\BOOKMARK [1][-]{section.0.1}{Introduction to Axiom}{}
\BOOKMARK [2][-]{subsection.0.1.1}{Symbolic Computation}{section.0.1}
\BOOKMARK [2][-]{subsection.0.1.2}{Numeric Computation}{section.0.1}
\BOOKMARK [2][-]{subsection.0.1.3}{Graphics}{section.0.1}
\BOOKMARK [2][-]{subsection.0.1.4}{HyperDoc}{section.0.1}
\BOOKMARK [2][-]{subsection.0.1.5}{Interactive Programming }{section.0.1}
\BOOKMARK [2][-]{subsection.0.1.6}{Data Structures}{section.0.1}
\BOOKMARK [2][-]{subsection.0.1.7}{Mathematical Structures}{section.0.1}
\BOOKMARK [2][-]{subsection.0.1.8}{Pattern Matching}{section.0.1}
\BOOKMARK [2][-]{subsection.0.1.9}{Polymorphic Algorithms}{section.0.1}
\BOOKMARK [2][-]{subsection.0.1.10}{Extensibility}{section.0.1}
\BOOKMARK [2][-]{subsection.0.1.11}{Types are Defined by Abstract Datatype Programs}{section.0.1}
\BOOKMARK [2][-]{subsection.0.1.12}{The Type of Basic Objects is a Domain or Subdomain}{section.0.1}
\BOOKMARK [2][-]{subsection.0.1.13}{Domains Have Types Called Categories}{section.0.1}
\BOOKMARK [2][-]{subsection.0.1.14}{Operations Can Refer To Abstract Types}{section.0.1}
\BOOKMARK [2][-]{subsection.0.1.15}{Categories Form Hierarchies}{section.0.1}
\BOOKMARK [2][-]{subsection.0.1.16}{Domains Belong to Categories by Assertion}{section.0.1}
\BOOKMARK [2][-]{subsection.0.1.17}{Packages Are Clusters of Polymorphic Operations}{section.0.1}
\BOOKMARK [2][-]{subsection.0.1.18}{The Interpreter Builds Domains Dynamically}{section.0.1}
\BOOKMARK [2][-]{subsection.0.1.19}{Axiom Code is Compiled}{section.0.1}
\BOOKMARK [2][-]{subsection.0.1.20}{Axiom is Extensible}{section.0.1}
\BOOKMARK [1][-]{section.0.2}{Using Axiom as a Pocket Calculator}{}
\BOOKMARK [2][-]{subsection.0.2.1}{Basic Arithmetic}{section.0.2}
\BOOKMARK [2][-]{subsection.0.2.2}{Type Conversion}{section.0.2}
\BOOKMARK [2][-]{subsection.0.2.3}{Useful Functions}{section.0.2}
\BOOKMARK [1][-]{section.0.3}{Using Axiom as a Symbolic Calculator}{}
\BOOKMARK [2][-]{subsection.0.3.1}{Expressions Involving Symbols}{section.0.3}
\BOOKMARK [2][-]{subsection.0.3.2}{Complex Numbers}{section.0.3}
\BOOKMARK [2][-]{subsection.0.3.3}{Number Representations}{section.0.3}
\BOOKMARK [2][-]{subsection.0.3.4}{Modular Arithmetic}{section.0.3}
\BOOKMARK [1][-]{section.0.4}{General Points about Axiom}{}
\BOOKMARK [2][-]{subsection.0.4.1}{Computation Without Output}{section.0.4}
\BOOKMARK [2][-]{subsection.0.4.2}{Accessing Earlier Results}{section.0.4}
\BOOKMARK [2][-]{subsection.0.4.3}{Splitting Expressions Over Several Lines}{section.0.4}
\BOOKMARK [2][-]{subsection.0.4.4}{Comments and Descriptions}{section.0.4}
\BOOKMARK [2][-]{subsection.0.4.5}{Control of Result Types}{section.0.4}
\BOOKMARK [1][-]{section.0.5}{Data Structures in Axiom}{}
\BOOKMARK [2][-]{subsection.0.5.1}{Lists}{section.0.5}
\BOOKMARK [2][-]{subsection.0.5.2}{Segmented Lists}{section.0.5}
\BOOKMARK [2][-]{subsection.0.5.3}{Streams}{section.0.5}
\BOOKMARK [2][-]{subsection.0.5.4}{Arrays, Vectors, Strings, and Bits}{section.0.5}
\BOOKMARK [2][-]{subsection.0.5.5}{Flexible Arrays}{section.0.5}
\BOOKMARK [1][-]{section.0.6}{Functions, Choices, and Loops}{}
\BOOKMARK [2][-]{subsection.0.6.1}{Reading Code from a File}{section.0.6}
\BOOKMARK [2][-]{subsection.0.6.2}{Blocks}{section.0.6}
\BOOKMARK [2][-]{subsection.0.6.3}{Functions}{section.0.6}
\BOOKMARK [2][-]{subsection.0.6.4}{Choices}{section.0.6}
\BOOKMARK [2][-]{subsection.0.6.5}{Loops}{section.0.6}
\BOOKMARK [0][-]{chapter.1}{An Overview of Axiom}{}
\BOOKMARK [1][-]{section.1.1}{Starting Up and Winding Down}{chapter.1}
\BOOKMARK [2][-]{subsection.1.1.1}{Clef}{section.1.1}
\BOOKMARK [1][-]{section.1.2}{Typographic Conventions}{chapter.1}
\BOOKMARK [1][-]{section.1.3}{The Axiom Language}{chapter.1}
\BOOKMARK [2][-]{subsection.1.3.1}{Arithmetic Expressions}{section.1.3}
\BOOKMARK [2][-]{subsection.1.3.2}{Previous Results}{section.1.3}
\BOOKMARK [2][-]{subsection.1.3.3}{Some Types}{section.1.3}
\BOOKMARK [2][-]{subsection.1.3.4}{Symbols, Variables, Assignments, and Declarations}{section.1.3}
\BOOKMARK [2][-]{subsection.1.3.5}{Conversion}{section.1.3}
\BOOKMARK [2][-]{subsection.1.3.6}{Calling Functions}{section.1.3}
