\BOOKMARK [0][-]{chapter.1}{Release Notes}{}
\BOOKMARK [1][-]{section.1.1}{releasenotes.ht}{chapter.1}
\BOOKMARK [2][-]{subsection.1.1.1}{What is new in Axiom}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.2}{Online Information}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.3}{January 2012 Release Notes}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.4}{November 2011 Release Notes}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.5}{September 2011 Release Notes}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.6}{July 2011 Release Notes}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.7}{May 2011 Release Notes}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.8}{March 2011 Release Notes}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.9}{January 2011 Release Notes}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.10}{November 2010 Release Notes}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.11}{September 2010 Release Notes}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.12}{July 2010 Release Notes}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.13}{May 2010 Release Notes}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.14}{March 2010 Release Notes}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.15}{January 2010 Release Notes}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.16}{November 2009 Release Notes}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.17}{September 2009 Release Notes}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.18}{July 2009 Release Notes}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.19}{May 2009 Release Notes}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.20}{March 2009 Release Notes}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.21}{January 2009 Release Notes}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.22}{November 23, 2008 Release Notes}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.23}{September 23, 2008 Release Notes}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.24}{July 23, 2008 Release Notes}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.25}{May 27, 2008 Release Notes}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.26}{March 25, 2008 Release Notes}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.27}{January 25, 2008 Release Notes}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.28}{November 23, 2007 Release Notes}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.29}{Feature Complete Release Feb 2005}{section.1.1}
\BOOKMARK [0][-]{chapter.2}{Special hyperdoc pages}{}
\BOOKMARK [1][-]{section.2.1}{util.ht}{chapter.2}
\BOOKMARK [2][-]{subsection.2.1.1}{Names of software and facilities}{section.2.1}
\BOOKMARK [2][-]{subsection.2.1.2}{Special hooks to Unix}{section.2.1}
\BOOKMARK [2][-]{subsection.2.1.3}{HyperDoc menu macros}{section.2.1}
\BOOKMARK [2][-]{subsection.2.1.4}{Bitmaps and bitmap manipulation macros}{section.2.1}
\BOOKMARK [2][-]{subsection.2.1.5}{HyperDoc button objects}{section.2.1}
\BOOKMARK [2][-]{subsection.2.1.6}{Standard HyperDoc button configurations}{section.2.1}
\BOOKMARK [2][-]{subsection.2.1.7}{HyperDoc graphics macros}{section.2.1}
\BOOKMARK [2][-]{subsection.2.1.8}{TeX and LaTeX compatibility macros}{section.2.1}
\BOOKMARK [2][-]{subsection.2.1.9}{Book and .ht page macros}{section.2.1}
\BOOKMARK [2][-]{subsection.2.1.10}{Browse macros}{section.2.1}
\BOOKMARK [2][-]{subsection.2.1.11}{Support for output and graph paste-ins}{section.2.1}
\BOOKMARK [2][-]{subsection.2.1.12}{Hook for including a local menu item on the rootpage}{section.2.1}
\BOOKMARK [2][-]{subsection.2.1.13}{Not Connected to Axiom}{section.2.1}
\BOOKMARK [2][-]{subsection.2.1.14}{Do You Really Want to Exit?}{section.2.1}
\BOOKMARK [2][-]{subsection.2.1.15}{Missing Page}{section.2.1}
\BOOKMARK [2][-]{subsection.2.1.16}{Something is Wrong}{section.2.1}
\BOOKMARK [2][-]{subsection.2.1.17}{Sorry!}{section.2.1}
\BOOKMARK [0][-]{chapter.3}{Hyperdoc pages}{}
\BOOKMARK [1][-]{section.3.1}{rootpage.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.1.1}{Axiom HyperDoc Top Level}{section.3.1}
\BOOKMARK [2][-]{subsection.3.1.2}{Axiom -- The Scientific Computation System}{section.3.1}
\BOOKMARK [2][-]{subsection.3.1.3}{System Commands}{section.3.1}
\BOOKMARK [2][-]{subsection.3.1.4}{Axiom Examples}{section.3.1}
\BOOKMARK [2][-]{subsection.3.1.5}{Axiom Reference}{section.3.1}
\BOOKMARK [2][-]{subsection.3.1.6}{NAG Documentation}{section.3.1}
\BOOKMARK [1][-]{section.3.2}{algebra.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.2.1}{Abstract Algebra}{section.3.2}
\BOOKMARK [2][-]{subsection.3.2.2}{Number Theory}{section.3.2}
\BOOKMARK [1][-]{section.3.3}{alist.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.3.1}{AssociationList}{section.3.3}
\BOOKMARK [1][-]{section.3.4}{array1.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.4.1}{OneDimensionalArray}{section.3.4}
\BOOKMARK [1][-]{section.3.5}{array2.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.5.1}{TwoDimensionalArray}{section.3.5}
\BOOKMARK [1][-]{section.3.6}{basic.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.6.1}{Basic Commands}{section.3.6}
\BOOKMARK [2][-]{subsection.3.6.2}{Calculus}{section.3.6}
\BOOKMARK [1][-]{section.3.7}{bbtree.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.7.1}{BalancedBinaryTree}{section.3.7}
\BOOKMARK [1][-]{section.3.8}{binary.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.8.1}{BinaryExpansion}{section.3.8}
\BOOKMARK [1][-]{section.3.9}{bmcat.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.9.1}{Bit Map Catalog}{section.3.9}
\BOOKMARK [1][-]{section.3.10}{bop.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.10.1}{BasicOperator}{section.3.10}
\BOOKMARK [1][-]{section.3.11}{bstree.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.11.1}{BinarySearchTree}{section.3.11}
\BOOKMARK [1][-]{section.3.12}{card.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.12.1}{CardinalNumber}{section.3.12}
\BOOKMARK [1][-]{section.3.13}{carten.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.13.1}{CartesianTensor}{section.3.13}
\BOOKMARK [1][-]{section.3.14}{cclass.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.14.1}{CharacterClass}{section.3.14}
\BOOKMARK [1][-]{section.3.15}{char.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.15.1}{Character}{section.3.15}
\BOOKMARK [2][-]{subsection.3.15.2}{CliffordAlgebra}{section.3.15}
\BOOKMARK [2][-]{subsection.3.15.3}{The Complex Numbers as a Clifford Algebra}{section.3.15}
\BOOKMARK [2][-]{subsection.3.15.4}{The Quaternion Numbers as a Clifford Algebra}{section.3.15}
\BOOKMARK [2][-]{subsection.3.15.5}{The Exterior Algebra on a Three Space}{section.3.15}
\BOOKMARK [2][-]{subsection.3.15.6}{The Dirac Spin Algebra}{section.3.15}
\BOOKMARK [1][-]{section.3.16}{complex.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.16.1}{Complex}{section.3.16}
\BOOKMARK [1][-]{section.3.17}{contfrac.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.17.1}{ContinuedFraction}{section.3.17}
\BOOKMARK [1][-]{section.3.18}{cphelp.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.18.1}{Control Panel Bits}{section.3.18}
\BOOKMARK [1][-]{section.3.19}{cycles.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.19.1}{CycleIndicators}{section.3.19}
\BOOKMARK [1][-]{section.3.20}{coverex.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.20.1}{Examples Of Axiom Commands}{section.3.20}
\BOOKMARK [2][-]{subsection.3.20.2}{Differentiation}{section.3.20}
\BOOKMARK [2][-]{subsection.3.20.3}{Integration}{section.3.20}
\BOOKMARK [2][-]{subsection.3.20.4}{Laplace Transforms}{section.3.20}
\BOOKMARK [2][-]{subsection.3.20.5}{Limits}{section.3.20}
\BOOKMARK [2][-]{subsection.3.20.6}{Matrices}{section.3.20}
\BOOKMARK [2][-]{subsection.3.20.7}{2-D Graphics}{section.3.20}
\BOOKMARK [2][-]{subsection.3.20.8}{3-D Graphics}{section.3.20}
\BOOKMARK [2][-]{subsection.3.20.9}{Series}{section.3.20}
\BOOKMARK [2][-]{subsection.3.20.10}{Summations}{section.3.20}
\BOOKMARK [1][-]{section.3.21}{decimal.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.21.1}{Decimal Expansion}{section.3.21}
\BOOKMARK [1][-]{section.3.22}{derham.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.22.1}{DeRhamComplex}{section.3.22}
\BOOKMARK [1][-]{section.3.23}{dfloat.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.23.1}{DoubleFloat}{section.3.23}
\BOOKMARK [1][-]{section.3.24}{dmp.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.24.1}{DistributedMultivariatePoly}{section.3.24}
\BOOKMARK [1][-]{section.3.25}{eq.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.25.1}{Equation}{section.3.25}
\BOOKMARK [1][-]{section.3.26}{eqtbl.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.26.1}{EqTable}{section.3.26}
\BOOKMARK [1][-]{section.3.27}{evalex.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.27.1}{Example of Standard Evaluation}{section.3.27}
\BOOKMARK [2][-]{subsection.3.27.2}{Example of Standard Evaluation}{section.3.27}
\BOOKMARK [1][-]{section.3.28}{exdiff.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.28.1}{Computing Derivatives}{section.3.28}
\BOOKMARK [2][-]{subsection.3.28.2}{Derivatives of Functions of Several Variables}{section.3.28}
\BOOKMARK [2][-]{subsection.3.28.3}{Derivatives of Higher Order}{section.3.28}
\BOOKMARK [2][-]{subsection.3.28.4}{Multiple Derivatives I}{section.3.28}
\BOOKMARK [2][-]{subsection.3.28.5}{Multiple Derivatives II}{section.3.28}
\BOOKMARK [2][-]{subsection.3.28.6}{Derivatives of Functions Involving Formal Integrals}{section.3.28}
\BOOKMARK [2][-]{subsection.3.28.7}{Exit}{section.3.28}
\BOOKMARK [1][-]{section.3.29}{exlap.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.29.1}{Laplace transform with a single pole}{section.3.29}
\BOOKMARK [2][-]{subsection.3.29.2}{Laplace transform of a trigonometric function}{section.3.29}
\BOOKMARK [2][-]{subsection.3.29.3}{Laplace transform requiring a definite integration}{section.3.29}
\BOOKMARK [2][-]{subsection.3.29.4}{Laplace transform of exponentials}{section.3.29}
\BOOKMARK [2][-]{subsection.3.29.5}{Laplace transform of an exponential integral}{section.3.29}
\BOOKMARK [2][-]{subsection.3.29.6}{Laplace transform of special functions}{section.3.29}
\BOOKMARK [1][-]{section.3.30}{exint.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.30.1}{Integral of a Rational Function}{section.3.30}
