In doing numerical operations like NDSolve and NMinimize, Mathematica by default uses machine numbers. But by setting the option WorkingPrecision->n you can tell it to use ...

Counting roots of polynomials. CountRoots accepts polynomials with Gaussian rational coefficients. The root count includes multiplicities. This gives the number of real roots ...

Converting between numbers and lists or strings of digits. Here is the list of base 16 digits for an integer. This gives a list of digits, together with the number of digits ...

Mathematica normally assumes that variables which appear in equations can stand for arbitrary complex numbers. But when you use Reduce, you can explicitly tell Mathematica ...

Mathematica allows you to export graphics and sounds in a wide variety of formats. If you use the notebook front end for Mathematica, then you can typically just copy and ...

In doing many kinds of calculations, you need to evaluate expressions when variables take on particular values. In many cases, you can do this simply by applying ...

Unless f is a flat function, a pattern like f[x_,y_] stands only for instances of the function with exactly two arguments. Sometimes you need to set up patterns that can ...

Converting between symbols and their names. Here is the symbol x. Its name is a string.

Functions in Mathematica are carefully set up so that you normally do not have to know how they work inside. But particularly for numerical functions that use iterative ...

Mathematica by default interprets any sequence of letters or letter-like forms as the name of a symbol. All these are treated by Mathematica as symbols. Symbols with built-in ...