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\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}January 2012 Release Notes}{4}{subsection.1.1.3}
\contentsline {subsection}{\numberline {1.1.4}November 2011 Release Notes}{7}{subsection.1.1.4}
\contentsline {subsection}{\numberline {1.1.5}September 2011 Release Notes}{10}{subsection.1.1.5}
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\contentsline {subsection}{\numberline {1.1.9}January 2011 Release Notes}{19}{subsection.1.1.9}
\contentsline {subsection}{\numberline {1.1.10}November 2010 Release Notes}{22}{subsection.1.1.10}
\contentsline {subsection}{\numberline {1.1.11}September 2010 Release Notes}{24}{subsection.1.1.11}
\contentsline {subsection}{\numberline {1.1.12}July 2010 Release Notes}{27}{subsection.1.1.12}
\contentsline {subsection}{\numberline {1.1.13}May 2010 Release Notes}{30}{subsection.1.1.13}
\contentsline {subsection}{\numberline {1.1.14}March 2010 Release Notes}{35}{subsection.1.1.14}
\contentsline {subsection}{\numberline {1.1.15}January 2010 Release Notes}{38}{subsection.1.1.15}
\contentsline {subsection}{\numberline {1.1.16}November 2009 Release Notes}{40}{subsection.1.1.16}
\contentsline {subsection}{\numberline {1.1.17}September 2009 Release Notes}{43}{subsection.1.1.17}
\contentsline {subsection}{\numberline {1.1.18}July 2009 Release Notes}{45}{subsection.1.1.18}
\contentsline {subsection}{\numberline {1.1.19}May 2009 Release Notes}{47}{subsection.1.1.19}
\contentsline {subsection}{\numberline {1.1.20}March 2009 Release Notes}{52}{subsection.1.1.20}
\contentsline {subsection}{\numberline {1.1.21}January 2009 Release Notes}{58}{subsection.1.1.21}
\contentsline {subsection}{\numberline {1.1.22}November 23, 2008 Release Notes}{63}{subsection.1.1.22}
\contentsline {subsection}{\numberline {1.1.23}September 23, 2008 Release Notes}{65}{subsection.1.1.23}
\contentsline {subsection}{\numberline {1.1.24}July 23, 2008 Release Notes}{68}{subsection.1.1.24}
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\contentsline {subsection}{\numberline {1.1.27}January 25, 2008 Release Notes}{76}{subsection.1.1.27}
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\contentsline {chapter}{\numberline {16}NAG Library Routines}{2661}{chapter.16}
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\contentsline {subsection}{\numberline {16.1.1}NAG On-line Documentation}{2661}{subsection.16.1.1}
\contentsline {subsection}{\numberline {16.1.2}NAG Documentation: summary}{2663}{subsection.16.1.2}
\contentsline {subsection}{\numberline {16.1.3}NAG Documentation: introduction}{2685}{subsection.16.1.3}
\contentsline {subsection}{\numberline {16.1.4}NAG Documentation: keyword in context}{2702}{subsection.16.1.4}
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\contentsline {subsection}{\numberline {16.2.1} Zeros of Polynomials}{2803}{subsection.16.2.1}
\contentsline {subsection}{\numberline {16.2.2} Roots of a complex polynomial equation}{2807}{subsection.16.2.2}
\contentsline {subsection}{\numberline {16.2.3} Roots of a real polynomial equation}{2812}{subsection.16.2.3}
\contentsline {subsection}{\numberline {16.2.4} Roots of One or More Transcendental Equations}{2818}{subsection.16.2.4}
\contentsline {subsection}{\numberline {16.2.5} Zero of a continuous function in a given interval}{2822}{subsection.16.2.5}
\contentsline {subsection}{\numberline {16.2.6} Solution of a system of nonlinear equations}{2826}{subsection.16.2.6}
\contentsline {subsection}{\numberline {16.2.7} Solution of a system of nonlinear equations}{2830}{subsection.16.2.7}
\contentsline {subsection}{\numberline {16.2.8} Checks the gradients of a set of non-linear functions}{2836}{subsection.16.2.8}