\BOOKMARK [2][-]{subsection.3.30.2}{Integral of a Rational Function with a Real Parameter}{section.3.30}
\BOOKMARK [2][-]{subsection.3.30.3}{Integral of a Rational Function with a Complex Parameter}{section.3.30}
\BOOKMARK [2][-]{subsection.3.30.4}{Two Similar Integrands Producing Very Different Results}{section.3.30}
\BOOKMARK [2][-]{subsection.3.30.5}{An Integral Which Does Not Exist}{section.3.30}
\BOOKMARK [2][-]{subsection.3.30.6}{A Trigonometric Function of a Quadratic}{section.3.30}
\BOOKMARK [2][-]{subsection.3.30.7}{Integrating a Function with a Hidden Algebraic Relation}{section.3.30}
\BOOKMARK [2][-]{subsection.3.30.8}{Details for integrating a function with a Hidden Algebraic Relation}{section.3.30}
\BOOKMARK [2][-]{subsection.3.30.9}{An Integral Involving a Root of a Transcendental Function}{section.3.30}
\BOOKMARK [2][-]{subsection.3.30.10}{An Integral of a Non-elementary Function}{section.3.30}
\BOOKMARK [1][-]{section.3.31}{exlimit.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.31.1}{Computing Limits}{section.3.31}
\BOOKMARK [2][-]{subsection.3.31.2}{Limits of Functions with Parameters}{section.3.31}
\BOOKMARK [2][-]{subsection.3.31.3}{One-sided Limits}{section.3.31}
\BOOKMARK [2][-]{subsection.3.31.4}{Two-sided Limits}{section.3.31}
\BOOKMARK [2][-]{subsection.3.31.5}{Limits at Infinity}{section.3.31}
\BOOKMARK [2][-]{subsection.3.31.6}{Real Limits vs. Complex Limits}{section.3.31}
\BOOKMARK [2][-]{subsection.3.31.7}{Complex Limits at Infinity}{section.3.31}
\BOOKMARK [1][-]{section.3.32}{exmatrix.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.32.1}{Basic Arithmetic Operations on Matrices}{section.3.32}
\BOOKMARK [2][-]{subsection.3.32.2}{Constructing new Matrices}{section.3.32}
\BOOKMARK [2][-]{subsection.3.32.3}{Trace of a Matrix}{section.3.32}
\BOOKMARK [2][-]{subsection.3.32.4}{Determinant of a Matrix}{section.3.32}
\BOOKMARK [2][-]{subsection.3.32.5}{Inverse of a Matrix}{section.3.32}
\BOOKMARK [2][-]{subsection.3.32.6}{Rank of a Matrix}{section.3.32}
\BOOKMARK [1][-]{section.3.33}{expr.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.33.1}{Expression}{section.3.33}
\BOOKMARK [1][-]{section.3.34}{explot2d.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.34.1}{Plotting Functions of One Variable}{section.3.34}
\BOOKMARK [2][-]{subsection.3.34.2}{Plotting Parametric Curves}{section.3.34}
\BOOKMARK [2][-]{subsection.3.34.3}{Plotting Using Polar Coordinates}{section.3.34}
\BOOKMARK [2][-]{subsection.3.34.4}{Plotting Plane Algebraic Curves}{section.3.34}
\BOOKMARK [1][-]{section.3.35}{explot3d.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.35.1}{Plotting Functions of Two Variables}{section.3.35}
\BOOKMARK [2][-]{subsection.3.35.2}{Plotting Parametric Surfaces}{section.3.35}
\BOOKMARK [2][-]{subsection.3.35.3}{Plotting Parametric Curves}{section.3.35}
\BOOKMARK [1][-]{section.3.36}{expose.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.36.1}{Exposure}{section.3.36}
\BOOKMARK [2][-]{subsection.3.36.2}{System Defined Exposure Groups}{section.3.36}
\BOOKMARK [2][-]{subsection.3.36.3}{What is an Exposure Group?}{section.3.36}
\BOOKMARK [2][-]{subsection.3.36.4}{Details on Exposure}{section.3.36}
\BOOKMARK [1][-]{section.3.37}{exseries.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.37.1}{Converting Expressions to Series}{section.3.37}
\BOOKMARK [2][-]{subsection.3.37.2}{Manipulating Power Series}{section.3.37}
\BOOKMARK [2][-]{subsection.3.37.3}{Functions on Power Series}{section.3.37}
\BOOKMARK [2][-]{subsection.3.37.4}{Substituting Numerical Values in Power Series}{section.3.37}
\BOOKMARK [1][-]{section.3.38}{exsum.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.38.1}{Summing the Entries of a List I}{section.3.38}
\BOOKMARK [2][-]{subsection.3.38.2}{Summing the Entries of a List II}{section.3.38}
\BOOKMARK [2][-]{subsection.3.38.3}{Approximating e}{section.3.38}
\BOOKMARK [2][-]{subsection.3.38.4}{Closed Form Summations}{section.3.38}
\BOOKMARK [2][-]{subsection.3.38.5}{Sums of Cubes}{section.3.38}
\BOOKMARK [2][-]{subsection.3.38.6}{Sums of Polynomials}{section.3.38}
\BOOKMARK [2][-]{subsection.3.38.7}{Sums of General Functions}{section.3.38}
\BOOKMARK [2][-]{subsection.3.38.8}{Infinite Sums}{section.3.38}
\BOOKMARK [1][-]{section.3.39}{farray.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.39.1}{FlexibleArray}{section.3.39}
\BOOKMARK [1][-]{section.3.40}{file.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.40.1}{File}{section.3.40}
\BOOKMARK [1][-]{section.3.41}{float.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.41.1}{Float}{section.3.41}
\BOOKMARK [2][-]{subsection.3.41.2}{Introduction to Float}{section.3.41}
\BOOKMARK [2][-]{subsection.3.41.3}{Conversion Functions}{section.3.41}
\BOOKMARK [2][-]{subsection.3.41.4}{Output Functions}{section.3.41}
\BOOKMARK [2][-]{subsection.3.41.5}{An Example: Determinant of a Hilbert Matrix}{section.3.41}
\BOOKMARK [2][-]{subsection.3.41.6}{Expanding Factored Objects}{section.3.41}
\BOOKMARK [2][-]{subsection.3.41.7}{Arithmetic with Factored Objects}{section.3.41}
\BOOKMARK [2][-]{subsection.3.41.8}{Creating New Factored Objects}{section.3.41}
\BOOKMARK [2][-]{subsection.3.41.9}{Factored Objects with Variables}{section.3.41}
\BOOKMARK [1][-]{section.3.42}{fr2.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.42.1}{FactoredFunctions2}{section.3.42}
\BOOKMARK [1][-]{section.3.43}{frac.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.43.1}{Fraction}{section.3.43}
\BOOKMARK [1][-]{section.3.44}{fparfrac.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.44.1}{FullPartialFracExpansion}{section.3.44}
\BOOKMARK [1][-]{section.3.45}{function.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.45.1}{Functions in Axiom}{section.3.45}
\BOOKMARK [2][-]{subsection.3.45.2}{Rational Functions}{section.3.45}
\BOOKMARK [2][-]{subsection.3.45.3}{Algebraic Functions}{section.3.45}
\BOOKMARK [2][-]{subsection.3.45.4}{Elementary Functions}{section.3.45}
\BOOKMARK [2][-]{subsection.3.45.5}{Simplification}{section.3.45}
\BOOKMARK [1][-]{section.3.46}{gbf.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.46.1}{GroebnerFactorizationPkg}{section.3.46}
\BOOKMARK [1][-]{section.3.47}{gloss.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.47.1}{Glossary}{section.3.47}
\BOOKMARK [1][-]{section.3.48}{graphics.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.48.1}{Graphics}{section.3.48}
\BOOKMARK [2][-]{subsection.3.48.2}{Graphics Examples}{section.3.48}
\BOOKMARK [2][-]{subsection.3.48.3}{Assorted Graphics Examples}{section.3.48}
\BOOKMARK [2][-]{subsection.3.48.4}{Three Dimensional Graphics}{section.3.48}
\BOOKMARK [2][-]{subsection.3.48.5}{Functions of One Variable}{section.3.48}
\BOOKMARK [2][-]{subsection.3.48.6}{Parametric Curves}{section.3.48}
\BOOKMARK [2][-]{subsection.3.48.7}{Polar Coordinates}{section.3.48}
\BOOKMARK [2][-]{subsection.3.48.8}{Implicit Curves}{section.3.48}
\BOOKMARK [2][-]{subsection.3.48.9}{Lists of Points}{section.3.48}
\BOOKMARK [2][-]{subsection.3.48.10}{Two Dimensional Graphics}{section.3.48}
\BOOKMARK [2][-]{subsection.3.48.11}{Functions of One Variable}{section.3.48}
\BOOKMARK [2][-]{subsection.3.48.12}{Parametric Curves}{section.3.48}
\BOOKMARK [2][-]{subsection.3.48.13}{Polar Coordinates}{section.3.48}
\BOOKMARK [2][-]{subsection.3.48.14}{Implicit Curves}{section.3.48}
\BOOKMARK [2][-]{subsection.3.48.15}{Lists of Points}{section.3.48}
\BOOKMARK [2][-]{subsection.3.48.16}{Representation Theory}{section.3.48}
\BOOKMARK [2][-]{subsection.3.48.17}{Group Theory}{section.3.48}
\BOOKMARK [1][-]{section.3.49}{gstbl.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.49.1}{GeneralSparseTable}{section.3.49}
\BOOKMARK [1][-]{section.3.50}{heap.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.50.1}{Heap}{section.3.50}
\BOOKMARK [1][-]{section.3.51}{hexadec.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.51.1}{HexadecimalExpansion}{section.3.51}
\BOOKMARK [1][-]{section.3.52}{int.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.52.1}{Integer}{section.3.52}
\BOOKMARK [2][-]{subsection.3.52.2}{Basic Functions}{section.3.52}
\BOOKMARK [2][-]{subsection.3.52.3}{Primes and Factorization}{section.3.52}
\BOOKMARK [2][-]{subsection.3.52.4}{Some Number Theoretic Functions}{section.3.52}
\BOOKMARK [1][-]{section.3.53}{intheory.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.53.1}{IntegerNumberTheoryFunctions}{section.3.53}
\BOOKMARK [1][-]{section.3.54}{kafile.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.54.1}{KeyedAccessFile}{section.3.54}
\BOOKMARK [1][-]{section.3.55}{kernel.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.55.1}{Kernel}{section.3.55}
\BOOKMARK [1][-]{section.3.56}{lazm3pk.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.56.1}{LazardSetSolvingPackage}{section.3.56}
\BOOKMARK [1][-]{section.3.57}{lexp.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.57.1}{LieExponentials}{section.3.57}
\BOOKMARK [1][-]{section.3.58}{lextripk.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.58.1}{LexTriangularPackage}{section.3.58}
\BOOKMARK [1][-]{section.3.59}{lib.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.59.1}{Library}{section.3.59}
\BOOKMARK [1][-]{section.3.60}{link.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.60.1}{The Axiom Link to NAG Software}{section.3.60}
\BOOKMARK [2][-]{subsection.3.60.2}{Use of the Link from HyperDoc}{section.3.60}
\BOOKMARK [2][-]{subsection.3.60.3}{C02 Zeros of Polynomials}{section.3.60}
\BOOKMARK [2][-]{subsection.3.60.4}{C05 Roots of One or More Transcendental Equations}{section.3.60}
\BOOKMARK [2][-]{subsection.3.60.5}{C06 Summation of Series}{section.3.60}
\BOOKMARK [2][-]{subsection.3.60.6}{D01 Quadrature}{section.3.60}
\BOOKMARK [2][-]{subsection.3.60.7}{D02 Ordinary Differential Equations}{section.3.60}
\BOOKMARK [2][-]{subsection.3.60.8}{D03 Partial Differential Equations}{section.3.60}
\BOOKMARK [2][-]{subsection.3.60.9}{E01 Interpolation}{section.3.60}
\BOOKMARK [2][-]{subsection.3.60.10}{E02 Curve and Surface Fitting}{section.3.60}
\BOOKMARK [2][-]{subsection.3.60.11}{E04 Minimizing or Maximizing a Function}{section.3.60}
\BOOKMARK [2][-]{subsection.3.60.12}{F01 Matrix Operations - Including Inversion}{section.3.60}
