\contentsline {chapter}{\numberline {1}Release Notes}{1}{chapter.1}
\contentsline {section}{\numberline {1.1}releasenotes.ht}{1}{section.1.1}
\contentsline {subsection}{\numberline {1.1.1}What is new in Axiom}{1}{subsection.1.1.1}
\contentsline {subsection}{\numberline {1.1.2}Online Information}{3}{subsection.1.1.2}
\contentsline {subsection}{\numberline {1.1.3}May 2012 Release Notes}{4}{subsection.1.1.3}
\contentsline {subsection}{\numberline {1.1.4}March 2012 Release Notes}{7}{subsection.1.1.4}
\contentsline {subsection}{\numberline {1.1.5}January 2012 Release Notes}{9}{subsection.1.1.5}
\contentsline {subsection}{\numberline {1.1.6}November 2011 Release Notes}{12}{subsection.1.1.6}
\contentsline {subsection}{\numberline {1.1.7}September 2011 Release Notes}{15}{subsection.1.1.7}
\contentsline {subsection}{\numberline {1.1.8}July 2011 Release Notes}{17}{subsection.1.1.8}
\contentsline {subsection}{\numberline {1.1.9}May 2011 Release Notes}{19}{subsection.1.1.9}
\contentsline {subsection}{\numberline {1.1.10}March 2011 Release Notes}{22}{subsection.1.1.10}
\contentsline {subsection}{\numberline {1.1.11}January 2011 Release Notes}{24}{subsection.1.1.11}
\contentsline {subsection}{\numberline {1.1.12}November 2010 Release Notes}{26}{subsection.1.1.12}
\contentsline {subsection}{\numberline {1.1.13}September 2010 Release Notes}{28}{subsection.1.1.13}
\contentsline {subsection}{\numberline {1.1.14}July 2010 Release Notes}{32}{subsection.1.1.14}
\contentsline {subsection}{\numberline {1.1.15}May 2010 Release Notes}{35}{subsection.1.1.15}
\contentsline {subsection}{\numberline {1.1.16}March 2010 Release Notes}{39}{subsection.1.1.16}
\contentsline {subsection}{\numberline {1.1.17}January 2010 Release Notes}{42}{subsection.1.1.17}
\contentsline {subsection}{\numberline {1.1.18}November 2009 Release Notes}{45}{subsection.1.1.18}
\contentsline {subsection}{\numberline {1.1.19}September 2009 Release Notes}{47}{subsection.1.1.19}
\contentsline {subsection}{\numberline {1.1.20}July 2009 Release Notes}{50}{subsection.1.1.20}
\contentsline {subsection}{\numberline {1.1.21}May 2009 Release Notes}{52}{subsection.1.1.21}
\contentsline {subsection}{\numberline {1.1.22}March 2009 Release Notes}{57}{subsection.1.1.22}
\contentsline {subsection}{\numberline {1.1.23}January 2009 Release Notes}{63}{subsection.1.1.23}
\contentsline {subsection}{\numberline {1.1.24}November 23, 2008 Release Notes}{68}{subsection.1.1.24}
\contentsline {subsection}{\numberline {1.1.25}September 23, 2008 Release Notes}{70}{subsection.1.1.25}
\contentsline {subsection}{\numberline {1.1.26}July 23, 2008 Release Notes}{73}{subsection.1.1.26}
\contentsline {subsection}{\numberline {1.1.27}May 27, 2008 Release Notes}{77}{subsection.1.1.27}
\contentsline {subsection}{\numberline {1.1.28}March 25, 2008 Release Notes}{78}{subsection.1.1.28}
\contentsline {subsection}{\numberline {1.1.29}January 25, 2008 Release Notes}{81}{subsection.1.1.29}
\contentsline {subsection}{\numberline {1.1.30}November 23, 2007 Release Notes}{87}{subsection.1.1.30}
\contentsline {subsection}{\numberline {1.1.31}Feature Complete Release Feb 2005}{91}{subsection.1.1.31}
\contentsline {chapter}{\numberline {2}Special hyperdoc pages}{93}{chapter.2}
\contentsline {section}{\numberline {2.1}util.ht}{93}{section.2.1}
\contentsline {subsection}{\numberline {2.1.1}Names of software and facilities}{93}{subsection.2.1.1}
\contentsline {subsection}{\numberline {2.1.2}Special hooks to Unix}{93}{subsection.2.1.2}
\contentsline {subsection}{\numberline {2.1.3}HyperDoc menu macros}{94}{subsection.2.1.3}
\contentsline {subsection}{\numberline {2.1.4}Bitmaps and bitmap manipulation macros}{95}{subsection.2.1.4}
\contentsline {subsection}{\numberline {2.1.5}HyperDoc button objects}{96}{subsection.2.1.5}
\contentsline {subsection}{\numberline {2.1.6}Standard HyperDoc button configurations}{96}{subsection.2.1.6}
\contentsline {subsection}{\numberline {2.1.7}HyperDoc graphics macros}{96}{subsection.2.1.7}
\contentsline {subsection}{\numberline {2.1.8}TeX and LaTeX compatibility macros}{97}{subsection.2.1.8}
\contentsline {subsection}{\numberline {2.1.9}Book and .ht page macros}{99}{subsection.2.1.9}
\contentsline {subsection}{\numberline {2.1.10}Browse macros}{102}{subsection.2.1.10}
\contentsline {subsection}{\numberline {2.1.11}Support for output and graph paste-ins}{103}{subsection.2.1.11}
\contentsline {subsection}{\numberline {2.1.12}Hook for including a local menu item on the rootpage}{103}{subsection.2.1.12}
\contentsline {subsection}{\numberline {2.1.13}Not Connected to Axiom}{104}{subsection.2.1.13}
\contentsline {subsection}{\numberline {2.1.14}Do You Really Want to Exit?}{104}{subsection.2.1.14}
\contentsline {subsection}{\numberline {2.1.15}Missing Page}{104}{subsection.2.1.15}
\contentsline {subsection}{\numberline {2.1.16}Something is Wrong}{105}{subsection.2.1.16}
\contentsline {subsection}{\numberline {2.1.17}Sorry!}{105}{subsection.2.1.17}
\contentsline {chapter}{\numberline {3}Hyperdoc pages}{107}{chapter.3}
\contentsline {section}{\numberline {3.1}rootpage.ht}{107}{section.3.1}
\contentsline {subsection}{\numberline {3.1.1}Axiom HyperDoc Top Level}{107}{subsection.3.1.1}
\contentsline {subsection}{\numberline {3.1.2}Axiom -- The Scientific Computation System}{109}{subsection.3.1.2}
\contentsline {subsection}{\numberline {3.1.3}System Commands}{110}{subsection.3.1.3}
\contentsline {subsection}{\numberline {3.1.4}Axiom Examples}{111}{subsection.3.1.4}
\contentsline {subsection}{\numberline {3.1.5}Axiom Reference}{113}{subsection.3.1.5}
\contentsline {subsection}{\numberline {3.1.6}NAG Documentation}{115}{subsection.3.1.6}
\contentsline {section}{\numberline {3.2}algebra.ht}{121}{section.3.2}
\contentsline {subsection}{\numberline {3.2.1}Abstract Algebra}{121}{subsection.3.2.1}
\contentsline {subsection}{\numberline {3.2.2}Number Theory}{122}{subsection.3.2.2}
\contentsline {section}{\numberline {3.3}alist.ht}{122}{section.3.3}
\contentsline {subsection}{\numberline {3.3.1}AssociationList}{122}{subsection.3.3.1}
\contentsline {section}{\numberline {3.4}array1.ht}{128}{section.3.4}
\contentsline {subsection}{\numberline {3.4.1}OneDimensionalArray}{128}{subsection.3.4.1}
\contentsline {section}{\numberline {3.5}array2.ht}{133}{section.3.5}
\contentsline {subsection}{\numberline {3.5.1}TwoDimensionalArray}{133}{subsection.3.5.1}
\contentsline {section}{\numberline {3.6}basic.ht}{145}{section.3.6}
\contentsline {subsection}{\numberline {3.6.1}Basic Commands}{145}{subsection.3.6.1}
\contentsline {subsection}{\numberline {3.6.2}Calculus}{146}{subsection.3.6.2}
\contentsline {section}{\numberline {3.7}bbtree.ht}{147}{section.3.7}
\contentsline {subsection}{\numberline {3.7.1}BalancedBinaryTree}{147}{subsection.3.7.1}
\contentsline {section}{\numberline {3.8}binary.ht}{153}{section.3.8}
\contentsline {subsection}{\numberline {3.8.1}BinaryExpansion}{153}{subsection.3.8.1}
\contentsline {section}{\numberline {3.9}bmcat.ht}{158}{section.3.9}
\contentsline {subsection}{\numberline {3.9.1}Bit Map Catalog}{158}{subsection.3.9.1}
\contentsline {section}{\numberline {3.10}bop.ht}{159}{section.3.10}
\contentsline {subsection}{\numberline {3.10.1}BasicOperator}{159}{subsection.3.10.1}
\contentsline {section}{\numberline {3.11}bstree.ht}{168}{section.3.11}
\contentsline {subsection}{\numberline {3.11.1}BinarySearchTree}{168}{subsection.3.11.1}
\contentsline {section}{\numberline {3.12}card.ht}{175}{section.3.12}
\contentsline {subsection}{\numberline {3.12.1}CardinalNumber}{175}{subsection.3.12.1}
\contentsline {section}{\numberline {3.13}carten.ht}{185}{section.3.13}
\contentsline {subsection}{\numberline {3.13.1}CartesianTensor}{185}{subsection.3.13.1}
\contentsline {section}{\numberline {3.14}cclass.ht}{211}{section.3.14}
\contentsline {subsection}{\numberline {3.14.1}CharacterClass}{211}{subsection.3.14.1}
\contentsline {section}{\numberline {3.15}char.ht}{218}{section.3.15}
\contentsline {subsection}{\numberline {3.15.1}Character}{218}{subsection.3.15.1}
\contentsline {subsection}{\numberline {3.15.2}CliffordAlgebra}{224}{subsection.3.15.2}
\contentsline {subsection}{\numberline {3.15.3}The Complex Numbers as a Clifford Algebra}{225}{subsection.3.15.3}
\contentsline {subsection}{\numberline {3.15.4}The Quaternion Numbers as a Clifford Algebra}{229}{subsection.3.15.4}
\contentsline {subsection}{\numberline {3.15.5}The Exterior Algebra on a Three Space}{234}{subsection.3.15.5}
\contentsline {subsection}{\numberline {3.15.6}The Dirac Spin Algebra}{240}{subsection.3.15.6}
\contentsline {section}{\numberline {3.16}complex.ht}{244}{section.3.16}
\contentsline {subsection}{\numberline {3.16.1}Complex}{244}{subsection.3.16.1}
\contentsline {section}{\numberline {3.17}contfrac.ht}{252}{section.3.17}
\contentsline {subsection}{\numberline {3.17.1}ContinuedFraction}{252}{subsection.3.17.1}
\contentsline {section}{\numberline {3.18}cphelp.ht}{269}{section.3.18}
\contentsline {subsection}{\numberline {3.18.1}Control Panel Bits}{269}{subsection.3.18.1}
\contentsline {section}{\numberline {3.19}cycles.ht}{269}{section.3.19}
\contentsline {subsection}{\numberline {3.19.1}CycleIndicators}{269}{subsection.3.19.1}
\contentsline {section}{\numberline {3.20}coverex.ht}{294}{section.3.20}
\contentsline {subsection}{\numberline {3.20.1}Examples Of Axiom Commands}{294}{subsection.3.20.1}
\contentsline {subsection}{\numberline {3.20.2}Differentiation}{295}{subsection.3.20.2}
\contentsline {subsection}{\numberline {3.20.3}Integration}{300}{subsection.3.20.3}
\contentsline {subsection}{\numberline {3.20.4}Laplace Transforms}{307}{subsection.3.20.4}
\contentsline {subsection}{\numberline {3.20.5}Limits}{310}{subsection.3.20.5}
\contentsline {subsection}{\numberline {3.20.6}Matrices}{315}{subsection.3.20.6}
\contentsline {subsection}{\numberline {3.20.7}2-D Graphics}{323}{subsection.3.20.7}
\contentsline {subsection}{\numberline {3.20.8}3-D Graphics}{325}{subsection.3.20.8}
\contentsline {subsection}{\numberline {3.20.9}Series}{327}{subsection.3.20.9}
\contentsline {subsection}{\numberline {3.20.10}Summations}{332}{subsection.3.20.10}
\contentsline {section}{\numberline {3.21}decimal.ht}{338}{section.3.21}
\contentsline {subsection}{\numberline {3.21.1}Decimal Expansion}{338}{subsection.3.21.1}
\contentsline {section}{\numberline {3.22}derham.ht}{342}{section.3.22}
\contentsline {subsection}{\numberline {3.22.1}DeRhamComplex}{342}{subsection.3.22.1}
\contentsline {section}{\numberline {3.23}dfloat.ht}{359}{section.3.23}
\contentsline {subsection}{\numberline {3.23.1}DoubleFloat}{359}{subsection.3.23.1}
\contentsline {section}{\numberline {3.24}dmp.ht}{365}{section.3.24}
\contentsline {subsection}{\numberline {3.24.1}DistributedMultivariatePoly}{365}{subsection.3.24.1}
\contentsline {section}{\numberline {3.25}eq.ht}{370}{section.3.25}
\contentsline {subsection}{\numberline {3.25.1}Equation}{370}{subsection.3.25.1}
\contentsline {section}{\numberline {3.26}eqtbl.ht}{376}{section.3.26}
\contentsline {subsection}{\numberline {3.26.1}EqTable}{376}{subsection.3.26.1}
\contentsline {section}{\numberline {3.27}evalex.ht}{379}{section.3.27}
\contentsline {subsection}{\numberline {3.27.1}Example of Standard Evaluation}{379}{subsection.3.27.1}
\contentsline {subsection}{\numberline {3.27.2}Example of Standard Evaluation}{380}{subsection.3.27.2}
\contentsline {section}{\numberline {3.28}exdiff.ht}{381}{section.3.28}
\contentsline {subsection}{\numberline {3.28.1}Computing Derivatives}{381}{subsection.3.28.1}
\contentsline {subsection}{\numberline {3.28.2}Derivatives of Functions of Several Variables}{382}{subsection.3.28.2}
\contentsline {subsection}{\numberline {3.28.3}Derivatives of Higher Order}{383}{subsection.3.28.3}
\contentsline {subsection}{\numberline {3.28.4}Multiple Derivatives I}{384}{subsection.3.28.4}
\contentsline {subsection}{\numberline {3.28.5}Multiple Derivatives II}{386}{subsection.3.28.5}
\contentsline {subsection}{\numberline {3.28.6}Derivatives of Functions Involving Formal Integrals}{386}{subsection.3.28.6}
\contentsline {subsection}{\numberline {3.28.7}Exit}{388}{subsection.3.28.7}
\contentsline {section}{\numberline {3.29}exlap.ht}{392}{section.3.29}
\contentsline {subsection}{\numberline {3.29.1}Laplace transform with a single pole}{392}{subsection.3.29.1}
\contentsline {subsection}{\numberline {3.29.2}Laplace transform of a trigonometric function}{392}{subsection.3.29.2}
\contentsline {subsection}{\numberline {3.29.3}Laplace transform requiring a definite integration}{393}{subsection.3.29.3}
\contentsline {subsection}{\numberline {3.29.4}Laplace transform of exponentials}{394}{subsection.3.29.4}
\contentsline {subsection}{\numberline {3.29.5}Laplace transform of an exponential integral}{395}{subsection.3.29.5}
\contentsline {subsection}{\numberline {3.29.6}Laplace transform of special functions}{396}{subsection.3.29.6}
