Functions like Read and Write handle ordinary printable text. But in dealing with external data files or devices it is sometimes necessary to go to a lower level, and work ...

Mathematica includes functions for performing a variety of specific algebraic transformations. Some are algorithmically straightforward; others include highly sophisticated ...

IrreduciblePolynomialQ[poly] tests whether poly is an irreducible polynomial over the rationals.IrreduciblePolynomialQ[poly, Modulus -> p] tests whether poly is irreducible ...

As with integers, operations related to division are key to many computations with polynomials. Mathematica includes not only highly optimized univariate polynomial-division ...

RSolve[eqn, a[n], n] solves a recurrence equation for a[n]. RSolve[{eqn_1, eqn_2, ...}, {a_1[n], a_2[n], ...}, n] solves a system of recurrence equations. RSolve[eqn, a[n_1, ...

A core activity in exploratory experimental mathematics is recognition of numbers: going backward from a number to find out how it can be generated. Mathematica provides ...

MaxValue[f, x] gives the maximum value of f with respect to x.MaxValue[f, {x, y, ...}] gives the maximum value of f with respect to x, y, .... MaxValue[{f, cons}, {x, y, ...

NMaximize[f, x] maximizes f numerically with respect to x.NMaximize[f, {x, y, ...}] maximizes f numerically with respect to x, y, .... NMaximize[{f, cons}, {x, y, ...}] ...

Reduce[expr, vars] reduces the statement expr by solving equations or inequalities for vars and eliminating quantifiers. Reduce[expr, vars, dom] does the reduction over the ...

In just one Mathematica command, you can easily specify a calculation that is far too complicated for any computer to do. For example, you could ask for ...