\BOOKMARK [2][-]{subsection.3.60.13}{F02 Eigenvalues and Eigenvectors}{section.3.60}
\BOOKMARK [2][-]{subsection.3.60.14}{F04 Simultaneous Linear Equations}{section.3.60}
\BOOKMARK [2][-]{subsection.3.60.15}{F07 Linear Equations \(LAPACK\)}{section.3.60}
\BOOKMARK [2][-]{subsection.3.60.16}{S -- Approximations of Special Functions}{section.3.60}
\BOOKMARK [1][-]{section.3.61}{list.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.61.1}{List}{section.3.61}
\BOOKMARK [2][-]{subsection.3.61.2}{Creating Lists}{section.3.61}
\BOOKMARK [2][-]{subsection.3.61.3}{Accessing List Elements}{section.3.61}
\BOOKMARK [2][-]{subsection.3.61.4}{Changing List Elements}{section.3.61}
\BOOKMARK [2][-]{subsection.3.61.5}{Other Functions}{section.3.61}
\BOOKMARK [2][-]{subsection.3.61.6}{Dot, Dot}{section.3.61}
\BOOKMARK [1][-]{section.3.62}{lodo.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.62.1}{LinearOrdinaryDifferentialOperator}{section.3.62}
\BOOKMARK [2][-]{subsection.3.62.2}{Differential Operators with Series Coefficients}{section.3.62}
\BOOKMARK [1][-]{section.3.63}{lodo1.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.63.1}{LinearOrdinaryDifferentialOperator1}{section.3.63}
\BOOKMARK [2][-]{subsection.3.63.2}{Differential Operators with Rational Function Coefficients}{section.3.63}
\BOOKMARK [1][-]{section.3.64}{lodo2.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.64.1}{LinearOrdinaryDifferentialOperator2}{section.3.64}
\BOOKMARK [2][-]{subsection.3.64.2}{Differential Operators with Constant Coefficients}{section.3.64}
\BOOKMARK [2][-]{subsection.3.64.3}{Differential Operators with Matrix Coefficients Operating on Vectors}{section.3.64}
\BOOKMARK [1][-]{section.3.65}{lpoly.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.65.1}{LiePolynomial}{section.3.65}
\BOOKMARK [1][-]{section.3.66}{magma.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.66.1}{Magma}{section.3.66}
\BOOKMARK [1][-]{section.3.67}{man0.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.67.1}{Reference Search}{section.3.67}
\BOOKMARK [2][-]{subsection.3.67.2}{Lisp Functions}{section.3.67}
\BOOKMARK [2][-]{subsection.3.67.3}{Axiom Browser}{section.3.67}
\BOOKMARK [2][-]{subsection.3.67.4}{The Hyperdoc Browse Facility}{section.3.67}
\BOOKMARK [1][-]{section.3.68}{mapping.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.68.1}{Domain Mapping\(T,S,...\)}{section.3.68}
\BOOKMARK [2][-]{subsection.3.68.2}{Domain Constructor Mapping}{section.3.68}
\BOOKMARK [1][-]{section.3.69}{mappkg1.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.69.1}{MappingPackage1}{section.3.69}
\BOOKMARK [1][-]{section.3.70}{mset.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.70.1}{MultiSet}{section.3.70}
\BOOKMARK [1][-]{section.3.71}{matrix.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.71.1}{Matrix}{section.3.71}
\BOOKMARK [2][-]{subsection.3.71.2}{Creating Matrices}{section.3.71}
\BOOKMARK [2][-]{subsection.3.71.3}{Operations on Matrices}{section.3.71}
\BOOKMARK [1][-]{section.3.72}{mkfunc.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.72.1}{MakeFunction}{section.3.72}
\BOOKMARK [1][-]{section.3.73}{mpoly.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.73.1}{MultivariatePolynomial}{section.3.73}
\BOOKMARK [1][-]{section.3.74}{newuser.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.74.1}{No More Help :-\(}{section.3.74}
\BOOKMARK [2][-]{subsection.3.74.2}{You Tried It!}{section.3.74}
\BOOKMARK [1][-]{section.3.75}{none.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.75.1}{None}{section.3.75}
\BOOKMARK [1][-]{section.3.76}{numbers.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.76.1}{Axiom Number Types}{section.3.76}
\BOOKMARK [2][-]{subsection.3.76.2}{Fraction}{section.3.76}
\BOOKMARK [2][-]{subsection.3.76.3}{Rational Number}{section.3.76}
\BOOKMARK [2][-]{subsection.3.76.4}{Integers}{section.3.76}
\BOOKMARK [2][-]{subsection.3.76.5}{Integer Examples}{section.3.76}
\BOOKMARK [2][-]{subsection.3.76.6}{Integer Example Proof}{section.3.76}
\BOOKMARK [2][-]{subsection.3.76.7}{Integer Problems}{section.3.76}
\BOOKMARK [2][-]{subsection.3.76.8}{Integer Problem Proof}{section.3.76}
\BOOKMARK [2][-]{subsection.3.76.9}{Solution to Problem \0431}{section.3.76}
\BOOKMARK [2][-]{subsection.3.76.10}{Solution to Problem \0432}{section.3.76}
\BOOKMARK [1][-]{section.3.77}{oct.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.77.1}{Octonion}{section.3.77}
\BOOKMARK [1][-]{section.3.78}{odpol.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.78.1}{OrderlyDifferentialPolynomial}{section.3.78}
\BOOKMARK [1][-]{section.3.79}{op.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.79.1}{Operator}{section.3.79}
\BOOKMARK [1][-]{section.3.80}{ovar.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.80.1}{OrderedVariableList}{section.3.80}
\BOOKMARK [1][-]{section.3.81}{perman.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.81.1}{Permanent}{section.3.81}
\BOOKMARK [1][-]{section.3.82}{pfr.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.82.1}{PartialFraction}{section.3.82}
\BOOKMARK [1][-]{section.3.83}{poly.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.83.1}{Polynomials}{section.3.83}
\BOOKMARK [2][-]{subsection.3.83.2}{The Specific Polynomial Types}{section.3.83}
\BOOKMARK [2][-]{subsection.3.83.3}{Basic Operations On Polynomials}{section.3.83}
\BOOKMARK [2][-]{subsection.3.83.4}{Polynomial Evaluation and Substitution}{section.3.83}
\BOOKMARK [2][-]{subsection.3.83.5}{Greatest Common Divisors, Resultants, and Discriminants}{section.3.83}
\BOOKMARK [2][-]{subsection.3.83.6}{Roots of Polynomials}{section.3.83}
\BOOKMARK [1][-]{section.3.84}{poly1.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.84.1}{Polynomial}{section.3.84}
\BOOKMARK [1][-]{section.3.85}{quat.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.85.1}{Quaternion}{section.3.85}
\BOOKMARK [1][-]{section.3.86}{radix.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.86.1}{RadixExpansion}{section.3.86}
\BOOKMARK [1][-]{section.3.87}{reclos.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.87.1}{RealClosure}{section.3.87}
\BOOKMARK [1][-]{section.3.88}{sregset.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.88.1}{SquareFreeRegularTriangularSet}{section.3.88}
\BOOKMARK [1][-]{section.3.89}{stbl.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.89.1}{SparseTable}{section.3.89}
\BOOKMARK [1][-]{section.3.90}{stream.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.90.1}{Stream}{section.3.90}
\BOOKMARK [1][-]{section.3.91}{string.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.91.1}{String}{section.3.91}
\BOOKMARK [1][-]{section.3.92}{strtbl.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.92.1}{StringTable}{section.3.92}
\BOOKMARK [1][-]{section.3.93}{symbol.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.93.1}{Symbol}{section.3.93}
\BOOKMARK [1][-]{section.3.94}{table.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.94.1}{Table}{section.3.94}
\BOOKMARK [1][-]{section.3.95}{textfile.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.95.1}{TextFile}{section.3.95}
\BOOKMARK [1][-]{section.3.96}{topics.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.96.1}{Axiom Topics}{section.3.96}
\BOOKMARK [2][-]{subsection.3.96.2}{Solving Equations}{section.3.96}
\BOOKMARK [2][-]{subsection.3.96.3}{Linear Algebra}{section.3.96}
\BOOKMARK [2][-]{subsection.3.96.4}{Calculus}{section.3.96}
\BOOKMARK [1][-]{section.3.97}{type.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.97.1}{Category Type}{section.3.97}
\BOOKMARK [1][-]{section.3.98}{union.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.98.1}{Domain Union\(a:A,...,b:B\)}{section.3.98}
\BOOKMARK [2][-]{subsection.3.98.2}{Domain Constructor Union}{section.3.98}
\BOOKMARK [2][-]{subsection.3.98.3}{Domain Union\(A,...,B\)}{section.3.98}
\BOOKMARK [2][-]{subsection.3.98.4}{Domain Constructor Union}{section.3.98}
\BOOKMARK [1][-]{section.3.99}{uniseg.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.99.1}{UniversalSegment}{section.3.99}
\BOOKMARK [1][-]{section.3.100}{up.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.100.1}{UnivariatePolynomial}{section.3.100}
\BOOKMARK [1][-]{section.3.101}{oreup.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.101.1}{UnivariateSkewPolynomial}{section.3.101}
\BOOKMARK [1][-]{section.3.102}{vector.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.102.1}{Vector}{section.3.102}
\BOOKMARK [1][-]{section.3.103}{void.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.103.1}{Void}{section.3.103}
\BOOKMARK [1][-]{section.3.104}{wutset.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.104.1}{WuWenTsunTriangularSet}{section.3.104}
\BOOKMARK [1][-]{section.3.105}{xmpexp.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.105.1}{Some Examples of Domains and Packages}{section.3.105}
\BOOKMARK [1][-]{section.3.106}{xpbwpoly.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.106.1}{XPBWPolynomial}{section.3.106}
\BOOKMARK [1][-]{section.3.107}{xpoly.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.107.1}{XPolynomial}{section.3.107}
\BOOKMARK [1][-]{section.3.108}{xpr.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.108.1}{XPolynomialRing}{section.3.108}
\BOOKMARK [1][-]{section.3.109}{zlindep.ht}{chapter.3}
\BOOKMARK [2][-]{subsection.3.109.1}{IntegerLinearDependence}{section.3.109}
\BOOKMARK [0][-]{chapter.4}{Users Guide Pages \(ug.ht\)}{}
\BOOKMARK [1][-]{subsection.4.0.2}{Users Guide}{chapter.4}
\BOOKMARK [0][-]{chapter.5}{Users Guide Chapter 0 \(ug00.ht\)}{}
\BOOKMARK [1][-]{subsection.5.0.3}{What's New for May 2008}{chapter.5}
\BOOKMARK [2][-]{subsection.5.0.4}{New polynomial domains and algorithms}{subsection.5.0.3}
\BOOKMARK [2][-]{subsection.5.0.5}{Enhancements to HyperDoc and Graphics}{subsection.5.0.3}
\BOOKMARK [2][-]{subsection.5.0.6}{Enhancements to NAGLink}{subsection.5.0.3}
\BOOKMARK [2][-]{subsection.5.0.7}{Enhancements to the Lisp system}{subsection.5.0.3}
\BOOKMARK [0][-]{chapter.6}{Users Guide Chapter 1 \(ug01.ht\)}{}
\BOOKMARK [1][-]{subsection.6.0.8}{An Overview of Axiom}{chapter.6}
\BOOKMARK [2][-]{subsection.6.0.9}{Starting Up and Winding Down}{subsection.6.0.8}
\BOOKMARK [2][-]{subsection.6.0.10}{Clef}{subsection.6.0.8}
\BOOKMARK [2][-]{subsection.6.0.11}{Typographic Conventions}{subsection.6.0.8}