\contentsline {section}{\numberline {3.30}exint.ht}{396}{section.3.30}
\contentsline {subsection}{\numberline {3.30.1}Integral of a Rational Function}{396}{subsection.3.30.1}
\contentsline {subsection}{\numberline {3.30.2}Integral of a Rational Function with a Real Parameter}{399}{subsection.3.30.2}
\contentsline {subsection}{\numberline {3.30.3}Integral of a Rational Function with a Complex Parameter}{400}{subsection.3.30.3}
\contentsline {subsection}{\numberline {3.30.4}Two Similar Integrands Producing Very Different Results}{400}{subsection.3.30.4}
\contentsline {subsection}{\numberline {3.30.5}An Integral Which Does Not Exist}{402}{subsection.3.30.5}
\contentsline {subsection}{\numberline {3.30.6}A Trigonometric Function of a Quadratic}{403}{subsection.3.30.6}
\contentsline {subsection}{\numberline {3.30.7}Integrating a Function with a Hidden Algebraic Relation}{404}{subsection.3.30.7}
\contentsline {subsection}{\numberline {3.30.8}Details for integrating a function with a Hidden Algebraic Relation}{405}{subsection.3.30.8}
\contentsline {subsection}{\numberline {3.30.9}An Integral Involving a Root of a Transcendental Function}{406}{subsection.3.30.9}
\contentsline {subsection}{\numberline {3.30.10}An Integral of a Non-elementary Function}{407}{subsection.3.30.10}
\contentsline {section}{\numberline {3.31}exlimit.ht}{407}{section.3.31}
\contentsline {subsection}{\numberline {3.31.1}Computing Limits}{407}{subsection.3.31.1}
\contentsline {subsection}{\numberline {3.31.2}Limits of Functions with Parameters}{408}{subsection.3.31.2}
\contentsline {subsection}{\numberline {3.31.3}One-sided Limits}{409}{subsection.3.31.3}
\contentsline {subsection}{\numberline {3.31.4}Two-sided Limits}{410}{subsection.3.31.4}
\contentsline {subsection}{\numberline {3.31.5}Limits at Infinity}{412}{subsection.3.31.5}
\contentsline {subsection}{\numberline {3.31.6}Real Limits vs. Complex Limits}{413}{subsection.3.31.6}
\contentsline {subsection}{\numberline {3.31.7}Complex Limits at Infinity}{414}{subsection.3.31.7}
\contentsline {section}{\numberline {3.32}exmatrix.ht}{416}{section.3.32}
\contentsline {subsection}{\numberline {3.32.1}Basic Arithmetic Operations on Matrices}{416}{subsection.3.32.1}
\contentsline {subsection}{\numberline {3.32.2}Constructing new Matrices}{419}{subsection.3.32.2}
\contentsline {subsection}{\numberline {3.32.3}Trace of a Matrix}{423}{subsection.3.32.3}
\contentsline {subsection}{\numberline {3.32.4}Determinant of a Matrix}{423}{subsection.3.32.4}
\contentsline {subsection}{\numberline {3.32.5}Inverse of a Matrix}{424}{subsection.3.32.5}
\contentsline {subsection}{\numberline {3.32.6}Rank of a Matrix}{425}{subsection.3.32.6}
\contentsline {section}{\numberline {3.33}expr.ht}{426}{section.3.33}
\contentsline {subsection}{\numberline {3.33.1}Expression}{426}{subsection.3.33.1}
\contentsline {section}{\numberline {3.34}explot2d.ht}{439}{section.3.34}
\contentsline {subsection}{\numberline {3.34.1}Plotting Functions of One Variable}{439}{subsection.3.34.1}
\contentsline {subsection}{\numberline {3.34.2}Plotting Parametric Curves}{439}{subsection.3.34.2}
\contentsline {subsection}{\numberline {3.34.3}Plotting Using Polar Coordinates}{440}{subsection.3.34.3}
\contentsline {subsection}{\numberline {3.34.4}Plotting Plane Algebraic Curves}{441}{subsection.3.34.4}
\contentsline {section}{\numberline {3.35}explot3d.ht}{441}{section.3.35}
\contentsline {subsection}{\numberline {3.35.1}Plotting Functions of Two Variables}{441}{subsection.3.35.1}
\contentsline {subsection}{\numberline {3.35.2}Plotting Parametric Surfaces}{442}{subsection.3.35.2}
\contentsline {subsection}{\numberline {3.35.3}Plotting Parametric Curves}{443}{subsection.3.35.3}
\contentsline {section}{\numberline {3.36}expose.ht}{444}{section.3.36}
\contentsline {subsection}{\numberline {3.36.1}Exposure}{444}{subsection.3.36.1}
\contentsline {subsection}{\numberline {3.36.2}System Defined Exposure Groups}{445}{subsection.3.36.2}
\contentsline {subsection}{\numberline {3.36.3}What is an Exposure Group?}{446}{subsection.3.36.3}
\contentsline {subsection}{\numberline {3.36.4}Details on Exposure}{447}{subsection.3.36.4}
\contentsline {section}{\numberline {3.37}exseries.ht}{447}{section.3.37}
\contentsline {subsection}{\numberline {3.37.1}Converting Expressions to Series}{447}{subsection.3.37.1}
\contentsline {subsection}{\numberline {3.37.2}Manipulating Power Series}{449}{subsection.3.37.2}
\contentsline {subsection}{\numberline {3.37.3}Functions on Power Series}{451}{subsection.3.37.3}
\contentsline {subsection}{\numberline {3.37.4}Substituting Numerical Values in Power Series}{452}{subsection.3.37.4}
\contentsline {section}{\numberline {3.38}exsum.ht}{454}{section.3.38}
\contentsline {subsection}{\numberline {3.38.1}Summing the Entries of a List I}{454}{subsection.3.38.1}
\contentsline {subsection}{\numberline {3.38.2}Summing the Entries of a List II}{455}{subsection.3.38.2}
\contentsline {subsection}{\numberline {3.38.3}Approximating $e$}{456}{subsection.3.38.3}
\contentsline {subsection}{\numberline {3.38.4}Closed Form Summations}{457}{subsection.3.38.4}
\contentsline {subsection}{\numberline {3.38.5}Sums of Cubes}{458}{subsection.3.38.5}
\contentsline {subsection}{\numberline {3.38.6}Sums of Polynomials}{460}{subsection.3.38.6}
\contentsline {subsection}{\numberline {3.38.7}Sums of General Functions}{461}{subsection.3.38.7}
\contentsline {subsection}{\numberline {3.38.8}Infinite Sums}{462}{subsection.3.38.8}
\contentsline {section}{\numberline {3.39}farray.ht}{462}{section.3.39}
\contentsline {subsection}{\numberline {3.39.1}FlexibleArray}{462}{subsection.3.39.1}
\contentsline {section}{\numberline {3.40}file.ht}{470}{section.3.40}
\contentsline {subsection}{\numberline {3.40.1}File}{470}{subsection.3.40.1}
\contentsline {section}{\numberline {3.41}float.ht}{477}{section.3.41}
\contentsline {subsection}{\numberline {3.41.1}Float}{477}{subsection.3.41.1}
\contentsline {subsection}{\numberline {3.41.2}Introduction to Float}{478}{subsection.3.41.2}
\contentsline {subsection}{\numberline {3.41.3}Conversion Functions}{480}{subsection.3.41.3}
\contentsline {subsection}{\numberline {3.41.4}Output Functions}{488}{subsection.3.41.4}
\contentsline {subsection}{\numberline {3.41.5}An Example: Determinant of a Hilbert Matrix}{492}{subsection.3.41.5}
\contentsline {subsection}{\numberline {3.41.6}Expanding Factored Objects}{511}{subsection.3.41.6}
\contentsline {subsection}{\numberline {3.41.7}Arithmetic with Factored Objects}{513}{subsection.3.41.7}
\contentsline {subsection}{\numberline {3.41.8}Creating New Factored Objects}{520}{subsection.3.41.8}
\contentsline {subsection}{\numberline {3.41.9}Factored Objects with Variables}{524}{subsection.3.41.9}
\contentsline {section}{\numberline {3.42}fr2.ht}{527}{section.3.42}
\contentsline {subsection}{\numberline {3.42.1}FactoredFunctions2}{527}{subsection.3.42.1}
\contentsline {section}{\numberline {3.43}frac.ht}{531}{section.3.43}
\contentsline {subsection}{\numberline {3.43.1}Fraction}{531}{subsection.3.43.1}
\contentsline {section}{\numberline {3.44}fparfrac.ht}{537}{section.3.44}
\contentsline {subsection}{\numberline {3.44.1}FullPartialFracExpansion}{537}{subsection.3.44.1}
\contentsline {section}{\numberline {3.45}function.ht}{548}{section.3.45}
\contentsline {subsection}{\numberline {3.45.1}Functions in Axiom}{548}{subsection.3.45.1}
\contentsline {subsection}{\numberline {3.45.2}Rational Functions}{549}{subsection.3.45.2}
\contentsline {subsection}{\numberline {3.45.3}Algebraic Functions}{552}{subsection.3.45.3}
\contentsline {subsection}{\numberline {3.45.4}Elementary Functions}{555}{subsection.3.45.4}
\contentsline {subsection}{\numberline {3.45.5}Simplification}{556}{subsection.3.45.5}
\contentsline {section}{\numberline {3.46}gbf.ht}{563}{section.3.46}
\contentsline {subsection}{\numberline {3.46.1}GroebnerFactorizationPkg}{563}{subsection.3.46.1}
\contentsline {section}{\numberline {3.47}gloss.ht}{567}{section.3.47}
\contentsline {subsection}{\numberline {3.47.1}Glossary}{567}{subsection.3.47.1}
\contentsline {section}{\numberline {3.48}graphics.ht}{589}{section.3.48}
\contentsline {subsection}{\numberline {3.48.1}Graphics}{589}{subsection.3.48.1}
\contentsline {subsection}{\numberline {3.48.2}Graphics Examples}{590}{subsection.3.48.2}
\contentsline {subsection}{\numberline {3.48.3}Assorted Graphics Examples}{591}{subsection.3.48.3}
\contentsline {subsection}{\numberline {3.48.4}Three Dimensional Graphics}{593}{subsection.3.48.4}
\contentsline {subsection}{\numberline {3.48.5}Functions of One Variable}{598}{subsection.3.48.5}
\contentsline {subsection}{\numberline {3.48.6}Parametric Curves}{600}{subsection.3.48.6}
\contentsline {subsection}{\numberline {3.48.7}Polar Coordinates}{602}{subsection.3.48.7}
\contentsline {subsection}{\numberline {3.48.8}Implicit Curves}{604}{subsection.3.48.8}
\contentsline {subsection}{\numberline {3.48.9}Lists of Points}{607}{subsection.3.48.9}
\contentsline {subsection}{\numberline {3.48.10}Two Dimensional Graphics}{630}{subsection.3.48.10}
\contentsline {subsection}{\numberline {3.48.11}Functions of One Variable}{631}{subsection.3.48.11}
\contentsline {subsection}{\numberline {3.48.12}Parametric Curves}{633}{subsection.3.48.12}
\contentsline {subsection}{\numberline {3.48.13}Polar Coordinates}{636}{subsection.3.48.13}
\contentsline {subsection}{\numberline {3.48.14}Implicit Curves}{638}{subsection.3.48.14}
\contentsline {subsection}{\numberline {3.48.15}Lists of Points}{639}{subsection.3.48.15}
\contentsline {subsection}{\numberline {3.48.16}Representation Theory}{671}{subsection.3.48.16}
\contentsline {subsection}{\numberline {3.48.17}Group Theory}{672}{subsection.3.48.17}
\contentsline {section}{\numberline {3.49}gstbl.ht}{673}{section.3.49}
\contentsline {subsection}{\numberline {3.49.1}GeneralSparseTable}{673}{subsection.3.49.1}
\contentsline {section}{\numberline {3.50}heap.ht}{677}{section.3.50}
\contentsline {subsection}{\numberline {3.50.1}Heap}{677}{subsection.3.50.1}
\contentsline {section}{\numberline {3.51}hexadec.ht}{679}{section.3.51}
\contentsline {subsection}{\numberline {3.51.1}HexadecimalExpansion}{679}{subsection.3.51.1}
\contentsline {section}{\numberline {3.52}int.ht}{683}{section.3.52}
\contentsline {subsection}{\numberline {3.52.1}Integer}{683}{subsection.3.52.1}
\contentsline {subsection}{\numberline {3.52.2}Basic Functions}{685}{subsection.3.52.2}
\contentsline {subsection}{\numberline {3.52.3}Primes and Factorization}{699}{subsection.3.52.3}
\contentsline {subsection}{\numberline {3.52.4}Some Number Theoretic Functions}{703}{subsection.3.52.4}
\contentsline {section}{\numberline {3.53}intheory.ht}{709}{section.3.53}
\contentsline {subsection}{\numberline {3.53.1}IntegerNumberTheoryFunctions}{709}{subsection.3.53.1}
\contentsline {section}{\numberline {3.54}kafile.ht}{721}{section.3.54}
\contentsline {subsection}{\numberline {3.54.1}KeyedAccessFile}{721}{subsection.3.54.1}
\contentsline {section}{\numberline {3.55}kernel.ht}{730}{section.3.55}
\contentsline {subsection}{\numberline {3.55.1}Kernel}{730}{subsection.3.55.1}
\contentsline {section}{\numberline {3.56}lazm3pk.ht}{739}{section.3.56}
\contentsline {subsection}{\numberline {3.56.1}LazardSetSolvingPackage}{739}{subsection.3.56.1}
\contentsline {section}{\numberline {3.57}lexp.ht}{765}{section.3.57}
\contentsline {subsection}{\numberline {3.57.1}LieExponentials}{765}{subsection.3.57.1}
\contentsline {section}{\numberline {3.58}lextripk.ht}{771}{section.3.58}
\contentsline {subsection}{\numberline {3.58.1}LexTriangularPackage}{771}{subsection.3.58.1}
\contentsline {section}{\numberline {3.59}lib.ht}{827}{section.3.59}
\contentsline {subsection}{\numberline {3.59.1}Library}{827}{subsection.3.59.1}
\contentsline {section}{\numberline {3.60}link.ht}{831}{section.3.60}
\contentsline {subsection}{\numberline {3.60.1}The Axiom Link to NAG Software}{831}{subsection.3.60.1}
\contentsline {subsection}{\numberline {3.60.2}Use of the Link from HyperDoc}{832}{subsection.3.60.2}
\contentsline {subsection}{\numberline {3.60.3}C02 Zeros of Polynomials}{833}{subsection.3.60.3}
\contentsline {subsection}{\numberline {3.60.4}C05 Roots of One or More Transcendental Equations}{834}{subsection.3.60.4}
\contentsline {subsection}{\numberline {3.60.5}C06 Summation of Series}{834}{subsection.3.60.5}
\contentsline {subsection}{\numberline {3.60.6}D01 Quadrature}{836}{subsection.3.60.6}
\contentsline {subsection}{\numberline {3.60.7}D02 Ordinary Differential Equations}{838}{subsection.3.60.7}
\contentsline {subsection}{\numberline {3.60.8}D03 Partial Differential Equations}{839}{subsection.3.60.8}
\contentsline {subsection}{\numberline {3.60.9}E01 Interpolation}{840}{subsection.3.60.9}
\contentsline {subsection}{\numberline {3.60.10}E02 Curve and Surface Fitting}{841}{subsection.3.60.10}