\contentsline {subsection}{\numberline {16.2.9} Discrete Fourier transform of real or complex data values}{2839}{subsection.16.2.9}
\contentsline {subsection}{\numberline {16.2.10} Discrete Fourier transform of n real data values}{2847}{subsection.16.2.10}
\contentsline {subsection}{\numberline {16.2.11} Discrete Fourier transform of a Hermitian sequence}{2850}{subsection.16.2.11}
\contentsline {subsection}{\numberline {16.2.12} Discrete Fourier transform of n complex data values}{2854}{subsection.16.2.12}
\contentsline {subsection}{\numberline {16.2.13} Circular convolution or correlation of two real vectors}{2857}{subsection.16.2.13}
\contentsline {subsection}{\numberline {16.2.14} Discrete Fourier transforms of m sequences}{2861}{subsection.16.2.14}
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\contentsline {subsection}{\numberline {16.2.18} Summation of Series}{2879}{subsection.16.2.18}
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\contentsline {subsection}{\numberline {16.3.2} Approximation of the integral over a finite interval}{2901}{subsection.16.3.2}
\contentsline {subsection}{\numberline {16.3.3} Adaptive integration over a finite integral}{2907}{subsection.16.3.3}
\contentsline {subsection}{\numberline {16.3.4} Approximate integration with local singular points}{2913}{subsection.16.3.4}
\contentsline {subsection}{\numberline {16.3.5} Approximate integration over a (semi-)infinite interval}{2919}{subsection.16.3.5}
\contentsline {subsection}{\numberline {16.3.6} Approximate sine or cosine transform over finite interval}{2925}{subsection.16.3.6}
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\contentsline {subsection}{\numberline {16.4.21} Evaluate cubic spline and 3 derivatives from B-spline}{3212}{subsection.16.4.21}
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\contentsline {subsection}{\numberline {16.4.28} Calculates values of a bicubic spline from B-spline}{3266}{subsection.16.4.28}
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\contentsline {subsection}{\numberline {16.4.31} Minimizing or Maximizing a Function}{3280}{subsection.16.4.31}
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\contentsline {subsection}{\numberline {16.4.35} Finding an unconstrained minimum of a sum of squares}{3325}{subsection.16.4.35}
\contentsline {subsection}{\numberline {16.4.36} Finding an unconstrained minimum of a sum of squares}{3331}{subsection.16.4.36}
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\contentsline {subsection}{\numberline {16.5.1} Linear Algebra}{3436}{subsection.16.5.1}
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\contentsline {subsection}{\numberline {16.5.3} Factorizes a real sparse matrix}{3443}{subsection.16.5.3}
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\contentsline {subsection}{\numberline {16.5.14} Calculates all the eigenvalues of a real symmetric matrix}{3507}{subsection.16.5.14}
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\contentsline {subsection}{\numberline {16.5.16} Calculates all the eigenvalues of $Ax=\lambda Bx$}{3512}{subsection.16.5.16}
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\contentsline {subsection}{\numberline {16.5.18} Calculates all the eigenvalues of a real unsymmetric matrix}{3519}{subsection.16.5.18}
\contentsline {subsection}{\numberline {16.5.19} Eigenvalues and eigenvectors of a real unsymmetric matrix}{3521}{subsection.16.5.19}
\contentsline {subsection}{\numberline {16.5.20} Calculates all the eigenvalues of a complex matrix}{3524}{subsection.16.5.20}
\contentsline {subsection}{\numberline {16.5.21} Eigenvalues and eigenvectors of a complex matrix}{3527}{subsection.16.5.21}