\BOOKMARK [2][-]{subsection.6.0.12}{The Axiom Language}{subsection.6.0.8}
\BOOKMARK [2][-]{subsection.6.0.13}{Arithmetic Expressions}{subsection.6.0.8}
\BOOKMARK [2][-]{subsection.6.0.14}{Previous Results}{subsection.6.0.8}
\BOOKMARK [2][-]{subsection.6.0.15}{Some Types}{subsection.6.0.8}
\BOOKMARK [2][-]{subsection.6.0.16}{Symbols, Variables, Assignments, and Declarations}{subsection.6.0.8}
\BOOKMARK [2][-]{subsection.6.0.17}{Conversion}{subsection.6.0.8}
\BOOKMARK [2][-]{subsection.6.0.18}{Calling Functions}{subsection.6.0.8}
\BOOKMARK [2][-]{subsection.6.0.19}{Some Predefined Macros}{subsection.6.0.8}
\BOOKMARK [2][-]{subsection.6.0.20}{Long Lines}{subsection.6.0.8}
\BOOKMARK [2][-]{subsection.6.0.21}{Comments}{subsection.6.0.8}
\BOOKMARK [2][-]{subsection.6.0.22}{Graphics}{subsection.6.0.8}
\BOOKMARK [2][-]{subsection.6.0.23}{Numbers}{subsection.6.0.8}
\BOOKMARK [2][-]{subsection.6.0.24}{Data Structures}{subsection.6.0.8}
\BOOKMARK [2][-]{subsection.6.0.25}{Expanding to Higher Dimensions}{subsection.6.0.8}
\BOOKMARK [2][-]{subsection.6.0.26}{Writing Your Own Functions}{subsection.6.0.8}
\BOOKMARK [2][-]{subsection.6.0.27}{Solution of Equations}{subsection.6.0.8}
\BOOKMARK [2][-]{subsection.6.0.28}{Records}{subsection.6.0.8}
\BOOKMARK [2][-]{subsection.6.0.29}{Subdomains Again}{subsection.6.0.8}
\BOOKMARK [2][-]{subsection.6.0.30}{Package Calling and Target Types}{subsection.6.0.8}
\BOOKMARK [2][-]{subsection.6.0.31}{Resolving Types}{subsection.6.0.8}
\BOOKMARK [2][-]{subsection.6.0.32}{Exposing Domains and Packages}{subsection.6.0.8}
\BOOKMARK [2][-]{subsection.6.0.33}{Commands for Snooping}{subsection.6.0.8}
\BOOKMARK [0][-]{chapter.7}{Users Guide Chapter 3 \(ug03.ht\)}{}
\BOOKMARK [1][-]{subsection.7.0.34}{Using Hyperdoc}{chapter.7}
\BOOKMARK [2][-]{subsection.7.0.35}{Headings}{subsection.7.0.34}
\BOOKMARK [2][-]{subsection.7.0.36}{Key Definitions}{subsection.7.0.34}
\BOOKMARK [2][-]{subsection.7.0.37}{Scroll Bars}{subsection.7.0.34}
\BOOKMARK [2][-]{subsection.7.0.38}{Input Areas}{subsection.7.0.34}
\BOOKMARK [2][-]{subsection.7.0.39}{Radio Buttons and Toggles}{subsection.7.0.34}
\BOOKMARK [2][-]{subsection.7.0.40}{Search Strings}{subsection.7.0.34}
\BOOKMARK [2][-]{subsection.7.0.41}{Logical Searches}{subsection.7.0.34}
\BOOKMARK [2][-]{subsection.7.0.42}{Example Pages}{subsection.7.0.34}
\BOOKMARK [2][-]{subsection.7.0.43}{X Window Resources for Hyperdoc}{subsection.7.0.34}
\BOOKMARK [0][-]{chapter.8}{Users Guide Chapter 4 \(ug04.ht\)}{}
\BOOKMARK [1][-]{subsection.8.0.44}{Input Files and Output Styles}{chapter.8}
\BOOKMARK [2][-]{subsection.8.0.45}{Input Files}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.46}{The .axiom.input File}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.47}{Common Features of Using Output Formats}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.48}{Monospace 2D Mathematical Format}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.49}{HTML Format}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.50}{Immediate and Delayed Assignments}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.51}{Blocks}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.52}{if-then-else}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.53}{Loops}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.54}{Compiling vs. Interpreting Loops}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.55}{return in Loops}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.56}{break in Loops}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.57}{break vs. => in Loop Bodies}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.58}{More Examples of break}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.59}{iterate in Loops}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.60}{while Loops}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.61}{for Loops}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.62}{for i in n..m repeat}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.63}{for i in n..m by s repeat}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.64}{for i in n.. repeat}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.65}{for x in l repeat}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.66}{``Such that'' Predicates}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.67}{Parallel Iteration}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.68}{Creating Lists and Streams with Iterators}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.69}{Addendum: Appending a Graph to a Viewport Window Containing a Graph}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.70}{Three-Dimensional Graphics}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.71}{Plotting Three-Dimensional Functions of Two Variables}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.72}{Plotting Three-Dimensional Parametric Space Curves}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.73}{Plotting 3D Parametric Surfaces}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.74}{Three-Dimensional Options}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.75}{The makeObject Command}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.76}{Building 3D Objects From Primitives}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.77}{Coordinate System Transformations}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.78}{Three-Dimensional Clipping}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.79}{Three-Dimensional Control-Panel}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.80}{Operations for Three-Dimensional Graphics}{subsection.8.0.44}
\BOOKMARK [2][-]{subsection.8.0.81}{Customization using .Xdefaults}{subsection.8.0.44}
\BOOKMARK [0][-]{chapter.9}{Users Guide Chapter 8 \(ug08.ht\)}{}
\BOOKMARK [1][-]{subsection.9.0.82}{Advanced Problem Solving}{chapter.9}
\BOOKMARK [2][-]{subsection.9.0.83}{Numeric Functions}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.84}{Polynomial Factorization}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.85}{Integer and Rational Number Coefficients}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.86}{Finite Field Coefficients}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.87}{Simple Algebraic Extension Field Coefficients}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.88}{Factoring Rational Functions}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.89}{Manipulating Symbolic Roots of a Polynomial}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.90}{Using a Single Root of a Polynomial}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.91}{Using All Roots of a Polynomial}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.92}{Computation of Eigenvalues and Eigenvectors}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.93}{Solution of Linear and Polynomial Equations}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.94}{Solution of Systems of Linear Equations}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.95}{Solution of a Single Polynomial Equation}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.96}{Solution of Systems of Polynomial Equations}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.97}{Limits}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.98}{Laplace Transforms}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.99}{Integration}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.100}{Working with Power Series}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.101}{Creation of Power Series}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.102}{Coefficients of Power Series}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.103}{Power Series Arithmetic}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.104}{Functions on Power Series}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.105}{Converting to Power Series}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.106}{Power Series from Formulas}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.107}{Substituting Numerical Values in Power Series}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.108}{Example: Bernoulli Polynomials and Sums of Powers}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.109}{Solution of Differential Equations}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.110}{Closed-Form Solutions of Linear Differential Equations}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.111}{Closed-Form Solutions of Non-Linear DEs}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.112}{Power Series Solutions of Differential Equations}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.113}{Finite Fields}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.114}{Modular Arithmetic and Prime Fields}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.115}{Extensions of Finite Fields}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.116}{Irreducible Mod Polynomial Representations}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.117}{Cyclic Group Representations}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.118}{Normal Basis Representations}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.119}{Conversion Operations for Finite Fields}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.120}{Utility Operations for Finite Fields}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.121}{Primary Decomposition of Ideals}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.122}{Computation of Galois Groups}{subsection.9.0.82}
\BOOKMARK [2][-]{subsection.9.0.123}{Non-Associative Algebras and Genetic Laws}{subsection.9.0.82}
\BOOKMARK [0][-]{chapter.10}{Users Guide Chapter 10 \(ug10.ht\)}{}
\BOOKMARK [1][-]{subsection.10.0.124}{Interactive Programming}{chapter.10}
\BOOKMARK [2][-]{subsection.10.0.125}{Drawing Ribbons Interactively}{subsection.10.0.124}
\BOOKMARK [2][-]{subsection.10.0.126}{A Ribbon Program}{subsection.10.0.124}
\BOOKMARK [2][-]{subsection.10.0.127}{Coloring and Positioning Ribbons}{subsection.10.0.124}
\BOOKMARK [2][-]{subsection.10.0.128}{Points, Lines, and Curves}{subsection.10.0.124}
\BOOKMARK [2][-]{subsection.10.0.129}{Browse}{subsection.10.0.124}
\BOOKMARK [2][-]{subsection.10.0.130}{Representation}{subsection.10.0.124}
\BOOKMARK [2][-]{subsection.10.0.131}{Multiple Representations}{subsection.10.0.124}