\contentsline {subsection}{\numberline {3.60.11}E04 Minimizing or Maximizing a Function}{843}{subsection.3.60.11}
\contentsline {subsection}{\numberline {3.60.12}F01 Matrix Operations - Including Inversion}{844}{subsection.3.60.12}
\contentsline {subsection}{\numberline {3.60.13}F02 Eigenvalues and Eigenvectors}{845}{subsection.3.60.13}
\contentsline {subsection}{\numberline {3.60.14}F04 Simultaneous Linear Equations}{847}{subsection.3.60.14}
\contentsline {subsection}{\numberline {3.60.15}F07 Linear Equations (LAPACK)}{849}{subsection.3.60.15}
\contentsline {subsection}{\numberline {3.60.16}S -- Approximations of Special Functions}{850}{subsection.3.60.16}
\contentsline {section}{\numberline {3.61}list.ht}{853}{section.3.61}
\contentsline {subsection}{\numberline {3.61.1}List}{853}{subsection.3.61.1}
\contentsline {subsection}{\numberline {3.61.2}Creating Lists}{854}{subsection.3.61.2}
\contentsline {subsection}{\numberline {3.61.3}Accessing List Elements}{856}{subsection.3.61.3}
\contentsline {subsection}{\numberline {3.61.4}Changing List Elements}{862}{subsection.3.61.4}
\contentsline {subsection}{\numberline {3.61.5}Other Functions}{866}{subsection.3.61.5}
\contentsline {subsection}{\numberline {3.61.6}Dot, Dot}{869}{subsection.3.61.6}
\contentsline {section}{\numberline {3.62}lodo.ht}{871}{section.3.62}
\contentsline {subsection}{\numberline {3.62.1}LinearOrdinaryDifferentialOperator}{871}{subsection.3.62.1}
\contentsline {subsection}{\numberline {3.62.2}Differential Operators with Series Coefficients}{871}{subsection.3.62.2}
\contentsline {section}{\numberline {3.63}lodo1.ht}{881}{section.3.63}
\contentsline {subsection}{\numberline {3.63.1}LinearOrdinaryDifferentialOperator1}{881}{subsection.3.63.1}
\contentsline {subsection}{\numberline {3.63.2}Differential Operators with Rational Function Coefficients}{882}{subsection.3.63.2}
\contentsline {section}{\numberline {3.64}lodo2.ht}{892}{section.3.64}
\contentsline {subsection}{\numberline {3.64.1}LinearOrdinaryDifferentialOperator2}{892}{subsection.3.64.1}
\contentsline {subsection}{\numberline {3.64.2}Differential Operators with Constant Coefficients}{893}{subsection.3.64.2}
\contentsline {subsection}{\numberline {3.64.3}Differential Operators with Matrix Coefficients Operating on Vectors}{898}{subsection.3.64.3}
\contentsline {section}{\numberline {3.65}lpoly.ht}{907}{section.3.65}
\contentsline {subsection}{\numberline {3.65.1}LiePolynomial}{907}{subsection.3.65.1}
\contentsline {section}{\numberline {3.66}magma.ht}{928}{section.3.66}
\contentsline {subsection}{\numberline {3.66.1}Magma}{928}{subsection.3.66.1}
\contentsline {section}{\numberline {3.67}man0.ht}{938}{section.3.67}
\contentsline {subsection}{\numberline {3.67.1}Reference Search}{938}{subsection.3.67.1}
\contentsline {subsection}{\numberline {3.67.2}Lisp Functions}{939}{subsection.3.67.2}
\contentsline {subsection}{\numberline {3.67.3}Axiom Browser}{949}{subsection.3.67.3}
\contentsline {subsection}{\numberline {3.67.4}The Hyperdoc Browse Facility}{950}{subsection.3.67.4}
\contentsline {section}{\numberline {3.68}mapping.ht}{951}{section.3.68}
\contentsline {subsection}{\numberline {3.68.1}Domain {\bf Mapping(T,S,...)}}{951}{subsection.3.68.1}
\contentsline {subsection}{\numberline {3.68.2}Domain Constructor {\bf Mapping}}{951}{subsection.3.68.2}
\contentsline {section}{\numberline {3.69}mappkg1.ht}{952}{section.3.69}
\contentsline {subsection}{\numberline {3.69.1}MappingPackage1}{952}{subsection.3.69.1}
\contentsline {section}{\numberline {3.70}mset.ht}{965}{section.3.70}
\contentsline {subsection}{\numberline {3.70.1}MultiSet}{965}{subsection.3.70.1}
\contentsline {section}{\numberline {3.71}matrix.ht}{970}{section.3.71}
\contentsline {subsection}{\numberline {3.71.1}Matrix}{970}{subsection.3.71.1}
\contentsline {subsection}{\numberline {3.71.2}Creating Matrices}{971}{subsection.3.71.2}
\contentsline {subsection}{\numberline {3.71.3}Operations on Matrices}{983}{subsection.3.71.3}
\contentsline {section}{\numberline {3.72}mkfunc.ht}{993}{section.3.72}
\contentsline {subsection}{\numberline {3.72.1}MakeFunction}{993}{subsection.3.72.1}
\contentsline {section}{\numberline {3.73}mpoly.ht}{998}{section.3.73}
\contentsline {subsection}{\numberline {3.73.1}MultivariatePolynomial}{998}{subsection.3.73.1}
\contentsline {section}{\numberline {3.74}newuser.ht}{1004}{section.3.74}
\contentsline {subsection}{\numberline {3.74.1}No More Help :-(}{1004}{subsection.3.74.1}
\contentsline {subsection}{\numberline {3.74.2}You Tried It!}{1005}{subsection.3.74.2}
\contentsline {section}{\numberline {3.75}none.ht}{1005}{section.3.75}
\contentsline {subsection}{\numberline {3.75.1}None}{1005}{subsection.3.75.1}
\contentsline {section}{\numberline {3.76}numbers.ht}{1008}{section.3.76}
\contentsline {subsection}{\numberline {3.76.1}Axiom Number Types}{1008}{subsection.3.76.1}
\contentsline {subsection}{\numberline {3.76.2}Fraction}{1010}{subsection.3.76.2}
\contentsline {subsection}{\numberline {3.76.3}Rational Number}{1012}{subsection.3.76.3}
\contentsline {subsection}{\numberline {3.76.4}Integers}{1016}{subsection.3.76.4}
\contentsline {subsection}{\numberline {3.76.5}Integer Examples}{1021}{subsection.3.76.5}
\contentsline {subsection}{\numberline {3.76.6}Integer Example Proof}{1023}{subsection.3.76.6}
\contentsline {subsection}{\numberline {3.76.7}Integer Problems}{1024}{subsection.3.76.7}
\contentsline {subsection}{\numberline {3.76.8}Integer Problem Proof}{1025}{subsection.3.76.8}
\contentsline {subsection}{\numberline {3.76.9}Solution to Problem \#1}{1025}{subsection.3.76.9}
\contentsline {subsection}{\numberline {3.76.10}Solution to Problem \#2}{1029}{subsection.3.76.10}
\contentsline {section}{\numberline {3.77}oct.ht}{1031}{section.3.77}
\contentsline {subsection}{\numberline {3.77.1}Octonion}{1031}{subsection.3.77.1}
\contentsline {section}{\numberline {3.78}odpol.ht}{1040}{section.3.78}
\contentsline {subsection}{\numberline {3.78.1}OrderlyDifferentialPolynomial}{1040}{subsection.3.78.1}
\contentsline {section}{\numberline {3.79}op.ht}{1058}{section.3.79}
\contentsline {subsection}{\numberline {3.79.1}Operator}{1058}{subsection.3.79.1}
\contentsline {section}{\numberline {3.80}ovar.ht}{1069}{section.3.80}
\contentsline {subsection}{\numberline {3.80.1}OrderedVariableList}{1069}{subsection.3.80.1}
\contentsline {section}{\numberline {3.81}perman.ht}{1072}{section.3.81}
\contentsline {subsection}{\numberline {3.81.1}Permanent}{1072}{subsection.3.81.1}
\contentsline {section}{\numberline {3.82}pfr.ht}{1075}{section.3.82}
\contentsline {subsection}{\numberline {3.82.1}PartialFraction}{1075}{subsection.3.82.1}
\contentsline {section}{\numberline {3.83}poly.ht}{1082}{section.3.83}
\contentsline {subsection}{\numberline {3.83.1}Polynomials}{1082}{subsection.3.83.1}
\contentsline {subsection}{\numberline {3.83.2}The Specific Polynomial Types}{1083}{subsection.3.83.2}
\contentsline {subsection}{\numberline {3.83.3}Basic Operations On Polynomials}{1084}{subsection.3.83.3}
\contentsline {subsection}{\numberline {3.83.4}Polynomial Evaluation and Substitution}{1091}{subsection.3.83.4}
\contentsline {subsection}{\numberline {3.83.5}Greatest Common Divisors, Resultants, and Discriminants}{1095}{subsection.3.83.5}
\contentsline {subsection}{\numberline {3.83.6}Roots of Polynomials}{1097}{subsection.3.83.6}
\contentsline {section}{\numberline {3.84}poly1.ht}{1097}{section.3.84}
\contentsline {subsection}{\numberline {3.84.1}Polynomial}{1097}{subsection.3.84.1}
\contentsline {section}{\numberline {3.85}quat.ht}{1121}{section.3.85}
\contentsline {subsection}{\numberline {3.85.1}Quaternion}{1121}{subsection.3.85.1}
\contentsline {section}{\numberline {3.86}radix.ht}{1127}{section.3.86}
\contentsline {subsection}{\numberline {3.86.1}RadixExpansion}{1127}{subsection.3.86.1}
\contentsline {section}{\numberline {3.87}reclos.ht}{1136}{section.3.87}
\contentsline {subsection}{\numberline {3.87.1}RealClosure}{1136}{subsection.3.87.1}
\contentsline {section}{\numberline {3.88}sregset.ht}{1231}{section.3.88}
\contentsline {subsection}{\numberline {3.88.1}SquareFreeRegularTriangularSet}{1231}{subsection.3.88.1}
\contentsline {section}{\numberline {3.89}stbl.ht}{1243}{section.3.89}
\contentsline {subsection}{\numberline {3.89.1}SparseTable}{1243}{subsection.3.89.1}
\contentsline {section}{\numberline {3.90}stream.ht}{1247}{section.3.90}
\contentsline {subsection}{\numberline {3.90.1}Stream}{1247}{subsection.3.90.1}
\contentsline {section}{\numberline {3.91}string.ht}{1253}{section.3.91}
\contentsline {subsection}{\numberline {3.91.1}String}{1253}{subsection.3.91.1}
\contentsline {section}{\numberline {3.92}strtbl.ht}{1268}{section.3.92}
\contentsline {subsection}{\numberline {3.92.1}StringTable}{1268}{subsection.3.92.1}
\contentsline {section}{\numberline {3.93}symbol.ht}{1271}{section.3.93}
\contentsline {subsection}{\numberline {3.93.1}Symbol}{1271}{subsection.3.93.1}
\contentsline {section}{\numberline {3.94}table.ht}{1282}{section.3.94}
\contentsline {subsection}{\numberline {3.94.1}Table}{1282}{subsection.3.94.1}
\contentsline {section}{\numberline {3.95}textfile.ht}{1291}{section.3.95}
\contentsline {subsection}{\numberline {3.95.1}TextFile}{1291}{subsection.3.95.1}
\contentsline {section}{\numberline {3.96}topics.ht}{1297}{section.3.96}
\contentsline {subsection}{\numberline {3.96.1}Axiom Topics}{1297}{subsection.3.96.1}
\contentsline {subsection}{\numberline {3.96.2}Solving Equations}{1299}{subsection.3.96.2}
\contentsline {subsection}{\numberline {3.96.3}Linear Algebra}{1300}{subsection.3.96.3}
\contentsline {subsection}{\numberline {3.96.4}Calculus}{1302}{subsection.3.96.4}
\contentsline {section}{\numberline {3.97}type.ht}{1303}{section.3.97}
\contentsline {subsection}{\numberline {3.97.1}Category {\bf Type}}{1303}{subsection.3.97.1}
\contentsline {section}{\numberline {3.98}union.ht}{1303}{section.3.98}
\contentsline {subsection}{\numberline {3.98.1}Domain {\bf Union(a:A,...,b:B)}}{1303}{subsection.3.98.1}
\contentsline {subsection}{\numberline {3.98.2}Domain Constructor {\bf Union}}{1304}{subsection.3.98.2}
\contentsline {subsection}{\numberline {3.98.3}Domain {\bf Union(A,...,B)}}{1305}{subsection.3.98.3}
\contentsline {subsection}{\numberline {3.98.4}Domain Constructor {\bf Union}}{1306}{subsection.3.98.4}
\contentsline {section}{\numberline {3.99}uniseg.ht}{1306}{section.3.99}
\contentsline {subsection}{\numberline {3.99.1}UniversalSegment}{1306}{subsection.3.99.1}
\contentsline {section}{\numberline {3.100}up.ht}{1311}{section.3.100}
\contentsline {subsection}{\numberline {3.100.1}UnivariatePolynomial}{1311}{subsection.3.100.1}
\contentsline {section}{\numberline {3.101}oreup.ht}{1329}{section.3.101}
\contentsline {subsection}{\numberline {3.101.1}UnivariateSkewPolynomial}{1329}{subsection.3.101.1}
\contentsline {section}{\numberline {3.102}vector.ht}{1335}{section.3.102}
\contentsline {subsection}{\numberline {3.102.1}Vector}{1335}{subsection.3.102.1}
\contentsline {section}{\numberline {3.103}void.ht}{1341}{section.3.103}
\contentsline {subsection}{\numberline {3.103.1}Void}{1341}{subsection.3.103.1}
\contentsline {section}{\numberline {3.104}wutset.ht}{1344}{section.3.104}
\contentsline {subsection}{\numberline {3.104.1}WuWenTsunTriangularSet}{1344}{subsection.3.104.1}
\contentsline {section}{\numberline {3.105}xmpexp.ht}{1353}{section.3.105}
\contentsline {subsection}{\numberline {3.105.1}Some Examples of Domains and Packages}{1353}{subsection.3.105.1}
\contentsline {section}{\numberline {3.106}xpbwpoly.ht}{1358}{section.3.106}
\contentsline {subsection}{\numberline {3.106.1}XPBWPolynomial}{1358}{subsection.3.106.1}
\contentsline {section}{\numberline {3.107}xpoly.ht}{1379}{section.3.107}
\contentsline {subsection}{\numberline {3.107.1}XPolynomial}{1379}{subsection.3.107.1}
\contentsline {section}{\numberline {3.108}xpr.ht}{1386}{section.3.108}
\contentsline {subsection}{\numberline {3.108.1}XPolynomialRing}{1386}{subsection.3.108.1}
\contentsline {section}{\numberline {3.109}zlindep.ht}{1447}{section.3.109}
\contentsline {subsection}{\numberline {3.109.1}IntegerLinearDependence}{1447}{subsection.3.109.1}
\contentsline {chapter}{\numberline {4}Users Guide Pages (ug.ht)}{1453}{chapter.4}
\contentsline {subsection}{\numberline {4.0.2}Users Guide}{1454}{subsection.4.0.2}
\contentsline {chapter}{\numberline {5}Users Guide Chapter 0 (ug00.ht)}{1457}{chapter.5}
\contentsline {subsection}{\numberline {5.0.3}What's New for May 2008}{1457}{subsection.5.0.3}
\contentsline {subsection}{\numberline {5.0.4}New polynomial domains and algorithms}{1458}{subsection.5.0.4}
\contentsline {subsection}{\numberline {5.0.5}Enhancements to HyperDoc and Graphics}{1459}{subsection.5.0.5}
\contentsline {subsection}{\numberline {5.0.6}Enhancements to NAGLink}{1460}{subsection.5.0.6}