\contentsline {subsection}{\numberline {16.5.22} Eigenvalues of a complex Hermitian matrix}{3530}{subsection.16.5.22}
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\contentsline {subsection}{\numberline {16.5.27} Singular value decomposition of a general real matrix}{3558}{subsection.16.5.27}
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\contentsline {subsection}{\numberline {16.5.29} Simultaneous Linear Equations}{3573}{subsection.16.5.29}
\contentsline {subsection}{\numberline {16.5.30} Approximate solution of a set of complex linear equations}{3579}{subsection.16.5.30}
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\contentsline {subsection}{\numberline {16.5.34} Solution of a set of real sparse linear equations}{3592}{subsection.16.5.34}
\contentsline {subsection}{\numberline {16.5.35} Real symmetric positive-definite tridiagonal linear equations}{3595}{subsection.16.5.35}
\contentsline {subsection}{\numberline {16.5.36} Solution of a linear least-squares problem, $Ax=b$}{3601}{subsection.16.5.36}
\contentsline {subsection}{\numberline {16.5.37} Sparse symmetric positive-definite system linear equations}{3607}{subsection.16.5.37}
\contentsline {subsection}{\numberline {16.5.38} Solves a system of real sparse symmetric linear equations}{3613}{subsection.16.5.38}
\contentsline {subsection}{\numberline {16.5.39} Solution of a system of real linear equations}{3624}{subsection.16.5.39}
\contentsline {subsection}{\numberline {16.5.40} Solves sparse unsymmetric equations}{3629}{subsection.16.5.40}
\contentsline {subsection}{\numberline {16.5.41} Linear Algebra Support Routines}{3643}{subsection.16.5.41}
\contentsline {subsection}{\numberline {16.5.42} Linear Equations (LAPACK)}{3676}{subsection.16.5.42}
\contentsline {subsection}{\numberline {16.5.43} Computes the LU factorization of a real m by n matrix}{3677}{subsection.16.5.43}
\contentsline {subsection}{\numberline {16.5.44} Solves a real system of linear equations}{3681}{subsection.16.5.44}
\contentsline {subsection}{\numberline {16.5.45} Factorization of a real symmetric positive-definite matrix}{3685}{subsection.16.5.45}
\contentsline {subsection}{\numberline {16.5.46} Real symmetric positive-definite system of linear equations}{3688}{subsection.16.5.46}
\contentsline {subsection}{\numberline {16.5.47} Sort vector of double precision numbers}{3695}{subsection.16.5.47}
\contentsline {subsection}{\numberline {16.5.48} Ranks a vector of double precision numbers}{3698}{subsection.16.5.48}
\contentsline {subsection}{\numberline {16.5.49} Ranks the rows of a matrix of double precision numbers}{3701}{subsection.16.5.49}
\contentsline {subsection}{\numberline {16.5.50} Ranks the columns of a matrix of double precision numbers}{3704}{subsection.16.5.50}
\contentsline {subsection}{\numberline {16.5.51} Rearranges a vector of double precision numbers}{3707}{subsection.16.5.51}
\contentsline {subsection}{\numberline {16.5.52} Inverts a permutation}{3709}{subsection.16.5.52}
\contentsline {section}{\numberline {16.6}nags.ht}{3712}{section.16.6}
\contentsline {subsection}{\numberline {16.6.1} Approximations of Special Functions}{3712}{subsection.16.6.1}
\contentsline {subsection}{\numberline {16.6.2} Exponential function $e^z$ , for complex $z$}{3725}{subsection.16.6.2}
\contentsline {subsection}{\numberline {16.6.3} Returns the value of the exponential integral $E(x)$}{3728}{subsection.16.6.3}
\contentsline {subsection}{\numberline {16.6.4} Returns the value of the cosine integral}{3731}{subsection.16.6.4}
\contentsline {subsection}{\numberline {16.6.5} Returns the value of the sine integral}{3734}{subsection.16.6.5}