\BOOKMARK [2][-]{subsection.10.0.132}{Add Domain}{subsection.10.0.124}
\BOOKMARK [2][-]{subsection.10.0.133}{Defaults}{subsection.10.0.124}
\BOOKMARK [2][-]{subsection.10.0.134}{Origins}{subsection.10.0.124}
\BOOKMARK [2][-]{subsection.10.0.135}{Short Forms}{subsection.10.0.124}
\BOOKMARK [2][-]{subsection.10.0.136}{Example 1: Clifford Algebra}{subsection.10.0.124}
\BOOKMARK [2][-]{subsection.10.0.137}{Example 2: Building A Query Facility}{subsection.10.0.124}
\BOOKMARK [2][-]{subsection.10.0.138}{A Little Query Language}{subsection.10.0.124}
\BOOKMARK [2][-]{subsection.10.0.139}{The Database Constructor}{subsection.10.0.124}
\BOOKMARK [2][-]{subsection.10.0.140}{Query Equations}{subsection.10.0.124}
\BOOKMARK [2][-]{subsection.10.0.141}{DataLists}{subsection.10.0.124}
\BOOKMARK [2][-]{subsection.10.0.142}{Index Cards}{subsection.10.0.124}
\BOOKMARK [2][-]{subsection.10.0.143}{Creating a Database}{subsection.10.0.124}
\BOOKMARK [2][-]{subsection.10.0.144}{Putting It All Together}{subsection.10.0.124}
\BOOKMARK [2][-]{subsection.10.0.145}{Example Queries}{subsection.10.0.124}
\BOOKMARK [0][-]{chapter.11}{Users Guide Chapter 14 \(ug14.ht\)}{}
\BOOKMARK [1][-]{subsection.11.0.146}{Browse}{chapter.11}
\BOOKMARK [2][-]{subsection.11.0.147}{The Front Page: Searching the Library}{subsection.11.0.146}
\BOOKMARK [2][-]{subsection.11.0.148}{The Constructor Page}{subsection.11.0.146}
\BOOKMARK [2][-]{subsection.11.0.149}{Constructor Page Buttons}{subsection.11.0.146}
\BOOKMARK [2][-]{subsection.11.0.150}{Cross Reference}{subsection.11.0.146}
\BOOKMARK [2][-]{subsection.11.0.151}{Views Of Constructors}{subsection.11.0.146}
\BOOKMARK [2][-]{subsection.11.0.152}{Giving Parameters to Constructors}{subsection.11.0.146}
\BOOKMARK [2][-]{subsection.11.0.153}{Miscellaneous Features of Browse}{subsection.11.0.146}
\BOOKMARK [2][-]{subsection.11.0.154}{The Description Page for Operations}{subsection.11.0.146}
\BOOKMARK [2][-]{subsection.11.0.155}{Views of Operations}{subsection.11.0.146}
\BOOKMARK [2][-]{subsection.11.0.156}{Capitalization Convention}{subsection.11.0.146}
\BOOKMARK [0][-]{chapter.12}{Users Guide Chapter 15 \(ug15.ht\)}{}
\BOOKMARK [1][-]{subsection.12.0.157}{What's New in Axiom Version 2.0}{chapter.12}
\BOOKMARK [2][-]{subsection.12.0.158}{Important Things to Read First}{subsection.12.0.157}
\BOOKMARK [2][-]{subsection.12.0.159}{The NAG Library Link}{subsection.12.0.157}
\BOOKMARK [2][-]{subsection.12.0.160}{Interpreting NAG Documentation}{subsection.12.0.157}
\BOOKMARK [2][-]{subsection.12.0.161}{Using the Link}{subsection.12.0.157}
\BOOKMARK [2][-]{subsection.12.0.162}{Providing values for Argument Subprograms}{subsection.12.0.157}
\BOOKMARK [2][-]{subsection.12.0.163}{General Fortran-generation utilities in Axiom}{subsection.12.0.157}
\BOOKMARK [2][-]{subsection.12.0.164}{Some technical information}{subsection.12.0.157}
\BOOKMARK [2][-]{subsection.12.0.165}{Interactive Front-end and Language}{subsection.12.0.157}
\BOOKMARK [2][-]{subsection.12.0.166}{Library}{subsection.12.0.157}
\BOOKMARK [2][-]{subsection.12.0.167}{HyperDoc}{subsection.12.0.157}
\BOOKMARK [2][-]{subsection.12.0.168}{Documentation}{subsection.12.0.157}
\BOOKMARK [0][-]{chapter.13}{Users Guide Chapter 16 \(ug16.ht\)}{}
\BOOKMARK [1][-]{subsection.13.0.169}{Axiom System Commands}{chapter.13}
\BOOKMARK [2][-]{subsection.13.0.170}{Introduction}{subsection.13.0.169}
\BOOKMARK [2][-]{subsection.13.0.171}{\)abbreviation}{subsection.13.0.169}
\BOOKMARK [2][-]{subsection.13.0.172}{\)boot}{subsection.13.0.169}
\BOOKMARK [2][-]{subsection.13.0.173}{\)cd}{subsection.13.0.169}
\BOOKMARK [2][-]{subsection.13.0.174}{\)close}{subsection.13.0.169}
\BOOKMARK [2][-]{subsection.13.0.175}{\)clear}{subsection.13.0.169}
\BOOKMARK [2][-]{subsection.13.0.176}{\)compile}{subsection.13.0.169}
\BOOKMARK [2][-]{subsection.13.0.177}{\)display}{subsection.13.0.169}
\BOOKMARK [2][-]{subsection.13.0.178}{\)edit}{subsection.13.0.169}
\BOOKMARK [2][-]{subsection.13.0.179}{\)fin}{subsection.13.0.169}
\BOOKMARK [2][-]{subsection.13.0.180}{\)frame}{subsection.13.0.169}
\BOOKMARK [2][-]{subsection.13.0.181}{\)help}{subsection.13.0.169}
\BOOKMARK [2][-]{subsection.13.0.182}{\)history}{subsection.13.0.169}
\BOOKMARK [2][-]{subsection.13.0.183}{\)library}{subsection.13.0.169}
\BOOKMARK [2][-]{subsection.13.0.184}{\)lisp}{subsection.13.0.169}
\BOOKMARK [2][-]{subsection.13.0.185}{\)load}{subsection.13.0.169}
\BOOKMARK [2][-]{subsection.13.0.186}{\)ltrace}{subsection.13.0.169}
\BOOKMARK [2][-]{subsection.13.0.187}{\)pquit}{subsection.13.0.169}
\BOOKMARK [2][-]{subsection.13.0.188}{\)quit}{subsection.13.0.169}
\BOOKMARK [2][-]{subsection.13.0.189}{\)read}{subsection.13.0.169}
\BOOKMARK [2][-]{subsection.13.0.190}{\)set}{subsection.13.0.169}
\BOOKMARK [2][-]{subsection.13.0.191}{\)show}{subsection.13.0.169}
\BOOKMARK [2][-]{subsection.13.0.192}{\)spool}{subsection.13.0.169}
\BOOKMARK [2][-]{subsection.13.0.193}{\)synonym}{subsection.13.0.169}
\BOOKMARK [2][-]{subsection.13.0.194}{\)system}{subsection.13.0.169}
\BOOKMARK [2][-]{subsection.13.0.195}{\)trace}{subsection.13.0.169}
\BOOKMARK [2][-]{subsection.13.0.196}{\)undo}{subsection.13.0.169}
\BOOKMARK [2][-]{subsection.13.0.197}{\)what}{subsection.13.0.169}
\BOOKMARK [0][-]{chapter.14}{Users Guide Chapter 21 \(ug21.ht\)}{}
\BOOKMARK [1][-]{subsection.14.0.198}{Programs for Axiom Images}{chapter.14}
\BOOKMARK [2][-]{subsection.14.0.199}{images1.input}{subsection.14.0.198}
\BOOKMARK [2][-]{subsection.14.0.200}{images2.input}{subsection.14.0.198}
\BOOKMARK [2][-]{subsection.14.0.201}{images3.input}{subsection.14.0.198}
\BOOKMARK [2][-]{subsection.14.0.202}{images5.input}{subsection.14.0.198}
\BOOKMARK [2][-]{subsection.14.0.203}{images6.input}{subsection.14.0.198}
\BOOKMARK [2][-]{subsection.14.0.204}{images7.input}{subsection.14.0.198}
\BOOKMARK [2][-]{subsection.14.0.205}{images8.input}{subsection.14.0.198}
\BOOKMARK [2][-]{subsection.14.0.206}{conformal.input}{subsection.14.0.198}
\BOOKMARK [2][-]{subsection.14.0.207}{tknot.input}{subsection.14.0.198}
\BOOKMARK [2][-]{subsection.14.0.208}{ntube.input}{subsection.14.0.198}
\BOOKMARK [2][-]{subsection.14.0.209}{dhtri.input}{subsection.14.0.198}
\BOOKMARK [2][-]{subsection.14.0.210}{tetra.input}{subsection.14.0.198}
\BOOKMARK [2][-]{subsection.14.0.211}{antoine.input}{subsection.14.0.198}
\BOOKMARK [2][-]{subsection.14.0.212}{scherk.input}{subsection.14.0.198}
\BOOKMARK [0][-]{chapter.15}{Hypertex Language Pages}{}
\BOOKMARK [1][-]{subsection.15.0.213}{Creating Hyperdoc Pages}{chapter.15}
\BOOKMARK [1][-]{section.15.1}{htxadvpage1.ht}{chapter.15}
\BOOKMARK [2][-]{subsection.15.1.1}{Input Areas}{section.15.1}
\BOOKMARK [2][-]{subsection.15.1.2}{HTXAdvPage1xPatch1 patch}{section.15.1}
\BOOKMARK [2][-]{subsection.15.1.3}{HTXAdvPage1xPatch1A patch}{section.15.1}
\BOOKMARK [2][-]{subsection.15.1.4}{HTXAdvPage1xPatch2 patch}{section.15.1}
\BOOKMARK [2][-]{subsection.15.1.5}{HTXAdvPage1xPatch2A patch}{section.15.1}
\BOOKMARK [1][-]{section.15.2}{htxadvpage2.ht}{chapter.15}
\BOOKMARK [2][-]{subsection.15.2.1}{Radio buttons}{section.15.2}
\BOOKMARK [1][-]{section.15.3}{htxadvpage3.ht}{chapter.15}
\BOOKMARK [2][-]{subsection.15.3.1}{Macros}{section.15.3}
\BOOKMARK [1][-]{section.15.4}{htxadvpage4.ht}{chapter.15}
\BOOKMARK [2][-]{subsection.15.4.1}{Patch and Paste}{section.15.4}
\BOOKMARK [2][-]{subsection.15.4.2}{patch1 patch}{section.15.4}
\BOOKMARK [2][-]{subsection.15.4.3}{Patch1 patch}{section.15.4}
\BOOKMARK [2][-]{subsection.15.4.4}{Patch2 patch}{section.15.4}
\BOOKMARK [1][-]{section.15.5}{htxadvpage5.ht}{chapter.15}
\BOOKMARK [2][-]{subsection.15.5.1}{Axiom paste-ins}{section.15.5}
\BOOKMARK [1][-]{section.15.6}{htxadvpage6.ht}{chapter.15}
\BOOKMARK [2][-]{subsection.15.6.1}{Miscellaneous}{section.15.6}
\BOOKMARK [2][-]{subsection.15.6.2}{HTXAdvPage6xPatch1 patch}{section.15.6}
\BOOKMARK [2][-]{subsection.15.6.3}{HTXAdvPage6xPatch1A patch}{section.15.6}
\BOOKMARK [2][-]{subsection.15.6.4}{HTXAdvPage6xPatch2 patch}{section.15.6}
\BOOKMARK [2][-]{subsection.15.6.5}{HTXAdvPage6xPatch2A patch}{section.15.6}
\BOOKMARK [2][-]{subsection.15.6.6}{HTXAdvPage6xPatch3 patch}{section.15.6}
\BOOKMARK [2][-]{subsection.15.6.7}{HTXAdvPage6xPatch3A patch}{section.15.6}
\BOOKMARK [1][-]{section.15.7}{htxadvtoppage.ht}{chapter.15}
\BOOKMARK [2][-]{subsection.15.7.1}{Advanced features in Hyperdoc}{section.15.7}
\BOOKMARK [1][-]{section.15.8}{htxformatpage1.ht}{chapter.15}
\BOOKMARK [2][-]{subsection.15.8.1}{Using the special characters}{section.15.8}
\BOOKMARK [2][-]{subsection.15.8.2}{HTXFormatPage1xPatch1 patch}{section.15.8}
\BOOKMARK [2][-]{subsection.15.8.3}{HTXFormatPage1xPatch2 patch}{section.15.8}
\BOOKMARK [1][-]{section.15.9}{htxformatpage2.ht}{chapter.15}
\BOOKMARK [2][-]{subsection.15.9.1}{Formatting without commands}{section.15.9}
\BOOKMARK [2][-]{subsection.15.9.2}{HTXFormatPage2xPatch1 patch}{section.15.9}
\BOOKMARK [2][-]{subsection.15.9.3}{HTXFormatPage2xPatch2 patch}{section.15.9}
\BOOKMARK [2][-]{subsection.15.9.4}{HTXFormatPage2xPatch2A patch}{section.15.9}
\BOOKMARK [2][-]{subsection.15.9.5}{HTXFormatPage2xPatch3 patch}{section.15.9}
\BOOKMARK [2][-]{subsection.15.9.6}{HTXFormatPage2xPatch3A patch}{section.15.9}
\BOOKMARK [2][-]{subsection.15.9.7}{HTXFormatPage2xPatch4 patch}{section.15.9}
\BOOKMARK [2][-]{subsection.15.9.8}{HTXFormatPage2xPatch4A patch}{section.15.9}
\BOOKMARK [1][-]{section.15.10}{htxformatpage3.ht}{chapter.15}
\BOOKMARK [2][-]{subsection.15.10.1}{Using different fonts}{section.15.10}
\BOOKMARK [2][-]{subsection.15.10.2}{HTXFormatPage3xPatch1 patch}{section.15.10}
\BOOKMARK [2][-]{subsection.15.10.3}{HTXFormatPage3xPatch2 patch}{section.15.10}
\BOOKMARK [2][-]{subsection.15.10.4}{HTXFormatPage3xPatch3 patch}{section.15.10}
\BOOKMARK [2][-]{subsection.15.10.5}{HTXFormatPage3xPatch4 patch}{section.15.10}
\BOOKMARK [1][-]{section.15.11}{htxformatpage4.ht}{chapter.15}
\BOOKMARK [2][-]{subsection.15.11.1}{Indentation}{section.15.11}
\BOOKMARK [2][-]{subsection.15.11.2}{HTXFormatPage4xPatch1 patch}{section.15.11}
\BOOKMARK [2][-]{subsection.15.11.3}{HTXFormatPage4xPatch1A patch}{section.15.11}
\BOOKMARK [2][-]{subsection.15.11.4}{HTXFormatPage4xPatch2 patch}{section.15.11}
\BOOKMARK [2][-]{subsection.15.11.5}{HTXFormatPage4xPatch2A patch}{section.15.11}
\BOOKMARK [2][-]{subsection.15.11.6}{HTXFormatPage4xPatch3 patch}{section.15.11}