\contentsline {subsection}{\numberline {5.0.7}Enhancements to the Lisp system}{1460}{subsection.5.0.7}
\contentsline {chapter}{\numberline {6}Users Guide Chapter 1 (ug01.ht)}{1467}{chapter.6}
\contentsline {subsection}{\numberline {6.0.8}An Overview of Axiom}{1467}{subsection.6.0.8}
\contentsline {subsection}{\numberline {6.0.9}Starting Up and Winding Down}{1468}{subsection.6.0.9}
\contentsline {subsection}{\numberline {6.0.10}Clef}{1471}{subsection.6.0.10}
\contentsline {subsection}{\numberline {6.0.11}Typographic Conventions}{1472}{subsection.6.0.11}
\contentsline {subsection}{\numberline {6.0.12}The Axiom Language}{1473}{subsection.6.0.12}
\contentsline {subsection}{\numberline {6.0.13}Arithmetic Expressions}{1474}{subsection.6.0.13}
\contentsline {subsection}{\numberline {6.0.14}Previous Results}{1476}{subsection.6.0.14}
\contentsline {subsection}{\numberline {6.0.15}Some Types}{1478}{subsection.6.0.15}
\contentsline {subsection}{\numberline {6.0.16}Symbols, Variables, Assignments, and Declarations}{1481}{subsection.6.0.16}
\contentsline {subsection}{\numberline {6.0.17}Conversion}{1487}{subsection.6.0.17}
\contentsline {subsection}{\numberline {6.0.18}Calling Functions}{1489}{subsection.6.0.18}
\contentsline {subsection}{\numberline {6.0.19}Some Predefined Macros}{1492}{subsection.6.0.19}
\contentsline {subsection}{\numberline {6.0.20}Long Lines}{1493}{subsection.6.0.20}
\contentsline {subsection}{\numberline {6.0.21}Comments}{1494}{subsection.6.0.21}
\contentsline {subsection}{\numberline {6.0.22}Graphics}{1494}{subsection.6.0.22}
\contentsline {subsection}{\numberline {6.0.23}Numbers}{1497}{subsection.6.0.23}
\contentsline {subsection}{\numberline {6.0.24}Data Structures}{1516}{subsection.6.0.24}
\contentsline {subsection}{\numberline {6.0.25}Expanding to Higher Dimensions}{1532}{subsection.6.0.25}
\contentsline {subsection}{\numberline {6.0.26}Writing Your Own Functions}{1537}{subsection.6.0.26}
\contentsline {subsection}{\numberline {6.0.27}Solution of Equations}{1585}{subsection.6.0.27}
\contentsline {subsection}{\numberline {6.0.28}Records}{1627}{subsection.6.0.28}
\contentsline {subsection}{\numberline {6.0.29}Subdomains Again}{1658}{subsection.6.0.29}
\contentsline {subsection}{\numberline {6.0.30}Package Calling and Target Types}{1665}{subsection.6.0.30}
\contentsline {subsection}{\numberline {6.0.31}Resolving Types}{1674}{subsection.6.0.31}
\contentsline {subsection}{\numberline {6.0.32}Exposing Domains and Packages}{1677}{subsection.6.0.32}
\contentsline {subsection}{\numberline {6.0.33}Commands for Snooping}{1681}{subsection.6.0.33}
\contentsline {chapter}{\numberline {7}Users Guide Chapter 3 (ug03.ht)}{1687}{chapter.7}
\contentsline {subsection}{\numberline {7.0.34}Using Hyperdoc}{1687}{subsection.7.0.34}
\contentsline {subsection}{\numberline {7.0.35}Headings}{1688}{subsection.7.0.35}
\contentsline {subsection}{\numberline {7.0.36}Key Definitions}{1689}{subsection.7.0.36}
\contentsline {subsection}{\numberline {7.0.37}Scroll Bars}{1690}{subsection.7.0.37}
\contentsline {subsection}{\numberline {7.0.38}Input Areas}{1691}{subsection.7.0.38}
\contentsline {subsection}{\numberline {7.0.39}Radio Buttons and Toggles}{1693}{subsection.7.0.39}
\contentsline {subsection}{\numberline {7.0.40}Search Strings}{1694}{subsection.7.0.40}
\contentsline {subsection}{\numberline {7.0.41}Logical Searches}{1695}{subsection.7.0.41}
\contentsline {subsection}{\numberline {7.0.42}Example Pages}{1696}{subsection.7.0.42}
\contentsline {subsection}{\numberline {7.0.43}X Window Resources for Hyperdoc}{1697}{subsection.7.0.43}
\contentsline {chapter}{\numberline {8}Users Guide Chapter 4 (ug04.ht)}{1701}{chapter.8}
\contentsline {subsection}{\numberline {8.0.44}Input Files and Output Styles}{1701}{subsection.8.0.44}
\contentsline {subsection}{\numberline {8.0.45}Input Files}{1702}{subsection.8.0.45}
\contentsline {subsection}{\numberline {8.0.46}The .axiom.input File}{1704}{subsection.8.0.46}
\contentsline {subsection}{\numberline {8.0.47}Common Features of Using Output Formats}{1705}{subsection.8.0.47}
\contentsline {subsection}{\numberline {8.0.48}Monospace 2D Mathematical Format}{1708}{subsection.8.0.48}
\contentsline {subsection}{\numberline {8.0.49}HTML Format}{1722}{subsection.8.0.49}
\contentsline {subsection}{\numberline {8.0.50}Immediate and Delayed Assignments}{1724}{subsection.8.0.50}
\contentsline {subsection}{\numberline {8.0.51}Blocks}{1732}{subsection.8.0.51}
\contentsline {subsection}{\numberline {8.0.52}if-then-else}{1741}{subsection.8.0.52}
\contentsline {subsection}{\numberline {8.0.53}Loops}{1744}{subsection.8.0.53}
\contentsline {subsection}{\numberline {8.0.54}Compiling vs. Interpreting Loops}{1746}{subsection.8.0.54}
\contentsline {subsection}{\numberline {8.0.55}return in Loops}{1746}{subsection.8.0.55}
\contentsline {subsection}{\numberline {8.0.56}break in Loops}{1750}{subsection.8.0.56}
\contentsline {subsection}{\numberline {8.0.57}break vs. {\tt =>} in Loop Bodies}{1753}{subsection.8.0.57}
\contentsline {subsection}{\numberline {8.0.58}More Examples of break}{1754}{subsection.8.0.58}
\contentsline {subsection}{\numberline {8.0.59}iterate in Loops}{1762}{subsection.8.0.59}
\contentsline {subsection}{\numberline {8.0.60}while Loops}{1763}{subsection.8.0.60}
\contentsline {subsection}{\numberline {8.0.61}for Loops}{1770}{subsection.8.0.61}
\contentsline {subsection}{\numberline {8.0.62}for i in n..m repeat}{1771}{subsection.8.0.62}
\contentsline {subsection}{\numberline {8.0.63}for i in n..m by s repeat}{1775}{subsection.8.0.63}
\contentsline {subsection}{\numberline {8.0.64}for i in n.. repeat}{1776}{subsection.8.0.64}
\contentsline {subsection}{\numberline {8.0.65}for x in l repeat}{1777}{subsection.8.0.65}
\contentsline {subsection}{\numberline {8.0.66}``Such that'' Predicates}{1780}{subsection.8.0.66}
\contentsline {subsection}{\numberline {8.0.67}Parallel Iteration}{1782}{subsection.8.0.67}
\contentsline {subsection}{\numberline {8.0.68}Creating Lists and Streams with Iterators}{1788}{subsection.8.0.68}
\contentsline {subsection}{\numberline {8.0.69}Addendum: Appending a Graph to a Viewport Window Containing a Graph}{1987}{subsection.8.0.69}
\contentsline {subsection}{\numberline {8.0.70}Three-Dimensional Graphics}{1990}{subsection.8.0.70}
\contentsline {subsection}{\numberline {8.0.71}Plotting Three-Dimensional Functions of Two Variables}{1991}{subsection.8.0.71}
\contentsline {subsection}{\numberline {8.0.72}Plotting Three-Dimensional Parametric Space Curves}{1993}{subsection.8.0.72}
\contentsline {subsection}{\numberline {8.0.73}Plotting 3D Parametric Surfaces}{1996}{subsection.8.0.73}
\contentsline {subsection}{\numberline {8.0.74}Three-Dimensional Options}{2000}{subsection.8.0.74}
\contentsline {subsection}{\numberline {8.0.75}The makeObject Command}{2010}{subsection.8.0.75}
\contentsline {subsection}{\numberline {8.0.76}Building 3D Objects From Primitives}{2012}{subsection.8.0.76}
\contentsline {subsection}{\numberline {8.0.77}Coordinate System Transformations}{2025}{subsection.8.0.77}
\contentsline {subsection}{\numberline {8.0.78}Three-Dimensional Clipping}{2032}{subsection.8.0.78}
\contentsline {subsection}{\numberline {8.0.79}Three-Dimensional Control-Panel}{2034}{subsection.8.0.79}
\contentsline {subsection}{\numberline {8.0.80}Operations for Three-Dimensional Graphics}{2039}{subsection.8.0.80}
\contentsline {subsection}{\numberline {8.0.81}Customization using .Xdefaults}{2046}{subsection.8.0.81}
\contentsline {chapter}{\numberline {9}Users Guide Chapter 8 (ug08.ht)}{2049}{chapter.9}
\contentsline {subsection}{\numberline {9.0.82}Advanced Problem Solving}{2049}{subsection.9.0.82}
\contentsline {subsection}{\numberline {9.0.83}Numeric Functions}{2051}{subsection.9.0.83}
\contentsline {subsection}{\numberline {9.0.84}Polynomial Factorization}{2073}{subsection.9.0.84}
\contentsline {subsection}{\numberline {9.0.85}Integer and Rational Number Coefficients}{2074}{subsection.9.0.85}
\contentsline {subsection}{\numberline {9.0.86}Finite Field Coefficients}{2076}{subsection.9.0.86}
\contentsline {subsection}{\numberline {9.0.87}Simple Algebraic Extension Field Coefficients}{2078}{subsection.9.0.87}
\contentsline {subsection}{\numberline {9.0.88}Factoring Rational Functions}{2083}{subsection.9.0.88}
\contentsline {subsection}{\numberline {9.0.89}Manipulating Symbolic Roots of a Polynomial}{2084}{subsection.9.0.89}
\contentsline {subsection}{\numberline {9.0.90}Using a Single Root of a Polynomial}{2085}{subsection.9.0.90}
\contentsline {subsection}{\numberline {9.0.91}Using All Roots of a Polynomial}{2089}{subsection.9.0.91}
\contentsline {subsection}{\numberline {9.0.92}Computation of Eigenvalues and Eigenvectors}{2095}{subsection.9.0.92}
\contentsline {subsection}{\numberline {9.0.93}Solution of Linear and Polynomial Equations}{2102}{subsection.9.0.93}
\contentsline {subsection}{\numberline {9.0.94}Solution of Systems of Linear Equations}{2103}{subsection.9.0.94}
\contentsline {subsection}{\numberline {9.0.95}Solution of a Single Polynomial Equation}{2107}{subsection.9.0.95}
\contentsline {subsection}{\numberline {9.0.96}Solution of Systems of Polynomial Equations}{2112}{subsection.9.0.96}
\contentsline {subsection}{\numberline {9.0.97}Limits}{2117}{subsection.9.0.97}
\contentsline {subsection}{\numberline {9.0.98}Laplace Transforms}{2124}{subsection.9.0.98}
\contentsline {subsection}{\numberline {9.0.99}Integration}{2129}{subsection.9.0.99}
\contentsline {subsection}{\numberline {9.0.100}Working with Power Series}{2136}{subsection.9.0.100}
\contentsline {subsection}{\numberline {9.0.101}Creation of Power Series}{2138}{subsection.9.0.101}
\contentsline {subsection}{\numberline {9.0.102}Coefficients of Power Series}{2144}{subsection.9.0.102}
\contentsline {subsection}{\numberline {9.0.103}Power Series Arithmetic}{2147}{subsection.9.0.103}
\contentsline {subsection}{\numberline {9.0.104}Functions on Power Series}{2150}{subsection.9.0.104}
\contentsline {subsection}{\numberline {9.0.105}Converting to Power Series}{2158}{subsection.9.0.105}
\contentsline {subsection}{\numberline {9.0.106}Power Series from Formulas}{2166}{subsection.9.0.106}
\contentsline {subsection}{\numberline {9.0.107}Substituting Numerical Values in Power Series}{2173}{subsection.9.0.107}
\contentsline {subsection}{\numberline {9.0.108}Example: Bernoulli Polynomials and Sums of Powers}{2175}{subsection.9.0.108}
\contentsline {subsection}{\numberline {9.0.109}Solution of Differential Equations}{2183}{subsection.9.0.109}
\contentsline {subsection}{\numberline {9.0.110}Closed-Form Solutions of Linear Differential Equations}{2184}{subsection.9.0.110}
\contentsline {subsection}{\numberline {9.0.111}Closed-Form Solutions of Non-Linear DEs}{2192}{subsection.9.0.111}
\contentsline {subsection}{\numberline {9.0.112}Power Series Solutions of Differential Equations}{2202}{subsection.9.0.112}
\contentsline {subsection}{\numberline {9.0.113}Finite Fields}{2207}{subsection.9.0.113}
\contentsline {subsection}{\numberline {9.0.114}Modular Arithmetic and Prime Fields}{2209}{subsection.9.0.114}
\contentsline {subsection}{\numberline {9.0.115}Extensions of Finite Fields}{2218}{subsection.9.0.115}
\contentsline {subsection}{\numberline {9.0.116}Irreducible Mod Polynomial Representations}{2221}{subsection.9.0.116}
\contentsline {subsection}{\numberline {9.0.117}Cyclic Group Representations}{2230}{subsection.9.0.117}
\contentsline {subsection}{\numberline {9.0.118}Normal Basis Representations}{2236}{subsection.9.0.118}
\contentsline {subsection}{\numberline {9.0.119}Conversion Operations for Finite Fields}{2244}{subsection.9.0.119}
\contentsline {subsection}{\numberline {9.0.120}Utility Operations for Finite Fields}{2252}{subsection.9.0.120}
\contentsline {subsection}{\numberline {9.0.121}Primary Decomposition of Ideals}{2269}{subsection.9.0.121}
\contentsline {subsection}{\numberline {9.0.122}Computation of Galois Groups}{2278}{subsection.9.0.122}
\contentsline {subsection}{\numberline {9.0.123}Non-Associative Algebras and Genetic Laws}{2297}{subsection.9.0.123}
\contentsline {chapter}{\numberline {10}Users Guide Chapter 10 (ug10.ht)}{2309}{chapter.10}
\contentsline {subsection}{\numberline {10.0.124}Interactive Programming}{2309}{subsection.10.0.124}
\contentsline {subsection}{\numberline {10.0.125}Drawing Ribbons Interactively}{2310}{subsection.10.0.125}
\contentsline {subsection}{\numberline {10.0.126}A Ribbon Program}{2316}{subsection.10.0.126}
\contentsline {subsection}{\numberline {10.0.127}Coloring and Positioning Ribbons}{2319}{subsection.10.0.127}
\contentsline {subsection}{\numberline {10.0.128}Points, Lines, and Curves}{2320}{subsection.10.0.128}
\contentsline {subsection}{\numberline {10.0.129}Browse}{2397}{subsection.10.0.129}
\contentsline {subsection}{\numberline {10.0.130}Representation}{2398}{subsection.10.0.130}