\BOOKMARK [2][-]{subsection.1.3.7}{Some Predefined Macros}{section.1.3}
\BOOKMARK [2][-]{subsection.1.3.8}{Long Lines}{section.1.3}
\BOOKMARK [2][-]{subsection.1.3.9}{Comments}{section.1.3}
\BOOKMARK [1][-]{section.1.4}{Numbers}{chapter.1}
\BOOKMARK [1][-]{section.1.5}{Data Structures}{chapter.1}
\BOOKMARK [1][-]{section.1.6}{Expanding to Higher Dimensions}{chapter.1}
\BOOKMARK [1][-]{section.1.7}{Writing Your Own Functions}{chapter.1}
\BOOKMARK [1][-]{section.1.8}{Polynomials}{chapter.1}
\BOOKMARK [1][-]{section.1.9}{Limits}{chapter.1}
\BOOKMARK [1][-]{section.1.10}{Series}{chapter.1}
\BOOKMARK [1][-]{section.1.11}{Derivatives}{chapter.1}
\BOOKMARK [1][-]{section.1.12}{Integration}{chapter.1}
\BOOKMARK [1][-]{section.1.13}{Differential Equations}{chapter.1}
\BOOKMARK [1][-]{section.1.14}{Solution of Equations}{chapter.1}
\BOOKMARK [1][-]{section.1.15}{System Commands}{chapter.1}
\BOOKMARK [2][-]{subsection.1.15.1}{Undo}{section.1.15}
\BOOKMARK [1][-]{section.1.16}{Graphics}{chapter.1}
\BOOKMARK [0][-]{chapter.2}{Using Types and Modes}{}
\BOOKMARK [1][-]{section.2.1}{The Basic Idea}{chapter.2}
\BOOKMARK [2][-]{subsection.2.1.1}{Domain Constructors}{section.2.1}
\BOOKMARK [1][-]{section.2.2}{Writing Types and Modes}{chapter.2}
\BOOKMARK [2][-]{subsection.2.2.1}{Types with No Arguments}{section.2.2}
\BOOKMARK [2][-]{subsection.2.2.2}{Types with One Argument}{section.2.2}
\BOOKMARK [2][-]{subsection.2.2.3}{Types with More Than One Argument}{section.2.2}
\BOOKMARK [2][-]{subsection.2.2.4}{Modes}{section.2.2}
\BOOKMARK [2][-]{subsection.2.2.5}{Abbreviations}{section.2.2}
\BOOKMARK [1][-]{section.2.3}{Declarations}{chapter.2}
\BOOKMARK [1][-]{section.2.4}{Records}{chapter.2}
\BOOKMARK [1][-]{section.2.5}{Unions}{chapter.2}
\BOOKMARK [2][-]{subsection.2.5.1}{Unions Without Selectors}{section.2.5}
\BOOKMARK [2][-]{subsection.2.5.2}{Unions With Selectors}{section.2.5}
\BOOKMARK [1][-]{section.2.6}{The ``Any'' Domain}{chapter.2}
\BOOKMARK [1][-]{section.2.7}{Conversion}{chapter.2}
\BOOKMARK [1][-]{section.2.8}{Subdomains Again}{chapter.2}
\BOOKMARK [1][-]{section.2.9}{Package Calling and Target Types}{chapter.2}
\BOOKMARK [1][-]{section.2.10}{Resolving Types}{chapter.2}
\BOOKMARK [1][-]{section.2.11}{Exposing Domains and Packages}{chapter.2}
\BOOKMARK [1][-]{section.2.12}{Commands for Snooping}{chapter.2}
\BOOKMARK [0][-]{chapter.3}{Using HyperDoc}{}
\BOOKMARK [1][-]{section.3.1}{Headings}{chapter.3}
\BOOKMARK [1][-]{section.3.2}{Key Definitions}{chapter.3}
\BOOKMARK [1][-]{section.3.3}{Scroll Bars}{chapter.3}
\BOOKMARK [1][-]{section.3.4}{Input Areas}{chapter.3}
\BOOKMARK [1][-]{section.3.5}{Radio Buttons and Toggles}{chapter.3}
\BOOKMARK [1][-]{section.3.6}{Search Strings}{chapter.3}
\BOOKMARK [2][-]{subsection.3.6.1}{Logical Searches}{section.3.6}
\BOOKMARK [1][-]{section.3.7}{Example Pages}{chapter.3}
\BOOKMARK [1][-]{section.3.8}{X Window Resources for HyperDoc}{chapter.3}
\BOOKMARK [0][-]{chapter.4}{Input Files and Output Styles}{}
\BOOKMARK [1][-]{section.4.1}{Input Files}{chapter.4}
\BOOKMARK [1][-]{section.4.2}{The .axiom.input File}{chapter.4}
\BOOKMARK [1][-]{section.4.3}{Common Features of Using Output Formats}{chapter.4}
\BOOKMARK [1][-]{section.4.4}{Monospace Two-Dimensional Mathematical Format}{chapter.4}
\BOOKMARK [1][-]{section.4.5}{TeX Format}{chapter.4}
\BOOKMARK [1][-]{section.4.6}{IBM Script Formula Format}{chapter.4}
\BOOKMARK [1][-]{section.4.7}{FORTRAN Format}{chapter.4}
\BOOKMARK [0][-]{chapter.5}{Overview of Interactive Language}{}
\BOOKMARK [1][-]{section.5.1}{Immediate and Delayed Assignments}{chapter.5}
\BOOKMARK [1][-]{section.5.2}{Blocks}{chapter.5}
\BOOKMARK [1][-]{section.5.3}{if-then-else}{chapter.5}
\BOOKMARK [1][-]{section.5.4}{Loops}{chapter.5}
\BOOKMARK [2][-]{subsection.5.4.1}{Compiling vs. Interpreting Loops}{section.5.4}
\BOOKMARK [2][-]{subsection.5.4.2}{return in Loops}{section.5.4}
\BOOKMARK [2][-]{subsection.5.4.3}{break in Loops}{section.5.4}
\BOOKMARK [2][-]{subsection.5.4.4}{break vs. => in Loop Bodies}{section.5.4}
\BOOKMARK [2][-]{subsection.5.4.5}{More Examples of break}{section.5.4}
