diff --git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet index 4dbb5c8..cc291b7 100644 --- a/books/bookvolbib.pamphlet +++ b/books/bookvolbib.pamphlet @@ -210,14 +210,21 @@ logarithms and exponentials. \bibitem[Bronstein 91a]{Bro91a} Bronstein, M.\\ The Risch differential equation on an algebraic curve''\\ in Watt [Wat91], pp241-246 ISBN 0-89791-437-6 LCCN QA76.95.I59 1991 +%\verb|axiom-developer.org/axiom-website/papers/Bro91a.pdf| REF:00120 -\bibitem[Bronstein 91b]{Bro91b} Bronstein, M.\\ -The Risch differential equation on an algebraic curve''\\ - In S.Watt, editor, {\sl Proceedings of ISSAC'91}, -pages 241-246, ACM Press, 1991. +\begin{adjustwidth}{2.5em}{0pt} +We present a new rational algorithm for solving Risch differential +equations over algebraic curves. This algorithm can also be used to +solve $n^{th}$-order linear ordinary differential equations with +coefficients in an algebraic extension of the rational functions. In +the general ("mixed function") case, this algorithm finds the +denominator of any solution of the equation. +\end{adjustwidth} -\bibitem[Bronstein 91c]{Bro91c} Bronstein, Manual\\ +\bibitem[Bronstein 91c]{Bro91c} Bronstein, Manuel\\ Computer Algebra and Indefinite Integrals''\\ +in Computer Aided Proofs in Analysis, K.R. Meyers et al. (eds) +Springer-Verlag, NY (1991) %\verb|axiom-developer.org/axiom-website/papers/Bro91c.pdf| \begin{adjustwidth}{2.5em}{0pt} @@ -269,6 +276,7 @@ In Bronstein [Bro93] pp157-160 ISBN 0-89791-604-2 LCCN QA76.95 I59 1993\\ \bibitem[Bronstein 92a]{Bro92a} Bronstein, Manuel\\ Integration and Differential Equations in Computer Algebra'' +\verb|citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.42.576| %\verb|axiom-developer.org/axiom-website/papers/Bro92a.pdf| \begin{adjustwidth}{2.5em}{0pt} @@ -881,6 +889,10 @@ ISBN 0-89791-199-7 LCCN QA155.7.E4 A281 1986 ACM order number 505860 On an installation of Buchberger's algorithm''\\ Journal of Symbolic Computation, 6(2-3) pp275-286 1988 CODEN JSYCEH ISSN 0747-7171 +\verb|www.sciencedirect.com/science/article/pii/S0747717188800488/pdf| +\verb|?md5=f6ccf63002ef3bc58aaa92e12ef18980&| +\verb|pid=1-s2.0-S0747717188800488-main.pdf| +%\verb|axiom-developer.org/axiom-website/papers/GM88.pdf| \bibitem[Geddes 92]{GCL92} Geddes, Keith; Czapor, O.; Stephen R.; Labahn, George\\ @@ -891,6 +903,15 @@ Kluwer Academic Publishers ISBN 0-7923-9259-0 (Sept 1992) Primary Decomposition of Ideals''\\ in [Wit87], pp12-13 +\bibitem[Gianni 88]{Gia88} Gianni, Patrizia.; Trager, Barry.; +Zacharias, Gail.\\ +Gr\"obner Bases and Primary Decomposition of Polynomial Ideals''\\ +J. Symbolic Computation 6, 149-167 (1988)\\ +\verb|www.sciencedirect.com/science/article/pii/S0747717188800403/pdf| +\verb|?md5=40c29b67947035884904fd4597ddf710&| +\verb|pid=1-s2.0-S0747717188800403-main.pdf| +%\verb|axiom-developer.org/axiom-website/papers/Gia88.pdf| + \bibitem[Gianni 89a]{Gia89} Gianni, P. (Patrizia) (ed)\\ Symbolic and Algebraic Computation. International Symposium ISSAC '88, Rome, Italy, July 4-8, 1988. Proceedings, @@ -1000,7 +1021,7 @@ In Petrick [Pet71], pp42-58. LCCN QA76.5.S94 1971\\ \verb|delivery.acm.org/10.1145/810000/806266/p42-griesmer.pdf|\\ SYMSAC'71 Proc. second ACM Symposium on Symbolic and Algebraic Manipulation pp45-48 -%\verb|axiom-developer.org/axiom-website/papers/GJ71.pdf| +%\verb|axiom-developer.org/axiom-website/papers/GJ71.pdf| REF:00027 \begin{adjustwidth}{2.5em}{0pt} The SCRATCHPAD/1 system is designed to provide an interactive symbolic @@ -1108,6 +1129,7 @@ Watson Research Center, Yorktown Heights, NY, USA, 1969 RC2968 July 1970 META/PLUS: The syntax extension facility for SCRATCHPAD''\\ Research Report RC 3259, International Business Machines, Inc., Thomas J. Watson Research Center, Yorktown Heights, NY, USA, 1971 +% REF:00040 \bibitem[Jenks 74]{Jen74} Jenks, R. D.