Mathematica has many powerful features, to handle a wide range of statistical needs. Some of the most elementary are outlined below.

x > y yields True if x is determined to be greater than y. x_1 > x_2 > x_3 yields True if the x_i form a strictly decreasing sequence.

Stack[] shows the current evaluation stack, giving a list of the tags associated with evaluations that are currently being done. Stack[pattern] gives a list of expressions ...

One of the most important features of Mathematica is that it is an extensible system. There is a certain amount of mathematical and other functionality that is built into ...

FullForm[expr] prints as the full form of expr, with no special syntax.

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 ...

Messages[symbol] gives all the messages assigned to a particular symbol.

AlgebraicNumberPolynomial[a, x] gives the polynomial in x corresponding to the AlgebraicNumber object a.

Structural operations on polynomials. Here is a polynomial in one variable. Expand expands out products and powers, writing the polynomial as a simple sum of terms.

RecurrenceTable[eqns, expr, {n, n_max}] generates a list of values of expr for successive n based on solving the recurrence equations eqns.RecurrenceTable[eqns, expr, nspec] ...