\BOOKMARK [2][-]{subsection.5.4.6}{iterate in Loops}{section.5.4}
\BOOKMARK [2][-]{subsection.5.4.7}{while Loops}{section.5.4}
\BOOKMARK [2][-]{subsection.5.4.8}{for Loops}{section.5.4}
\BOOKMARK [2][-]{subsection.5.4.9}{for i in n..m repeat}{section.5.4}
\BOOKMARK [2][-]{subsection.5.4.10}{for i in n..m by s repeat}{section.5.4}
\BOOKMARK [2][-]{subsection.5.4.11}{for i in n.. repeat}{section.5.4}
\BOOKMARK [2][-]{subsection.5.4.12}{for x in l repeat}{section.5.4}
\BOOKMARK [2][-]{subsection.5.4.13}{``Such that'' Predicates}{section.5.4}
\BOOKMARK [2][-]{subsection.5.4.14}{Parallel Iteration}{section.5.4}
\BOOKMARK [2][-]{subsection.5.4.15}{Mixing Loop Modifiers}{section.5.4}
\BOOKMARK [1][-]{section.5.5}{Creating Lists and Streams with Iterators}{chapter.5}
\BOOKMARK [1][-]{section.5.6}{An Example: Streams of Primes}{chapter.5}
\BOOKMARK [0][-]{chapter.6}{User-Defined Functions, Macros and Rules}{}
\BOOKMARK [1][-]{section.6.1}{Functions vs. Macros}{chapter.6}
\BOOKMARK [1][-]{section.6.2}{Macros}{chapter.6}
\BOOKMARK [1][-]{section.6.3}{Introduction to Functions}{chapter.6}
\BOOKMARK [1][-]{section.6.4}{Declaring the Type of Functions}{chapter.6}
\BOOKMARK [1][-]{section.6.5}{One-Line Functions}{chapter.6}
\BOOKMARK [1][-]{section.6.6}{Declared vs. Undeclared Functions}{chapter.6}
\BOOKMARK [1][-]{section.6.7}{Functions vs. Operations}{chapter.6}
\BOOKMARK [1][-]{section.6.8}{Delayed Assignments vs. Functions with No Arguments}{chapter.6}
\BOOKMARK [1][-]{section.6.9}{How Axiom Determines What Function to Use}{chapter.6}
\BOOKMARK [1][-]{section.6.10}{Compiling vs. Interpreting}{chapter.6}
\BOOKMARK [1][-]{section.6.11}{Piece-Wise Function Definitions}{chapter.6}
\BOOKMARK [2][-]{subsection.6.11.1}{A Basic Example}{section.6.11}
\BOOKMARK [2][-]{subsection.6.11.2}{Picking Up the Pieces}{section.6.11}
\BOOKMARK [2][-]{subsection.6.11.3}{Predicates}{section.6.11}
\BOOKMARK [1][-]{section.6.12}{Caching Previously Computed Results}{chapter.6}
\BOOKMARK [1][-]{section.6.13}{Recurrence Relations}{chapter.6}
\BOOKMARK [1][-]{section.6.14}{Making Functions from Objects}{chapter.6}
\BOOKMARK [1][-]{section.6.15}{Functions Defined with Blocks}{chapter.6}
\BOOKMARK [1][-]{section.6.16}{Free and Local Variables}{chapter.6}
\BOOKMARK [1][-]{section.6.17}{Anonymous Functions}{chapter.6}
\BOOKMARK [2][-]{subsection.6.17.1}{Some Examples}{section.6.17}
\BOOKMARK [2][-]{subsection.6.17.2}{Declaring Anonymous Functions}{section.6.17}
\BOOKMARK [1][-]{section.6.18}{Example: A Database}{chapter.6}
\BOOKMARK [1][-]{section.6.19}{Example: A Famous Triangle}{chapter.6}
\BOOKMARK [1][-]{section.6.20}{Example: Testing for Palindromes}{chapter.6}
\BOOKMARK [1][-]{section.6.21}{Rules and Pattern Matching}{chapter.6}
\BOOKMARK [0][-]{chapter.7}{Graphics}{}
\BOOKMARK [1][-]{section.7.1}{Two-Dimensional Graphics}{chapter.7}
\BOOKMARK [2][-]{subsection.7.1.1}{Plotting Two-Dimensional Functions of One Variable}{section.7.1}
\BOOKMARK [2][-]{subsection.7.1.2}{Plotting Two-Dimensional Parametric Plane Curves}{section.7.1}
\BOOKMARK [2][-]{subsection.7.1.3}{Plotting Plane Algebraic Curves}{section.7.1}
\BOOKMARK [2][-]{subsection.7.1.4}{Two-Dimensional Options}{section.7.1}
\BOOKMARK [2][-]{subsection.7.1.5}{Color}{section.7.1}
\BOOKMARK [2][-]{subsection.7.1.6}{Palette}{section.7.1}
\BOOKMARK [2][-]{subsection.7.1.7}{Two-Dimensional Control-Panel}{section.7.1}
\BOOKMARK [2][-]{subsection.7.1.8}{Operations for Two-Dimensional Graphics}{section.7.1}
\BOOKMARK [2][-]{subsection.7.1.9}{Addendum: Building Two-Dimensional Graphs}{section.7.1}
\BOOKMARK [2][-]{subsection.7.1.10}{Addendum: Appending a Graph to a Viewport Window Containing a Graph}{section.7.1}
\BOOKMARK [1][-]{section.7.2}{Three-Dimensional Graphics}{chapter.7}
\BOOKMARK [2][-]{subsection.7.2.1}{Plotting Three-Dimensional Functions of Two Variables}{section.7.2}
\BOOKMARK [2][-]{subsection.7.2.2}{Plotting Three-Dimensional Parametric Space Curves}{section.7.2}
\BOOKMARK [2][-]{subsection.7.2.3}{Plotting Three-Dimensional Parametric Surfaces}{section.7.2}
\BOOKMARK [2][-]{subsection.7.2.4}{Axiom Images}{section.7.2}
