1887 lines
45 KiB
HTML
1887 lines
45 KiB
HTML
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<!DOCTYPE HTML>
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<meta content="text/html; charset=utf-8" http-equiv="Content-Type">
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<title>Ratios and Rational Numbers · Learn Lisp The Hard Way</title>
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<meta name="generator" content="GitBook 3.2.3">
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<meta name="author" content=""the Phoeron" Colin J.E. Lupton">
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<link rel="next" href="1-06-07-floating-point.html" />
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<body>
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<div class="book">
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<li class="header">LEARN LISP THE HARD WAY</li>
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<li class="chapter " data-level="1.1" data-path="./">
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CHANGELOG
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</a>
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</li>
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<li class="chapter " data-level="1.3" data-path="TODO.html">
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<a href="TODO.html">
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TODO
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</a>
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</li>
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<li class="header">PREFACE</li>
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<li class="chapter " data-level="2.1" data-path="preface.html">
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<a href="preface.html">
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TANSTAAFL
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</a>
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</li>
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<li class="chapter " data-level="2.2" data-path="preface-part-two.html">
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<a href="preface-part-two.html">
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The Hard Way is Easier
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</a>
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</li>
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<li class="chapter " data-level="2.3" data-path="preface-part-three.html">
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<a href="preface-part-three.html">
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Who Is This Book For?
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</a>
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</li>
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<li class="chapter " data-level="2.4" data-path="introduction.html">
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<a href="introduction.html">
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Lisp: A Future History
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</a>
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</li>
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<li class="chapter " data-level="2.5" data-path="acknowledgements.html">
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<a href="acknowledgements.html">
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Acknowledgements
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</a>
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</li>
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<li class="header">PART ONE</li>
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<li class="chapter " data-level="3.1" data-path="1-0-0-overview.html">
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<a href="1-0-0-overview.html">
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Grokking Lisp
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</a>
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<ul class="articles">
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<li class="chapter " data-level="3.1.1" data-path="1-01-00-lisp-bootcamp.html">
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<a href="1-01-00-lisp-bootcamp.html">
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Common Lisp Bootcamp
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</a>
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<ul class="articles">
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<li class="chapter " data-level="3.1.1.1" data-path="1-01-01-syntax-overview.html">
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<a href="1-01-01-syntax-overview.html">
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Syntax Overview in 5 Minutes
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</a>
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</li>
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<li class="chapter " data-level="3.1.1.2" data-path="1-01-02-repl.html">
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<a href="1-01-02-repl.html">
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The REPL
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</a>
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</li>
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<li class="chapter " data-level="3.1.1.3" data-path="1-01-03-expressions.html">