\\ The SCRATCHPAD language''\\ @@ -1198,6 +1220,7 @@ In Jan{\ss}en Springer-Verlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc., 1992 ISBN 0-387-97855-0 (New York), 3-540-97855-0 (Berlin) 742pp LCCN QA76.95.J46 1992 +% REF:00116 \bibitem[Jenks 94]{JT94} Jenks, R. D.; Trager, B. M.\\ How to make AXIOM into a Scratchpad''\\ @@ -1223,7 +1246,17 @@ SIGSAM Communications in Computer Algebra, 157 2006\\ Integration of Algebraic Functions: A Simple Heuristic for Finding the Logarithmic Part''\\ ISSAC July 2008 ACM 978-1-59593-904 pp133-140 -\verb|www.kauers.de/publications.html| +\verb|www.risc.jku.at/publications/download/risc_3427/Ka01.pdf| +%\verb|axiom-developer.org/axiom-website/papers/Kau08.pdf| + +\begin{adjustwidth}{2.5em}{0pt} +A new method is proposed for finding the logarithmic part of an +integral over an algebraic function. The method uses Gr\"obner bases +and is easy to implement. It does not have the feature of finding a +closed form of an integral whenever there is one. But it very often +does, as we will show by a comparison with the built-in integrators of +some computer algebra systems. +\end{adjustwidth} \bibitem[Keady 94]{KN94} Keady, G.; Nolan, G.\\ Production of Argument SubPrograms in the AXIOM -- NAG @@ -1818,6 +1851,25 @@ LCCN QA268.A35 1998 Conference held jointly with ISSAC '88 An algorithm for solving parametric linear systems''\\ Journal of Symbolic Computations, 13(4) pp353-394, April 1992 CODEN JSYCEH ISSN 0747-7171 +\verb|www.sciencedirect.com/science/article/pii/S0747717108801046/pdf| +\verb|?md5=00aa65e18e6ea5c4a008c8dfdfcd4b83&| +\verb|pid=1-s2.0-S0747717108801046-main.pdf| +%\verb|axiom-developer.org/axiom-website/papers/Sit92.pdf| + +\begin{adjustwidth}{2.5em}{0pt} +We present a theoretical foundation for studying parametric systesm of +linear equations and prove an efficient algorithm for identifying all +parametric values (including degnerate cases) for which the system is +consistent. The algorithm gives a small set of regimes where for each +regime, the solutions of the specialized systems may be given +uniformly. For homogeneous linear systems, or for systems were the +right hand side is arbitrary, this small set is irredunant. We discuss +in detail practical issues concerning implementations, with particular +emphasis on simplification of results. Examples are given based on a +close implementation of the algorithm in SCRATCHPAD II. We also give a +complexity analysis of the Gaussian elimination method and compare +that with our algorithm. +\end{adjustwidth} \bibitem[Sit 06]{Sit06} Sit, Emil\\ Tools for Repeatable Research''\\ @@ -2253,6 +2305,30 @@ December 4, 2000. DASL - Data Approximation Subroutine Library''\\ National Physical Laboratory. (1982) +\bibitem[Arnon 88]{Arno88} Arno, D.S.; MIgnotte, M.