basis with symbolic back substitution for polynomial systems, and finally bounded multivariate Newton-Raphson. Rational polynomial systems may have denominators cleared for symbolic work; candidates are checked against the original domain.

Searches numerically for isolated real solutions of a multivariate system. Each equation is interpreted as `equation = 0`. The solver starts Newton-Raphson at every point in a Cartesian grid, approximates the Jacobian with central differences, and merges nearby converged solutions.

Finds all complex roots of a univariate polynomial numerically. Coefficient arrays use ascending powers: the element at index `k` is the coefficient of `x^k`. Polynomial and string inputs are converted to that representation before solving. Linear and quadratic inputs are handled directly; higher degrees use simultaneous Aberth iteration followed by Newton refinement.

A finite set of solution descriptors with solver-specific metadata.

Applies a bounded set of exact transformations to one equation in one variable. Polynomial equations through degree four use closed-form formulas. Other recognized forms are solved by isolating and inverting elementary functions, exponentials, logarithmic sums, or a single square-root term. Unsupported input is reported by solve as `unsolved` so a caller can select a different strategy.

Options for bounded numerical root searches with FunctionSolver.

Options for the bounded multi-start search performed by MultivariateSolver.

Metadata returned by a single numerical root-refinement attempt.

Describes whether the stored descriptors represent finite solutions, indexed families, or all values.

Describes whether accepted solutions were produced by numerical strategies, symbolic strategies, or both.