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<a href="1-01-03-expressions.html">
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Expressions, Parentheses, and Return Values
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</a>
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</li>
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<li class="chapter " data-level="3.1.1.4" data-path="1-01-04-lists-cons-cells.html">
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<a href="1-01-04-lists-cons-cells.html">
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Lists, Cons-Cells, and Memory
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</a>
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</li>
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<li class="chapter " data-level="3.1.1.5" data-path="1-01-05-symbols.html">
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<a href="1-01-05-symbols.html">
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Symbols and Namespaces
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</a>
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</li>
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<li class="chapter " data-level="3.1.1.6" data-path="1-01-06-prefix-notation.html">
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<a href="1-01-06-prefix-notation.html">
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Prefix Notation
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</a>
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</li>
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<li class="chapter " data-level="3.1.1.7" data-path="1-01-07-style-guide.html">
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<a href="1-01-07-style-guide.html">
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Common Lisp Style Guide
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</a>
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</li>
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<li class="chapter " data-level="3.1.1.8" data-path="1-01-08-configuration.html">
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<a href="1-01-08-configuration.html">
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Configuring Your Development Environment
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</a>
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</li>
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</ul>
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</li>
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<li class="chapter " data-level="3.1.2" data-path="1-02-00-input-output.html">
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<a href="1-02-00-input-output.html">
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Printing, Streams, and Strings
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</a>
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<ul class="articles">
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<li class="chapter " data-level="3.1.2.1" data-path="1-02-01-strings.html">
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<a href="1-02-01-strings.html">
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Strings
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</a>
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</li>
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<li class="chapter " data-level="3.1.2.2" data-path="1-02-02-more-strings.html">
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<a href="1-02-02-more-strings.html">
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More Strings
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</a>
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</li>
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<li class="chapter " data-level="3.1.2.3" data-path="1-02-03-unicode.html">
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<a href="1-02-03-unicode.html">
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Unicode and Strings
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</a>
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</li>
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<li class="chapter " data-level="3.1.2.4" data-path="1-02-04-chars.html">
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<a href="1-02-04-chars.html">
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Characters
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</a>
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</li>
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<li class="chapter " data-level="3.1.2.5" data-path="1-02-05-more-chars.html">
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<a href="1-02-05-more-chars.html">
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More Characters
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</a>
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</li>
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<li class="chapter " data-level="3.1.2.6" data-path="1-02-06-char-codes.html">
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<a href="1-02-06-char-codes.html">
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Character Codes
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</a>
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</li>
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<li class="chapter " data-level="3.1.2.7" data-path="1-02-07-strings-from-chars.html">