\contentsline {subsection}{\numberline {10.0.131}Multiple Representations}{2399}{subsection.10.0.131}
\contentsline {subsection}{\numberline {10.0.132}Add Domain}{2401}{subsection.10.0.132}
\contentsline {subsection}{\numberline {10.0.133}Defaults}{2402}{subsection.10.0.133}
\contentsline {subsection}{\numberline {10.0.134}Origins}{2403}{subsection.10.0.134}
\contentsline {subsection}{\numberline {10.0.135}Short Forms}{2404}{subsection.10.0.135}
\contentsline {subsection}{\numberline {10.0.136}Example 1: Clifford Algebra}{2405}{subsection.10.0.136}
\contentsline {subsection}{\numberline {10.0.137}Example 2: Building A Query Facility}{2408}{subsection.10.0.137}
\contentsline {subsection}{\numberline {10.0.138}A Little Query Language}{2409}{subsection.10.0.138}
\contentsline {subsection}{\numberline {10.0.139}The Database Constructor}{2412}{subsection.10.0.139}
\contentsline {subsection}{\numberline {10.0.140}Query Equations}{2415}{subsection.10.0.140}
\contentsline {subsection}{\numberline {10.0.141}DataLists}{2416}{subsection.10.0.141}
\contentsline {subsection}{\numberline {10.0.142}Index Cards}{2417}{subsection.10.0.142}
\contentsline {subsection}{\numberline {10.0.143}Creating a Database}{2418}{subsection.10.0.143}
\contentsline {subsection}{\numberline {10.0.144}Putting It All Together}{2419}{subsection.10.0.144}
\contentsline {subsection}{\numberline {10.0.145}Example Queries}{2420}{subsection.10.0.145}
\contentsline {chapter}{\numberline {11}Users Guide Chapter 14 (ug14.ht)}{2433}{chapter.11}
\contentsline {subsection}{\numberline {11.0.146}Browse}{2433}{subsection.11.0.146}
\contentsline {subsection}{\numberline {11.0.147}The Front Page: Searching the Library}{2434}{subsection.11.0.147}
\contentsline {subsection}{\numberline {11.0.148}The Constructor Page}{2436}{subsection.11.0.148}
\contentsline {subsection}{\numberline {11.0.149}Constructor Page Buttons}{2438}{subsection.11.0.149}
\contentsline {subsection}{\numberline {11.0.150}Cross Reference}{2440}{subsection.11.0.150}
\contentsline {subsection}{\numberline {11.0.151}Views Of Constructors}{2444}{subsection.11.0.151}
\contentsline {subsection}{\numberline {11.0.152}Giving Parameters to Constructors}{2446}{subsection.11.0.152}
\contentsline {subsection}{\numberline {11.0.153}Miscellaneous Features of Browse}{2447}{subsection.11.0.153}
\contentsline {subsection}{\numberline {11.0.154}The Description Page for Operations}{2448}{subsection.11.0.154}
\contentsline {subsection}{\numberline {11.0.155}Views of Operations}{2449}{subsection.11.0.155}
\contentsline {subsection}{\numberline {11.0.156}Capitalization Convention}{2452}{subsection.11.0.156}
\contentsline {chapter}{\numberline {12}Users Guide Chapter 15 (ug15.ht)}{2455}{chapter.12}
\contentsline {subsection}{\numberline {12.0.157}What's New in Axiom Version 2.0}{2455}{subsection.12.0.157}
\contentsline {subsection}{\numberline {12.0.158}Important Things to Read First}{2456}{subsection.12.0.158}
\contentsline {subsection}{\numberline {12.0.159}The NAG Library Link}{2456}{subsection.12.0.159}
\contentsline {subsection}{\numberline {12.0.160}Interpreting NAG Documentation}{2457}{subsection.12.0.160}
\contentsline {subsection}{\numberline {12.0.161}Using the Link}{2460}{subsection.12.0.161}
\contentsline {subsection}{\numberline {12.0.162}Providing values for Argument Subprograms}{2463}{subsection.12.0.162}
\contentsline {subsection}{\numberline {12.0.163}General Fortran-generation utilities in Axiom}{2467}{subsection.12.0.163}
\contentsline {subsection}{\numberline {12.0.164}Some technical information}{2492}{subsection.12.0.164}
\contentsline {subsection}{\numberline {12.0.165}Interactive Front-end and Language}{2493}{subsection.12.0.165}
\contentsline {subsection}{\numberline {12.0.166}Library}{2494}{subsection.12.0.166}
\contentsline {subsection}{\numberline {12.0.167}HyperDoc}{2496}{subsection.12.0.167}
\contentsline {subsection}{\numberline {12.0.168}Documentation}{2497}{subsection.12.0.168}
\contentsline {chapter}{\numberline {13}Users Guide Chapter 16 (ug16.ht)}{2499}{chapter.13}
\contentsline {subsection}{\numberline {13.0.169}Axiom System Commands}{2500}{subsection.13.0.169}
\contentsline {subsection}{\numberline {13.0.170}Introduction}{2502}{subsection.13.0.170}
\contentsline {subsection}{\numberline {13.0.171})abbreviation}{2504}{subsection.13.0.171}
\contentsline {subsection}{\numberline {13.0.172})boot}{2506}{subsection.13.0.172}
\contentsline {subsection}{\numberline {13.0.173})cd}{2507}{subsection.13.0.173}
\contentsline {subsection}{\numberline {13.0.174})close}{2508}{subsection.13.0.174}
\contentsline {subsection}{\numberline {13.0.175})clear}{2509}{subsection.13.0.175}
\contentsline {subsection}{\numberline {13.0.176})compile}{2511}{subsection.13.0.176}
\contentsline {subsection}{\numberline {13.0.177})display}{2514}{subsection.13.0.177}
\contentsline {subsection}{\numberline {13.0.178})edit}{2516}{subsection.13.0.178}
\contentsline {subsection}{\numberline {13.0.179})fin}{2517}{subsection.13.0.179}
\contentsline {subsection}{\numberline {13.0.180})frame}{2518}{subsection.13.0.180}
\contentsline {subsection}{\numberline {13.0.181})help}{2520}{subsection.13.0.181}
\contentsline {subsection}{\numberline {13.0.182})history}{2521}{subsection.13.0.182}
\contentsline {subsection}{\numberline {13.0.183})library}{2525}{subsection.13.0.183}
\contentsline {subsection}{\numberline {13.0.184})lisp}{2527}{subsection.13.0.184}
\contentsline {subsection}{\numberline {13.0.185})load}{2528}{subsection.13.0.185}
\contentsline {subsection}{\numberline {13.0.186})ltrace}{2528}{subsection.13.0.186}
\contentsline {subsection}{\numberline {13.0.187})pquit}{2529}{subsection.13.0.187}
\contentsline {subsection}{\numberline {13.0.188})quit}{2531}{subsection.13.0.188}
\contentsline {subsection}{\numberline {13.0.189})read}{2532}{subsection.13.0.189}
\contentsline {subsection}{\numberline {13.0.190})set}{2533}{subsection.13.0.190}
\contentsline {subsection}{\numberline {13.0.191})show}{2535}{subsection.13.0.191}
\contentsline {subsection}{\numberline {13.0.192})spool}{2536}{subsection.13.0.192}
\contentsline {subsection}{\numberline {13.0.193})synonym}{2537}{subsection.13.0.193}
\contentsline {subsection}{\numberline {13.0.194})system}{2538}{subsection.13.0.194}
\contentsline {subsection}{\numberline {13.0.195})trace}{2540}{subsection.13.0.195}
\contentsline {subsection}{\numberline {13.0.196})undo}{2546}{subsection.13.0.196}
\contentsline {subsection}{\numberline {13.0.197})what}{2548}{subsection.13.0.197}
\contentsline {chapter}{\numberline {14}Users Guide Chapter 21 (ug21.ht)}{2551}{chapter.14}
\contentsline {subsection}{\numberline {14.0.198}Programs for Axiom Images}{2551}{subsection.14.0.198}
\contentsline {subsection}{\numberline {14.0.199}images1.input}{2552}{subsection.14.0.199}
\contentsline {subsection}{\numberline {14.0.200}images2.input}{2553}{subsection.14.0.200}
\contentsline {subsection}{\numberline {14.0.201}images3.input}{2553}{subsection.14.0.201}
\contentsline {subsection}{\numberline {14.0.202}images5.input}{2554}{subsection.14.0.202}
\contentsline {subsection}{\numberline {14.0.203}images6.input}{2556}{subsection.14.0.203}
\contentsline {subsection}{\numberline {14.0.204}images7.input}{2557}{subsection.14.0.204}
\contentsline {subsection}{\numberline {14.0.205}images8.input}{2558}{subsection.14.0.205}
\contentsline {subsection}{\numberline {14.0.206}conformal.input}{2559}{subsection.14.0.206}
\contentsline {subsection}{\numberline {14.0.207}tknot.input}{2563}{subsection.14.0.207}
\contentsline {subsection}{\numberline {14.0.208}ntube.input}{2563}{subsection.14.0.208}
\contentsline {subsection}{\numberline {14.0.209}dhtri.input}{2566}{subsection.14.0.209}
\contentsline {subsection}{\numberline {14.0.210}tetra.input}{2567}{subsection.14.0.210}
\contentsline {subsection}{\numberline {14.0.211}antoine.input}{2569}{subsection.14.0.211}
\contentsline {subsection}{\numberline {14.0.212}scherk.input}{2570}{subsection.14.0.212}
\contentsline {chapter}{\numberline {15}Hypertex Language Pages}{2573}{chapter.15}
\contentsline {subsection}{\numberline {15.0.213}Creating Hyperdoc Pages}{2573}{subsection.15.0.213}
\contentsline {section}{\numberline {15.1}htxadvpage1.ht}{2574}{section.15.1}
\contentsline {subsection}{\numberline {15.1.1}Input Areas}{2574}{subsection.15.1.1}
\contentsline {subsection}{\numberline {15.1.2}HTXAdvPage1xPatch1 patch}{2575}{subsection.15.1.2}
\contentsline {subsection}{\numberline {15.1.3}HTXAdvPage1xPatch1A patch}{2575}{subsection.15.1.3}
\contentsline {subsection}{\numberline {15.1.4}HTXAdvPage1xPatch2 patch}{2576}{subsection.15.1.4}
\contentsline {subsection}{\numberline {15.1.5}HTXAdvPage1xPatch2A patch}{2576}{subsection.15.1.5}
\contentsline {section}{\numberline {15.2}htxadvpage2.ht}{2577}{section.15.2}
\contentsline {subsection}{\numberline {15.2.1}Radio buttons}{2577}{subsection.15.2.1}
\contentsline {section}{\numberline {15.3}htxadvpage3.ht}{2580}{section.15.3}
\contentsline {subsection}{\numberline {15.3.1}Macros}{2580}{subsection.15.3.1}
\contentsline {section}{\numberline {15.4}htxadvpage4.ht}{2581}{section.15.4}
\contentsline {subsection}{\numberline {15.4.1}Patch and Paste}{2581}{subsection.15.4.1}
\contentsline {subsection}{\numberline {15.4.2}patch1 patch}{2584}{subsection.15.4.2}
\contentsline {subsection}{\numberline {15.4.3}Patch1 patch}{2584}{subsection.15.4.3}
\contentsline {subsection}{\numberline {15.4.4}Patch2 patch}{2585}{subsection.15.4.4}
\contentsline {section}{\numberline {15.5}htxadvpage5.ht}{2585}{section.15.5}
\contentsline {subsection}{\numberline {15.5.1}Axiom paste-ins}{2585}{subsection.15.5.1}
\contentsline {section}{\numberline {15.6}htxadvpage6.ht}{2588}{section.15.6}
\contentsline {subsection}{\numberline {15.6.1}Miscellaneous}{2588}{subsection.15.6.1}
\contentsline {subsection}{\numberline {15.6.2}HTXAdvPage6xPatch1 patch}{2590}{subsection.15.6.2}
\contentsline {subsection}{\numberline {15.6.3}HTXAdvPage6xPatch1A patch}{2590}{subsection.15.6.3}
\contentsline {subsection}{\numberline {15.6.4}HTXAdvPage6xPatch2 patch}{2590}{subsection.15.6.4}
\contentsline {subsection}{\numberline {15.6.5}HTXAdvPage6xPatch2A patch}{2591}{subsection.15.6.5}
\contentsline {subsection}{\numberline {15.6.6}HTXAdvPage6xPatch3 patch}{2591}{subsection.15.6.6}
\contentsline {subsection}{\numberline {15.6.7}HTXAdvPage6xPatch3A patch}{2591}{subsection.15.6.7}
\contentsline {section}{\numberline {15.7}htxadvtoppage.ht}{2592}{section.15.7}
\contentsline {subsection}{\numberline {15.7.1}Advanced features in Hyperdoc}{2592}{subsection.15.7.1}
\contentsline {section}{\numberline {15.8}htxformatpage1.ht}{2593}{section.15.8}
\contentsline {subsection}{\numberline {15.8.1}Using the special characters}{2593}{subsection.15.8.1}
\contentsline {subsection}{\numberline {15.8.2}HTXFormatPage1xPatch1 patch}{2594}{subsection.15.8.2}
\contentsline {subsection}{\numberline {15.8.3}HTXFormatPage1xPatch2 patch}{2594}{subsection.15.8.3}
\contentsline {section}{\numberline {15.9}htxformatpage2.ht}{2595}{section.15.9}
\contentsline {subsection}{\numberline {15.9.1}Formatting without commands}{2595}{subsection.15.9.1}
\contentsline {subsection}{\numberline {15.9.2}HTXFormatPage2xPatch1 patch}{2596}{subsection.15.9.2}
\contentsline {subsection}{\numberline {15.9.3}HTXFormatPage2xPatch2 patch}{2597}{subsection.15.9.3}
\contentsline {subsection}{\numberline {15.9.4}HTXFormatPage2xPatch2A patch}{2597}{subsection.15.9.4}
\contentsline {subsection}{\numberline {15.9.5}HTXFormatPage2xPatch3 patch}{2598}{subsection.15.9.5}
\contentsline {subsection}{\numberline {15.9.6}HTXFormatPage2xPatch3A patch}{2598}{subsection.15.9.6}
\contentsline {subsection}{\numberline {15.9.7}HTXFormatPage2xPatch4 patch}{2599}{subsection.15.9.7}
\contentsline {subsection}{\numberline {15.9.8}HTXFormatPage2xPatch4A patch}{2599}{subsection.15.9.8}
\contentsline {section}{\numberline {15.10}htxformatpage3.ht}{2599}{section.15.10}
\contentsline {subsection}{\numberline {15.10.1}Using different fonts}{2599}{subsection.15.10.1}
\contentsline {subsection}{\numberline {15.10.2}HTXFormatPage3xPatch1 patch}{2601}{subsection.15.10.2}
\contentsline {subsection}{\numberline {15.10.3}HTXFormatPage3xPatch2 patch}{2602}{subsection.15.10.3}
\contentsline {subsection}{\numberline {15.10.4}HTXFormatPage3xPatch3 patch}{2602}{subsection.15.10.4}
\contentsline {subsection}{\numberline {15.10.5}HTXFormatPage3xPatch4 patch}{2603}{subsection.15.10.5}
\contentsline {section}{\numberline {15.11}htxformatpage4.ht}{2603}{section.15.11}
\contentsline {subsection}{\numberline {15.11.1}Indentation}{2603}{subsection.15.11.1}
\contentsline {subsection}{\numberline {15.11.2}HTXFormatPage4xPatch1 patch}{2606}{subsection.15.11.2}
