diff --git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet index ce05d16..b0fc641 100644 --- a/books/bookvolbib.pamphlet +++ b/books/bookvolbib.pamphlet @@ -4698,6 +4698,28 @@ completed to solutions of the original system. \verb|e-collection.library.ethz.ch/eserv/eth:39463/eth-39463-01.pdf| %\verb|axiom-developer.org/axiom-website/papers/Mohr94.pdf| +\bibitem[Von Mohrenschildt 98]{Mohr98} Von Mohrenschildt, Martin\\ +``A Normal Form for Function Rings of Piecewise Functions''\\ +J. Symbolic Computation (1998) Vol 26 pp607-619\\ +\verb|www.cas.mcmaster.ca/~mohrens/JSC.pdf| +%\verb|axiom-developer.org/axiom-website/papers/Mohr98.pdf| + +\begin{adjustwidth}{2.5em}{0pt} +Computer algebra systems often have to deal with piecewise continuous +functions. These are, for example, the absolute value function, +signum, piecewise defined functions but also functions that are the +supremum or infimum of two functions. We present a new algebraic +approach to these types of problems. This paper presents a normal form +for a function ring containing piecewise polynomial functions of an +expression. The main result is that this normal form can be used to +decide extensional equality of two piecewise functions. Also we define +supremum and infimum for piecewise functions; in fact, we show that +the function ring forms a lattice. Additionally, a method to solve +equalities and inequalities in this function ring is +presented. Finally, we give a ``user interface'' to the algebraic +representation of the piecewise functions. +\end{adjustwidth} + \bibitem[Weber 06]{Webe06} Weber, Andreas\\ ``Quantifier Elimination on Real Closed Fields and Differential Equations''\\ \verb|cg.cs.uni-bonn.de/personal-pages/weber/publications/pdf/WeberA/Weber2006a.pdf| @@ -4822,6 +4844,22 @@ Cambridge Unversity Press, Cambridge, 1916 {\sl Nouvelles Annales de Math\'{e}matiques} ($2^{eme}$ s\'{e}rie), 11:145-148, 1872 +\bibitem[Jeffrey 99]{Jeff99} Jeffrey, D.J.; Labahn, G.; Mohrenschildt, M.v.; +Rich, A.D.\\ +``Integration of the signum, piecewise and related functions''\\ +\verb|cs.uwaterloo.ca/~glabahn/Papers/issac99-2.pdf| +%\verb|axiom-developer.org/axiom-website/papers/Jeff99.pdf| + +\begin{adjustwidth}{2.5em}{0pt} +When a computer algebra system has an assumption facility, it is +possible to distinguish between integration problems with respect to a +real variable, and those with respect to a complex variable. Here, a +class of integration problems is defined in which the integrand +consists of compositions of continuous functions and signum functions, +and integration is with respect to a real variable. Algorithms are +given for evaluating such integrals. +\end{adjustwidth} + \bibitem[Knowles 93]{Know93} Knowles, P.\\ ``Integration of a class of transcendental liouvillian functions with error-functions i''\\ diff --git a/changelog b/changelog index a5e4752..05799e3 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,5 @@ +20140707 tpd src/axiom-website/patches.html 20140707.02.tpd.patch +20140707 tpd books/bookvolbib add Mohr98, Jeff99 20140707 tpd src/axiom-website/patches.html 20140707.01.tpd.patch 20140707 tpd books/bookvolbib add many new references 20140706 tpd src/axiom-website/patches.html 20140706.01.tpd.patch diff --git a/patch b/patch index 9938a85..2fa739f 100644 --- a/patch +++ b/patch @@ -1,3 +1,3 @@ -books/bookvolbib add many new references +books/bookvolbib add Mohr98, Jeff99 More web searching for Axiom related references. diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 31533dc..2b91091 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -4530,6 +4530,8 @@ books/bookvolbib add Lamport book "Specifying Systems" books/bookvolbib add references Meij91, Mohr94 20140707.01.tpd.patch books/bookvolbib add many new references +20140707.02.tpd.patch +books/bookvolbib add Mohr98, Jeff99