When numerically solving Hamiltonian dynamical systems it is advantageous if the numerical method yields a symplectic map. If the Hamiltonian can be written in separable ...

SQLSelect selects and returns data from a database. An alternative, using raw SQL, is described in "Selecting Data with Raw SQL". If you find that the examples in this ...

The arithmetic used by Mathematica is a mixture of variable-precision software arithmetic and whatever is provided by the manufacturer of the floating-point hardware (or the ...

All the functionality of NumericalMath`OrderStar` is now available in the newly created Function Approximations Package. OrderStar has been renamed OrderStarPlot. ...

LowerTriangularize[m] gives a matrix in which all but the lower triangular elements of m are replaced with zeros. LowerTriangularize[m, k] replaces with zeros only the ...

UpperTriangularize[m] gives a matrix in which all but the upper triangular elements of m are replaced with zeros. UpperTriangularize[m, k] replaces with zeros only the ...

Pochhammer[a, n] gives the Pochhammer symbol (a) n.

The ability to generate pseudorandom numbers is important for simulating events, estimating probabilities and other quantities, making randomized assignments or selections, ...

This section is designed to discuss how to make compiled functions run efficiently. It will cover features that make them run faster, as well as problems that can make them ...

PaddedForm[expr, n] prints with all numbers in expr padded to leave room for a total of n digits. PaddedForm[expr, {n, f}] prints with approximate real numbers having exactly ...