\\ +On Mechanical Quantifier Elimination for Elementary Algebra and Geometry''\\ +J. Symbolic Computation 5, 237-259 (1988) +\verb|http://www.sciencedirect.com/science/article/pii/S0747717188800142/|\\ +\verb|pdf?md5=62052077d84e6078cc024bc8e29c23c1&| +\verb|pid=1-s2.0-S0747717188800142-main.pdf| +%\verb|axiom-developer.org/axiom-website/papers/Arno88.pdf| + +\begin{adjustwidth}{2.5em}{0pt} +We give solutions to two problems of elementary algebra and geometry: +(1) find conditions on real numbers $p$, $q$, and $r$ so that the +polynomial function $f(x)=x^4+px^2+qx+r$ is nonnegative for all real +$x$ and (2) find conditions on real numbers $a$, $b$, and $c$ so that +the ellipse $\frac{(x-e)^2}{q^2}+\frac{y^2}{b^2}-1=0$ lies inside the +unit circle $y^2+x^2-1=0$. Our solutions are obtained by following the +basic outline of the method of quantifier elimination by cylindrical +algebraic decomposition (Collins, 1975), but we have developed, and +have been considerably aided by, modified versions of certain of its +steps. We have found three equally simple but not obviously equivalent +solutions for the first problem, illustrating the difficulty of +obtaining unique simplest'' solutions to quantifier elimination +problems of elementary algebra and geometry. +\end{adjustwidth} + \bibitem[Aubry 99]{ALM99} P. Aubry; D. Lazard; M. Moreno Maza\\ On the Theories of Triangular Sets''\\ Journal of Symbolic Computation 1999 Vol 28 pp105-124 @@ -2365,6 +2441,7 @@ Mathematics of Computation, vol. 35, num. 35, Oct. 1980, 1379-1381 The Transcendental Risch Differential Equation''\\ J. Symbolic Computation (1990) 9, pp49-60 Feb 1988\\ IBM Research Report RC13460 IBM Corp. Yorktown Heights, NY +\verb|www.sciencedirect.com/science/article/pii/S0747717108800065| %\verb|axiom-developer.org/axiom-website/papers/Bro88.pdf| \begin{adjustwidth}{2.5em}{0pt} @@ -2417,6 +2494,20 @@ In Bronstein [Bro93] pp157-160 ISBN 0-89791-604-2 LCCN QA76.95 I59 1993\\ \bibitem[Bronstein 98]{REF-Bro98} Bronstein, M.\\ The lazy hermite reduction''\\ Rapport de Recherche RR-3562, INRIA, 1998 +%\verb|axiom-developer.org/axiom-website/papers/REF-Bro98.pdf| + +\begin{adjustwidth}{2.5em}{0pt} +The Hermite reduction is a symbolic integration technique that reduces +algebraic functions to integrands having only simple affine +poles. While it is very effective in the case of simple radical +extensions, its use in more general algebraic extensions requires the +precomputation of an integral basis, which makes the reduction +impractical for either multiple algebraic extensions or complicated +ground fields. In this paper, we show that the Hermite reduction can +be performed without {\sl a priori} computation of either a primitive +element or integral basis, computing the smallest order necessary for +a particular integrand along the way. +\end{adjustwidth} \bibitem[Bronstein 98b]{Bro98b} Bronstein, Manuel\\ Symbolic Integration Tutorial''\\ @@ -2637,6 +2728,62 @@ Journal of Pure and Applied Algebra V145 No 2 Jan 2000 pp149-163 equations''\\ A.E.R.E. Report R.8730. HMSO. (1977) +\bibitem[Duval 94a]{Duva94a} Duval, D.; Reynaud, J.C.\\ +Sketches and Computation (Part I): Basic Definitions and Static Evaluation''\\ +Mathematical Structures in Computer Science, 4, p 185-238 Cambridge University Press (1994) +\verb|journals.cambridge.org/abstract_S0960129500000438| +%\verb|axiom-developer.org/axiom-website/papers/Duva94a.pdf| + +\begin{adjustwidth}{2.5em}{0pt} +We define a categorical framework, based on the notion of {\sl +sketch}, for specification and evaluation in the sense of algebraic +specifications and algebraic programming. This framework goes far +beyond our initial motivations, which was to specify computation with +algebraic numbers. We begin by redefining sketches in