diff --git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet index 905cf1b..2472ed4 100644 --- a/books/bookvolbib.pamphlet +++ b/books/bookvolbib.pamphlet @@ -3697,6 +3697,23 @@ Math. Tables Aids Comput. 10 91--96. (1956) \subsection{Z} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\bibitem[Zakrajsek 02]{Zak02} Zakrajsek, Helena\\ +Applications of Hermite transform in computer algebra''\\ +\verb|www.imfm.si/preprinti/PDF/00835.pdf| +%\verb|axiom-developer.org/axiom-website/papers/Zak02.pdf| + +\begin{adjustwidth}{2.5em}{0pt} +let $L$ be a linear differential operator with polynomial coefficients. +We show that there is an isomorphism of differential operators +${\bf D_\alpha}$ and an integral transform ${\bf H_\alpha}$ (called the +Hermite transform) on functions for which $({\bf D_\alpha}{\bf L})f(x)=0$ +implies ${\bf L}{\bf H_alpha}(f)(x)=0$. We present an algorithm that +computes the Hermite transform of a rational function and use it to find +$n+1$ linearly independent solutions of ${\bf L}y=0$ when +$({\bf D_\alpha}{\bf L})f(x)=0$ has a rational solution with $n$ +distinct finite poles. +\end{adjustwidth} + \bibitem[Zhi 97]{Zhi97} Zhi, Lihong\\ Optimal Algorithm for Algebraic Factoring''\\ \verb|www.mmrc.iss.ac.cn/~lzhi/Publications/zopfac.pdf| @@ -3905,7 +3922,7 @@ subjects encountered during the thesis. \bibitem[Shoup 93]{ST-PGCD-Sh93} Shoup, Victor\\ Factoring Polynomials over Finite Fields: Asymptotic Complexity vs Reality*''\\ -Proc. IMACS Symposium, Lille, France, (1993) +Proc. IMACS Symposium, Lille, France, (1993)\\ \verb|www.shoup.net/papers/lille.pdf| %\verb|axiom-developer.org/axiom-website/papers/ST-PGCD-Sh93.pdf| @@ -3956,7 +3973,7 @@ comparison of the two algorithms using implementations in Maple. \bibitem[Wang 78]{Wang78} Wang, Paul S.\\ An Improved Multivariate Polynomial Factoring Algorithm''\\ -Mathematics of Computation, Vol 32, No 144 Oct 1978, pp1215-1231 +Mathematics of Computation, Vol 32, No 144 Oct 1978, pp1215-1231\\ \verb|www.ams.org/journals/mcom/1978-32-144/S0025-5718-1978-0568284-3/| \verb|S0025-5718-1978-0568284-3.pdf| %\verb|axiom-developer.org/axiom-website/papers/Wang78.pdf| @@ -4460,6 +4477,34 @@ in Lecture Notes in Computer Science, Springer ISBN 978-3-540-85520-0 \subsection{Numerics} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\bibitem[Atkinson 09]{Atk09} Atkinson, Kendall; Han, Welmin; Stewear, David\\ +Numerical Solution of Ordinary Differential Equations''\\ +\verb|homepage.math.uiowa.edu/~atkinson/papers/NAODE_Book.pdf| +%\verb|axiom-developer.org/axiom-website/papers/Atk09.pdf| + +\begin{adjustwidth}{2.5em}{0pt} +This book is an expanded version of supplementary notes that we used +for a course on ordinary differential equations for upper-division +undergraduate students and beginning graduate students in mathematics, +engineering, and sciences. The book introduces the numerical analysis +of differential equations, describing the mathematical background for +understanding numerical methods and giving information on what to +expect when using them. As a reason for studying numerical methods as +a part of a more general course on differential equations, many of the +basic ideas of the numerical analysis of differential equations are +tied closely to theoretical behavior associated with the problem being +solved. For example, the criteria for the stability of a numerical +method is closely connected to the stability of the differential +equation problem being solved. +\end{adjustwidth} + +\bibitem[Crank 96]{Cran96} Crank, J.; Nicolson, P.