When exchanging expressions with external programs, the Mathematica kernel uses the convention of wrapping the expressions inside packets which identify what role the ...

Packed into functions like Solve and Reduce are a wealth of sophisticated algorithms, many created specifically for Mathematica. Routinely handling both dense and sparse ...

DefaultAxesStyle is a low-level option for graphics functions that specifies the default style to use in displaying axes and axes-like constructs.

LeastSquares[m, b] finds an x that solves the linear least-squares problem for the matrix equation m.x == b.

RealBlockDiagonalForm is an option for SchurDecomposition and related functions which specifies whether 2*2 blocks of real values should be used on matrix diagonals in place ...

Functions for grouping together elements of lists. Here is a list. This groups the elements of the list in pairs, throwing away the single element left at the end.

Mathematica usually keeps the elements of a list in exactly the order you originally entered them. If you want to treat a Mathematica list like a mathematical set, however, ...

Functions for rearranging lists. This sorts the elements of a list into a standard order. In simple cases like this, the order is alphabetical or numerical. This sorts the ...

Simplifying with assumptions. Mathematica does not automatically simplify this, since it is only true for some values of x. Sqrt[x^2] is equal to x for x≥0, but not otherwise.

Select[list, crit] picks out all elements e_i of list for which crit[e_i] is True. Select[list, crit, n] picks out the first n elements for which crit[e_i] is True.