Numerical root finding. NSolve gives you numerical approximations to all the roots of a polynomial equation. You can also use NSolve to solve sets of simultaneous equations ...

IsolatingInterval[a] gives a rational isolating interval for the algebraic number a.IsolatingInterval[a, dx] gives an isolating interval of width at most dx.

ProductLog[z] gives the principal solution for w in z == w e^w. ProductLog[k, z] gives the k\[Null]^th solution.

When Solve cannot find solutions in terms of radicals to polynomial equations, it returns a symbolic form of the result in terms of Root objects. You can get numerical ...

MultiplicativeOrder[k, n] gives the multiplicative order of k modulo n, defined as the smallest integer m such that k^m \[Congruent] 1 mod n. MultiplicativeOrder[k, n, {r_1, ...

NSolve[expr, vars] attempts to find numerical approximations to the solutions of the system expr of equations or inequalities for the variables vars. NSolve[expr, vars, ...

Two decades of intense R&D at Wolfram Research have given Mathematica by far the world's broadest and deepest coverage of special functions—and greatly expanded the whole ...

Although Diophantine equations provide classic examples of undecidability, Mathematica in practice succeeds in solving a remarkably wide range of such equations—automatically ...

RootLocusPlot[g, {k, k_min, k_max}] generates the root locus plot of a rational function g of k ranging from k_min to k_max.RootLocusPlot[sys, ...] plots the root loci of a ...

SqrtBox[x] is a low-level box construct that represents the displayed object Sqrt[x] in notebook expressions.