\BOOKMARK [2][-]{subsection.7.2.5}{Three-Dimensional Options}{section.7.2}
\BOOKMARK [2][-]{subsection.7.2.6}{The makeObject Command}{section.7.2}
\BOOKMARK [2][-]{subsection.7.2.7}{Building Three-Dimensional Objects From Primitives}{section.7.2}
\BOOKMARK [2][-]{subsection.7.2.8}{Coordinate System Transformations}{section.7.2}
\BOOKMARK [2][-]{subsection.7.2.9}{Three-Dimensional Clipping}{section.7.2}
\BOOKMARK [2][-]{subsection.7.2.10}{Three-Dimensional Control-Panel}{section.7.2}
\BOOKMARK [2][-]{subsection.7.2.11}{Operations for Three-Dimensional Graphics}{section.7.2}
\BOOKMARK [2][-]{subsection.7.2.12}{Customization using .Xdefaults}{section.7.2}
\BOOKMARK [0][-]{chapter.8}{Advanced Problem Solving}{}
\BOOKMARK [1][-]{section.8.1}{Numeric Functions}{chapter.8}
\BOOKMARK [1][-]{section.8.2}{Polynomial Factorization}{chapter.8}
\BOOKMARK [2][-]{subsection.8.2.1}{Integer and Rational Number Coefficients}{section.8.2}
\BOOKMARK [2][-]{subsection.8.2.2}{Finite Field Coefficients}{section.8.2}
\BOOKMARK [2][-]{subsection.8.2.3}{Simple Algebraic Extension Field Coefficients}{section.8.2}
\BOOKMARK [2][-]{subsection.8.2.4}{Factoring Rational Functions}{section.8.2}
\BOOKMARK [1][-]{section.8.3}{Manipulating Symbolic Roots of a Polynomial}{chapter.8}
\BOOKMARK [2][-]{subsection.8.3.1}{Using a Single Root of a Polynomial}{section.8.3}
\BOOKMARK [2][-]{subsection.8.3.2}{Using All Roots of a Polynomial}{section.8.3}
\BOOKMARK [1][-]{section.8.4}{Computation of Eigenvalues and Eigenvectors}{chapter.8}
\BOOKMARK [1][-]{section.8.5}{Solution of Linear and Polynomial Equations}{chapter.8}
\BOOKMARK [2][-]{subsection.8.5.1}{Solution of Systems of Linear Equations}{section.8.5}
\BOOKMARK [2][-]{subsection.8.5.2}{Solution of a Single Polynomial Equation}{section.8.5}
\BOOKMARK [2][-]{subsection.8.5.3}{Solution of Systems of Polynomial Equations}{section.8.5}
\BOOKMARK [1][-]{section.8.6}{Limits}{chapter.8}
\BOOKMARK [1][-]{section.8.7}{Laplace Transforms}{chapter.8}
\BOOKMARK [1][-]{section.8.8}{Integration}{chapter.8}
\BOOKMARK [1][-]{section.8.9}{Working with Power Series}{chapter.8}
\BOOKMARK [2][-]{subsection.8.9.1}{Creation of Power Series}{section.8.9}
\BOOKMARK [2][-]{subsection.8.9.2}{Coefficients of Power Series}{section.8.9}
\BOOKMARK [2][-]{subsection.8.9.3}{Power Series Arithmetic}{section.8.9}
\BOOKMARK [2][-]{subsection.8.9.4}{Functions on Power Series}{section.8.9}
\BOOKMARK [2][-]{subsection.8.9.5}{Converting to Power Series}{section.8.9}
\BOOKMARK [2][-]{subsection.8.9.6}{Power Series from Formulas}{section.8.9}
\BOOKMARK [2][-]{subsection.8.9.7}{Substituting Numerical Values in Power Series}{section.8.9}
\BOOKMARK [2][-]{subsection.8.9.8}{Example: Bernoulli Polynomials and Sums of Powers}{section.8.9}
\BOOKMARK [1][-]{section.8.10}{Solution of Differential Equations}{chapter.8}
\BOOKMARK [2][-]{subsection.8.10.1}{Closed-Form Solutions of Linear Differential Equations}{section.8.10}
\BOOKMARK [2][-]{subsection.8.10.2}{Closed-Form Solutions of Non-Linear Differential Equations}{section.8.10}
\BOOKMARK [2][-]{subsection.8.10.3}{Power Series Solutions of Differential Equations}{section.8.10}
\BOOKMARK [1][-]{section.8.11}{Finite Fields}{chapter.8}
\BOOKMARK [2][-]{subsection.8.11.1}{Modular Arithmetic and Prime Fields}{section.8.11}
\BOOKMARK [2][-]{subsection.8.11.2}{Extensions of Finite Fields}{section.8.11}
\BOOKMARK [2][-]{subsection.8.11.3}{Irreducible Modulus Polynomial Representations}{section.8.11}
\BOOKMARK [2][-]{subsection.8.11.4}{Cyclic Group Representations}{section.8.11}
\BOOKMARK [2][-]{subsection.8.11.5}{Normal Basis Representations}{section.8.11}
\BOOKMARK [2][-]{subsection.8.11.6}{Conversion Operations for Finite Fields}{section.8.11}
\BOOKMARK [2][-]{subsection.8.11.7}{Utility Operations for Finite Fields}{section.8.11}
\BOOKMARK [1][-]{section.8.12}{Primary Decomposition of Ideals}{chapter.8}
\BOOKMARK [1][-]{section.8.13}{Computation of Galois Groups}{chapter.8}
\BOOKMARK [1][-]{section.8.14}{Non-Associative Algebras and Modelling Genetic Laws}{chapter.8}
\BOOKMARK [0][-]{chapter.9}{Some Examples of Domains and Packages}{}