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<a href="1-02-07-strings-from-chars.html">
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Strings from Chars
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</a>
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</li>
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<li class="chapter " data-level="3.1.2.8" data-path="1-02-08-printing.html">
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<a href="1-02-08-printing.html">
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Printing
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</a>
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</li>
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<li class="chapter " data-level="3.1.2.9" data-path="1-02-09-more-printing.html">
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<a href="1-02-09-more-printing.html">
|
||
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More Printing
|
||
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</a>
|
||
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</li>
|
||
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<li class="chapter " data-level="3.1.2.10" data-path="1-02-10-prin1.html">
|
||
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|
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<a href="1-02-10-prin1.html">
|
||
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Printing With prin1
|
||
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</a>
|
||
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||
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</li>
|
||
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<li class="chapter " data-level="3.1.2.11" data-path="1-02-11-princ.html">
|
||
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||
|
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<a href="1-02-11-princ.html">
|
||
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|
||
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|
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Printing With princ
|
||
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</a>
|
||
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||
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|
||
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||
|
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</li>
|
||
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|
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<li class="chapter " data-level="3.1.2.12" data-path="1-02-12-format.html">
|
||
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|
||
|
|
<a href="1-02-12-format.html">
|
||
|
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|
||
|
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|
||
|
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A Brief Introduction to Format
|
||
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|
||
|
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</a>
|
||
|
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|
||
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|
||
|
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||
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</li>
|
||
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|
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<li class="chapter " data-level="3.1.2.13" data-path="1-02-13-more-format.html">
|
||
|
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|
||
|
|
<a href="1-02-13-more-format.html">
|
||
|
|
|
||
|
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|
||
|
|
A Little Bit More on Format
|
||
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|
||
|
|
</a>
|
||
|
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|
||
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|
||
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</li>
|
||
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<li class="chapter " data-level="3.1.2.14" data-path="1-02-14-pathnames.html">
|
||
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|
||
|
|
<a href="1-02-14-pathnames.html">
|
||
|
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|
||
|
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|
||
|
|
Pathnames
|
||
|
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|
||
|
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</a>
|
||
|
|
|
||
|
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|
||
|
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|
||
|
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</li>
|
||
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|
||
|
|
<li class="chapter " data-level="3.1.2.15" data-path="1-02-15-streams.html">
|
||
|
|
|
||
|
|
<a href="1-02-15-streams.html">
|
||
|
|
|
||
|
|
|
||
|
|
Streams
|
||
|
|
|
||
|
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</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
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|
||
|
|
<li class="chapter " data-level="3.1.2.16" data-path="1-02-16-file-streams.html">
|
||
|
|
|
||
|
|
<a href="1-02-16-file-streams.html">
|
||
|
|
|
||
|
|
|
||
|
|
File Streams
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.2.17" data-path="1-02-17-binary-streams.html">
|
||
|
|
|
||
|
|
<a href="1-02-17-binary-streams.html">
|
||
|
|
|
||
|
|
|
||
|
|
Binary Streams
