Even more so than for other special functions, you need to be very careful about the arguments you give to elliptic integrals and elliptic functions. There are several ...

Hundreds of thousands of mathematical results derived at Wolfram Research give Mathematica unprecedented strength in the transformation and simplification of hypergeometric ...

Eigensystem[m] gives a list {values, vectors} of the eigenvalues and eigenvectors of the square matrix m. Eigensystem[{m, a}] gives the generalized eigenvalues and ...

Discriminant[poly, var] computes the discriminant of the polynomial poly with respect to the variable var.Discriminant[poly, var, Modulus -> p] computes the discriminant ...

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 ...

Convergents and QuadraticIrrationalQ have been added to the built-in Mathematica kernel.

Factoring a quadratic polynomial in one variable is straightforward. But Mathematica routinely factors degree-100 polynomials in 3 variables—by making use of a tower of ...

The essence of most methods is in the local quadratic model that is used to determine the next step. The FindMinimum function in Mathematica has five essentially different ...

Differentiation Total Derivatives Derivatives of Unknown Functions

FrobeniusSolve[{a_1, ..., a_n}, b] gives a list of all solutions of the Frobenius equation a_1 x_1 + ... + a_n x_n = b.FrobeniusSolve[{a_1, ..., a_n}, b, m] gives at most m ...