\BOOKMARK [1][-]{section.9.1}{ApplicationProgramInterface}{chapter.9}
\BOOKMARK [1][-]{section.9.2}{ArrayStack}{chapter.9}
\BOOKMARK [1][-]{section.9.3}{AssociationList}{chapter.9}
\BOOKMARK [1][-]{section.9.4}{BalancedBinaryTree}{chapter.9}
\BOOKMARK [1][-]{section.9.5}{BasicOperator}{chapter.9}
\BOOKMARK [1][-]{section.9.6}{BinaryExpansion}{chapter.9}
\BOOKMARK [1][-]{section.9.7}{BinarySearchTree}{chapter.9}
\BOOKMARK [1][-]{section.9.8}{CardinalNumber}{chapter.9}
\BOOKMARK [1][-]{section.9.9}{CartesianTensor}{chapter.9}
\BOOKMARK [1][-]{section.9.10}{Character}{chapter.9}
\BOOKMARK [1][-]{section.9.11}{CharacterClass}{chapter.9}
\BOOKMARK [1][-]{section.9.12}{CliffordAlgebra}{chapter.9}
\BOOKMARK [2][-]{subsection.9.12.1}{The Complex Numbers as a Clifford Algebra}{section.9.12}
\BOOKMARK [2][-]{subsection.9.12.2}{The Quaternion Numbers as a Clifford Algebra}{section.9.12}
\BOOKMARK [2][-]{subsection.9.12.3}{The Exterior Algebra on a Three Space}{section.9.12}
\BOOKMARK [2][-]{subsection.9.12.4}{The Dirac Spin Algebra}{section.9.12}
\BOOKMARK [1][-]{section.9.13}{Complex}{chapter.9}
\BOOKMARK [1][-]{section.9.14}{ContinuedFraction}{chapter.9}
\BOOKMARK [1][-]{section.9.15}{CycleIndicators}{chapter.9}
\BOOKMARK [1][-]{section.9.16}{DeRhamComplex}{chapter.9}
\BOOKMARK [1][-]{section.9.17}{DecimalExpansion}{chapter.9}
\BOOKMARK [1][-]{section.9.18}{Dequeue}{chapter.9}
\BOOKMARK [1][-]{section.9.19}{DistributedMultivariatePolynomial}{chapter.9}
\BOOKMARK [1][-]{section.9.20}{DoubleFloat}{chapter.9}
\BOOKMARK [1][-]{section.9.21}{EqTable}{chapter.9}
\BOOKMARK [1][-]{section.9.22}{Equation}{chapter.9}
\BOOKMARK [1][-]{section.9.23}{EuclideanGroebnerBasisPackage}{chapter.9}
\BOOKMARK [1][-]{section.9.24}{Exit}{chapter.9}
\BOOKMARK [1][-]{section.9.25}{Expression}{chapter.9}
\BOOKMARK [1][-]{section.9.26}{Factored}{chapter.9}
\BOOKMARK [2][-]{subsection.9.26.1}{Decomposing Factored Objects}{section.9.26}
\BOOKMARK [2][-]{subsection.9.26.2}{Expanding Factored Objects}{section.9.26}
\BOOKMARK [2][-]{subsection.9.26.3}{Arithmetic with Factored Objects}{section.9.26}
\BOOKMARK [2][-]{subsection.9.26.4}{Creating New Factored Objects}{section.9.26}
\BOOKMARK [2][-]{subsection.9.26.5}{Factored Objects with Variables}{section.9.26}
\BOOKMARK [1][-]{section.9.27}{FactoredFunctions2}{chapter.9}
\BOOKMARK [1][-]{section.9.28}{File}{chapter.9}
\BOOKMARK [1][-]{section.9.29}{FileName}{chapter.9}
\BOOKMARK [1][-]{section.9.30}{FlexibleArray}{chapter.9}
\BOOKMARK [1][-]{section.9.31}{Float}{chapter.9}
\BOOKMARK [2][-]{subsection.9.31.1}{Introduction to Float}{section.9.31}
\BOOKMARK [2][-]{subsection.9.31.2}{Conversion Functions}{section.9.31}
\BOOKMARK [2][-]{subsection.9.31.3}{Output Functions}{section.9.31}
\BOOKMARK [2][-]{subsection.9.31.4}{An Example: Determinant of a Hilbert Matrix}{section.9.31}
\BOOKMARK [1][-]{section.9.32}{Fraction}{chapter.9}
\BOOKMARK [1][-]{section.9.33}{FullPartialFractionExpansion}{chapter.9}
\BOOKMARK [1][-]{section.9.34}{GeneralDistributedMultivariatePolynomial}{chapter.9}
\BOOKMARK [1][-]{section.9.35}{GeneralSparseTable}{chapter.9}
\BOOKMARK [1][-]{section.9.36}{GroebnerFactorizationPackage}{chapter.9}
\BOOKMARK [1][-]{section.9.37}{GroebnerPackage}{chapter.9}
\BOOKMARK [1][-]{section.9.38}{Heap}{chapter.9}
\BOOKMARK [1][-]{section.9.39}{HexadecimalExpansion}{chapter.9}
\BOOKMARK [1][-]{section.9.40}{HomogeneousDistributedMultivariatePolynomial}{chapter.9}
\BOOKMARK [1][-]{section.9.41}{Integer}{chapter.9}
\BOOKMARK [2][-]{subsection.9.41.1}{Basic Functions}{section.9.41}
\BOOKMARK [2][-]{subsection.9.41.2}{Primes and Factorization}{section.9.41}
\BOOKMARK [2][-]{subsection.9.41.3}{Some Number Theoretic Functions}{section.9.41}
\BOOKMARK [1][-]{section.9.42}{IntegerLinearDependence}{chapter.9}
\BOOKMARK [1][-]{section.9.43}{IntegerNumberTheoryFunctions}{chapter.9}
\BOOKMARK [1][-]{section.9.44}{Kernel}{chapter.9}
\BOOKMARK [1][-]{section.9.45}{KeyedAccessFile}{chapter.9}
\BOOKMARK [1][-]{section.9.46}{LexTriangularPackage}{chapter.9}
\BOOKMARK [1][-]{section.9.47}{LazardSetSolvingPackage}{chapter.9}
\BOOKMARK [1][-]{section.9.48}{Library}{chapter.9}