\BOOKMARK [2][-]{subsection.15.11.7}{HTXFormatPage4xPatch3A patch}{section.15.11}
\BOOKMARK [2][-]{subsection.15.11.8}{HTXFormatPage4xPatch4 patch}{section.15.11}
\BOOKMARK [2][-]{subsection.15.11.9}{HTXFormatPage4xPatch5 patch}{section.15.11}
\BOOKMARK [2][-]{subsection.15.11.10}{HTXFormatPage4xPatch5A patch}{section.15.11}
\BOOKMARK [1][-]{section.15.12}{htxformatpage5.ht}{chapter.15}
\BOOKMARK [2][-]{subsection.15.12.1}{Creating Lists and Tables}{section.15.12}
\BOOKMARK [2][-]{subsection.15.12.2}{HTXFormatPage5xPatch1 patch}{section.15.12}
\BOOKMARK [2][-]{subsection.15.12.3}{HTXFormatPage5xPatch1A patch}{section.15.12}
\BOOKMARK [2][-]{subsection.15.12.4}{HTXFormatPage5xPatch2 patch}{section.15.12}
\BOOKMARK [2][-]{subsection.15.12.5}{HTXFormatPage5xPatch2A patch}{section.15.12}
\BOOKMARK [2][-]{subsection.15.12.6}{HTXFormatPage5xPatch3 patch}{section.15.12}
\BOOKMARK [2][-]{subsection.15.12.7}{HTXFormatPage5xPatch3A patch}{section.15.12}
\BOOKMARK [1][-]{section.15.13}{htxformatpage6}{chapter.15}
\BOOKMARK [2][-]{subsection.15.13.1}{Boxes and Lines}{section.15.13}
\BOOKMARK [2][-]{subsection.15.13.2}{HTXFormatPage6xPatch1 patch}{section.15.13}
\BOOKMARK [2][-]{subsection.15.13.3}{HTXFormatPage6xPatch2 patch}{section.15.13}
\BOOKMARK [1][-]{section.15.14}{htxformatpage7}{chapter.15}
\BOOKMARK [2][-]{subsection.15.14.1}{Micro-Spacing}{section.15.14}
\BOOKMARK [2][-]{subsection.15.14.2}{HTXFormatPage7xPatch1 patch}{section.15.14}
\BOOKMARK [2][-]{subsection.15.14.3}{HTXFormatPage7xPatch2 patch}{section.15.14}
\BOOKMARK [2][-]{subsection.15.14.4}{HTXFormatPage7xPatch2A patch}{section.15.14}
\BOOKMARK [2][-]{subsection.15.14.5}{HTXFormatPage7xPatch3 patch}{section.15.14}
\BOOKMARK [2][-]{subsection.15.14.6}{HTXFormatPage7xPatch3A patch}{section.15.14}
\BOOKMARK [1][-]{section.15.15}{htxformatpage8}{chapter.15}
\BOOKMARK [2][-]{subsection.15.15.1}{Bitmaps and Images}{section.15.15}
\BOOKMARK [2][-]{subsection.15.15.2}{HTXFormatPage8xPatch1 patch}{section.15.15}
\BOOKMARK [2][-]{subsection.15.15.3}{HTXFormatPage8xPatch2 patch}{section.15.15}
\BOOKMARK [2][-]{subsection.15.15.4}{HTXFormatPage8xPatch2A patch}{section.15.15}
\BOOKMARK [1][-]{section.15.16}{htxformattoppage.ht}{chapter.15}
\BOOKMARK [2][-]{subsection.15.16.1}{Formatting in Hyperdoc}{section.15.16}
\BOOKMARK [1][-]{section.15.17}{htxintropage1.ht}{chapter.15}
\BOOKMARK [2][-]{subsection.15.17.1}{What Hyperdoc does}{section.15.17}
\BOOKMARK [1][-]{section.15.18}{htxintropage2.ht}{chapter.15}
\BOOKMARK [2][-]{subsection.15.18.1}{How Hyperdoc does it}{section.15.18}
\BOOKMARK [1][-]{section.15.19}{htxintropage3.ht}{chapter.15}
\BOOKMARK [2][-]{subsection.15.19.1}{A simple text page}{section.15.19}
\BOOKMARK [1][-]{section.15.20}{htxintrotoppage.ht}{chapter.15}
\BOOKMARK [2][-]{subsection.15.20.1}{First Steps}{section.15.20}
\BOOKMARK [1][-]{section.15.21}{htxlinkpage1.ht}{chapter.15}
\BOOKMARK [2][-]{subsection.15.21.1}{Linking to a named page}{section.15.21}
\BOOKMARK [2][-]{subsection.15.21.2}{HTXLinkPage1xPatch1 patch}{section.15.21}
\BOOKMARK [2][-]{subsection.15.21.3}{HTXLinkPage1xPatch1A patch}{section.15.21}
\BOOKMARK [2][-]{subsection.15.21.4}{Test Help Page}{section.15.21}
\BOOKMARK [1][-]{section.15.22}{htxlinkpage2.ht}{chapter.15}
\BOOKMARK [2][-]{subsection.15.22.1}{Standard Pages}{section.15.22}
\BOOKMARK [2][-]{subsection.15.22.2}{HTXLinkPage2xPatch1 patch}{section.15.22}
\BOOKMARK [2][-]{subsection.15.22.3}{HTXLinkPage2xPatch1A patch}{section.15.22}
\BOOKMARK [1][-]{section.15.23}{htxlinkpage3.ht}{chapter.15}
\BOOKMARK [2][-]{subsection.15.23.1}{Active Axiom commands}{section.15.23}
\BOOKMARK [2][-]{subsection.15.23.2}{HTXLinkPage3xPatch1 patch}{section.15.23}
\BOOKMARK [2][-]{subsection.15.23.3}{HTXLinkPage3xPatch1A patch}{section.15.23}
\BOOKMARK [2][-]{subsection.15.23.4}{HTXLinkPage3xPatch2 patch}{section.15.23}
\BOOKMARK [2][-]{subsection.15.23.5}{HTXLinkPage3xPatch2A patch}{section.15.23}
\BOOKMARK [2][-]{subsection.15.23.6}{HTXLinkPage3xPatch3 patch}{section.15.23}
\BOOKMARK [2][-]{subsection.15.23.7}{HTXLinkPage3xPatch3A patch}{section.15.23}
\BOOKMARK [1][-]{section.15.24}{htxlinkpage4.ht}{chapter.15}
\BOOKMARK [2][-]{subsection.15.24.1}{Linking to Lisp}{section.15.24}
\BOOKMARK [2][-]{subsection.15.24.2}{HTXLinkPage4xPatch1 patch}{section.15.24}
\BOOKMARK [2][-]{subsection.15.24.3}{HTXLinkPage4xPatch1A patch}{section.15.24}
\BOOKMARK [2][-]{subsection.15.24.4}{HTXLinkPage4xPatch2 patch}{section.15.24}
\BOOKMARK [2][-]{subsection.15.24.5}{HTXLinkPage4xPatch2A patch}{section.15.24}
\BOOKMARK [2][-]{subsection.15.24.6}{HTXLinkPage4xPatch3 patch}{section.15.24}
\BOOKMARK [2][-]{subsection.15.24.7}{HTXLinkPage4xPatch3A patch}{section.15.24}
\BOOKMARK [2][-]{subsection.15.24.8}{HTXLinkPage4xPatch4 patch}{section.15.24}
\BOOKMARK [2][-]{subsection.15.24.9}{HTXLinkPage4xPatch4A patch}{section.15.24}
\BOOKMARK [2][-]{subsection.15.24.10}{HTXLinkPage4xPatch5 patch}{section.15.24}
\BOOKMARK [2][-]{subsection.15.24.11}{HTXLinkPage4xPatch5A patch}{section.15.24}
\BOOKMARK [1][-]{section.15.25}{htxlinkpage5.ht}{chapter.15}
\BOOKMARK [2][-]{subsection.15.25.1}{Linking to Unix}{section.15.25}
\BOOKMARK [2][-]{subsection.15.25.2}{HTXLinkPage5xPatch1 patch}{section.15.25}
\BOOKMARK [2][-]{subsection.15.25.3}{HTXLinkPage5xPatch1A patch}{section.15.25}
\BOOKMARK [2][-]{subsection.15.25.4}{HTXLinkPage5xPatch2 patch}{section.15.25}
\BOOKMARK [2][-]{subsection.15.25.5}{HTXLinkPage5xPatch2A patch}{section.15.25}
\BOOKMARK [1][-]{section.15.26}{htxlinkpage6.ht}{chapter.15}
\BOOKMARK [2][-]{subsection.15.26.1}{How to use your pages with Hyperdoc}{section.15.26}
\BOOKMARK [2][-]{subsection.15.26.2}{HTXLinkPage6xPatch1 patch}{section.15.26}
\BOOKMARK [2][-]{subsection.15.26.3}{HTXLinkPage6xPatch1A patch}{section.15.26}
\BOOKMARK [2][-]{subsection.15.26.4}{HTXLinkPage6xPatch2 patch}{section.15.26}
\BOOKMARK [2][-]{subsection.15.26.5}{HTXLinkPage6xPatch2A patch}{section.15.26}
\BOOKMARK [1][-]{section.15.27}{htxlinktoppage.ht}{chapter.15}
\BOOKMARK [2][-]{subsection.15.27.1}{Actions in Hyperdoc}{section.15.27}
\BOOKMARK [1][-]{section.15.28}{htxtoppage.ht}{chapter.15}
\BOOKMARK [2][-]{subsection.15.28.1}{Extending Hyperdoc}{section.15.28}
\BOOKMARK [1][-]{section.15.29}{htxtrypage.ht}{chapter.15}
\BOOKMARK [2][-]{subsection.15.29.1}{Try out Hyperdoc}{section.15.29}
\BOOKMARK [0][-]{chapter.16}{NAG Library Routines}{}
\BOOKMARK [1][-]{section.16.1}{nagaux.ht}{chapter.16}
\BOOKMARK [2][-]{subsection.16.1.1}{NAG On-line Documentation}{section.16.1}
\BOOKMARK [2][-]{subsection.16.1.2}{NAG Documentation: summary}{section.16.1}
\BOOKMARK [2][-]{subsection.16.1.3}{NAG Documentation: introduction}{section.16.1}
\BOOKMARK [2][-]{subsection.16.1.4}{NAG Documentation: keyword in context}{section.16.1}
\BOOKMARK [2][-]{subsection.16.1.5}{NAG Documentation: conversion}{section.16.1}
\BOOKMARK [1][-]{section.16.2}{nagc.ht}{chapter.16}
\BOOKMARK [2][-]{subsection.16.2.1}{ Zeros of Polynomials}{section.16.2}
\BOOKMARK [2][-]{subsection.16.2.2}{ Roots of a complex polynomial equation}{section.16.2}
\BOOKMARK [2][-]{subsection.16.2.3}{ Roots of a real polynomial equation}{section.16.2}
\BOOKMARK [2][-]{subsection.16.2.4}{ Roots of One or More Transcendental Equations}{section.16.2}
\BOOKMARK [2][-]{subsection.16.2.5}{ Zero of a continuous function in a given interval}{section.16.2}
\BOOKMARK [2][-]{subsection.16.2.6}{ Solution of a system of nonlinear equations}{section.16.2}
\BOOKMARK [2][-]{subsection.16.2.7}{ Solution of a system of nonlinear equations}{section.16.2}
\BOOKMARK [2][-]{subsection.16.2.8}{ Checks the gradients of a set of non-linear functions}{section.16.2}
\BOOKMARK [2][-]{subsection.16.2.9}{ Discrete Fourier transform of real or complex data values}{section.16.2}
\BOOKMARK [2][-]{subsection.16.2.10}{ Discrete Fourier transform of n real data values}{section.16.2}
\BOOKMARK [2][-]{subsection.16.2.11}{ Discrete Fourier transform of a Hermitian sequence}{section.16.2}
\BOOKMARK [2][-]{subsection.16.2.12}{ Discrete Fourier transform of n complex data values}{section.16.2}
\BOOKMARK [2][-]{subsection.16.2.13}{ Circular convolution or correlation of two real vectors}{section.16.2}
\BOOKMARK [2][-]{subsection.16.2.14}{ Discrete Fourier transforms of m sequences}{section.16.2}
\BOOKMARK [2][-]{subsection.16.2.15}{ Discrete Fourier transforms of m Hermitian sequences}{section.16.2}
\BOOKMARK [2][-]{subsection.16.2.16}{ Discrete Fourier transforms of m complex sequences}{section.16.2}
\BOOKMARK [2][-]{subsection.16.2.17}{ Discrete Fourier transform of bivariate complex data}{section.16.2}
\BOOKMARK [2][-]{subsection.16.2.18}{ Summation of Series}{section.16.2}
\BOOKMARK [2][-]{subsection.16.2.19}{ Complex conjugate of a sequence of n data values}{section.16.2}
\BOOKMARK [2][-]{subsection.16.2.20}{ Complex conjugates of m Hermitian sequences}{section.16.2}
\BOOKMARK [2][-]{subsection.16.2.21}{ Form real and imaginary parts of m Hermitian sequences}{section.16.2}
\BOOKMARK [1][-]{section.16.3}{nagd.ht}{chapter.16}
\BOOKMARK [2][-]{subsection.16.3.1}{ Quadrature}{section.16.3}
\BOOKMARK [2][-]{subsection.16.3.2}{ Approximation of the integral over a finite interval}{section.16.3}
\BOOKMARK [2][-]{subsection.16.3.3}{ Adaptive integration over a finite integral}{section.16.3}
\BOOKMARK [2][-]{subsection.16.3.4}{ Approximate integration with local singular points}{section.16.3}
\BOOKMARK [2][-]{subsection.16.3.5}{ Approximate integration over a \(semi-\)infinite interval}{section.16.3}
\BOOKMARK [2][-]{subsection.16.3.6}{ Approximate sine or cosine transform over finite interval}{section.16.3}
\BOOKMARK [2][-]{subsection.16.3.7}{ Adaptive integration of weighted function over an interval}{section.16.3}
\BOOKMARK [2][-]{subsection.16.3.8}{ Hilbert transform over finite interval}{section.16.3}
\BOOKMARK [2][-]{subsection.16.3.9}{ Approximate Sine or Cosine over [a,]}{section.16.3}
\BOOKMARK [2][-]{subsection.16.3.10}{ Weights and abscissae for Gaussian quadrature formula}{section.16.3}
\BOOKMARK [2][-]{subsection.16.3.11}{ Multidimensional integrals with finite limits}{section.16.3}
\BOOKMARK [2][-]{subsection.16.3.12}{ Third-order finite-difference integration}{section.16.3}
\BOOKMARK [2][-]{subsection.16.3.13}{ Monte Carlo integration over hyper-rectangular regions}{section.16.3}