\contentsline {subsection}{\numberline {15.11.3}HTXFormatPage4xPatch1A patch}{2606}{subsection.15.11.3}
\contentsline {subsection}{\numberline {15.11.4}HTXFormatPage4xPatch2 patch}{2606}{subsection.15.11.4}
\contentsline {subsection}{\numberline {15.11.5}HTXFormatPage4xPatch2A patch}{2607}{subsection.15.11.5}
\contentsline {subsection}{\numberline {15.11.6}HTXFormatPage4xPatch3 patch}{2607}{subsection.15.11.6}
\contentsline {subsection}{\numberline {15.11.7}HTXFormatPage4xPatch3A patch}{2608}{subsection.15.11.7}
\contentsline {subsection}{\numberline {15.11.8}HTXFormatPage4xPatch4 patch}{2608}{subsection.15.11.8}
\contentsline {subsection}{\numberline {15.11.9}HTXFormatPage4xPatch5 patch}{2609}{subsection.15.11.9}
\contentsline {subsection}{\numberline {15.11.10}HTXFormatPage4xPatch5A patch}{2609}{subsection.15.11.10}
\contentsline {section}{\numberline {15.12}htxformatpage5.ht}{2610}{section.15.12}
\contentsline {subsection}{\numberline {15.12.1}Creating Lists and Tables}{2610}{subsection.15.12.1}
\contentsline {subsection}{\numberline {15.12.2}HTXFormatPage5xPatch1 patch}{2612}{subsection.15.12.2}
\contentsline {subsection}{\numberline {15.12.3}HTXFormatPage5xPatch1A patch}{2613}{subsection.15.12.3}
\contentsline {subsection}{\numberline {15.12.4}HTXFormatPage5xPatch2 patch}{2613}{subsection.15.12.4}
\contentsline {subsection}{\numberline {15.12.5}HTXFormatPage5xPatch2A patch}{2614}{subsection.15.12.5}
\contentsline {subsection}{\numberline {15.12.6}HTXFormatPage5xPatch3 patch}{2614}{subsection.15.12.6}
\contentsline {subsection}{\numberline {15.12.7}HTXFormatPage5xPatch3A patch}{2615}{subsection.15.12.7}
\contentsline {section}{\numberline {15.13}htxformatpage6}{2615}{section.15.13}
\contentsline {subsection}{\numberline {15.13.1}Boxes and Lines}{2615}{subsection.15.13.1}
\contentsline {subsection}{\numberline {15.13.2}HTXFormatPage6xPatch1 patch}{2616}{subsection.15.13.2}
\contentsline {subsection}{\numberline {15.13.3}HTXFormatPage6xPatch2 patch}{2617}{subsection.15.13.3}
\contentsline {section}{\numberline {15.14}htxformatpage7}{2617}{section.15.14}
\contentsline {subsection}{\numberline {15.14.1}Micro-Spacing}{2617}{subsection.15.14.1}
\contentsline {subsection}{\numberline {15.14.2}HTXFormatPage7xPatch1 patch}{2619}{subsection.15.14.2}
\contentsline {subsection}{\numberline {15.14.3}HTXFormatPage7xPatch2 patch}{2620}{subsection.15.14.3}
\contentsline {subsection}{\numberline {15.14.4}HTXFormatPage7xPatch2A patch}{2620}{subsection.15.14.4}
\contentsline {subsection}{\numberline {15.14.5}HTXFormatPage7xPatch3 patch}{2620}{subsection.15.14.5}
\contentsline {subsection}{\numberline {15.14.6}HTXFormatPage7xPatch3A patch}{2621}{subsection.15.14.6}
\contentsline {section}{\numberline {15.15}htxformatpage8}{2622}{section.15.15}
\contentsline {subsection}{\numberline {15.15.1}Bitmaps and Images}{2622}{subsection.15.15.1}
\contentsline {subsection}{\numberline {15.15.2}HTXFormatPage8xPatch1 patch}{2623}{subsection.15.15.2}
\contentsline {subsection}{\numberline {15.15.3}HTXFormatPage8xPatch2 patch}{2624}{subsection.15.15.3}
\contentsline {subsection}{\numberline {15.15.4}HTXFormatPage8xPatch2A patch}{2624}{subsection.15.15.4}
\contentsline {section}{\numberline {15.16}htxformattoppage.ht}{2624}{section.15.16}
\contentsline {subsection}{\numberline {15.16.1}Formatting in Hyperdoc}{2624}{subsection.15.16.1}
\contentsline {section}{\numberline {15.17}htxintropage1.ht}{2625}{section.15.17}
\contentsline {subsection}{\numberline {15.17.1}What Hyperdoc does}{2625}{subsection.15.17.1}
\contentsline {section}{\numberline {15.18}htxintropage2.ht}{2626}{section.15.18}
\contentsline {subsection}{\numberline {15.18.1}How Hyperdoc does it}{2626}{subsection.15.18.1}
\contentsline {section}{\numberline {15.19}htxintropage3.ht}{2628}{section.15.19}
\contentsline {subsection}{\numberline {15.19.1}A simple text page}{2628}{subsection.15.19.1}
\contentsline {section}{\numberline {15.20}htxintrotoppage.ht}{2630}{section.15.20}
\contentsline {subsection}{\numberline {15.20.1}First Steps}{2630}{subsection.15.20.1}
\contentsline {section}{\numberline {15.21}htxlinkpage1.ht}{2631}{section.15.21}
\contentsline {subsection}{\numberline {15.21.1}Linking to a named page}{2631}{subsection.15.21.1}
\contentsline {subsection}{\numberline {15.21.2}HTXLinkPage1xPatch1 patch}{2633}{subsection.15.21.2}
\contentsline {subsection}{\numberline {15.21.3}HTXLinkPage1xPatch1A patch}{2633}{subsection.15.21.3}
\contentsline {subsection}{\numberline {15.21.4}Test Help Page}{2634}{subsection.15.21.4}
\contentsline {section}{\numberline {15.22}htxlinkpage2.ht}{2634}{section.15.22}
\contentsline {subsection}{\numberline {15.22.1}Standard Pages}{2634}{subsection.15.22.1}
\contentsline {subsection}{\numberline {15.22.2}HTXLinkPage2xPatch1 patch}{2636}{subsection.15.22.2}
\contentsline {subsection}{\numberline {15.22.3}HTXLinkPage2xPatch1A patch}{2636}{subsection.15.22.3}
\contentsline {section}{\numberline {15.23}htxlinkpage3.ht}{2637}{section.15.23}
\contentsline {subsection}{\numberline {15.23.1}Active Axiom commands}{2637}{subsection.15.23.1}
\contentsline {subsection}{\numberline {15.23.2}HTXLinkPage3xPatch1 patch}{2640}{subsection.15.23.2}
\contentsline {subsection}{\numberline {15.23.3}HTXLinkPage3xPatch1A patch}{2641}{subsection.15.23.3}
\contentsline {subsection}{\numberline {15.23.4}HTXLinkPage3xPatch2 patch}{2641}{subsection.15.23.4}
\contentsline {subsection}{\numberline {15.23.5}HTXLinkPage3xPatch2A patch}{2641}{subsection.15.23.5}
\contentsline {subsection}{\numberline {15.23.6}HTXLinkPage3xPatch3 patch}{2642}{subsection.15.23.6}
\contentsline {subsection}{\numberline {15.23.7}HTXLinkPage3xPatch3A patch}{2642}{subsection.15.23.7}
\contentsline {section}{\numberline {15.24}htxlinkpage4.ht}{2643}{section.15.24}
\contentsline {subsection}{\numberline {15.24.1}Linking to Lisp}{2643}{subsection.15.24.1}
\contentsline {subsection}{\numberline {15.24.2}HTXLinkPage4xPatch1 patch}{2647}{subsection.15.24.2}
\contentsline {subsection}{\numberline {15.24.3}HTXLinkPage4xPatch1A patch}{2648}{subsection.15.24.3}
\contentsline {subsection}{\numberline {15.24.4}HTXLinkPage4xPatch2 patch}{2648}{subsection.15.24.4}
\contentsline {subsection}{\numberline {15.24.5}HTXLinkPage4xPatch2A patch}{2648}{subsection.15.24.5}
\contentsline {subsection}{\numberline {15.24.6}HTXLinkPage4xPatch3 patch}{2649}{subsection.15.24.6}
\contentsline {subsection}{\numberline {15.24.7}HTXLinkPage4xPatch3A patch}{2649}{subsection.15.24.7}
\contentsline {subsection}{\numberline {15.24.8}HTXLinkPage4xPatch4 patch}{2650}{subsection.15.24.8}
\contentsline {subsection}{\numberline {15.24.9}HTXLinkPage4xPatch4A patch}{2650}{subsection.15.24.9}
\contentsline {subsection}{\numberline {15.24.10}HTXLinkPage4xPatch5 patch}{2650}{subsection.15.24.10}
\contentsline {subsection}{\numberline {15.24.11}HTXLinkPage4xPatch5A patch}{2651}{subsection.15.24.11}
\contentsline {section}{\numberline {15.25}htxlinkpage5.ht}{2652}{section.15.25}
\contentsline {subsection}{\numberline {15.25.1}Linking to Unix}{2652}{subsection.15.25.1}
\contentsline {subsection}{\numberline {15.25.2}HTXLinkPage5xPatch1 patch}{2653}{subsection.15.25.2}
\contentsline {subsection}{\numberline {15.25.3}HTXLinkPage5xPatch1A patch}{2654}{subsection.15.25.3}
\contentsline {subsection}{\numberline {15.25.4}HTXLinkPage5xPatch2 patch}{2654}{subsection.15.25.4}
\contentsline {subsection}{\numberline {15.25.5}HTXLinkPage5xPatch2A patch}{2654}{subsection.15.25.5}
\contentsline {section}{\numberline {15.26}htxlinkpage6.ht}{2655}{section.15.26}
\contentsline {subsection}{\numberline {15.26.1}How to use your pages with Hyperdoc}{2655}{subsection.15.26.1}
\contentsline {subsection}{\numberline {15.26.2}HTXLinkPage6xPatch1 patch}{2657}{subsection.15.26.2}
\contentsline {subsection}{\numberline {15.26.3}HTXLinkPage6xPatch1A patch}{2659}{subsection.15.26.3}
\contentsline {subsection}{\numberline {15.26.4}HTXLinkPage6xPatch2 patch}{2659}{subsection.15.26.4}
\contentsline {subsection}{\numberline {15.26.5}HTXLinkPage6xPatch2A patch}{2660}{subsection.15.26.5}
\contentsline {section}{\numberline {15.27}htxlinktoppage.ht}{2660}{section.15.27}
\contentsline {subsection}{\numberline {15.27.1}Actions in Hyperdoc}{2660}{subsection.15.27.1}
\contentsline {section}{\numberline {15.28}htxtoppage.ht}{2661}{section.15.28}
\contentsline {subsection}{\numberline {15.28.1}Extending Hyperdoc}{2661}{subsection.15.28.1}
\contentsline {section}{\numberline {15.29}htxtrypage.ht}{2662}{section.15.29}
\contentsline {subsection}{\numberline {15.29.1}Try out Hyperdoc}{2662}{subsection.15.29.1}
\contentsline {chapter}{\numberline {16}NAG Library Routines}{2665}{chapter.16}
\contentsline {section}{\numberline {16.1}nagaux.ht}{2665}{section.16.1}
\contentsline {subsection}{\numberline {16.1.1}NAG On-line Documentation}{2665}{subsection.16.1.1}
\contentsline {subsection}{\numberline {16.1.2}NAG Documentation: summary}{2667}{subsection.16.1.2}
\contentsline {subsection}{\numberline {16.1.3}NAG Documentation: introduction}{2689}{subsection.16.1.3}
\contentsline {subsection}{\numberline {16.1.4}NAG Documentation: keyword in context}{2706}{subsection.16.1.4}
\contentsline {subsection}{\numberline {16.1.5}NAG Documentation: conversion}{2804}{subsection.16.1.5}
\contentsline {section}{\numberline {16.2}nagc.ht}{2807}{section.16.2}
\contentsline {subsection}{\numberline {16.2.1} Zeros of Polynomials}{2807}{subsection.16.2.1}
\contentsline {subsection}{\numberline {16.2.2} Roots of a complex polynomial equation}{2811}{subsection.16.2.2}
\contentsline {subsection}{\numberline {16.2.3} Roots of a real polynomial equation}{2816}{subsection.16.2.3}
\contentsline {subsection}{\numberline {16.2.4} Roots of One or More Transcendental Equations}{2822}{subsection.16.2.4}
\contentsline {subsection}{\numberline {16.2.5} Zero of a continuous function in a given interval}{2826}{subsection.16.2.5}
\contentsline {subsection}{\numberline {16.2.6} Solution of a system of nonlinear equations}{2830}{subsection.16.2.6}
\contentsline {subsection}{\numberline {16.2.7} Solution of a system of nonlinear equations}{2834}{subsection.16.2.7}
\contentsline {subsection}{\numberline {16.2.8} Checks the gradients of a set of non-linear functions}{2840}{subsection.16.2.8}
\contentsline {subsection}{\numberline {16.2.9} Discrete Fourier transform of real or complex data values}{2843}{subsection.16.2.9}
\contentsline {subsection}{\numberline {16.2.10} Discrete Fourier transform of n real data values}{2851}{subsection.16.2.10}
\contentsline {subsection}{\numberline {16.2.11} Discrete Fourier transform of a Hermitian sequence}{2854}{subsection.16.2.11}
\contentsline {subsection}{\numberline {16.2.12} Discrete Fourier transform of n complex data values}{2858}{subsection.16.2.12}
\contentsline {subsection}{\numberline {16.2.13} Circular convolution or correlation of two real vectors}{2861}{subsection.16.2.13}
\contentsline {subsection}{\numberline {16.2.14} Discrete Fourier transforms of m sequences}{2865}{subsection.16.2.14}
\contentsline {subsection}{\numberline {16.2.15} Discrete Fourier transforms of m Hermitian sequences}{2870}{subsection.16.2.15}
\contentsline {subsection}{\numberline {16.2.16} Discrete Fourier transforms of m complex sequences}{2874}{subsection.16.2.16}
\contentsline {subsection}{\numberline {16.2.17} Discrete Fourier transform of bivariate complex data}{2878}{subsection.16.2.17}
\contentsline {subsection}{\numberline {16.2.18} Summation of Series}{2883}{subsection.16.2.18}
\contentsline {subsection}{\numberline {16.2.19} Complex conjugate of a sequence of n data values}{2885}{subsection.16.2.19}
\contentsline {subsection}{\numberline {16.2.20} Complex conjugates of m Hermitian sequences}{2887}{subsection.16.2.20}
\contentsline {subsection}{\numberline {16.2.21} Form real and imaginary parts of m Hermitian sequences}{2889}{subsection.16.2.21}
\contentsline {section}{\numberline {16.3}nagd.ht}{2892}{section.16.3}
\contentsline {subsection}{\numberline {16.3.1} Quadrature}{2892}{subsection.16.3.1}
\contentsline {subsection}{\numberline {16.3.2} Approximation of the integral over a finite interval}{2905}{subsection.16.3.2}
\contentsline {subsection}{\numberline {16.3.3} Adaptive integration over a finite integral}{2911}{subsection.16.3.3}
\contentsline {subsection}{\numberline {16.3.4} Approximate integration with local singular points}{2917}{subsection.16.3.4}
\contentsline {subsection}{\numberline {16.3.5} Approximate integration over a (semi-)infinite interval}{2923}{subsection.16.3.5}
\contentsline {subsection}{\numberline {16.3.6} Approximate sine or cosine transform over finite interval}{2929}{subsection.16.3.6}
\contentsline {subsection}{\numberline {16.3.7} Adaptive integration of weighted function over an interval}{2935}{subsection.16.3.7}
\contentsline {subsection}{\numberline {16.3.8} Hilbert transform over finite interval}{2941}{subsection.16.3.8}