\contentsline {subsection}{\numberline {16.6.6} Returns the value of the Gamma function}{3737}{subsection.16.6.6}
\contentsline {subsection}{\numberline {16.6.7} Returns a value for the logarithm of the Gamma function}{3740}{subsection.16.6.7}
\contentsline {subsection}{\numberline {16.6.8} Incomplete gamma functions P(a,x) and Q(a,x)}{3744}{subsection.16.6.8}
\contentsline {subsection}{\numberline {16.6.9} Returns the value of the complementary error function}{3747}{subsection.16.6.9}
\contentsline {subsection}{\numberline {16.6.10} Returns the value of the error function erfx}{3751}{subsection.16.6.10}
\contentsline {subsection}{\numberline {16.6.11} Returns the value of the Bessel Function $Y_0(x)$}{3753}{subsection.16.6.11}
\contentsline {subsection}{\numberline {16.6.12} Returns the value of the Bessel Function $Y_1(x)$}{3757}{subsection.16.6.12}
\contentsline {subsection}{\numberline {16.6.13} Returns the value of the Bessel Function $J_0(x)$}{3762}{subsection.16.6.13}
\contentsline {subsection}{\numberline {16.6.14} Returns the value of the Bessel Function $J_1(x)$}{3766}{subsection.16.6.14}
\contentsline {subsection}{\numberline {16.6.15} Returns a value for the Airy function, $Ai(x)$}{3769}{subsection.16.6.15}
\contentsline {subsection}{\numberline {16.6.16} Returns a value of the Airy function, $Bi(x)$}{3774}{subsection.16.6.16}
\contentsline {subsection}{\numberline {16.6.17} Value of the derivative of the Airy function $Ai(x)$}{3778}{subsection.16.6.17}
\contentsline {subsection}{\numberline {16.6.18} Value for the derivative of the Airy function $Bi(x)$}{3782}{subsection.16.6.18}
\contentsline {subsection}{\numberline {16.6.19} Values for the Bessel functions $Y_{\nu +n}(z)$}{3786}{subsection.16.6.19}
\contentsline {subsection}{\numberline {16.6.20} Values for the Bessel functions $J_{\nu +n}(z)$}{3791}{subsection.16.6.20}
\contentsline {subsection}{\numberline {16.6.21} Value of the Airy function $Ai(z)$ or derivative $Ai'(z)$}{3796}{subsection.16.6.21}
\contentsline {subsection}{\numberline {16.6.22} Value of the Airy function $Bi(z)$ or derivative $Bi'(z)$}{3800}{subsection.16.6.22}
\contentsline {subsection}{\numberline {16.6.23} Returns a sequence of values for the Hankel functions}{3804}{subsection.16.6.23}
\contentsline {subsection}{\numberline {16.6.24} Returns the value of the modified Bessel Function $K_0(x)$}{3810}{subsection.16.6.24}
\contentsline {subsection}{\numberline {16.6.25} Returns the value of the modified Bessel Function $K_1(x)$}{3813}{subsection.16.6.25}
\contentsline {subsection}{\numberline {16.6.26} Returns the value of the modified Bessel Function $I_0(x)$}{3817}{subsection.16.6.26}
\contentsline {subsection}{\numberline {16.6.27} Returns a value for the modified Bessel Function $I_1(x)$}{3821}{subsection.16.6.27}
\contentsline {subsection}{\numberline {16.6.28} Sequence of values for the modified Bessel $K_{\nu _n}(z)$}{3824}{subsection.16.6.28}
\contentsline {subsection}{\numberline {16.6.29} Sequence of values for the modified Bessel $I_{\nu +n}$}{3829}{subsection.16.6.29}
\contentsline {subsection}{\numberline {16.6.30} Returns a value for the Kelvin function ber x}{3833}{subsection.16.6.30}
\contentsline {subsection}{\numberline {16.6.31} Returns a value for the Kelvin function bei x}{3837}{subsection.16.6.31}
\contentsline {subsection}{\numberline {16.6.32} Returns a value for the Kelvin function ker x}{3840}{subsection.16.6.32}
\contentsline {subsection}{\numberline {16.6.33} Returns a value for the Kelvin function keix}{3844}{subsection.16.6.33}
\contentsline {subsection}{\numberline {16.6.34} Returns a value for the Fresnel Integral $S(x)$}{3848}{subsection.16.6.34}