order to deal +explicitly with programs. Expressions and terms are carefully defined +and studied, then {\sl quasi-projective sketches} are introduced. We +describe {\sl static evaluation} in these sketches: we propose a +rigorous basis for evaluation in the corresponding structures. These +structures admit an initial model, but are not necessarily +equational. In Part II (Duval and Reynaud 1994), we study a more +general process, called {\sl dynamic evaluation}, for structures that +may have no initial model. +\end{adjustwidth} + +\bibitem[Duval 94b]{Duva94b} Duval, D.; Reynaud, J.C.\\ +Sketches and Computation (Part II): Dynamic Evaluation and Applications''\\ +Mathematical Structures in Computer Science, 4, p 239-271. Cambridge University Press (1994)\\ +\verb|journals.cambridge.org/abstract_S096012950000044X| +%\verb|axiom-developer.org/axiom-website/papers/Duva94b.pdf| + +\begin{adjustwidth}{2.5em}{0pt} +In the first part of this paper (Duval and Reynaud 1994), we defined a +categorical framework, based on the notion of {\sl sketch}, for +specification and evaluation in the senses of algebraic specification +and algebraic programming. {\sl Static evaluation} in {\sl +quasi-projective sketches} was defined in Part I; in this paper, {\sl +dynamic evaluation} is introduced. It deals with more general +structures, which may have no initial model. Until now, this process +has not been used in algebraic specification systems, but computer +algebra systems are beginning to use it as a basic tool. Finally, we +give some applications of dynamic evaluation to computation in field +extensions. +\end{adjustwidth} + +\bibitem[Duval 94c]{Duva94c} Duval, Dominique\\ +Algebraic Numbers: An Example of Dynamic Evaluation''\\ +J. Symbolic Computation 18, 429-445 (1994)\\ +\verb|www.sciencedirect.com/science/article/pii/S0747717106000551| +%\verb|axiom-developer.org/axiom-website/papers/Duva94c.pdf| + +\begin{adjustwidth}{2.5em}{0pt} +Dynamic evaluation is presented through examples: computations +involving algebraic numbers, automatic case discussion according to +the characteristic of a field. Implementation questions are addressed +too. Finally, branches are presented as dual'' to binary functions, +according to the approach of sketch theory. +\end{adjustwidth} + \subsection{F} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \bibitem[Fletcher 01]{Fl01} Fletcher, John P.\\ @@ -2824,6 +2971,14 @@ Numerical Analysis Report. 134 Manchester University. (1987) The consistency of the continuum hypothesis''\\ Ann. Math. Studies, Princeton Univ. Press, 1940 +\bibitem[Goldman 87]{Gold87} Goldman, L.\\ +Integrals of multinomial systems of ordinary differential equations''\\ +J. of Pure and Applied Algebra, 45, 225-240 (1987)\\ +\verb|www.sciencedirect.com/science/article/pii/0022404987900727/pdf| +\verb|?md5=5a0c70643eab514ccf47d80e4fc6ec5a&| +\verb|pid=1-s2.0-0022404987900727-main.pdf| +%\verb|axiom-developer.org/axiom-website/papers/Gold87.pdf| + \bibitem[Gollan 90]{GG90} H. Gollan; J. Grabmeier\\ Algorithms in Representation Theory and their Realization in the Computer Algebra System Scratchpad''\\ @@ -3017,6 +3172,10 @@ Ph. D. Thesis, University of Linz, Austria, 1991 Algorithmic properties of polynomial rings''\\ Journal of Symbolic Computation 1998 +\bibitem[Kaltofen 84]{Kalt84} Kaltofen, E.\\ +A Note on the Risch Differential Equation''\\ +Proc. EUROSAM pp 359-366 (1984) + \bibitem[Kantor 89]{Kan89} Kantor,I.L.; Solodovnikov, A.S.