\contentsline {subsection}{\numberline {16.3.9} Approximate Sine or Cosine over [$a$,$\infty $]}{2947}{subsection.16.3.9}
\contentsline {subsection}{\numberline {16.3.10} Weights and abscissae for Gaussian quadrature formula}{2954}{subsection.16.3.10}
\contentsline {subsection}{\numberline {16.3.11} Multidimensional integrals with finite limits}{2960}{subsection.16.3.11}
\contentsline {subsection}{\numberline {16.3.12} Third-order finite-difference integration}{2965}{subsection.16.3.12}
\contentsline {subsection}{\numberline {16.3.13} Monte Carlo integration over hyper-rectangular regions}{2968}{subsection.16.3.13}
\contentsline {subsection}{\numberline {16.3.14} Ordinary Differential Equations}{2973}{subsection.16.3.14}
\contentsline {subsection}{\numberline {16.3.15} First-order ODE over an interval with initial conditions}{2980}{subsection.16.3.15}
\contentsline {subsection}{\numberline {16.3.16} First-order ODE with initial conditions and user function}{2988}{subsection.16.3.16}
\contentsline {subsection}{\numberline {16.3.17} First-order ODE with variable-order, variable-step}{2996}{subsection.16.3.17}
\contentsline {subsection}{\numberline {16.3.18} Stiff First-order ODE with variable order and step}{3005}{subsection.16.3.18}
\contentsline {subsection}{\numberline {16.3.19} Two-point boundary-value ODE}{3014}{subsection.16.3.19}
\contentsline {subsection}{\numberline {16.3.20} Two-point boundary value ODE with deferred correction}{3021}{subsection.16.3.20}
\contentsline {subsection}{\numberline {16.3.21} Eignevalue of regular singular 2nd-order Sturm-Liouville}{3029}{subsection.16.3.21}
\contentsline {subsection}{\numberline {16.3.22} Two-point boundary-value ODE equation systems}{3052}{subsection.16.3.22}
\contentsline {subsection}{\numberline {16.3.23} Partial differential equations}{3066}{subsection.16.3.23}
\contentsline {subsection}{\numberline {16.3.24} Discrete elliptic PDE on rectangular region}{3073}{subsection.16.3.24}
\contentsline {subsection}{\numberline {16.3.25} Discrete 2nd-order elliptic PDE on rectangular regions}{3081}{subsection.16.3.25}
\contentsline {subsection}{\numberline {16.3.26} Helmholtz equation in 3 dimensions}{3094}{subsection.16.3.26}
\contentsline {section}{\numberline {16.4}nage.ht}{3104}{section.16.4}
\contentsline {subsection}{\numberline {16.4.1} Interpolation}{3104}{subsection.16.4.1}
\contentsline {subsection}{\numberline {16.4.2} Cubic spline interpolant}{3109}{subsection.16.4.2}
\contentsline {subsection}{\numberline {16.4.3} Monoticity-preserving piecewise cubic Hermite interpolant}{3114}{subsection.16.4.3}
\contentsline {subsection}{\numberline {16.4.4} Piecewise cubic Hermite interpolant}{3117}{subsection.16.4.4}
\contentsline {subsection}{\numberline {16.4.5} Piecewise cubic Hermite interpolant and 1st deriv}{3120}{subsection.16.4.5}
\contentsline {subsection}{\numberline {16.4.6} Definite integral of piecewise cubic Hermite interpolant}{3123}{subsection.16.4.6}
\contentsline {subsection}{\numberline {16.4.7} Bicubic spline interpolated surface}{3125}{subsection.16.4.7}
\contentsline {subsection}{\numberline {16.4.8} Two-D surface interpolating a set of scattered data points}{3132}{subsection.16.4.8}
\contentsline {subsection}{\numberline {16.4.9} Evaluate 2D interpolant function from E01SAF}{3135}{subsection.16.4.9}
\contentsline {subsection}{\numberline {16.4.10} Generate 2D surface interpolating a scattered data points}{3138}{subsection.16.4.10}
\contentsline {subsection}{\numberline {16.4.11} Evaluate 2D interpolating function from E01SEF}{3144}{subsection.16.4.11}
\contentsline {subsection}{\numberline {16.4.12} Curve and Surface Fitting}{3147}{subsection.16.4.12}
\contentsline {subsection}{\numberline {16.4.13} Least-squares polynomial approximations}{3172}{subsection.16.4.13}
\contentsline {subsection}{\numberline {16.4.14} Evaluate polynomial from Chebyshev-series representation}{3178}{subsection.16.4.14}
\contentsline {subsection}{\numberline {16.4.15} Constrained weighted least-squares polynomial}{3182}{subsection.16.4.15}
\contentsline {subsection}{\numberline {16.4.16} Coefficients of polynomial derivative}{3190}{subsection.16.4.16}
\contentsline {subsection}{\numberline {16.4.17} Find coefficients of indefinite integral of polynomial}{3195}{subsection.16.4.17}
\contentsline {subsection}{\numberline {16.4.18} Evaluate polynomial in Chebyshev-series representation}{3200}{subsection.16.4.18}
\contentsline {subsection}{\numberline {16.4.19} Weighted least-squares aprrox to data points}{3205}{subsection.16.4.19}
\contentsline {subsection}{\numberline {16.4.20} Evaluates a cubic spline from its B-spline representation}{3212}{subsection.16.4.20}
\contentsline {subsection}{\numberline {16.4.21} Evaluate cubic spline and 3 derivatives from B-spline}{3216}{subsection.16.4.21}
\contentsline {subsection}{\numberline {16.4.22} Definite integral of cubic spline from B-spline}{3221}{subsection.16.4.22}
\contentsline {subsection}{\numberline {16.4.23} Cubic spline approximation to an arbitrary set points}{3225}{subsection.16.4.23}
\contentsline {subsection}{\numberline {16.4.24} Minimal, weighted least-squares bicubic spline fit}{3234}{subsection.16.4.24}
\contentsline {subsection}{\numberline {16.4.25} Bicubic spline approximation to a set of data values}{3243}{subsection.16.4.25}
\contentsline {subsection}{\numberline {16.4.26} Bicubic spline approximation to a set of scattered data}{3254}{subsection.16.4.26}
\contentsline {subsection}{\numberline {16.4.27} Calculates values of a bicubic spline from B-spline}{3266}{subsection.16.4.27}
\contentsline {subsection}{\numberline {16.4.28} Calculates values of a bicubic spline from B-spline}{3270}{subsection.16.4.28}
\contentsline {subsection}{\numberline {16.4.29} Calculates $l_1$ solution to over-determined system equations}{3274}{subsection.16.4.29}
\contentsline {subsection}{\numberline {16.4.30} Sorts two-dimensional data into rectangular panels}{3280}{subsection.16.4.30}
\contentsline {subsection}{\numberline {16.4.31} Minimizing or Maximizing a Function}{3284}{subsection.16.4.31}
\contentsline {subsection}{\numberline {16.4.32} Minimizes a nonlinear function of several variable}{3309}{subsection.16.4.32}
\contentsline {subsection}{\numberline {16.4.33} Supply optional parameters to E04DGF from file}{3324}{subsection.16.4.33}
\contentsline {subsection}{\numberline {16.4.34} Supply individual optional params to E04DGF}{3327}{subsection.16.4.34}
\contentsline {subsection}{\numberline {16.4.35} Finding an unconstrained minimum of a sum of squares}{3329}{subsection.16.4.35}
\contentsline {subsection}{\numberline {16.4.36} Finding an unconstrained minimum of a sum of squares}{3335}{subsection.16.4.36}
\contentsline {subsection}{\numberline {16.4.37} Finding a minimum of a function}{3342}{subsection.16.4.37}
\contentsline {subsection}{\numberline {16.4.38} Solving linear programming problems}{3348}{subsection.16.4.38}
\contentsline {subsection}{\numberline {16.4.39} Solving linear or quadratic problems}{3357}{subsection.16.4.39}
\contentsline {subsection}{\numberline {16.4.40} Minimize an arbitrary smooth constrainted function}{3377}{subsection.16.4.40}
\contentsline {subsection}{\numberline {16.4.41} Supply optional parameters to E04UCF from file}{3428}{subsection.16.4.41}
\contentsline {subsection}{\numberline {16.4.42} Supply individual optional params to E04UCF}{3431}{subsection.16.4.42}
\contentsline {subsection}{\numberline {16.4.43} Estimates of elements of the variance-covariance matrix}{3434}{subsection.16.4.43}
\contentsline {section}{\numberline {16.5}nagf.ht}{3440}{section.16.5}
\contentsline {subsection}{\numberline {16.5.1} Linear Algebra}{3440}{subsection.16.5.1}
\contentsline {subsection}{\numberline {16.5.2} Matrix Factorization}{3444}{subsection.16.5.2}
\contentsline {subsection}{\numberline {16.5.3} Factorizes a real sparse matrix}{3447}{subsection.16.5.3}
\contentsline {subsection}{\numberline {16.5.4} Factorizes a real sparse matrix}{3457}{subsection.16.5.4}
\contentsline {subsection}{\numberline {16.5.5} Incomplete Cholesky factorization}{3463}{subsection.16.5.5}
\contentsline {subsection}{\numberline {16.5.6} Cholesky factor of a symmetric positive-definite matrix}{3470}{subsection.16.5.6}
\contentsline {subsection}{\numberline {16.5.7} QR factorization of the real m by n matrix A}{3475}{subsection.16.5.7}
\contentsline {subsection}{\numberline {16.5.8} $B:=QB$ or $B:=Q^T B$}{3480}{subsection.16.5.8}
\contentsline {subsection}{\numberline {16.5.9} First ncolq columns of the real m by m orthogonal matrix}{3485}{subsection.16.5.9}
\contentsline {subsection}{\numberline {16.5.10} QR factorization of the complex m by n matrix A}{3489}{subsection.16.5.10}
\contentsline {subsection}{\numberline {16.5.11} $B:=QB$ or $B:=Q^H B$}{3494}{subsection.16.5.11}
\contentsline {subsection}{\numberline {16.5.12} First ncolq columns of the complex m by m unitary matrix}{3500}{subsection.16.5.12}
\contentsline {subsection}{\numberline {16.5.13} Eigenvalues and Eigenvectors}{3505}{subsection.16.5.13}
\contentsline {subsection}{\numberline {16.5.14} Calculates all the eigenvalues of a real symmetric matrix}{3511}{subsection.16.5.14}
\contentsline {subsection}{\numberline {16.5.15} Eigenvalues and eigenvectors of a real symmetric matrix}{3513}{subsection.16.5.15}
\contentsline {subsection}{\numberline {16.5.16} Calculates all the eigenvalues of $Ax=\lambda Bx$}{3516}{subsection.16.5.16}
\contentsline {subsection}{\numberline {16.5.17} Eigenvalues and eigenvectors of $Ax=\lambda Bx$}{3519}{subsection.16.5.17}
\contentsline {subsection}{\numberline {16.5.18} Calculates all the eigenvalues of a real unsymmetric matrix}{3523}{subsection.16.5.18}
\contentsline {subsection}{\numberline {16.5.19} Eigenvalues and eigenvectors of a real unsymmetric matrix}{3525}{subsection.16.5.19}
\contentsline {subsection}{\numberline {16.5.20} Calculates all the eigenvalues of a complex matrix}{3528}{subsection.16.5.20}
\contentsline {subsection}{\numberline {16.5.21} Eigenvalues and eigenvectors of a complex matrix}{3531}{subsection.16.5.21}
\contentsline {subsection}{\numberline {16.5.22} Eigenvalues of a complex Hermitian matrix}{3534}{subsection.16.5.22}
\contentsline {subsection}{\numberline {16.5.23} Eigenvalues/eigenvectors complex Hermitian matrix}{3537}{subsection.16.5.23}
\contentsline {subsection}{\numberline {16.5.24} Eigenvalues and eigenvectors of a real symmetric matrix}{3540}{subsection.16.5.24}
\contentsline {subsection}{\numberline {16.5.25} Eigenvalues of generalized eigenproblem $Ax=\lambda Bx$}{3544}{subsection.16.5.25}
\contentsline {subsection}{\numberline {16.5.26} Eigenvalues and eigenvectors of real sparse symmetric problem}{3549}{subsection.16.5.26}
\contentsline {subsection}{\numberline {16.5.27} Singular value decomposition of a general real matrix}{3562}{subsection.16.5.27}
\contentsline {subsection}{\numberline {16.5.28} Singular value decomposition of a general complex matrix}{3570}{subsection.16.5.28}
\contentsline {subsection}{\numberline {16.5.29} Simultaneous Linear Equations}{3577}{subsection.16.5.29}
\contentsline {subsection}{\numberline {16.5.30} Approximate solution of a set of complex linear equations}{3583}{subsection.16.5.30}
\contentsline {subsection}{\numberline {16.5.31} Approximate solution of a set of real linear equations}{3586}{subsection.16.5.31}
\contentsline {subsection}{\numberline {16.5.32} Real symmetric positive-definite linear equations}{3589}{subsection.16.5.32}
\contentsline {subsection}{\numberline {16.5.33} Set of real linear equations with a single right-hand side}{3593}{subsection.16.5.33}
\contentsline {subsection}{\numberline {16.5.34} Solution of a set of real sparse linear equations}{3596}{subsection.16.5.34}
\contentsline {subsection}{\numberline {16.5.35} Real symmetric positive-definite tridiagonal linear equations}{3599}{subsection.16.5.35}
\contentsline {subsection}{\numberline {16.5.36} Solution of a linear least-squares problem, $Ax=b$}{3605}{subsection.16.5.36}
\contentsline {subsection}{\numberline {16.5.37} Sparse symmetric positive-definite system linear equations}{3611}{subsection.16.5.37}
\contentsline {subsection}{\numberline {16.5.38} Solves a system of real sparse symmetric linear equations}{3617}{subsection.16.5.38}
\contentsline {subsection}{\numberline {16.5.39} Solution of a system of real linear equations}{3628}{subsection.16.5.39}
\contentsline {subsection}{\numberline {16.5.40} Solves sparse unsymmetric equations}{3633}{subsection.16.5.40}
\contentsline {subsection}{\numberline {16.5.41} Linear Algebra Support Routines}{3647}{subsection.16.5.41}
\contentsline {subsection}{\numberline {16.5.42} Linear Equations (LAPACK)}{3680}{subsection.16.5.42}