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.2.18" data-path="1-02-18-prompting-users.html">
|
||
|
|
|
||
|
|
<a href="1-02-18-prompting-users.html">
|
||
|
|
|
||
|
|
|
||
|
|
Prompting Users
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.2.19" data-path="1-02-19-pretty-printing.html">
|
||
|
|
|
||
|
|
<a href="1-02-19-pretty-printing.html">
|
||
|
|
|
||
|
|
|
||
|
|
Pretty-Printing
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
|
||
|
|
</ul>
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.3" data-path="1-03-0-getting-input-from-users.html">
|
||
|
|
|
||
|
|
<a href="1-03-0-getting-input-from-users.html">
|
||
|
|
|
||
|
|
|
||
|
|
Extra Credit: Getting Input from Users
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.4" data-path="1-04-0-lists.html">
|
||
|
|
|
||
|
|
<a href="1-04-0-lists.html">
|
||
|
|
|
||
|
|
|
||
|
|
Lists and List-Operations
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.5" data-path="1-05-0-lookups-trees.html">
|
||
|
|
|
||
|
|
<a href="1-05-0-lookups-trees.html">
|
||
|
|
|
||
|
|
|
||
|
|
Extra Credit: Look-up Lists and Trees
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.6" data-path="1-06-0-math.html">
|
||
|
|
|
||
|
|
<a href="1-06-0-math.html">
|
||
|
|
|
||
|
|
|
||
|
|
Numbers and Math
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
<ul class="articles">
|
||
|
|
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.6.1" data-path="1-06-01-integers.html">
|
||
|
|
|
||
|
|
<a href="1-06-01-integers.html">
|
||
|
|
|
||
|
|
|
||
|
|
Integers
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.6.2" data-path="1-06-02-more-integers.html">
|
||
|
|
|
||
|
|
<a href="1-06-02-more-integers.html">
|
||
|
|
|
||
|
|
|
||
|
|
More Integers
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.6.3" data-path="1-06-03-hexadecimal-notation.html">
|
||
|
|
|
||
|
|
<a href="1-06-03-hexadecimal-notation.html">
|
||
|
|
|
||
|
|
|
||
|
|
Hexadecimal Integer Notation
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.6.4" data-path="1-06-04-octal-notation.html">
|
||
|
|
|
||
|
|
<a href="1-06-04-octal-notation.html">
|
||
|
|
|
||
|
|
|
||
|
|
Octal Integer Notation
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.6.5" data-path="1-06-05-binary-notation.html">
|
||
|
|
|
||
|
|
<a href="1-06-05-binary-notation.html">
|
||
|
|
|
||
|
|
|
||
|
|
Binary Integer Notation
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter active" data-level="3.1.6.6" data-path="1-06-06-ratios.html">
|
||
|
|
|
||
|
|
<a href="1-06-06-ratios.html">
|
||
|
|
|
||
|
|
|
||
|
|
Ratios and Rational Numbers
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.6.7" data-path="1-06-07-floating-point.html">
|
||
|
|
|
||
|
|
<a href="1-06-07-floating-point.html">
|
||
|
|
|
||
|
|
|
||
|
|
Floating-point Numbers
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.6.8" data-path="1-06-08-constants.html">
|
||
|
|
|
||
|
|
<a href="1-06-08-constants.html">
|
||
|
|
|
||
|
|
|
||
|
|
Numeric Constants
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.6.9" data-path="1-06-09-complex-numbers.html">
|
||
|
|
|
||
|
|
<a href="1-06-09-complex-numbers.html">
|
||
|
|
|
||
|
|
|
||
|
|
Complex Numbers
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.6.10" data-path="1-06-10-arithmetic.html">
|
||
|
|
|
||
|
|
<a href="1-06-10-arithmetic.html">
|
||
|
|
|
||
|
|
|
||
|
|
Arithmetic
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.6.11" data-path="1-06-11-more-arithmetic.html">
|
||
|
|
|
||
|
|
<a href="1-06-11-more-arithmetic.html">
|
||
|
|
|
||
|
|
|
||
|
|
More Arithmetic
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.6.12" data-path="1-06-12-even-more-arithmetic.html">
|
||
|
|
|
||
|
|
<a href="1-06-12-even-more-arithmetic.html">
|
||
|
|
|
||
|
|
|
||
|
|
Even More Arithmetic
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.6.13" data-path="1-06-13-exponents.html">
|
||
|
|
|
||
|
|
<a href="1-06-13-exponents.html">
|
||
|
|
|
||
|
|
|
||
|
|
Exponents
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.6.14" data-path="1-06-14-logarithms.html">
|
||
|
|
|
||
|
|
<a href="1-06-14-logarithms.html">
|
||
|
|
|
||
|
|
|
||
|
|
Logarithms
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.6.15" data-path="1-06-15-trigonometry.html">
|
||
|
|
|
||
|
|
<a href="1-06-15-trigonometry.html">
|
||
|
|
|
||
|
|
|
||
|
|
Trigonometry
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.6.16" data-path="1-06-16-psuedorandom-numbers.html">
|
||
|
|
|
||
|
|
<a href="1-06-16-psuedorandom-numbers.html">
|
||
|
|
|
||
|
|
|
||
|
|
Pseudo-Random Numbers
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
|
||
|
|
</ul>
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.7" data-path="1-07-0-arrays.html">
|
||
|
|
|
||
|
|
<a href="1-07-0-arrays.html">
|
||
|
|
|
||
|
|
|
||
|
|
Extra Credit: Arrays and Vectors
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.8" data-path="1-08-0-variables.html">
|
||
|
|
|
||
|
|
<a href="1-08-0-variables.html">
|
||
|
|
|
||
|
|
|
||
|
|
Variables, Parameters, and Constants
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.9" data-path="1-09-0-closures.html">
|
||
|
|
|
||
|
|
<a href="1-09-0-closures.html">
|
||
|
|
|
||
|
|
|
||
|
|
Extra Credit: Closures
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.10" data-path="1-10-0-functions.html">
|
||
|
|
|
||
|
|
<a href="1-10-0-functions.html">
|
||
|
|
|
||
|
|
|
||
|
|
Functions and Macros
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.11" data-path="1-11-0-text-adventure.html">