\BOOKMARK [1][-]{section.9.49}{LieExponentials}{chapter.9}
\BOOKMARK [1][-]{section.9.50}{LiePolynomial}{chapter.9}
\BOOKMARK [1][-]{section.9.51}{LinearOrdinaryDifferentialOperator}{chapter.9}
\BOOKMARK [2][-]{subsection.9.51.1}{Differential Operators with Series Coefficients}{section.9.51}
\BOOKMARK [1][-]{section.9.52}{LinearOrdinaryDifferentialOperator1}{chapter.9}
\BOOKMARK [2][-]{subsection.9.52.1}{Differential Operators with Rational Function Coefficients}{section.9.52}
\BOOKMARK [1][-]{section.9.53}{LinearOrdinaryDifferentialOperator2}{chapter.9}
\BOOKMARK [2][-]{subsection.9.53.1}{Differential Operators with Constant Coefficients}{section.9.53}
\BOOKMARK [2][-]{subsection.9.53.2}{ Differential Operators with Matrix Coefficients Operating on Vectors}{section.9.53}
\BOOKMARK [1][-]{section.9.54}{List}{chapter.9}
\BOOKMARK [2][-]{subsection.9.54.1}{Creating Lists}{section.9.54}
\BOOKMARK [2][-]{subsection.9.54.2}{Accessing List Elements}{section.9.54}
\BOOKMARK [2][-]{subsection.9.54.3}{Changing List Elements}{section.9.54}
\BOOKMARK [2][-]{subsection.9.54.4}{Other Functions}{section.9.54}
\BOOKMARK [2][-]{subsection.9.54.5}{Dot, Dot}{section.9.54}
\BOOKMARK [1][-]{section.9.55}{LyndonWord}{chapter.9}
\BOOKMARK [1][-]{section.9.56}{Magma}{chapter.9}
\BOOKMARK [1][-]{section.9.57}{MakeFunction}{chapter.9}
\BOOKMARK [1][-]{section.9.58}{MappingPackage1}{chapter.9}
\BOOKMARK [1][-]{section.9.59}{Matrix}{chapter.9}
\BOOKMARK [2][-]{subsection.9.59.1}{Creating Matrices}{section.9.59}
\BOOKMARK [2][-]{subsection.9.59.2}{Operations on Matrices}{section.9.59}
\BOOKMARK [1][-]{section.9.60}{Multiset}{chapter.9}
\BOOKMARK [1][-]{section.9.61}{MultivariatePolynomial}{chapter.9}
\BOOKMARK [1][-]{section.9.62}{None}{chapter.9}
\BOOKMARK [1][-]{section.9.63}{NottinghamGroup}{chapter.9}
\BOOKMARK [1][-]{section.9.64}{Octonion}{chapter.9}
\BOOKMARK [1][-]{section.9.65}{OneDimensionalArray}{chapter.9}
\BOOKMARK [1][-]{section.9.66}{Operator}{chapter.9}
\BOOKMARK [1][-]{section.9.67}{OrderedVariableList}{chapter.9}
\BOOKMARK [1][-]{section.9.68}{OrderlyDifferentialPolynomial}{chapter.9}
\BOOKMARK [1][-]{section.9.69}{PartialFraction}{chapter.9}
\BOOKMARK [1][-]{section.9.70}{Permanent}{chapter.9}
\BOOKMARK [1][-]{section.9.71}{Permutation}{chapter.9}
\BOOKMARK [1][-]{section.9.72}{Polynomial}{chapter.9}
\BOOKMARK [1][-]{section.9.73}{Quaternion}{chapter.9}
\BOOKMARK [1][-]{section.9.74}{Queue}{chapter.9}
\BOOKMARK [1][-]{section.9.75}{RadixExpansion}{chapter.9}
\BOOKMARK [1][-]{section.9.76}{RealClosure}{chapter.9}
\BOOKMARK [1][-]{section.9.77}{RealSolvePackage}{chapter.9}
\BOOKMARK [1][-]{section.9.78}{RegularTriangularSet}{chapter.9}
\BOOKMARK [1][-]{section.9.79}{RomanNumeral}{chapter.9}
\BOOKMARK [1][-]{section.9.80}{Segment}{chapter.9}
\BOOKMARK [1][-]{section.9.81}{SegmentBinding}{chapter.9}
\BOOKMARK [1][-]{section.9.82}{Set}{chapter.9}
\BOOKMARK [1][-]{section.9.83}{SingleInteger}{chapter.9}
\BOOKMARK [1][-]{section.9.84}{SparseTable}{chapter.9}
\BOOKMARK [1][-]{section.9.85}{SquareMatrix}{chapter.9}
\BOOKMARK [1][-]{section.9.86}{SquareFreeRegularTriangularSet}{chapter.9}
\BOOKMARK [1][-]{section.9.87}{Stack}{chapter.9}
\BOOKMARK [1][-]{section.9.88}{Stream}{chapter.9}
\BOOKMARK [1][-]{section.9.89}{String}{chapter.9}
\BOOKMARK [1][-]{section.9.90}{StringTable}{chapter.9}
\BOOKMARK [1][-]{section.9.91}{Symbol}{chapter.9}
\BOOKMARK [1][-]{section.9.92}{Table}{chapter.9}
\BOOKMARK [1][-]{section.9.93}{TextFile}{chapter.9}
\BOOKMARK [1][-]{section.9.94}{TwoDimensionalArray}{chapter.9}
\BOOKMARK [1][-]{section.9.95}{TwoDimensionalViewport}{chapter.9}
\BOOKMARK [1][-]{section.9.96}{UnivariatePolynomial}{chapter.9}
\BOOKMARK [1][-]{section.9.97}{UnivariateSkewPolynomial}{chapter.9}
\BOOKMARK [2][-]{subsection.9.97.1}{A second example}{section.9.97}
\BOOKMARK [2][-]{subsection.9.97.2}{A third example}{section.9.97}
\BOOKMARK [2][-]{subsection.9.97.3}{A fourth example}{section.9.97}
\BOOKMARK [1][-]{section.9.98}{UniversalSegment}{chapter.9}
\BOOKMARK [1][-]{section.9.99}{Vector}{chapter.9}
\BOOKMARK [1][-]{section.9.100}{Void}{chapter.9}