\\ +A practical method for numerical evaluations of solutions of partial differential equations of heat-conduction type''\\ +Advances in Computational Mathematics Vol 6 pp207-226 (1996)\\ +\verb|www.acms.arizona.edu/FemtoTheory/MK_personal/opti547/literature/| +\verb|CNMethod-original.pdf| +%\verb|axiom-developer.org/axiom-website/papers/Cran96.pdf| + \bibitem[Lef\'evre 06]{Lef06} Lef\'evre, Vincent; Stehl\'e, Damien; Zimmermann, Paul\\ Worst Cases for the Exponential Function @@ -4885,9 +4930,25 @@ MacRobert and others. An integral involving regular radial Coulomb wave function is also obtained as a particular case. \end{adjustwidth} +\bibitem[Bronstein 89]{Bro89a} Bronstein, M.\\ +An Algorithm for the Integration of Elementary Functions''\\ +Lecture Notes in Computer Science Vol 378 pp491-497 (1989) +%\verb|axiom-developer.org/axiom-website/papers/Bro89a.pdf| + +\begin{adjustwidth}{2.5em}{0pt} +Trager (1984) recently gave a new algorithm for the indefinite +integration of algebraic functions. His approach was rational'' in +the sense that the only algebraic extension computed in the smallest +one necessary to express the answer. We outline a generalization of +this approach that allows us to integrate mixed elementary +functions. Using only rational techniques, we are able to normalize +the integrand, and to check a necessary condition for elementary +integrability. +\end{adjustwidth} + \bibitem[Bronstein 97]{Bro97} Bronstein, M.\\ Symbolic Integration I--Transcendental Functions.''\\ -Springer, Heidelberg, 1997 ISBN 3-540-21493-3 +Springer, Heidelberg, 1997 ISBN 3-540-21493-3\\ \verb|evil-wire.org/arrrXiv/Mathematics/Bronstein,_Symbolic_Integration_I,1997.pdf| %\verb|axiom-developer.org/axiom-website/papers/Bro97.pdf| @@ -4897,9 +4958,38 @@ Springer, Heidelberg, 1997 ISBN 3-540-21493-3 \verb|www-sop.inria.fr/cafe/Manuel.Bronstein/pmint/examples| %\verb|axiom-developer.org/axiom-website/papers/Bro05a.txt| +\bibitem[Charlwood 07]{Charl07} Charlwood, Kevin\\ +Integration on Computer Algebra Systems''\\ +The Electronic J of Math. and Tech. Vol 2, No 3, ISSN 1933-2823 +\verb|12000.org/my_notes/ten_hard_integrals/paper.pdf| +%\verb|axiom-developer.org/axiom-website/papers/Charl07.pdf| + +\begin{adjustwidth}{2.5em}{0pt} +In this article, we consider ten indefinite integrals and the ability +of three computer algebra systems (CAS) to evaluate them in +closed-form, appealing only to the class of real, elementary +functions. Although these systems have been widely available for many +years and have undergone major enhancements in new versions, it is +interesting to note that there are still indefinite integrals that +escape the capacity of these systems to provide antiderivatves. When +this occurs, we consider what a user may do to find a solution with +the aid of a CAS. +\end{adjustwidth} + +\bibitem[Charlwood 08]{Charl08} Charlwood, Kevin\\ +Symbolic Integration Problems''\\ +\verb|www.apmaths.uwo.ca/~arich/IndependentTestResults/CharlwoodIntegrationProblems.pdf| +%\verb|axiom-developer.org/axiom-website/papers/Charl08.pdf| + +\begin{adjustwidth}{2.5em}{0pt} +A list of the 50 example integration problems from Kevin Charlwood's 2008 +article Integration on Computer Algebra Systems''. Each integral along +with its optimal antiderivative (that is, the best antiderivative found +so far) is shown. +\end{adjustwidth} + \bibitem[Cherry 84]{Che84} Cherry, G.W.\\ -Integration in Finite Terms with Special Functions: -The Error Function''\\ +Integration in Finite Terms with Special Functions: The Error Function''\\ J. Symbolic Computation (1985) Vol 1 pp283-302 %\verb|axiom-developer.org/axiom-website/papers/Che84.pdf| @@ -4925,6 +5015,26 @@ SIAM J. Comput. Vol 15 pp1-21 February 1986 \bibitem[Cherry 89]{Che89} Cherry, G.W.