\\ Hypercomplex Numbers''\\ Springer Verlag Heidelberg, 1989, ISBN 0-387-96980-2 @@ -3046,6 +3205,14 @@ ISBN 0-937073-81-4 Stanford CA (1992) (Sorting and Searching) Addison-Wesley 1998 +\bibitem[Kobayashi 89]{Koba89} Kobayashi, H.; Moritsugu, S.; Hogan, R.W.\\ +On Radical Zero-Dimensional Ideals''\\ +J. Symbolic Computations 8, 545-552 (1989)\\ +\verb|www.sciencedirect.com/science/article/pii/S0747717189800604/pdf| +\verb|?md5=f06dc6269514c90dcae57f0184bcbe65&| +\verb|pid=1-s2.0-S0747717189800604-main.pdf| +%\verb|axiom-developer.org/axiom-website/papers/Koba88.pdf| + \bibitem[Kolchin 73]{Kol73} Kolchin, E.R.\\ Differential Algebra and Algebraic Groups''\\ (Academic Press, 1973). @@ -3579,6 +3746,19 @@ Princeton. 517--523. 1968 Computers in Algebra and Number Theory, SIAM-AMS Proc., Vol. 4, American Math. Soc., 1991, pp191-195 +\bibitem[Singer 89]{Sing89} Singer, M.F.\\ +Formal Solutions of Differential Equations'' +J. Symbolic COmputation 10, No.1 59-94 (1990) +%\verb|axiom-developer.org/axiom-website/papers/Sing89.pdf| + +\begin{adjustwidth}{2.5em}{0pt} +We give a survey of some methods for finding formal solutions of +differential equations. These include methods for finding power series +solutions, elementary and liouvillian solutions, first integrals, Lie +theoretic methods, transform methods, asymptotic methods. A brief +discussion of difference equations is also included. +\end{adjustwidth} + \bibitem[Sit 92]{REF-Sit92} Sit, William\\ An Algorithm for Parametric Linear Systems''\\ J. Sym. Comp., April 1992 @@ -4984,6 +5164,27 @@ to show that all the solutions of a factor of such a system can be completed to solutions of the original system. \end{adjustwidth} +\bibitem[Davenport 86]{Dav86} Davenport, J.H.\\ +The Risch Differential Equation Problem''\\ +SIAM J. COMPUT. Vol 15, No. 4 1986 +%\verb|axiom-developer.org/axiom-website/papers/Dav86.pdf| + +\begin{adjustwidth}{2.5em}{0pt} +We propose a new algorithm, similar to Hermite's method for the +integration of rational functions, for the resolution of Risch +differential equations in closed form, or proving that they have no +resolution. By requiring more of the presentation of our differential +fields (in particular that the exponentials be weakly normalized), we +can avoid the introduction of arbitrary constants which have to be +solved for later. + +We also define a class of fields known as exponentially reduced, and +show that solutions of Risch differential equations which arise from +integrating in these fields satisfy the natural'' degree constraints +in their main variables, and we conjecture (after Risch and Norman) +that this is true in all variables. +\end{adjustwidth} + \bibitem[Singer 9]{Sing91.pdf} singer, Michael F.\\ Liouvillian Solutions of Linear Differential Equations with Liouvillian Coefficients''\\ J. Symbolic Computation V11 No 3 pp251-273 (1991)\\ @@ -5330,6 +5531,17 @@ where the algebraic expressions depend on a parameter as well as on the variable of integration. \end{adjustwidth} +\bibitem[Davenport 82a]{Dav82a} Davenport, J.H.\\ +The Parallel Risch Algorithm (I) +%\verb|axiom-developer.org/axiom-website/papers/Dav82a.pdf| + +\begin{adjustwidth}{2.5em}{0pt} +In this paper we review the so-called parallel Risch'' algorithm for +the integration of transcendental functions, and explain what the +problems with it are. We prove a positive result in the case of +logarithmic integrands. +\end{adjustwidth} + \bibitem[Davenport 82]{Dav82} Davenport, J.H.