\BOOKMARK [2][-]{subsection.16.3.14}{ Ordinary Differential Equations}{section.16.3}
\BOOKMARK [2][-]{subsection.16.3.15}{ First-order ODE over an interval with initial conditions}{section.16.3}
\BOOKMARK [2][-]{subsection.16.3.16}{ First-order ODE with initial conditions and user function}{section.16.3}
\BOOKMARK [2][-]{subsection.16.3.17}{ First-order ODE with variable-order, variable-step}{section.16.3}
\BOOKMARK [2][-]{subsection.16.3.18}{ Stiff First-order ODE with variable order and step}{section.16.3}
\BOOKMARK [2][-]{subsection.16.3.19}{ Two-point boundary-value ODE}{section.16.3}
\BOOKMARK [2][-]{subsection.16.3.20}{ Two-point boundary value ODE with deferred correction}{section.16.3}
\BOOKMARK [2][-]{subsection.16.3.21}{ Eignevalue of regular singular 2nd-order Sturm-Liouville}{section.16.3}
\BOOKMARK [2][-]{subsection.16.3.22}{ Two-point boundary-value ODE equation systems}{section.16.3}
\BOOKMARK [2][-]{subsection.16.3.23}{ Partial differential equations}{section.16.3}
\BOOKMARK [2][-]{subsection.16.3.24}{ Discrete elliptic PDE on rectangular region}{section.16.3}
\BOOKMARK [2][-]{subsection.16.3.25}{ Discrete 2nd-order elliptic PDE on rectangular regions}{section.16.3}
\BOOKMARK [2][-]{subsection.16.3.26}{ Helmholtz equation in 3 dimensions}{section.16.3}
\BOOKMARK [1][-]{section.16.4}{nage.ht}{chapter.16}
\BOOKMARK [2][-]{subsection.16.4.1}{ Interpolation}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.2}{ Cubic spline interpolant}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.3}{ Monoticity-preserving piecewise cubic Hermite interpolant}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.4}{ Piecewise cubic Hermite interpolant}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.5}{ Piecewise cubic Hermite interpolant and 1st deriv}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.6}{ Definite integral of piecewise cubic Hermite interpolant}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.7}{ Bicubic spline interpolated surface}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.8}{ Two-D surface interpolating a set of scattered data points}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.9}{ Evaluate 2D interpolant function from E01SAF}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.10}{ Generate 2D surface interpolating a scattered data points}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.11}{ Evaluate 2D interpolating function from E01SEF}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.12}{ Curve and Surface Fitting}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.13}{ Least-squares polynomial approximations}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.14}{ Evaluate polynomial from Chebyshev-series representation}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.15}{ Constrained weighted least-squares polynomial}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.16}{ Coefficients of polynomial derivative}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.17}{ Find coefficients of indefinite integral of polynomial}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.18}{ Evaluate polynomial in Chebyshev-series representation}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.19}{ Weighted least-squares aprrox to data points}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.20}{ Evaluates a cubic spline from its B-spline representation}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.21}{ Evaluate cubic spline and 3 derivatives from B-spline}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.22}{ Definite integral of cubic spline from B-spline}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.23}{ Cubic spline approximation to an arbitrary set points}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.24}{ Minimal, weighted least-squares bicubic spline fit}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.25}{ Bicubic spline approximation to a set of data values}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.26}{ Bicubic spline approximation to a set of scattered data}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.27}{ Calculates values of a bicubic spline from B-spline}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.28}{ Calculates values of a bicubic spline from B-spline}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.29}{ Calculates l1 solution to over-determined system equations}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.30}{ Sorts two-dimensional data into rectangular panels}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.31}{ Minimizing or Maximizing a Function}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.32}{ Minimizes a nonlinear function of several variable}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.33}{ Supply optional parameters to E04DGF from file}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.34}{ Supply individual optional params to E04DGF}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.35}{ Finding an unconstrained minimum of a sum of squares}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.36}{ Finding an unconstrained minimum of a sum of squares}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.37}{ Finding a minimum of a function}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.38}{ Solving linear programming problems}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.39}{ Solving linear or quadratic problems}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.40}{ Minimize an arbitrary smooth constrainted function}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.41}{ Supply optional parameters to E04UCF from file}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.42}{ Supply individual optional params to E04UCF}{section.16.4}
\BOOKMARK [2][-]{subsection.16.4.43}{ Estimates of elements of the variance-covariance matrix}{section.16.4}
\BOOKMARK [1][-]{section.16.5}{nagf.ht}{chapter.16}
\BOOKMARK [2][-]{subsection.16.5.1}{ Linear Algebra}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.2}{ Matrix Factorization}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.3}{ Factorizes a real sparse matrix}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.4}{ Factorizes a real sparse matrix}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.5}{ Incomplete Cholesky factorization}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.6}{ Cholesky factor of a symmetric positive-definite matrix}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.7}{ QR factorization of the real m by n matrix A}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.8}{ B:=QB or B:=QT B}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.9}{ First ncolq columns of the real m by m orthogonal matrix}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.10}{ QR factorization of the complex m by n matrix A}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.11}{ B:=QB or B:=QH B}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.12}{ First ncolq columns of the complex m by m unitary matrix}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.13}{ Eigenvalues and Eigenvectors}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.14}{ Calculates all the eigenvalues of a real symmetric matrix}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.15}{ Eigenvalues and eigenvectors of a real symmetric matrix}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.16}{ Calculates all the eigenvalues of Ax=Bx}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.17}{ Eigenvalues and eigenvectors of Ax=Bx}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.18}{ Calculates all the eigenvalues of a real unsymmetric matrix}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.19}{ Eigenvalues and eigenvectors of a real unsymmetric matrix}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.20}{ Calculates all the eigenvalues of a complex matrix}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.21}{ Eigenvalues and eigenvectors of a complex matrix}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.22}{ Eigenvalues of a complex Hermitian matrix}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.23}{ Eigenvalues/eigenvectors complex Hermitian matrix}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.24}{ Eigenvalues and eigenvectors of a real symmetric matrix}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.25}{ Eigenvalues of generalized eigenproblem Ax=Bx}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.26}{ Eigenvalues and eigenvectors of real sparse symmetric problem}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.27}{ Singular value decomposition of a general real matrix}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.28}{ Singular value decomposition of a general complex matrix}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.29}{ Simultaneous Linear Equations}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.30}{ Approximate solution of a set of complex linear equations}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.31}{ Approximate solution of a set of real linear equations}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.32}{ Real symmetric positive-definite linear equations}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.33}{ Set of real linear equations with a single right-hand side}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.34}{ Solution of a set of real sparse linear equations}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.35}{ Real symmetric positive-definite tridiagonal linear equations}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.36}{ Solution of a linear least-squares problem, Ax=b}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.37}{ Sparse symmetric positive-definite system linear equations}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.38}{ Solves a system of real sparse symmetric linear equations}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.39}{ Solution of a system of real linear equations}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.40}{ Solves sparse unsymmetric equations}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.41}{ Linear Algebra Support Routines}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.42}{ Linear Equations \(LAPACK\)}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.43}{ Computes the LU factorization of a real m by n matrix}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.44}{ Solves a real system of linear equations}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.45}{ Factorization of a real symmetric positive-definite matrix}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.46}{ Real symmetric positive-definite system of linear equations}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.47}{ Sort vector of double precision numbers}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.48}{ Ranks a vector of double precision numbers}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.49}{ Ranks the rows of a matrix of double precision numbers}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.50}{ Ranks the columns of a matrix of double precision numbers}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.51}{ Rearranges a vector of double precision numbers}{section.16.5}
