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Numerical Recipes Notice
Numerical Recipes Notice
Numerical Recipes
Types of License Offered

Here are the types of licenses that we offer. Note that some types are
automatically acquired with the purchase of media from Cambridge University
Press, or of an unlocking password from the Numerical Recipes On-Line Software
Store, while other types of licenses require that you communicate specifically with
Numerical Recipes Software (email: or fax: 781 863-1739). Our
Web site has additional information.

- "Immediate License" If you are the individual owner of a copy of this book and
you type one or more of its routines into your computer, we authorize you to use
them on that computer for your own personal and noncommercial purposes. You
are not authorized to transfer or distribute machine-readable copies to any other
person, or to use the routines on more than one machine, or to distribute executable
programs containing our routines. This is the only free license.

- "Single-Screen License" This is the most common type of low-cost license, with
terms governed by our Single Screen (Shrinkwrap) License document (complete
terms available through ourWeb site). Basically, this license lets you use Numerical
Recipes routines on any one screen (PC, workstation, X-terminal, etc.). You may
also, under this license, transfer pre-compiled, executable programs incorporating
our routines to other, unlicensed, screens or computers, providing that (i) your
application is noncommercial (i.e., does not involve the selling of your program
for a fee), (ii) the programs were first developed, compiled, and successfully run
on a licensed screen, and (iii) our routines are bound into the programs in such a
manner that they cannot be accessed as individual routines and cannot practicably
be unbound and used in other programs. That is, under this license, your program
user must not be able to use our programs as part of a program library or "mix-andmatch"
workbench. Conditions for other types of commercial or noncommercial
distribution may be found on our Web site (

- "Multi-Screen, Server, Site, and Corporate Licenses" The terms of the Single
Screen License can be extended to designated groups of machines, defined by
number of screens, number of machines, locations, or ownership. Significant
discounts from the corresponding single-screen prices are available when the
estimated number of screens exceeds 40. Contact Numerical Recipes Software
(email: or fax: 781 863-1739) for details.

- "Course Right-to-Copy License" Instructors at accredited educational institutions
who have adopted this book for a course, and who have already purchased a Single
Screen License (either acquired with the purchase of media, or from the Numerical
Recipes On-Line Software Store), may license the programs for use in that course
as follows: Mail your name, title, and address; the course name, number, dates,
and estimated enrollment; and advance payment of $5 per (estimated) student'
to Numerical Recipes Software, at this address: P.O. Box 243, Cambridge, MA
02238 (USA). You will receive by return mail a license authorizing you to make
copies of the programs for use by your students, and/or to transfer the programs to
a machine accessible to your students (but only for the duration of the course).

About Copyrights on Computer Programs
Like artistic or literary compositions, computer programs are protected by
copyright. Generally it is an infringement for you to copy into your computer a
program from a copyrighted source. (It is also not a friendly thing to do, since it
deprives the program's author of compensation for his or her creative effort.) Under
copyright law, all "derivative works" (modified versions, or translations into another
computer language) also come under the same copyright as the original work.
Copyright does not protect ideas, but only the expression of those ideas in
a particular form. In the case of a computer program, the ideas consist of the
program's methodology and algorithm, including the necessary sequence of steps
adopted by the programmer. The expression of those ideas is the program source
code (particularly any arbitrary or stylistic choices embodied in it), its derived object
code, and any other derivative works.

If you analyze the ideas contained in a program, and then express those
ideas in your own completely different implementation, then that new program
implementation belongs to you. That is what we have done for those programs in
this book that are not entirely of our own devising. When programs in this book are
said to be "based" on programs published in copyright sources, we mean that the
ideas are the same. The expression of these ideas as source code is our own. We
believe that no material in this book infringes on an existing copyright.

Several registered trademarks appear within the text of this book: Sun is a
trademark of Sun Microsystems, Inc. SPARC and SPARCstation are trademarks
of SPARC International, Inc. Microsoft, Windows 95, Windows NT, PowerStation,
and MS are trademarks of Microsoft Corporation. DEC, VMS, Alpha AXP, and
ULTRIX are trademarks of Digital Equipment Corporation. IBM is a trademark of
International Business Machines Corporation. Apple and Macintosh are trademarks
of Apple Computer, Inc. UNIX is a trademark licensed exclusively through X/Open
Co. Ltd. IMSL is a trademark of Visual Numerics, Inc. NAG refers to proprietary
computer software of Numerical Algorithms Group (USA) Inc. PostScript and
Adobe Illustrator are trademarks of Adobe Systems Incorporated. Last, and no doubt
least, Numerical Recipes (when identifying products) is a trademark of Numerical
Recipes Software.

The fact that ideas are legally "free as air" in no way supersedes the ethical
requirement that ideas be credited to their known originators. When programs in
this book are based on known sources, whether copyrighted or in the public domain,
published or "handed-down," we have attempted to give proper attribution. Unfortunately,
the lineage of many programs in common circulation is often unclear. We
would be grateful to readers for new or corrected information regarding attributions,
which we will attempt to incorporate in subsequent printings.