\\ An Analysis of the Rational Exponential Integral''\\ SIAM J. Computing Vol 18 pp 893-905 (1989) +%\verb|axiom-developer.org/axiom-website/papers/Che89.pdf| + +\begin{adjustwidth}{2.5em}{0pt} +In this paper an algorithm is presented for integrating expressions of +the form $\int{ge^f~dx}$, where $f$ and $g$ are rational functions of +$x$, in terms of a class of special functions called the special +incomplete $\Gamma$ functions. This class of special functions +includes the exponential integral, the error functions, the sine and +cosing integrals, and the Fresnel integrals. The algorithm presented +here is an improvement over those published previously for integrating +with special functions in the following ways: (i) This algorithm +combines all the above special functions into one algorithm, whereas +previously they were treated separately, (ii) Previous algorithms +require that the underlying field of constants be algebraically +closed. This algorithm, however, works over any field of +characteristic zero in which the basic field operations can be carried +out. (iii) This algorithm does not rely on Risch's solution of the +differential equation $y^\prime + fy = g$. Instead, a more direct +method of undetermined coefficients is used. +\end{adjustwidth} \bibitem[Churchill 06]{Chur06} Churchill, R.C.\\ Liouville's Theorem on Integration Terms of Elementary Functions''\\ @@ -4988,6 +5098,24 @@ Algorithms for Computer Algebra, Ch 12 pp511-573 (1992) The Integration of Functions of a Single Variable''\\ Cambridge Unversity Press, Cambridge, 1916 +\bibitem[Harrington 78]{Harr87} Harrington, S.J.\\ +A new symbolic integration system in reduce''\\ +\verb|comjnl.oxfordjournals.or/content/22/2/127.full.pdf| +%\verb|axiom-developer.org/axiom-website/papers/Harr87.pdf| + +\begin{adjustwidth}{2.5em}{0pt} +A new integration system, employing both algorithmic and pattern match +integration schemes is presented. The organization of the system +differs from that of earlier programs in its emphasis on the +algorithmic approach to integration, its modularity and its ease of +revision. The new Norman-Rish algorithm and its implementation at the +University of Cambridge are employed, supplemented by a powerful +collection of simplification and transformation rules. The facility +for user defined integrals and functions is also included. The program +is both fast and powerful, and can be easily modified to incorporate +anticipated developments in symbolic integration. +\end{adjustwidth} + \bibitem[Hermite 1872]{Her1872} Hermite, E.\\ Sur l'int\'{e}gration des fractions rationelles.''\\ {\sl Nouvelles Annales de Math\'{e}matiques} @@ -5044,6 +5172,16 @@ and integration is with respect to a real variable. Algorithms are given for evaluating such integrals. \end{adjustwidth} +\bibitem[Kiymaz 04]{Kiym04} Kiymaz, Onur; Mirasyedioglu, Seref\\ +A new symbolic computation for formal integration with exact power series''\\ +%\verb|axiom-developer.org/axiom-website/Kiym04.pdf| + +\begin{adjustwidth}{2.5em}{0pt} +This paper describes a new symbolic algorithm for formal integration +of a class of functions in the context of exact power series by using +generalized hypergeometric series and computer algebraic technique. +\end{adjustwidth} + \bibitem[Knowles 93]{Know93} Knowles, P.