nerdamer/solve

Returns polynomial roots as a Vector. Unlike solve(), which returns a SolutionSet with solver metadata, this function preserves the roots API's Vector return type. Numeric constants retain the historical square-root interpretation. Univariate polynomials delegate to PolynomialSolver and therefore return numerical roots.

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 limited-range 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 multivariate Newton-Raphson over a fixed search interval. 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. Expression, Polynomial, and string inputs are converted directly to numerical complex coefficients 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 defined 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 numerical root searches over a fixed interval with FunctionSolver.

Options for the finite-range 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.