Mathematica's extensive base of state-of-the-art algorithms, efficient handling of very long integers, and powerful built-in language make it uniquely suited to both research ...

You can use lists as tables of values. You can generate the tables, for example, by evaluating an expression for a sequence of different parameter values. This gives a table ...

In Mathematica's unified symbolic architecture, every Mathematica notebook you see is represented as a symbolic expression that can be manipulated and controlled ...

SparseArray[{pos_1 -> val_1, pos_2 -> val_2, ...}] yields a sparse array in which values val_i appear at positions pos_i. SparseArray[{pos_1, pos_2, ...} -> {val_1, val_2, ...

Particularly when you write procedural programs in Mathematica, you will often need to modify the value of a particular variable repeatedly. You can always do this by ...

Mathematica automatically handles hundreds of data formats and subformats—all coherently integrated through Mathematica's uniform use of symbolic expressions. For each ...

Mathematica has been used to make many important discoveries in discrete mathematics over the past two decades. Its integration of highly efficient and often original ...

SortBy[list, f] sorts the elements of list in the order defined by applying f to each of them.

Ordering[list] gives the positions in list at which each successive element of Sort[list] appears. Ordering[list, n] gives the positions in list at which the first n elements ...

Importing and exporting lists and tables of data. This exports a list of data to the file out1. Here are the contents of the file.