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If you have a mathematics background, you’ll already be well
aware that PHP doesn’t come with any special functions for working
with advanced mathematical concepts — complex numbers, fractions, polynomials,
statistics and matrices. However, this deficiency is more than made up by PEAR,
the PHP Extension and Application Repository, which has a number of ready-made
packages for working with complex mathematical units. These packages provide a
robust, well-tested code base for application developers, and also save you the time and
effort you would otherwise spend in “rolling your own” math

This document will list ten PEAR
packages (Table A) of specific
interest to developers working with complex math in their projects. Take a
look, and try them out — you never know you might find something that solves a
problem you’re currently facing. One warning, though: if you didn’t like math
class in school, what follows may bring back some unpleasant memories!

Note: You can
install PEAR packages directly from the Web, by following the instructions

Table A

Package Name



This package lets you perform basic and advanced
arithmetic operations on complex numbers (numbers containing both real and imaginary
parts). It includes an object-oriented interface that supports methods for
trigonometric and logarithmic operations on these numbers.

Use this
package when you need to perform trigonometric, hyperbolic or exponential
operations on complex numbers.


This package lets you generate “fraction
objects” by passing the fraction’s numerator and denominator as
arguments to the class. It includes methods to add, subtract, divide and
multiply fractions, as well as calculate reciprocals and compare two or more
fractions to find out which is greater.

Use this
package when you need to work with fractional values in PHP.


A derivative is the rate of change of a given function
with respect to its components, and one of the most important concepts in
calculus. This package provides an object-oriented framework to find the
derivative of any mathematical expression to a given level. It includes
support for basic rules (addition, subtraction, division, multiplication) and
a cache to speed up derivation.

Use this
package when working with derivatives.


A polynomial is a multi-component expression involving
variables raised to various powers. This package provides the tools required
to solve polynomial equations, including the ability to perform basic
arithmetic operations on polynomials; calculate polynomial derivatives and
degrees; and evaluate the polynomial for a particular value of its variables.

Use this
package to simplify the solving of complex polynomial equations.


This package provides an object-oriented framework to
mathematical operations involving matrices. Here, a matrix is represented by
an array of arrays, and the class provides functions to add, subtract,
multiply and divide these arrays; determine if the matrix is square; and
calculate important matrix values like the determinant and norm.

Use this
package when you need to work with matrices of numbers.


The Fibonacci sequence is a connected sequence of numbers
first discovered by an Italian mathematician. This package provides methods
to calculate one or more members of the sequence, a task often required in
applications like pseudorandom number generators, visual arts and music. It
can also be used to test if a particular integer belongs to the Fibonacci

Use this
package when you need to calculate and manipulate Fibonacci numbers.


This package provides an object-oriented framework for
working with vectors. It includes support for important calculations such as
calculating the distance (Cartesian, Manhattan and chessboard) between
vectors; reversing, conjugating, scaling and normalizing vectors; and finding
vector lengths and magnitudes.

Use this
package when you need to perform vector calculations in 2D or 3D space.


This package provides a framework for working with binary
data, including conversions to big endian, little endian, decimal, integer
and hexadecimal format; pack and unpack options; and the ability to easily
add and subtract binary numbers.

Use this
package when you need to perform calculations with binary data.


This package provides a diverse array of utility functions
to statistically analyze a data set. Some of the things you can do with it
include calculating the means (standard, inter-quartile, harmonic and
geometric), median and mode; finding the standard, absolute and
inter-quartile deviation; calculating the coefficient of variation; finding
raw moments; and calculating skewness and kurtosis
of the distribution.

Use this
package when you need to quickly perform basic statistical analysis on a data


This package provides an easy way to statistically analyze
a set of numerical data by categorizing them and plotting a graphical
frequency distribution. It includes the ability to define “bins”,
assign data points to bins, and generate a histogram distribution of the data
set, either numerically or graphically in 2D or 3D space

Use this
package to understand the frequency distribution of a data set.