\contentsline {subsection}{\numberline {16.6.35} Returns a value for the Fresnel Integral $C(x)$}{3852}{subsection.16.6.35}
\contentsline {subsection}{\numberline {16.6.36} Returns a value of an elementary integral}{3857}{subsection.16.6.36}
\contentsline {subsection}{\numberline {16.6.37} Value of the symmetrised elliptic integral of first kind}{3860}{subsection.16.6.37}
\contentsline {subsection}{\numberline {16.6.38} Value of the symmetrised elliptic integral of second kind}{3864}{subsection.16.6.38}
\contentsline {subsection}{\numberline {16.6.39} Value of the symmetrised elliptic integral of third kind}{3869}{subsection.16.6.39}
\contentsline {section}{\numberline {16.7}nagx.ht}{3874}{section.16.7}
\contentsline {subsection}{\numberline {16.7.1} Mathematical Constants}{3874}{subsection.16.7.1}
\contentsline {subsection}{\numberline {16.7.2} Machine Constants}{3875}{subsection.16.7.2}
\contentsline {subsection}{\numberline {16.7.3} Input/Output Utilities}{3882}{subsection.16.7.3}
\contentsline {subsection}{\numberline {16.7.4} Value of the current error message unit number}{3884}{subsection.16.7.4}
\contentsline {subsection}{\numberline {16.7.5} Value of the current advisory message unit number}{3887}{subsection.16.7.5}
\contentsline {subsection}{\numberline {16.7.6} Print a real matrix stored in a two-dimensional array}{3889}{subsection.16.7.6}
\contentsline {subsection}{\numberline {16.7.7} Print a complex matrix stored in a 2D array}{3892}{subsection.16.7.7}
\contentsline {subsection}{\numberline {16.7.8} Date and Time Utilities}{3896}{subsection.16.7.8}
\contentsline {subsection}{\numberline {16.7.9} Returns the current date and time}{3898}{subsection.16.7.9}
\contentsline {subsection}{\numberline {16.7.10} From seven-integer format time and date to character string}{3899}{subsection.16.7.10}
\contentsline {subsection}{\numberline {16.7.11} Compares two date/time character strings}{3902}{subsection.16.7.11}
\contentsline {subsection}{\numberline {16.7.12} Amount of processor time used}{3905}{subsection.16.7.12}
\contentsline {chapter}{\numberline {17}NAG ASP Example Code}{3907}{chapter.17}
\contentsline {section}{\numberline {17.1}aspex.ht}{3907}{section.17.1}
\contentsline {subsection}{\numberline {17.1.1}Asp1 Example Code}{3907}{subsection.17.1.1}
\contentsline {subsection}{\numberline {17.1.2}Asp10 Example Code}{3907}{subsection.17.1.2}
\contentsline {subsection}{\numberline {17.1.3}Asp12 Example Code}{3908}{subsection.17.1.3}
\contentsline {subsection}{\numberline {17.1.4}Asp19 Example Code}{3908}{subsection.17.1.4}
\contentsline {subsection}{\numberline {17.1.5}Asp20 Example Code}{3911}{subsection.17.1.5}
\contentsline {subsection}{\numberline {17.1.6}Asp24 Example Code}{3911}{subsection.17.1.6}
\contentsline {subsection}{\numberline {17.1.7}Asp27 Example Code}{3912}{subsection.17.1.7}
\contentsline {subsection}{\numberline {17.1.8}Asp28 Example Code}{3912}{subsection.17.1.8}
\contentsline {subsection}{\numberline {17.1.9}Asp29 Example Code}{3915}{subsection.17.1.9}
\contentsline {subsection}{\numberline {17.1.10}Asp30 Example Code}{3916}{subsection.17.1.10}
\contentsline {subsection}{\numberline {17.1.11}Asp31 Example Code}{3917}{subsection.17.1.11}
\contentsline {subsection}{\numberline {17.1.12}Asp33 Example Code}{3917}{subsection.17.1.12}
\contentsline {subsection}{\numberline {17.1.13}Asp34 Example Code}{3918}{subsection.17.1.13}
\contentsline {subsection}{\numberline {17.1.14}Asp35 Example Code}{3918}{subsection.17.1.14}
\contentsline {subsection}{\numberline {17.1.15}Asp4 Example Code}{3919}{subsection.17.1.15}
