Groups admit many different representations. In particular, all finite groups can be represented as permutation groups, that is, they are always isomorphic to a subgroup of ...

A possible way of working with permutations is by relating them to the reorderings of the elements of a list. This is the standard point of view in the combinatorial approach ...

Permutations are basic elements in algebra. They have a natural non-commutative product (as matrices do as well), and hence can encode highly nontrivial structures in a ...

Functions to pick out pieces of polynomials. Here is an algebraic expression. This gives the coefficient of x in e.

Turning conditions into numbers. Boole[expr] is a basic function that turns True and False into 1 and 0. It is sometimes known as the characteristic function or indicator ...

The leading term of a polynomial can be chosen in many different ways. For multivariate polynomials, sorting by the total degree of the monomials is often useful. Different ...

Functions like Factor usually assume that all coefficients in the polynomials they produce must involve only rational numbers. But by setting the option Extension you can ...

The Mathematica side of a MathLink connection is set up to work exactly the same on all computer systems. But inevitably there are differences between external programs on ...

The mathematical operations we have discussed so far are exact. Given precise input, their results are exact formulas. In many situations, however, you do not need an exact ...

The fundamental operation that Mathematica performs is evaluation. Whenever you enter an expression, Mathematica evaluates the expression, then returns the result. Evaluation ...