INSIDE THE INTEGRATOR
The Wolfram Mathematica Online Integrator uses webMathematica technology to bring the
computational capabilities of Mathematica to the web.
The heart of The Integrator is Mathematica's
built-in Integrate function--the same one you use
when accessing Mathematica directly. When you type in an
integral, the Integrator uses webMathematica to send the
integral to the Mathematica kernel, which computes the result
using the Integrate function. The result is then embedded
into the web page as typeset output.
How the Integrate Function Works
Mathematica's Integrate function represents the fruits
of a huge amount of mathematical and computational research. It
doesn't do integrals the way people do. Instead, it uses powerful,
general algorithms that often involve very sophisticated math. There
are a couple of approaches that it most commonly takes. One involves
working out the general form for an integral, then differentiating
this form and solving equations to match up undetermined symbolic
parameters. Even for quite simple integrands, the equations generated
in this way can be highly complex and require Mathematica's
strong algebraic computation capabilities to solve. Another approach
that Mathematica uses in working out integrals is to convert
them to generalized hypergeometric functions, then use collections of
relations about these highly general mathematical functions.
How Mathematica Typesetting
Works
One of Mathematica's achievements was the introduction of
a new generation of capabilities for typesetting mathematical
formulas. New algorithms for optimal layout of mathematical formulas,
as well as new families of fonts, were developed
for Mathematica. In The Integrator, the results
of Mathematica's typesetting are automatically converted to
GIF. Alternatively, you can request the answer in InputForm, a
text-based format, which can be pasted into Mathematica,
Word, or other applications.
How webMathematica Works
webMathematica provides the ideal solution to interactive
computations over the web. Using J/Link, webMathematica connects Mathematica to your web server, enabling interactive
evaluation on your website. For more information about this technology
and how it works, see the webMathematica site.