\\ On the Parallel Risch Algorithm (III): Use of Tangents''\\ SIGSAM V16 no. 3 pp3-6 August 1982 @@ -5354,10 +5566,12 @@ we need to understand what we mean by differentiation. \bibitem[Geddes 92a]{GCL92a} Geddes, K.O.; Czapor, S.R.; Labahn, G.\\ The Risch Integration Algorithm''\\ Algorithms for Computer Algebra, Ch 12 pp511-573 (1992) +%\verb|axiom-developer.org/axiom-website/papers/GCL92a.pdf| \bibitem[Hardy 1916]{Hard16} Hardy, G.H.\\ The Integration of Functions of a Single Variable''\\ Cambridge Unversity Press, Cambridge, 1916 +% REF:00002 \bibitem[Harrington 78]{Harr87} Harrington, S.J.\\ A new symbolic integration system in reduce''\\ @@ -5381,10 +5595,13 @@ anticipated developments in symbolic integration. Sur l'int\'{e}gration des fractions rationelles.''\\ {\sl Nouvelles Annales de Math\'{e}matiques} ($2^{eme}$ s\'{e}rie), 11:145-148, 1872 +% REF:00022 \bibitem[Horowitz 71]{Horo71} Horowitz, Ellis\\ -Algorithms for Partial Fraction Decomposition and Rational Function Integration'' -%\verb|axiom-developer.org/axiom-website/papers/Horo71.pdf| +Algorithms for Partial Fraction Decomposition and Rational Function Integration''\\ +SYMSAC '71 Proc. ACM Symp. on Symbolic and Algebraic Manipulation (1971) +pp441-457 +%\verb|axiom-developer.org/axiom-website/papers/Horo71.pdf| REF:00018 \begin{adjustwidth}{2.5em}{0pt} Algorithms for symbolic partial fraction decomposition and indefinite @@ -5543,7 +5760,7 @@ divisible by $Q$. \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| +%\verb|axiom-developer.org/axiom-website/papers/Mos76.pdf| REF:00048 \begin{adjustwidth}{2.5em}{0pt} Risch's decision procedure for determining the integrability in closed @@ -5556,8 +5773,9 @@ of current research. \bibitem[Moses 71a]{Mos71a} Moses, Joel\\ Symbolic Integration: The Stormy Decade''\\ +CACM Aug 1971 Vol 14 No 8 pp548-560 \verb|www-inst.eecs.berkeley.edu/~cs282/sp02/readings/moses-int.pdf| -%\verb|axiom-developer.org/axiom-website/papers/Mos71a.pdf| +%\verb|axiom-developer.org/axiom-website/papers/Mos71a.pdf| REF:00017 \begin{adjustwidth}{2.5em}{0pt} Three approaches to symbolic integration in the 1960's are @@ -5573,10 +5791,28 @@ functions and programs for solving differential equations and for finding the definite integral are also described. \end{adjustwidth} +\bibitem[Norman 79]{Nor79} Norman, A.C.; Davenport, J.H.\\ +Symbolic Integration -- The Dust Settles?''\\ +%\verb|axiom-developer.org/axiom-website/papers/Nor79.pdf| + +\begin{adjustwidth}{2.5em}{0pt} +By the end of the 1960s it had been shown that a computer could find +indefinite integrals with a competence exceeding that of typical +undergraduates. This practical advance was backed up by algorithmic +interpretations of a number of clasical results on integration, and by +some significant mathematical extensions to these same results. At +that time it would have been possible to claim that all the major +barriers in the way of a complete system for automated analysis had +been breached. In this paper we survey the work that has grown out of +the above-mentioned early results, showing where the development has +been smooth and where it has spurred work in seemingly unrelated fields. +\end{adjustwidth} + \bibitem[Ostrowski 46]{Ost46} Ostrowski, A.\\ Sur l'int\'egrabilit\'e \'el\'ementaire de quelques classes d'expressions''\\ Comm. Math. Helv., Vol 18 pp 283-308, (1946) +% REF:00008 \bibitem[Raab 12]{Raab12} Raab, Clemens G.