An operator is a special sign indicating what should be done with some data – operands. The simplest operators are arithmetic operators, for example, in expressions 2+3, a-b, c*d, e/f, 2^3, etc. Here, the signs +, -, *, /, and ^ are arithmetic binary operators because two operands are used with them. There are also unary operators working with one operand, such as the operator for calculating the factorial !, used in the form N! In the most modern systems the composition of operators is considerably extended, among them there are symbols for differentiation, integration, calculation of sums and products of series, etc. They are often derived using palettes of mathematical signs.

A function in programming languages is an object that has a name and returns the result of converting a list of function parameters. Many functions are built into mathematical systems, such as elementary functions like eXp(x), ln(x), sin(x), etc. These functions have one variable, but they can also be functions of two or more variables. Usually function parameters are entered in parentheses, but there are exceptions. In Mathematica, for example, function parameters (arguments) are given in square brackets, e.g., Sin[x], while in Derive class systems, function names are given in capital letters, e.g., SIN(x).

Let’s name the elementary functions in Mathcad 8/2000:

trigonometric functions – angle(x, y), sin(z), cos(z), tan(z), sec(z), csc(z),cot(z);
hyperbolic functions – sinh(z), cosh(z), tanh(z), sech(z), csch(z), coth(z);
inverse trigonometric functions – asin(z), acos(z), atan(z), asec(z), acsc(z), acot(z);
inverse hyperbolic functions – asinh(z), acosh(z), atanh(z), asech(z), acsch(z), acoth(z);
exp(z),ln(z),log(z);

functions of a complex argument:

Re(z) – extraction of the real part of z;
Im(z) – extraction of the imaginary part of z;
arg (z) – calculating the argument z.

This set (taking into account the differences in function notations noted above) is characteristic of all the computer mathematics systems described below. The set of special mathematical and other functions in computer mathematics systems is also quite extensive. Maple V and Mathematica are particularly abundant.

Although the number of mathematical functions can be in the hundreds, computer mathematics systems allow you to define your own functions (and sometimes even operators). These functions are called user functions. Usually they are specified in the form

function_name(list_parameters):=function_body

The function body is an expression that contains the variables defined in the parameter list. Such variables are local.