|
||
|
|
|
||
|
|
<a href="1-11-0-text-adventure.html">
|
||
|
|
|
||
|
|
|
||
|
|
Extra Credit: A Simple Text Adventure
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.12" data-path="1-12-0-namespaces.html">
|
||
|
|
|
||
|
|
<a href="1-12-0-namespaces.html">
|
||
|
|
|
||
|
|
|
||
|
|
Namespaces, Symbols, Packages, and Systems
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.13" data-path="1-13-0-simple-web-app.html">
|
||
|
|
|
||
|
|
<a href="1-13-0-simple-web-app.html">
|
||
|
|
|
||
|
|
|
||
|
|
Extra Credit: A Simple Web Application
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.14" data-path="1-14-0-conditionals.html">
|
||
|
|
|
||
|
|
<a href="1-14-0-conditionals.html">
|
||
|
|
|
||
|
|
|
||
|
|
Conditionals
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.15" data-path="1-15-0-command-line-utility.html">
|
||
|
|
|
||
|
|
<a href="1-15-0-command-line-utility.html">
|
||
|
|
|
||
|
|
|
||
|
|
Extra Credit: Command-Line Utilities
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.16" data-path="1-16-0-map-loop.html">
|
||
|
|
|
||
|
|
<a href="1-16-0-map-loop.html">
|
||
|
|
|
||
|
|
|
||
|
|
Mapping and Looping
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.17" data-path="1-17-0-iterate.html">
|
||
|
|
|
||
|
|
<a href="1-17-0-iterate.html">
|
||
|
|
|
||
|
|
|
||
|
|
Extra Credit: Revisiting Loops with Iterate
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.18" data-path="1-18-0-format.html">
|
||
|
|
|
||
|
|
<a href="1-18-0-format.html">
|
||
|
|
|
||
|
|
|
||
|
|
Format Strings
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.19" data-path="1-19-0-dsl.html">
|
||
|
|
|
||
|
|
<a href="1-19-0-dsl.html">
|
||
|
|
|
||
|
|
|
||
|
|
Extra Credit: Domain Specific Languages
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="3.1.20" data-path="1-20-0-review.html">
|
||
|
|
|
||
|
|
<a href="1-20-0-review.html">
|
||
|
|
|
||
|
|
|
||
|
|
Part One in Review
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
|
||
|
|
</ul>
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
<li class="header">PART TWO</li>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
<li class="chapter " data-level="4.1" data-path="2-0-0-overview.html">
|
||
|
|
|
||
|
|
<a href="2-0-0-overview.html">
|
||
|
|
|
||
|
|
|
||
|
|
The Suffusion of Blue
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
<ul class="articles">
|
||
|
|
|
||
|
|
|
||
|
|
<li class="chapter " data-level="4.1.1" data-path="2-01-0-programming-paradigms.html">
|
||
|
|
|
||
|
|
<a href="2-01-0-programming-paradigms.html">
|
||
|
|
|
||
|
|
|
||
|
|
Programming Paradigms
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="4.1.2" data-path="2-02-0-regex.html">
|
||
|
|
|
||
|
|
<a href="2-02-0-regex.html">
|
||
|
|
|
||
|
|
|
||
|
|
Extra Credit: Regular Expressions
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="4.1.3" data-path="2-03-0-objects-control.html">
|
||
|
|
|
||
|
|
<a href="2-03-0-objects-control.html">
|
||
|
|
|
||
|
|
|
||
|
|
Objects and Control Structures
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="4.1.4" data-path="2-04-0-data-persistence.html">
|
||
|
|
|
||
|
|
<a href="2-04-0-data-persistence.html">
|
||
|
|
|
||
|
|
|
||
|
|
Extra Credit: Persistence and Databases
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="4.1.5" data-path="2-05-0-extended-types.html">
|
||
|
|
|
||
|
|
<a href="2-05-0-extended-types.html">
|
||
|
|
|
||
|
|
|
||
|
|
Extended Types
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="4.1.6" data-path="2-06-0-threads-memos-parallel.html">
|
||
|
|
|
||
|
|
<a href="2-06-0-threads-memos-parallel.html">
|
||
|
|
|
||
|
|
|
||
|
|
Extra Credit: Concurrency and Memoization
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="4.1.7" data-path="2-07-0-logic-and-more-math.html">
|
||
|
|
|
||
|
|
<a href="2-07-0-logic-and-more-math.html">
|
||
|
|
|
||
|
|
|
||
|
|
Logic and Advanced Math
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="4.1.8" data-path="2-08-0-number-theory.html">
|
||
|
|
|
||
|
|
<a href="2-08-0-number-theory.html">
|
||
|
|
|
||
|
|
|
||
|
|
Extra Credit: Number Theory
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="4.1.9" data-path="2-09-0-binary-octets-bits.html">
|
||
|
|
|
||
|
|
<a href="2-09-0-binary-octets-bits.html">
|
||
|
|
|
||
|
|
|
||
|
|
Binary Streams, Octet-Vectors, and Bit-Vectors
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="4.1.10" data-path="2-10-0-improved-text-adventure-engine.html">
|
||
|
|
|
||
|
|
<a href="2-10-0-improved-text-adventure-engine.html">
|
||
|
|
|
||
|
|
|
||
|
|
Extra Credit: An Improved Text Adventure Engine
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="4.1.11" data-path="2-11-0-conditions.html">
|
||
|
|
|
||
|
|
<a href="2-11-0-conditions.html">
|
||
|
|
|
||
|
|
|
||
|
|
Conditions and Error Handling
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="4.1.12" data-path="2-12-0-2d-game.html">
|
||
|
|
|
||
|
|
<a href="2-12-0-2d-game.html">
|
||
|
|
|
||
|
|
|
||
|
|
Extra Credit: Write a 2D Game
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="4.1.13" data-path="2-13-0-compiler.html">
|
||
|
|
|
||
|
|
<a href="2-13-0-compiler.html">
|
||
|
|
|
||
|
|
|
||
|
|
The Compiler
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="4.1.14" data-path="2-14-0-tree-shaker.html">
|
||
|
|
|
||
|
|
<a href="2-14-0-tree-shaker.html">
|
||
|
|
|
||
|
|
|
||
|
|
Extra Credit: Write a Tree-Shaker