\\ Definite Integration in Differential Fields''\\ @@ -5713,11 +5949,11 @@ Research Report RC-2042, IBM Research, Yorktown Heights, NY, USA, 1969 {\sl Transactions of the American Mathematical Society} 139:167-189, 1969 %\verb|axiom-developer.org/axiom-website/papers/Ris69b.pdf| -\bibitem[Risch 69c]{Ris69c} Risch, Robert\\ +\bibitem[Risch 70]{Ris70} Risch, Robert\\ The Solution of the Problem of Integration in Finite Terms''\\ \verb|www.ams.org/journals/bull/1970-76-03/S0002-9904-1970-12454-5/| \verb|S0002-9904-1970-12454-5.pdf| -%\verb|axiom-developer.org/axiom-website/papers/Ris69c.pdf| +%\verb|axiom-developer.org/axiom-website/papers/Ris70.pdf| REF:00013 \begin{adjustwidth}{2.5em}{0pt} The problem of integration in finite terms asks for an algorithm for @@ -5740,12 +5976,13 @@ involved. \bibitem[Ritt 48]{Ritt48} Ritt, J.F.\\ Integration in Finite Terms''\\ Columbia University Press, New York 1948 +% REF:00046 \bibitem[Rosenlicht 68]{Ro68} Rosenlicht, Maxwell\\ Liouville's Theorem on Functions with Elementary Integrals''\\ 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| REF:00047 \begin{adjustwidth}{2.5em}{0pt} Defining a function with one variable to be elemetary if it has an @@ -5767,14 +6004,14 @@ simplicity and generalization. \bibitem[Rosenlicht 72]{Ro72} Rosenlicht, Maxwell\\ Integration in finite terms''\\ {\sl American Mathematical Monthly}, 79:963-972, 1972 -%\verb|axiom-developer.org/axiom-website/papers/Ro72.pdf| +%\verb|axiom-developer.org/axiom-website/papers/Ro72.pdf| REF:00045 \bibitem[Rothstein 76]{Ro76} Rothstein, Michael\\ Aspects of symbolic integration and simplifcation of exponential and primitive functions''\\ PhD thesis, University of Wisconsin-Madison (1976) \verb|www.cs.kent.edu/~rothstei/dis.pdf| -#\verb|axiom-developer.org/axiom-website/papers/Ro76.pdf| +%\verb|axiom-developer.org/axiom-website/papers/Ro76.pdf| REF:00051 \begin{adjustwidth}{2.5em}{0pt} In this thesis we cover some aspects of the theory necessary to obtain @@ -5805,7 +6042,7 @@ In this paper a generalization of the Risch Structure Theorem is reported. The generalization applies to fields $F(t_1,\ldots,t_n)$ where $F$ is a differential field (in our applications $F$ will be a finitely generated extension of $Q$, the field of rational numbers) and each $t_i$ -is either algebraic over $F_{i-1}=F(t_1,\ldots,t_{i-1}), is an exponential +is either algebraic over$F_{i-1}=F(t_1,\ldots,t_{i-1})$, is an exponential of an element in$F_{i-1}$, or is an integral of an element in$F_{i-1}$. If$t_i$is an integral and can be expressed using logarithms, it must be so expressed for the generalized structure theorem to apply. @@ -5814,7 +6051,7 @@ so expressed for the generalized structure theorem to apply. \bibitem[Rothstein 76b]{Ro76b} Rothstein, Michael; Caviness, B.F.\\ A structure theorem for exponential and primitive functions''\\ SIAM J. Computing Vol 8 No 3 (1979) -%\verb|axiom-developer.org/axiom-website/papers/Ro76b.pdf| +%\verb|axiom-developer.org/axiom-website/papers/Ro76b.pdf| REF:00104 \begin{adjustwidth}{2.5em}{0pt} In this paper a new theorem is proved that generalizes a result of @@ -5863,6 +6100,41 @@ rational operations has an integral which can be expressed in terms of elementary functions and error functions. \end{adjustwidth} +\bibitem[Slagle 61]{Slag61} Slagle, J.