NRoots[lhs == rhs, var] yields a disjunction of equations which represent numerical approximations to the roots of a polynomial equation.

ForAll[x, expr] represents the statement that expr is True for all values of x. ForAll[x, cond, expr] states that expr is True for all x satisfying the condition cond. ...

NumberFieldSignature[a] gives the signature of the field \[DoubleStruckCapitalQ][a] generated by the algebraic number a.

PolynomialReduce[poly, {poly_1, poly_2, ...}, {x_1, x_2, ...}] yields a list representing a reduction of poly in terms of the poly_i. The list has the form {{a_1, a_2, ...}, ...

Mathematica's symbolic character allows a powerful unification of the notion of conditionals in programming and in mathematics.

The Mathematica functions Reduce, Resolve, and FindInstance allow you to solve a wide variety of problems that can be expressed in terms of equations and inequalities. The ...

One-dimensional Laplace transforms. The Laplace transform of a function f(t) is given by ∫_0^∞f(t)e^-stt. The inverse Laplace transform of F(s) is given for suitable γ by ( ...

QuadraticIrrationalQ[x] gives True if x is a quadratic irrational and False otherwise.

Huge numerical datasets are routine for Mathematica. Its powerful array primitives make large-scale array manipulation both easy to specify and highly efficient. And its ...

x^y gives x to the power y.