\BOOKMARK [1][-]{section.9.101}{WuWenTsunTriangularSet}{chapter.9}
\BOOKMARK [1][-]{section.9.102}{XPBWPolynomial}{chapter.9}
\BOOKMARK [1][-]{section.9.103}{XPolynomial}{chapter.9}
\BOOKMARK [1][-]{section.9.104}{XPolynomialRing}{chapter.9}
\BOOKMARK [1][-]{section.9.105}{ZeroDimensionalSolvePackage}{chapter.9}
\BOOKMARK [0][-]{chapter.10}{Interactive Programming}{}
\BOOKMARK [1][-]{section.10.1}{Drawing Ribbons Interactively}{chapter.10}
\BOOKMARK [1][-]{section.10.2}{A Ribbon Program}{chapter.10}
\BOOKMARK [1][-]{section.10.3}{Coloring and Positioning Ribbons}{chapter.10}
\BOOKMARK [1][-]{section.10.4}{Points, Lines, and Curves}{chapter.10}
\BOOKMARK [1][-]{section.10.5}{A Bouquet of Arrows}{chapter.10}
\BOOKMARK [1][-]{section.10.6}{Diversion: When Things Go Wrong}{chapter.10}
\BOOKMARK [1][-]{section.10.7}{Drawing Complex Vector Fields}{chapter.10}
\BOOKMARK [1][-]{section.10.8}{Drawing Complex Functions}{chapter.10}
\BOOKMARK [1][-]{section.10.9}{Functions Producing Functions}{chapter.10}
\BOOKMARK [1][-]{section.10.10}{Automatic Newton Iteration Formulas}{chapter.10}
\BOOKMARK [0][-]{chapter.11}{Packages}{}
\BOOKMARK [1][-]{section.11.1}{Names, Abbreviations, and File Structure}{chapter.11}
\BOOKMARK [1][-]{section.11.2}{Syntax}{chapter.11}
\BOOKMARK [1][-]{section.11.3}{Abstract Datatypes}{chapter.11}
\BOOKMARK [1][-]{section.11.4}{Capsules}{chapter.11}
\BOOKMARK [1][-]{section.11.5}{Input Files vs. Packages}{chapter.11}
\BOOKMARK [1][-]{section.11.6}{Compiling Packages}{chapter.11}
\BOOKMARK [1][-]{section.11.7}{Parameters}{chapter.11}
\BOOKMARK [1][-]{section.11.8}{Conditionals}{chapter.11}
\BOOKMARK [1][-]{section.11.9}{Testing}{chapter.11}
\BOOKMARK [1][-]{section.11.10}{How Packages Work}{chapter.11}
\BOOKMARK [0][-]{chapter.12}{Categories}{}
\BOOKMARK [1][-]{section.12.1}{Definitions}{chapter.12}
\BOOKMARK [1][-]{section.12.2}{Exports}{chapter.12}
\BOOKMARK [1][-]{section.12.3}{Documentation}{chapter.12}
\BOOKMARK [1][-]{section.12.4}{Hierarchies}{chapter.12}
\BOOKMARK [1][-]{section.12.5}{Membership}{chapter.12}
\BOOKMARK [1][-]{section.12.6}{Defaults}{chapter.12}
\BOOKMARK [1][-]{section.12.7}{Axioms}{chapter.12}
\BOOKMARK [1][-]{section.12.8}{Correctness}{chapter.12}
\BOOKMARK [1][-]{section.12.9}{Attributes}{chapter.12}
\BOOKMARK [1][-]{section.12.10}{Parameters}{chapter.12}
\BOOKMARK [1][-]{section.12.11}{Conditionals}{chapter.12}
\BOOKMARK [1][-]{section.12.12}{Anonymous Categories}{chapter.12}
\BOOKMARK [0][-]{chapter.13}{Domains}{}
\BOOKMARK [1][-]{section.13.1}{Domains vs. Packages}{chapter.13}
\BOOKMARK [1][-]{section.13.2}{Definitions}{chapter.13}
\BOOKMARK [1][-]{section.13.3}{Category Assertions}{chapter.13}
\BOOKMARK [1][-]{section.13.4}{A Demo}{chapter.13}
\BOOKMARK [1][-]{section.13.5}{Browse}{chapter.13}
\BOOKMARK [1][-]{section.13.6}{Representation}{chapter.13}
\BOOKMARK [1][-]{section.13.7}{Multiple Representations}{chapter.13}
\BOOKMARK [1][-]{section.13.8}{Add Domain}{chapter.13}
\BOOKMARK [1][-]{section.13.9}{Defaults}{chapter.13}
\BOOKMARK [1][-]{section.13.10}{Origins}{chapter.13}
\BOOKMARK [1][-]{section.13.11}{Short Forms}{chapter.13}
\BOOKMARK [1][-]{section.13.12}{Example 1: Clifford Algebra}{chapter.13}
\BOOKMARK [1][-]{section.13.13}{Example 2: Building A Query Facility}{chapter.13}
\BOOKMARK [2][-]{subsection.13.13.1}{A Little Query Language}{section.13.13}
\BOOKMARK [2][-]{subsection.13.13.2}{The Database Constructor}{section.13.13}
\BOOKMARK [2][-]{subsection.13.13.3}{Query Equations}{section.13.13}
\BOOKMARK [2][-]{subsection.13.13.4}{DataLists}{section.13.13}
\BOOKMARK [2][-]{subsection.13.13.5}{Index Cards}{section.13.13}
\BOOKMARK [2][-]{subsection.13.13.6}{Creating a Database}{section.13.13}
\BOOKMARK [2][-]{subsection.13.13.7}{Putting It All Together}{section.13.13}
\BOOKMARK [2][-]{subsection.13.13.8}{Example Queries}{section.13.13}
\BOOKMARK [0][-]{chapter.14}{Browse}{}
\BOOKMARK [1][-]{section.14.1}{The Front Page: Searching the Library}{chapter.14}
\BOOKMARK [1][-]{section.14.2}{The Constructor Page}{chapter.14}
\BOOKMARK [2][-]{subsection.14.2.1}{Constructor Page Buttons}{section.14.2}