\BOOKMARK [2][-]{subsection.16.5.52}{ Inverts a permutation}{section.16.5}
\BOOKMARK [1][-]{section.16.6}{nags.ht}{chapter.16}
\BOOKMARK [2][-]{subsection.16.6.1}{ Approximations of Special Functions}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.2}{ Exponential function ez , for complex z}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.3}{ Returns the value of the exponential integral E\(x\)}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.4}{ Returns the value of the cosine integral}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.5}{ Returns the value of the sine integral}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.6}{ Returns the value of the Gamma function}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.7}{ Returns a value for the logarithm of the Gamma function}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.8}{ Incomplete gamma functions P\(a,x\) and Q\(a,x\)}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.9}{ Returns the value of the complementary error function}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.10}{ Returns the value of the error function erfx}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.11}{ Returns the value of the Bessel Function Y0\(x\)}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.12}{ Returns the value of the Bessel Function Y1\(x\)}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.13}{ Returns the value of the Bessel Function J0\(x\)}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.14}{ Returns the value of the Bessel Function J1\(x\)}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.15}{ Returns a value for the Airy function, Ai\(x\)}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.16}{ Returns a value of the Airy function, Bi\(x\)}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.17}{ Value of the derivative of the Airy function Ai\(x\)}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.18}{ Value for the derivative of the Airy function Bi\(x\)}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.19}{ Values for the Bessel functions Y+n\(z\)}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.20}{ Values for the Bessel functions J+n\(z\)}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.21}{ Value of the Airy function Ai\(z\) or derivative Ai'\(z\)}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.22}{ Value of the Airy function Bi\(z\) or derivative Bi'\(z\)}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.23}{ Returns a sequence of values for the Hankel functions}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.24}{ Returns the value of the modified Bessel Function K0\(x\)}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.25}{ Returns the value of the modified Bessel Function K1\(x\)}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.26}{ Returns the value of the modified Bessel Function I0\(x\)}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.27}{ Returns a value for the modified Bessel Function I1\(x\)}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.28}{ Sequence of values for the modified Bessel Kn\(z\)}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.29}{ Sequence of values for the modified Bessel I+n}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.30}{ Returns a value for the Kelvin function ber x}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.31}{ Returns a value for the Kelvin function bei x}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.32}{ Returns a value for the Kelvin function ker x}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.33}{ Returns a value for the Kelvin function keix}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.34}{ Returns a value for the Fresnel Integral S\(x\)}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.35}{ Returns a value for the Fresnel Integral C\(x\)}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.36}{ Returns a value of an elementary integral}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.37}{ Value of the symmetrised elliptic integral of first kind}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.38}{ Value of the symmetrised elliptic integral of second kind}{section.16.6}
\BOOKMARK [2][-]{subsection.16.6.39}{ Value of the symmetrised elliptic integral of third kind}{section.16.6}
\BOOKMARK [1][-]{section.16.7}{nagx.ht}{chapter.16}
\BOOKMARK [2][-]{subsection.16.7.1}{ Mathematical Constants}{section.16.7}
\BOOKMARK [2][-]{subsection.16.7.2}{ Machine Constants}{section.16.7}
\BOOKMARK [2][-]{subsection.16.7.3}{ Input/Output Utilities}{section.16.7}
\BOOKMARK [2][-]{subsection.16.7.4}{ Value of the current error message unit number}{section.16.7}
\BOOKMARK [2][-]{subsection.16.7.5}{ Value of the current advisory message unit number}{section.16.7}
\BOOKMARK [2][-]{subsection.16.7.6}{ Print a real matrix stored in a two-dimensional array}{section.16.7}
\BOOKMARK [2][-]{subsection.16.7.7}{ Print a complex matrix stored in a 2D array}{section.16.7}
\BOOKMARK [2][-]{subsection.16.7.8}{ Date and Time Utilities}{section.16.7}
\BOOKMARK [2][-]{subsection.16.7.9}{ Returns the current date and time}{section.16.7}
\BOOKMARK [2][-]{subsection.16.7.10}{ From seven-integer format time and date to character string}{section.16.7}
\BOOKMARK [2][-]{subsection.16.7.11}{ Compares two date/time character strings}{section.16.7}
\BOOKMARK [2][-]{subsection.16.7.12}{ Amount of processor time used}{section.16.7}
\BOOKMARK [0][-]{chapter.17}{NAG ASP Example Code}{}
\BOOKMARK [1][-]{section.17.1}{aspex.ht}{chapter.17}
\BOOKMARK [2][-]{subsection.17.1.1}{Asp1 Example Code}{section.17.1}
\BOOKMARK [2][-]{subsection.17.1.2}{Asp10 Example Code}{section.17.1}
\BOOKMARK [2][-]{subsection.17.1.3}{Asp12 Example Code}{section.17.1}
\BOOKMARK [2][-]{subsection.17.1.4}{Asp19 Example Code}{section.17.1}
\BOOKMARK [2][-]{subsection.17.1.5}{Asp20 Example Code}{section.17.1}
\BOOKMARK [2][-]{subsection.17.1.6}{Asp24 Example Code}{section.17.1}
\BOOKMARK [2][-]{subsection.17.1.7}{Asp27 Example Code}{section.17.1}
\BOOKMARK [2][-]{subsection.17.1.8}{Asp28 Example Code}{section.17.1}
\BOOKMARK [2][-]{subsection.17.1.9}{Asp29 Example Code}{section.17.1}
\BOOKMARK [2][-]{subsection.17.1.10}{Asp30 Example Code}{section.17.1}
\BOOKMARK [2][-]{subsection.17.1.11}{Asp31 Example Code}{section.17.1}
\BOOKMARK [2][-]{subsection.17.1.12}{Asp33 Example Code}{section.17.1}
\BOOKMARK [2][-]{subsection.17.1.13}{Asp34 Example Code}{section.17.1}
\BOOKMARK [2][-]{subsection.17.1.14}{Asp35 Example Code}{section.17.1}
\BOOKMARK [2][-]{subsection.17.1.15}{Asp4 Example Code}{section.17.1}
\BOOKMARK [2][-]{subsection.17.1.16}{Asp41 Example Code}{section.17.1}
\BOOKMARK [2][-]{subsection.17.1.17}{Asp42 Example Code}{section.17.1}
\BOOKMARK [2][-]{subsection.17.1.18}{Asp49 Example Code}{section.17.1}
\BOOKMARK [2][-]{subsection.17.1.19}{Asp50 Example Code}{section.17.1}
\BOOKMARK [2][-]{subsection.17.1.20}{Asp55 Example Code}{section.17.1}
\BOOKMARK [2][-]{subsection.17.1.21}{Asp6 Example Code}{section.17.1}
\BOOKMARK [2][-]{subsection.17.1.22}{Asp7 Example Code}{section.17.1}
\BOOKMARK [2][-]{subsection.17.1.23}{Asp73 Example Code}{section.17.1}
\BOOKMARK [2][-]{subsection.17.1.24}{Asp74 Example Code}{section.17.1}
\BOOKMARK [2][-]{subsection.17.1.25}{Asp77 Example Code}{section.17.1}
\BOOKMARK [2][-]{subsection.17.1.26}{Asp78 Example Code}{section.17.1}
\BOOKMARK [2][-]{subsection.17.1.27}{Asp8 Example Code}{section.17.1}
\BOOKMARK [2][-]{subsection.17.1.28}{Asp80 Example Code}{section.17.1}
\BOOKMARK [2][-]{subsection.17.1.29}{Asp9 Example Code}{section.17.1}
\BOOKMARK [0][-]{chapter.18}{NAG ANNA Expert System}{}
\BOOKMARK [1][-]{section.18.1}{annaex.ht}{chapter.18}
\BOOKMARK [2][-]{subsection.18.1.1}{Axiom/NAG Expert System}{section.18.1}
\BOOKMARK [2][-]{subsection.18.1.2}{Integration}{section.18.1}
\BOOKMARK [2][-]{subsection.18.1.3}{Ordinary Differential Equations}{section.18.1}
\BOOKMARK [2][-]{subsection.18.1.4}{Optimization}{section.18.1}
\BOOKMARK [2][-]{subsection.18.1.5}{Partial Differential Equations}{section.18.1}
\BOOKMARK [2][-]{subsection.18.1.6}{Examples Using the Axiom/NAG Expert System}{section.18.1}
\BOOKMARK [2][-]{subsection.18.1.7}{Examples Using the Axiom/NAG Expert System}{section.18.1}
\BOOKMARK [2][-]{subsection.18.1.8}{Examples Using the Axiom/NAG Expert System}{section.18.1}
\BOOKMARK [2][-]{subsection.18.1.9}{Examples Using the Axiom/NAG Expert System}{section.18.1}
\BOOKMARK [2][-]{subsection.18.1.10}{About the Axiom/NAG Expert System}{section.18.1}
\BOOKMARK [2][-]{subsection.18.1.11}{Introduction to the Axiom/NAG Expert System}{section.18.1}
\BOOKMARK [2][-]{subsection.18.1.12}{Example using the Axiom/NAG Expert System}{section.18.1}
\BOOKMARK [2][-]{subsection.18.1.13}{Example using the Axiom/NAG Expert System}{section.18.1}
\BOOKMARK [2][-]{subsection.18.1.14}{Example using the Axiom/NAG Expert System}{section.18.1}
\BOOKMARK [2][-]{subsection.18.1.15}{Decision Agents}{section.18.1}
\BOOKMARK [2][-]{subsection.18.1.16}{Inference Mechanisms}{section.18.1}
\BOOKMARK [2][-]{subsection.18.1.17}{Method Domains}{section.18.1}
\BOOKMARK [2][-]{subsection.18.1.18}{Measure Functions}{section.18.1}
\BOOKMARK [2][-]{subsection.18.1.19}{Computational Agents}{section.18.1}
\BOOKMARK [0][-]{chapter.19}{ANNA Algebra Code}{}
\BOOKMARK [0][-]{chapter.20}{Page hierarchy layout}{}
\BOOKMARK [0][-]{chapter.21}{Makefile}{}
