When you enter a piece of input such as 2+2, Mathematica first recognizes the + as an operator and constructs the expression Plus[2,2], then uses the built-in rules for Plus ...

Sometimes you may want to set up functions where certain arguments, if omitted, are given "default values". The pattern x_:v stands for an object that can be omitted, and if ...

Many aspects of the Mathematica front end such as the styles of cells, the appearance of notebooks, or the parameters used in typesetting are controlled by options. For ...

The Padé approximation is a rational function that can be thought of as a generalization of a Taylor polynomial. A rational function is the ratio of polynomials. Because ...

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 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 ...

The built-in functions in Mathematica operate in a wide variety of ways. But many of the mathematical functions share an important approach: they are set up so as to reduce ...

Functions like Read and Find are most often used for processing text and data from external files. In some cases, however, you may find it convenient to use these same ...

When you define a complicated function, you will often want to let some of the arguments of the function be "optional". If you do not give those arguments explicitly, you ...