\\ Integration of a class of transcendental liouvillian functions with error-functions i''\\ @@ -5071,6 +5209,28 @@ $\mathcal{E}\mathcal{L}$-elementary extensions of Singer, Saunders and Caviness and contains the Gamma function. \end{adjustwidth} +\bibitem[Leslie 09]{Lesl09} Leslie, Martin\\ +Why you can't integrate exp($x^2$)''\\ +\verb|math.arizona.edu/~mleslie/files/integrationtalk.pdf| +%\verb|axiom-developer.org/axiom-website/papers/Lesl09.pdf| + +\bibitem[Lichtblau 11]{Lich11} Lichtblau, Daniel\\ +Symbolic definite (and indefinite) integration: methods and open issues''\\ +ACM Comm. in Computer Algebra Issue 175, Vol 45, No.1 (2011)\\ +\verb|www.sigsam.org/bulletin/articles/175/issue175.pdf| +%\verb|axiom-developer.org/axiom-website/papers/Lich11.pdf| + +\begin{adjustwidth}{2.5em}{0pt} +The computation of definite integrals presents one with a variety of +choices. There are various methods such as Newton-Leibniz or Slater's +convolution method. There are questions such as whether to split or +merge sums, how to search for singularities on the path of +integration, when to issue conditional results, how to assess +(possibly conditional) convergence, and more. These various +considerations moreover interact with one another in a multitude of +ways. Herein we discuss these various issues and illustrate with examples. +\end{adjustwidth} + \bibitem[Liouville 1833a]{Lio1833a} Liouville, Joseph\\ Premier m\'{e}moire sur la d\'{e}termination des int\'{e}grales dont la valeur est @@ -5099,6 +5259,26 @@ transcendentes''\\ Journal f\"ur die Reine und Angewandte Mathematik, Vol 13(2) pp 93-118, (1835) +\bibitem[Marc 94]{Marc94} Marchisotto, Elena Anne; Zakeri, Gholem-All\\ +An Invitation to Integration in Finite Terms''\\ +College Mathematics Journal Vol 25 No 4 (1994) pp295-308\\ +\verb|www.rangevoting.org/MarchisottoZint.pdf| +%\verb|axiom-developer.org/axiom-website/papers/Marc94.pdf| + +\bibitem[Moses 76]{Mos76} Moses, Joel\\ +An introduction to the Risch Integration Algorithm''\\ +ACM Proc. 1976 annual conference pp425-428 +%\verb|axiom-developer.org/axiom-website/papers/Mos76.pdf| + +\begin{adjustwidth}{2.5em}{0pt} +Risch's decision procedure for determining the integrability in closed +form of the elementary functions of the calculus is presented via +examples. The exponential and logarithmic cases of the algorithsm had +been implemented for the MACSYMA system several years ago. The +implementation of the algebraic case of the algorithm is the subject +of current research. +\end{adjustwidth} + \bibitem[Moses 71a]{Mos71a} Moses, Joel\\ Symbolic Integration: The Stormy Decade''\\ \verb|www-inst.eecs.berkeley.edu/~cs282/sp02/readings/moses-int.pdf| @@ -5214,9 +5394,9 @@ Columbia University Press, New York 1948 \bibitem[Rosenlicht 68]{Ro68} Rosenlicht, Maxwell\\ Liouville's Theorem on Functions with Elementary Integrals''\\ -Pacific Journal of Mathematics Vol 24 No 1 (1968) +Pacific Journal of Mathematics Vol 24 No 1 (1968)\\ \verb|msp.org/pjm/1968/24-1/pjm-v24-n1-p16-p.pdf| -\verb|axiom-developer.org/axiom-website/papers/Ro68.pdf| +%\verb|axiom-developer.org/axiom-website/papers/Ro68.pdf| \begin{adjustwidth}{2.5em}{0pt} Defining a function with one variable to be elemetary if it has an @@ -5261,7 +5441,7 @@ Proc. Amer. Math. Soc. Vol 23 pp689-691 (1969) \bibitem[Singer 85]{Sing85} Singer, M.F.; Saunders, B.D.; Caviness, B.F.\\ An extension of Liouville's theorem on integration in finite terms''\\ -SIAM J. of Comp. Vol 14 pp965-990 (1985) +SIAM J. of Comp. Vol 14 pp965-990 (1985)\\ \verb|www4.ncsu.edu/~singer/papers/singer_saunders_caviness.pdf| %\verb|axiom-developer.org/axiom-website/papers/Sing85.pdf| @@ -5298,9 +5478,36 @@ for finding a least degree extension field in which the integral can be expressed. \end{adjustwidth} +\bibitem[Trager 76a]{Tr76a} Trager, Barry Marshall\\ +Algorithms for Manipulating Algebraic Functions''\\ +MIT Master's Thesis.