\contentsline {subsection}{\numberline {17.1.16}Asp41 Example Code}{3919}{subsection.17.1.16}
\contentsline {subsection}{\numberline {17.1.17}Asp42 Example Code}{3920}{subsection.17.1.17}
\contentsline {subsection}{\numberline {17.1.18}Asp49 Example Code}{3921}{subsection.17.1.18}
\contentsline {subsection}{\numberline {17.1.19}Asp50 Example Code}{3922}{subsection.17.1.19}
\contentsline {subsection}{\numberline {17.1.20}Asp55 Example Code}{3923}{subsection.17.1.20}
\contentsline {subsection}{\numberline {17.1.21}Asp6 Example Code}{3924}{subsection.17.1.21}
\contentsline {subsection}{\numberline {17.1.22}Asp7 Example Code}{3924}{subsection.17.1.22}
\contentsline {subsection}{\numberline {17.1.23}Asp73 Example Code}{3925}{subsection.17.1.23}
\contentsline {subsection}{\numberline {17.1.24}Asp74 Example Code}{3925}{subsection.17.1.24}
\contentsline {subsection}{\numberline {17.1.25}Asp77 Example Code}{3926}{subsection.17.1.25}
\contentsline {subsection}{\numberline {17.1.26}Asp78 Example Code}{3927}{subsection.17.1.26}
\contentsline {subsection}{\numberline {17.1.27}Asp8 Example Code}{3927}{subsection.17.1.27}
\contentsline {subsection}{\numberline {17.1.28}Asp80 Example Code}{3928}{subsection.17.1.28}
\contentsline {subsection}{\numberline {17.1.29}Asp9 Example Code}{3928}{subsection.17.1.29}
\contentsline {chapter}{\numberline {18}NAG ANNA Expert System}{3931}{chapter.18}
\contentsline {section}{\numberline {18.1}annaex.ht}{3931}{section.18.1}
\contentsline {subsection}{\numberline {18.1.1}Axiom/NAG Expert System}{3931}{subsection.18.1.1}
\contentsline {subsection}{\numberline {18.1.2}Integration}{3932}{subsection.18.1.2}
\contentsline {subsection}{\numberline {18.1.3}Ordinary Differential Equations}{3933}{subsection.18.1.3}
\contentsline {subsection}{\numberline {18.1.4}Optimization}{3933}{subsection.18.1.4}
\contentsline {subsection}{\numberline {18.1.5}Partial Differential Equations}{3934}{subsection.18.1.5}
\contentsline {subsection}{\numberline {18.1.6}Examples Using the Axiom/NAG Expert System}{3935}{subsection.18.1.6}
\contentsline {subsection}{\numberline {18.1.7}Examples Using the Axiom/NAG Expert System}{3936}{subsection.18.1.7}
\contentsline {subsection}{\numberline {18.1.8}Examples Using the Axiom/NAG Expert System}{3937}{subsection.18.1.8}
\contentsline {subsection}{\numberline {18.1.9}Examples Using the Axiom/NAG Expert System}{3939}{subsection.18.1.9}
\contentsline {subsection}{\numberline {18.1.10}About the Axiom/NAG Expert System}{3940}{subsection.18.1.10}
\contentsline {subsection}{\numberline {18.1.11}Introduction to the Axiom/NAG Expert System}{3941}{subsection.18.1.11}
\contentsline {subsection}{\numberline {18.1.12}Example using the Axiom/NAG Expert System}{3942}{subsection.18.1.12}
\contentsline {subsection}{\numberline {18.1.13}Example using the Axiom/NAG Expert System}{3947}{subsection.18.1.13}
\contentsline {subsection}{\numberline {18.1.14}Example using the Axiom/NAG Expert System}{3948}{subsection.18.1.14}
\contentsline {subsection}{\numberline {18.1.15}Decision Agents}{3949}{subsection.18.1.15}
\contentsline {subsection}{\numberline {18.1.16}Inference Mechanisms}{3950}{subsection.18.1.16}
\contentsline {subsection}{\numberline {18.1.17}Method Domains}{3951}{subsection.18.1.17}
\contentsline {subsection}{\numberline {18.1.18}Measure Functions}{3952}{subsection.18.1.18}
\contentsline {subsection}{\numberline {18.1.19}Computational Agents}{3953}{subsection.18.1.19}
\contentsline {chapter}{\numberline {19}ANNA Algebra Code}{3955}{chapter.19}
\contentsline {chapter}{\numberline {20}Page hierarchy layout}{3957}{chapter.20}
\contentsline {chapter}{\numberline {21}Makefile}{3991}{chapter.21}