\contentsline {subsection}{\numberline {16.5.43} Computes the LU factorization of a real m by n matrix}{3681}{subsection.16.5.43}
\contentsline {subsection}{\numberline {16.5.44} Solves a real system of linear equations}{3685}{subsection.16.5.44}
\contentsline {subsection}{\numberline {16.5.45} Factorization of a real symmetric positive-definite matrix}{3689}{subsection.16.5.45}
\contentsline {subsection}{\numberline {16.5.46} Real symmetric positive-definite system of linear equations}{3692}{subsection.16.5.46}
\contentsline {subsection}{\numberline {16.5.47} Sort vector of double precision numbers}{3699}{subsection.16.5.47}
\contentsline {subsection}{\numberline {16.5.48} Ranks a vector of double precision numbers}{3702}{subsection.16.5.48}
\contentsline {subsection}{\numberline {16.5.49} Ranks the rows of a matrix of double precision numbers}{3705}{subsection.16.5.49}
\contentsline {subsection}{\numberline {16.5.50} Ranks the columns of a matrix of double precision numbers}{3708}{subsection.16.5.50}
\contentsline {subsection}{\numberline {16.5.51} Rearranges a vector of double precision numbers}{3711}{subsection.16.5.51}
\contentsline {subsection}{\numberline {16.5.52} Inverts a permutation}{3713}{subsection.16.5.52}
\contentsline {section}{\numberline {16.6}nags.ht}{3716}{section.16.6}
\contentsline {subsection}{\numberline {16.6.1} Approximations of Special Functions}{3716}{subsection.16.6.1}
\contentsline {subsection}{\numberline {16.6.2} Exponential function $e^z$ , for complex $z$}{3729}{subsection.16.6.2}
\contentsline {subsection}{\numberline {16.6.3} Returns the value of the exponential integral $E(x)$}{3732}{subsection.16.6.3}
\contentsline {subsection}{\numberline {16.6.4} Returns the value of the cosine integral}{3735}{subsection.16.6.4}
\contentsline {subsection}{\numberline {16.6.5} Returns the value of the sine integral}{3738}{subsection.16.6.5}
\contentsline {subsection}{\numberline {16.6.6} Returns the value of the Gamma function}{3741}{subsection.16.6.6}
\contentsline {subsection}{\numberline {16.6.7} Returns a value for the logarithm of the Gamma function}{3744}{subsection.16.6.7}
\contentsline {subsection}{\numberline {16.6.8} Incomplete gamma functions P(a,x) and Q(a,x)}{3748}{subsection.16.6.8}
\contentsline {subsection}{\numberline {16.6.9} Returns the value of the complementary error function}{3751}{subsection.16.6.9}
\contentsline {subsection}{\numberline {16.6.10} Returns the value of the error function erfx}{3755}{subsection.16.6.10}
\contentsline {subsection}{\numberline {16.6.11} Returns the value of the Bessel Function $Y_0(x)$}{3757}{subsection.16.6.11}
\contentsline {subsection}{\numberline {16.6.12} Returns the value of the Bessel Function $Y_1(x)$}{3761}{subsection.16.6.12}
\contentsline {subsection}{\numberline {16.6.13} Returns the value of the Bessel Function $J_0(x)$}{3766}{subsection.16.6.13}
\contentsline {subsection}{\numberline {16.6.14} Returns the value of the Bessel Function $J_1(x)$}{3770}{subsection.16.6.14}
\contentsline {subsection}{\numberline {16.6.15} Returns a value for the Airy function, $Ai(x)$}{3773}{subsection.16.6.15}
\contentsline {subsection}{\numberline {16.6.16} Returns a value of the Airy function, $Bi(x)$}{3778}{subsection.16.6.16}
\contentsline {subsection}{\numberline {16.6.17} Value of the derivative of the Airy function $Ai(x)$}{3782}{subsection.16.6.17}
\contentsline {subsection}{\numberline {16.6.18} Value for the derivative of the Airy function $Bi(x)$}{3786}{subsection.16.6.18}
\contentsline {subsection}{\numberline {16.6.19} Values for the Bessel functions $Y_{\nu +n}(z)$}{3790}{subsection.16.6.19}
\contentsline {subsection}{\numberline {16.6.20} Values for the Bessel functions $J_{\nu +n}(z)$}{3795}{subsection.16.6.20}
\contentsline {subsection}{\numberline {16.6.21} Value of the Airy function $Ai(z)$ or derivative $Ai'(z)$}{3800}{subsection.16.6.21}
\contentsline {subsection}{\numberline {16.6.22} Value of the Airy function $Bi(z)$ or derivative $Bi'(z)$}{3804}{subsection.16.6.22}
\contentsline {subsection}{\numberline {16.6.23} Returns a sequence of values for the Hankel functions}{3808}{subsection.16.6.23}
\contentsline {subsection}{\numberline {16.6.24} Returns the value of the modified Bessel Function $K_0(x)$}{3814}{subsection.16.6.24}
\contentsline {subsection}{\numberline {16.6.25} Returns the value of the modified Bessel Function $K_1(x)$}{3817}{subsection.16.6.25}
\contentsline {subsection}{\numberline {16.6.26} Returns the value of the modified Bessel Function $I_0(x)$}{3821}{subsection.16.6.26}
\contentsline {subsection}{\numberline {16.6.27} Returns a value for the modified Bessel Function $I_1(x)$}{3825}{subsection.16.6.27}
\contentsline {subsection}{\numberline {16.6.28} Sequence of values for the modified Bessel $K_{\nu _n}(z)$}{3828}{subsection.16.6.28}
\contentsline {subsection}{\numberline {16.6.29} Sequence of values for the modified Bessel $I_{\nu +n}$}{3833}{subsection.16.6.29}
\contentsline {subsection}{\numberline {16.6.30} Returns a value for the Kelvin function ber x}{3837}{subsection.16.6.30}
\contentsline {subsection}{\numberline {16.6.31} Returns a value for the Kelvin function bei x}{3841}{subsection.16.6.31}
\contentsline {subsection}{\numberline {16.6.32} Returns a value for the Kelvin function ker x}{3844}{subsection.16.6.32}
\contentsline {subsection}{\numberline {16.6.33} Returns a value for the Kelvin function keix}{3848}{subsection.16.6.33}
\contentsline {subsection}{\numberline {16.6.34} Returns a value for the Fresnel Integral $S(x)$}{3852}{subsection.16.6.34}
\contentsline {subsection}{\numberline {16.6.35} Returns a value for the Fresnel Integral $C(x)$}{3856}{subsection.16.6.35}
\contentsline {subsection}{\numberline {16.6.36} Returns a value of an elementary integral}{3861}{subsection.16.6.36}
\contentsline {subsection}{\numberline {16.6.37} Value of the symmetrised elliptic integral of first kind}{3864}{subsection.16.6.37}
\contentsline {subsection}{\numberline {16.6.38} Value of the symmetrised elliptic integral of second kind}{3868}{subsection.16.6.38}
\contentsline {subsection}{\numberline {16.6.39} Value of the symmetrised elliptic integral of third kind}{3873}{subsection.16.6.39}
\contentsline {section}{\numberline {16.7}nagx.ht}{3878}{section.16.7}
\contentsline {subsection}{\numberline {16.7.1} Mathematical Constants}{3878}{subsection.16.7.1}
\contentsline {subsection}{\numberline {16.7.2} Machine Constants}{3879}{subsection.16.7.2}
\contentsline {subsection}{\numberline {16.7.3} Input/Output Utilities}{3886}{subsection.16.7.3}
\contentsline {subsection}{\numberline {16.7.4} Value of the current error message unit number}{3888}{subsection.16.7.4}
\contentsline {subsection}{\numberline {16.7.5} Value of the current advisory message unit number}{3891}{subsection.16.7.5}
\contentsline {subsection}{\numberline {16.7.6} Print a real matrix stored in a two-dimensional array}{3893}{subsection.16.7.6}
\contentsline {subsection}{\numberline {16.7.7} Print a complex matrix stored in a 2D array}{3896}{subsection.16.7.7}
\contentsline {subsection}{\numberline {16.7.8} Date and Time Utilities}{3900}{subsection.16.7.8}
\contentsline {subsection}{\numberline {16.7.9} Returns the current date and time}{3902}{subsection.16.7.9}
\contentsline {subsection}{\numberline {16.7.10} From seven-integer format time and date to character string}{3903}{subsection.16.7.10}
\contentsline {subsection}{\numberline {16.7.11} Compares two date/time character strings}{3906}{subsection.16.7.11}
\contentsline {subsection}{\numberline {16.7.12} Amount of processor time used}{3909}{subsection.16.7.12}
\contentsline {chapter}{\numberline {17}NAG ASP Example Code}{3911}{chapter.17}
\contentsline {section}{\numberline {17.1}aspex.ht}{3911}{section.17.1}
\contentsline {subsection}{\numberline {17.1.1}Asp1 Example Code}{3911}{subsection.17.1.1}
\contentsline {subsection}{\numberline {17.1.2}Asp10 Example Code}{3911}{subsection.17.1.2}
\contentsline {subsection}{\numberline {17.1.3}Asp12 Example Code}{3912}{subsection.17.1.3}
\contentsline {subsection}{\numberline {17.1.4}Asp19 Example Code}{3912}{subsection.17.1.4}
\contentsline {subsection}{\numberline {17.1.5}Asp20 Example Code}{3915}{subsection.17.1.5}
\contentsline {subsection}{\numberline {17.1.6}Asp24 Example Code}{3915}{subsection.17.1.6}
\contentsline {subsection}{\numberline {17.1.7}Asp27 Example Code}{3916}{subsection.17.1.7}
\contentsline {subsection}{\numberline {17.1.8}Asp28 Example Code}{3916}{subsection.17.1.8}
\contentsline {subsection}{\numberline {17.1.9}Asp29 Example Code}{3919}{subsection.17.1.9}
\contentsline {subsection}{\numberline {17.1.10}Asp30 Example Code}{3920}{subsection.17.1.10}
\contentsline {subsection}{\numberline {17.1.11}Asp31 Example Code}{3921}{subsection.17.1.11}
\contentsline {subsection}{\numberline {17.1.12}Asp33 Example Code}{3921}{subsection.17.1.12}
\contentsline {subsection}{\numberline {17.1.13}Asp34 Example Code}{3922}{subsection.17.1.13}
\contentsline {subsection}{\numberline {17.1.14}Asp35 Example Code}{3922}{subsection.17.1.14}
\contentsline {subsection}{\numberline {17.1.15}Asp4 Example Code}{3923}{subsection.17.1.15}
\contentsline {subsection}{\numberline {17.1.16}Asp41 Example Code}{3923}{subsection.17.1.16}
\contentsline {subsection}{\numberline {17.1.17}Asp42 Example Code}{3924}{subsection.17.1.17}
\contentsline {subsection}{\numberline {17.1.18}Asp49 Example Code}{3925}{subsection.17.1.18}
\contentsline {subsection}{\numberline {17.1.19}Asp50 Example Code}{3926}{subsection.17.1.19}
\contentsline {subsection}{\numberline {17.1.20}Asp55 Example Code}{3927}{subsection.17.1.20}
\contentsline {subsection}{\numberline {17.1.21}Asp6 Example Code}{3928}{subsection.17.1.21}
\contentsline {subsection}{\numberline {17.1.22}Asp7 Example Code}{3928}{subsection.17.1.22}
\contentsline {subsection}{\numberline {17.1.23}Asp73 Example Code}{3929}{subsection.17.1.23}
\contentsline {subsection}{\numberline {17.1.24}Asp74 Example Code}{3929}{subsection.17.1.24}
\contentsline {subsection}{\numberline {17.1.25}Asp77 Example Code}{3930}{subsection.17.1.25}
\contentsline {subsection}{\numberline {17.1.26}Asp78 Example Code}{3931}{subsection.17.1.26}
\contentsline {subsection}{\numberline {17.1.27}Asp8 Example Code}{3931}{subsection.17.1.27}
\contentsline {subsection}{\numberline {17.1.28}Asp80 Example Code}{3932}{subsection.17.1.28}
\contentsline {subsection}{\numberline {17.1.29}Asp9 Example Code}{3932}{subsection.17.1.29}
\contentsline {chapter}{\numberline {18}NAG ANNA Expert System}{3935}{chapter.18}
\contentsline {section}{\numberline {18.1}annaex.ht}{3935}{section.18.1}
\contentsline {subsection}{\numberline {18.1.1}Axiom/NAG Expert System}{3935}{subsection.18.1.1}
\contentsline {subsection}{\numberline {18.1.2}Integration}{3936}{subsection.18.1.2}
\contentsline {subsection}{\numberline {18.1.3}Ordinary Differential Equations}{3937}{subsection.18.1.3}
\contentsline {subsection}{\numberline {18.1.4}Optimization}{3937}{subsection.18.1.4}
\contentsline {subsection}{\numberline {18.1.5}Partial Differential Equations}{3938}{subsection.18.1.5}
\contentsline {subsection}{\numberline {18.1.6}Examples Using the Axiom/NAG Expert System}{3939}{subsection.18.1.6}
\contentsline {subsection}{\numberline {18.1.7}Examples Using the Axiom/NAG Expert System}{3940}{subsection.18.1.7}
\contentsline {subsection}{\numberline {18.1.8}Examples Using the Axiom/NAG Expert System}{3941}{subsection.18.1.8}
\contentsline {subsection}{\numberline {18.1.9}Examples Using the Axiom/NAG Expert System}{3943}{subsection.18.1.9}
\contentsline {subsection}{\numberline {18.1.10}About the Axiom/NAG Expert System}{3944}{subsection.18.1.10}
\contentsline {subsection}{\numberline {18.1.11}Introduction to the Axiom/NAG Expert System}{3945}{subsection.18.1.11}
\contentsline {subsection}{\numberline {18.1.12}Example using the Axiom/NAG Expert System}{3946}{subsection.18.1.12}
\contentsline {subsection}{\numberline {18.1.13}Example using the Axiom/NAG Expert System}{3951}{subsection.18.1.13}
\contentsline {subsection}{\numberline {18.1.14}Example using the Axiom/NAG Expert System}{3952}{subsection.18.1.14}
\contentsline {subsection}{\numberline {18.1.15}Decision Agents}{3953}{subsection.18.1.15}
\contentsline {subsection}{\numberline {18.1.16}Inference Mechanisms}{3954}{subsection.18.1.16}
\contentsline {subsection}{\numberline {18.1.17}Method Domains}{3955}{subsection.18.1.17}
\contentsline {subsection}{\numberline {18.1.18}Measure Functions}{3956}{subsection.18.1.18}
\contentsline {subsection}{\numberline {18.1.19}Computational Agents}{3957}{subsection.18.1.19}
\contentsline {chapter}{\numberline {19}ANNA Algebra Code}{3959}{chapter.19}
\contentsline {chapter}{\numberline {20}Page hierarchy layout}{3961}{chapter.20}
\contentsline {chapter}{\numberline {21}Makefile}{3995}{chapter.21}