\\ +\verb|www.dm.unipi.it/pages/gianni/public_html/Alg-Comp/fattorizzazione-EA.pdf| +%\verb|axiom-developer.org/axiom-website/papers/Tr76a.pdf| + +\begin{adjustwidth}{2.5em}{0pt} +Given a base field $k$, of characteristic zero, with effective +procedures for performing arithmetic and factoring polynomials, this +thesis presents algorithms for extending those capabilities to +elements of a finite algebraic symbolic manipulation system. An +algebraic factorization algorithm along with a constructive version of +the primitive element theorem is used to construct splitting fields of +polynomials. These fields provide a context in which we can operate +symbolically with all the roots of a set of polynomials. One +application for this capability is rational function integrations. +Previously presented symbolic algorithms concentrated on finding the +rational part and were only able to compute the complete +integral in special cases. This thesis presents an algorithm for +finding an algebraic extension field of least degreee in which the +integral can be expressed, and then constructs the integral in that +field. The problem of algebraic function integration is also +examined, and a highly efficient procedure is presented for generating +the algebraic part of integrals whose function fields are defined by a +single radical extension of the rational functions. +\end{adjustwidth} + \bibitem[Trager 84]{Tr84} Trager, Barry\\ On the integration of algebraic functions''\\ -PhD thesis, MIT, Computer Science, 1984 +PhD thesis, MIT, Computer Science, 1984\\ \verb|www.dm.unipi.it/pages/gianni/public_html/Alg-Comp/thesis.pdf| %\verb|axiom-developer.org/axiom-website/papers/Tr84.pdf| @@ -5362,6 +5569,17 @@ mentioned algorithms in the field of ODE's conclude this paper. This is used as a reference for the LeftOreRing category, in particular, the least left common multiple (lcmCoef) function. +\bibitem[Abramov 97]{Abra97} Abramov, Sergei A.; van Hoeij, Mark\\ +A method for the Integration of Solutions of Ore Equations''\\ +Proc ISSAC 97 pp172-175 (1997) +%\verb|axiom-developer.org/axiom-website/papers/Abra97.pdf| + +\begin{adjustwidth}{2.5em}{0pt} +We introduce the notion of the adjoint Ore ring and give a definition +of adjoint polynomial, operator and equation. We apply this for +integrating solutions of Ore equations. +\end{adjustwidth} + \bibitem[Delenclos 06]{DL06} Delenclos, Jonathon; Leroy, Andr\'e\\ Noncommutative Symmetric functions and $W$-polynomials''\\ \verb|arxiv.org/pdf/math/0606614.pdf| diff --git a/changelog b/changelog index 9068c57..cc966a4 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,5 @@ +20140807 tpd src/axiom-website/patches.html 20140807.01.tpd.patch +20140807 tpd books/bookvolbib add bibliographic references 20140806 tpd src/axiom-website/patches.html 20140806.01.tpd.patch 20140806 tpd Makefile merge include, lib, clef 20140806 tpd books/Makefile merge include, lib, clef diff --git a/patch b/patch index b397b99..6c307c9 100644 --- a/patch +++ b/patch @@ -1,4 +1,4 @@ -merge and remove include, lib, and clef into books +books/bookvolbib add bibliographic references -The include, lib, and clef subdirectories have been merged into -the related books. The directories were removed from the src tree. +add addition bibliographic references, some from Raoul Bourquin, +in the subsection on integration. diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 3bd3b93..612cc52 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -4604,6 +4604,8 @@ src/axiom-website/download.html add binary links
Makefile, src/Makefile remove src/scripts directory
20140806.01.tpd.patch merge and remove include, lib, and clef into books