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="4.1.15" data-path="2-15-0-docs-and-inspection.html">
|
||
|
|
|
||
|
|
<a href="2-15-0-docs-and-inspection.html">
|
||
|
|
|
||
|
|
|
||
|
|
Documentation and Inspection
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="4.1.16" data-path="2-16-0-foreign-libs.html">
|
||
|
|
|
||
|
|
<a href="2-16-0-foreign-libs.html">
|
||
|
|
|
||
|
|
|
||
|
|
Extra Credit: Foreign Libraries in Lisp
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="4.1.17" data-path="2-17-0-debugging-testing.html">
|
||
|
|
|
||
|
|
<a href="2-17-0-debugging-testing.html">
|
||
|
|
|
||
|
|
|
||
|
|
Debugging and Unit Testing
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="4.1.18" data-path="2-18-0-ffi.html">
|
||
|
|
|
||
|
|
<a href="2-18-0-ffi.html">
|
||
|
|
|
||
|
|
|
||
|
|
Extra Credit: Write a Foreign Function Interface
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="4.1.19" data-path="2-19-0-essential-libs.html">
|
||
|
|
|
||
|
|
<a href="2-19-0-essential-libs.html">
|
||
|
|
|
||
|
|
|
||
|
|
Essential Lisp Libraries
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="4.1.20" data-path="2-20-0-packaging-libs.html">
|
||
|
|
|
||
|
|
<a href="2-20-0-packaging-libs.html">
|
||
|
|
|
||
|
|
|
||
|
|
Extra Credit: Packaging Lisp Libraries
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="4.1.21" data-path="2-21-0-review.html">
|
||
|
|
|
||
|
|
<a href="2-21-0-review.html">
|
||
|
|
|
||
|
|
|
||
|
|
Detailed Syntax Review
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
|
||
|
|
</ul>
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
<li class="header">PART THREE</li>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
<li class="chapter " data-level="5.1" data-path="3-00-00-overview.html">
|
||
|
|
|
||
|
|
<a href="3-00-00-overview.html">
|
||
|
|
|
||
|
|
|
||
|
|
Lisp So(u)rcery
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
<ul class="articles">
|
||
|
|
|
||
|
|
|
||
|
|
<li class="chapter " data-level="5.1.1" data-path="3-01-00-web-apps.html">
|
||
|
|
|
||
|
|
<a href="3-01-00-web-apps.html">
|
||
|
|
|
||
|
|
|
||
|
|
Real-world Web Apps
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="5.1.2" data-path="3-02-00-typesetting.html">
|
||
|
|
|
||
|
|
<a href="3-02-00-typesetting.html">
|
||
|
|
|
||
|
|
|
||
|
|
Typesetting
|
||
|
|
|
||
|
|
</a>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</li>
|
||
|
|
|
||
|
|
<li class="chapter " data-level="5.1.3" data-path="3-03-00-mobile.html">
|
||
|
|
|
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A Simple LispOS
|
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<h1>
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<a href="index.html" >Ratios and Rational Numbers</a>
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|
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|
<h1 id="exercise-166">Exercise 1.6.6</h1>
|
||
|
|
<h2 id="ratios">Ratios</h2>
|
||
|
|
<h3 id="in-the-repl">In the REPL</h3>
|
||
|
|
<pre><code class="lang-lisp">3/17
|
||
|
|
|
||
|
|
1/2
|
||
|
|
|
||
|
|
(typep 1/2 'integer)
|
||
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|
||
|
|
(typep 1/2 'number)
|
||
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|
||
|
|
(type-of 1/2)
|
||
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|
||
|
|
.5
|
||
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|
||
|
|
(type-of .5)
|
||
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|
||
|
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1/2
|
||
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|
|
||
|
|
4/8
|
||
|
|
|
||
|
|
32/64
|
||
|
|
</code></pre>
|
||
|
|
<h3 id="what-you-should-see">What You Should See</h3>
|
||
|
|
<p>Ratios are a primitive numeric type in Common Lisp.</p>
|
||
|
|
<pre><code class="lang-lisp">* <span class="hljs-number">3/17</span>
|
||
|
|
<span class="hljs-number">3/17</span>
|
||
|
|
|
||
|
|
* <span class="hljs-number">1/2</span>
|
||
|
|
<span class="hljs-number">1/2</span>
|
||
|
|
</code></pre>
|
||
|
|
<p>Ratios are not integers, but they are still numbers.</p>
|
||
|
|
<pre><code class="lang-lisp">* (<span class="hljs-name">typep</span> <span class="hljs-number">1/2</span> 'integer)
|
||
|
|
NIL
|
||
|
|
|
||
|
|
* (<span class="hljs-name">typep</span> <span class="hljs-number">1/2</span> 'number)
|
||
|
|
T
|
||
|
|
</code></pre>
|
||
|
|
<p>These are not the same things as their float equivalents.</p>
|
||
|
|
<pre><code class="lang-lisp">* (type-of 1/2)
|
||
|
|
RATIO
|
||
|
|
|
||
|
|
* .5
|
||
|
|
0.5
|
||
|
|
|
||
|
|
* (type-of .5)
|
||
|
|
SINGLE-FLOAT
|
||
|
|
</code></pre>
|
||
|
|
<p>They are always reduced to lowest terms.</p>
|
||
|
|
<pre><code class="lang-lisp">* <span class="hljs-number">1/2</span>
|
||
|
|
<span class="hljs-number">1/2</span>
|
||
|
|
|
||
|
|
* <span class="hljs-number">4/8</span>
|
||
|
|
<span class="hljs-number">1/2</span>
|
||
|
|
|
||
|
|
* <span class="hljs-number">32/64</span>
|
||
|
|
<span class="hljs-number">1/2</span>
|
||
|
|
</code></pre>
|
||
|
|
|
||
|
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</section>
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<h1 class="search-results-title"><span class='search-results-count'></span> results matching "<span class='search-query'></span>"</h1>
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</div>
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</div>
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