\\ +A heuristic program that solves symbolic integration problems in freshman calculus''\\ +Ph.D Diss. MIT, May 1961; also Computers and Thought, Feigenbaum and Feldman. +% REF:00014 + +\bibitem[Terelius 09]{Tere09} Terelius, Bjorn\\ +Symbolic Integration''\\ +%\verb|axiom-developer.org/axiom-website/papers/Tere09.pdf| + +\begin{adjustwidth}{2.5em}{0pt} +Symbolic integration is the problem of expressing an indefinite integral +$\int{f}$of a given function$f$as a finite combination$g$of elementary +functions, or more generally, to determine whether a certain class of +functions contains an element$g$such that$g^\prime = f$. + +In the first part of this thesis, we compare different algorithms for +symbolic integration. Specifically, we review the integration rules +taught in calculus courses and how they can be used systematically to +create a reasonable, but somewhat limited, integration method. Then we +present the differential algebra required to prove the transcendental +cases of Risch's algorithm. Risch's algorithm decides if the integral +of an elementary function is elementary and if so computes it. The +presentation is mostly self-contained and, we hope, simpler than +previous descriptions of the algorithm. Finally, we describe +Risch-Norman's algorithm which, although it is not a decision +procedure, works well in practice and is considerably simpler than the +full Risch algorithm. + +In the second part of this thesis, we briefly discuss an +implementation of a computer algebra system and some of the +experiences it has given us. We also demonstrate an implementation of +the rule-based approach and how it can be used, not only to compute +integrals, but also to generate readable derivations of the results. +\end{adjustwidth} + \bibitem[Trager 76]{Tr76} Trager, Barry\\ Algebraic factoring and rational function integration''\\ In {Proceedings of SYMSAC'76} pages 219-226, 1976 @@ -5884,7 +6156,7 @@ be expressed. Algorithms for Manipulating Algebraic Functions''\\ MIT Master's Thesis.\\ \verb|www.dm.unipi.it/pages/gianni/public_html/Alg-Comp/fattorizzazione-EA.pdf| -%\verb|axiom-developer.org/axiom-website/papers/Tr76a.pdf| +%\verb|axiom-developer.org/axiom-website/papers/Tr76a.pdf| REF:00050 \begin{adjustwidth}{2.5em}{0pt} Given a base field$k$, of characteristic zero, with effective @@ -6013,5 +6285,12 @@ basis for various algorithms in Ore rings, in particular, in differential, shift, and$q\$-shift rings. \end{adjustwidth} +\subsection{Number Theory} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\bibitem[Shoup 08]{Sho08} Shoup, Victor\\ +A Computational Introduction to Number Theory''\\ +\verb|shoup.net/ntb/ntb-v2.pdf| +%\verb|axiom-developer.org/axiom-website/papers/Sho08.pdf| + \end{thebibliography} \end{document} diff --git a/changelog b/changelog index 49887d8..34888f8 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,5 @@ +20140825 tpd src/axiom-website/patches.html 20140825.02.tpd.patch +20140825 tpd books/bookvolbib fix typos 20140825 tpd src/axiom-website/patches.html 20140825.01.tpd.patch 20140825 tpd buglist add 7259 from taylorseries.input 20140825 tpd src/input/Makefile add taylorseries.input diff --git a/patch b/patch index b98bb6a..633e02e 100644 --- a/patch +++ b/patch @@ -1,3 +1,3 @@ -src/input/taylorseries.input add taylor series regression test +books/bookvolbib fix typos -Ralf Hemmecke / Bill Page taylor series regression test +minor typo fixes diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 44d2389..c4b9cc5 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -4610,6 +4610,8 @@ books/bookvolbib add bibliographic references