\BOOKMARK [2][-]{subsection.14.2.2}{Cross Reference}{section.14.2}
\BOOKMARK [2][-]{subsection.14.2.3}{Views Of Constructors}{section.14.2}
\BOOKMARK [2][-]{subsection.14.2.4}{Giving Parameters to Constructors}{section.14.2}
\BOOKMARK [1][-]{section.14.3}{Miscellaneous Features of Browse}{chapter.14}
\BOOKMARK [2][-]{subsection.14.3.1}{The Description Page for Operations}{section.14.3}
\BOOKMARK [2][-]{subsection.14.3.2}{Views of Operations}{section.14.3}
\BOOKMARK [2][-]{subsection.14.3.3}{Capitalization Convention}{section.14.3}
\BOOKMARK [0][-]{chapter.15}{What's New in Axiom Version 2.0}{}
\BOOKMARK [1][-]{section.15.1}{Important Things to Read First}{chapter.15}
\BOOKMARK [1][-]{section.15.2}{The NAG Library Link}{chapter.15}
\BOOKMARK [2][-]{subsection.15.2.1}{Interpreting NAG Documentation}{section.15.2}
\BOOKMARK [2][-]{subsection.15.2.2}{Using the Link}{section.15.2}
\BOOKMARK [2][-]{subsection.15.2.3}{Providing values for Argument Subprograms}{section.15.2}
\BOOKMARK [2][-]{subsection.15.2.4}{General Fortran-generation utilities in Axiom}{section.15.2}
\BOOKMARK [2][-]{subsection.15.2.5}{Some technical information}{section.15.2}
\BOOKMARK [1][-]{section.15.3}{Interactive Front-end and Language}{chapter.15}
\BOOKMARK [1][-]{section.15.4}{Library}{chapter.15}
\BOOKMARK [1][-]{section.15.5}{HyperTex}{chapter.15}
\BOOKMARK [1][-]{section.15.6}{Documentation}{chapter.15}
\BOOKMARK [0][-]{appendix.A}{Axiom System Commands}{}
\BOOKMARK [1][-]{section.A.1}{Introduction}{appendix.A}
\BOOKMARK [1][-]{section.A.2}{\)abbreviation}{appendix.A}
\BOOKMARK [1][-]{section.A.3}{\)boot}{appendix.A}
\BOOKMARK [1][-]{section.A.4}{\)browse}{appendix.A}
\BOOKMARK [1][-]{section.A.5}{\)cd}{appendix.A}
\BOOKMARK [1][-]{section.A.6}{\)close}{appendix.A}
\BOOKMARK [1][-]{section.A.7}{\)clear}{appendix.A}
\BOOKMARK [1][-]{section.A.8}{\)compile}{appendix.A}
\BOOKMARK [1][-]{section.A.9}{\)display}{appendix.A}
\BOOKMARK [1][-]{section.A.10}{\)edit}{appendix.A}
\BOOKMARK [1][-]{section.A.11}{\)fin}{appendix.A}
\BOOKMARK [1][-]{section.A.12}{\)frame}{appendix.A}
\BOOKMARK [1][-]{section.A.13}{\)help}{appendix.A}
\BOOKMARK [1][-]{section.A.14}{\)history}{appendix.A}
\BOOKMARK [1][-]{section.A.15}{\)include}{appendix.A}
\BOOKMARK [1][-]{section.A.16}{\)library}{appendix.A}
\BOOKMARK [1][-]{section.A.17}{\)lisp}{appendix.A}
\BOOKMARK [1][-]{section.A.18}{\)load}{appendix.A}
\BOOKMARK [1][-]{section.A.19}{\)trace}{appendix.A}
\BOOKMARK [1][-]{section.A.20}{\)pquit}{appendix.A}
\BOOKMARK [1][-]{section.A.21}{\)quit}{appendix.A}
\BOOKMARK [1][-]{section.A.22}{\)read}{appendix.A}
\BOOKMARK [1][-]{section.A.23}{\)set}{appendix.A}
\BOOKMARK [1][-]{section.A.24}{\)show}{appendix.A}
\BOOKMARK [1][-]{section.A.25}{\)spool}{appendix.A}
\BOOKMARK [1][-]{section.A.26}{\)synonym}{appendix.A}
\BOOKMARK [1][-]{section.A.27}{\)system}{appendix.A}
\BOOKMARK [1][-]{section.A.28}{\)trace}{appendix.A}
\BOOKMARK [1][-]{section.A.29}{\)undo}{appendix.A}
\BOOKMARK [1][-]{section.A.30}{\)what}{appendix.A}
\BOOKMARK [0][-]{appendix.B}{Categories}{}
\BOOKMARK [0][-]{appendix.C}{Domains}{}
\BOOKMARK [0][-]{appendix.D}{Packages}{}
\BOOKMARK [0][-]{appendix.E}{Operations}{}
\BOOKMARK [0][-]{appendix.F}{Programs for AXIOM Images}{}
\BOOKMARK [1][-]{section.F.1}{images1.input}{appendix.F}
\BOOKMARK [1][-]{section.F.2}{images2.input}{appendix.F}
\BOOKMARK [1][-]{section.F.3}{images3.input}{appendix.F}
\BOOKMARK [1][-]{section.F.4}{images5.input}{appendix.F}
\BOOKMARK [1][-]{section.F.5}{images6.input}{appendix.F}
\BOOKMARK [1][-]{section.F.6}{images7.input}{appendix.F}
\BOOKMARK [1][-]{section.F.7}{images8.input}{appendix.F}
\BOOKMARK [1][-]{section.F.8}{conformal.input}{appendix.F}
\BOOKMARK [1][-]{section.F.9}{tknot.input}{appendix.F}
\BOOKMARK [1][-]{section.F.10}{ntube.input}{appendix.F}
\BOOKMARK [1][-]{section.F.11}{dhtri.input}{appendix.F}
\BOOKMARK [1][-]{section.F.12}{tetra.input}{appendix.F}
\BOOKMARK [1][-]{section.F.13}{antoine.input}{appendix.F}
\BOOKMARK [1][-]{section.F.14}{scherk.input}{appendix.F}
\BOOKMARK [0][-]{appendix.G}{Glossary}{}
\BOOKMARK [0][-]{appendix.H}{License}{}
