From d077dc08163d05b12484a154039d931cef2e27d1 Mon Sep 17 00:00:00 2001
From: Tim Daly
Date: Sun, 26 Jun 2016 08:00:01 0400
Subject: [PATCH] books/bookvol10.3 Add Riob92, Emir04 domain RECLOS
RealClosure
Goal: Axiom Literate Programming

books/bookvol10.3.pamphlet  6 +
changelog  2 +
patch  252 +
src/axiomwebsite/patches.html  2 +
4 files changed, 11 insertions(+), 251 deletions()
diff git a/books/bookvol10.3.pamphlet b/books/bookvol10.3.pamphlet
index a3d93e0..d2a2109 100644
 a/books/bookvol10.3.pamphlet
+++ b/books/bookvol10.3.pamphlet
@@ 166084,11 +166084,17 @@ o )show RealClosure
\cross{RECLOS}{?rem?} &
\end{tabular}
+See: Rioboo\cite{Riob92}, Emiris\cite{Emir04}
+\label{domain RECLOS RealClosure}
\begin{chunk}{domain RECLOS RealClosure}
)abbrev domain RECLOS RealClosure
++ Author: Renaud Rioboo
++ Date Created: summer 1988
++ Date Last Updated: January 2004
+++ References:
+++ Riob92 Real algebraic closure of an ordered field,
+++ Implementation in Axiom
+++ Emir04 Comparing real algebraic numbers of small degree
++ Description:
++ This domain implements the real closure of an ordered field.
++ Note:
diff git a/changelog b/changelog
index 2bb2dc8..2cc857e 100644
 a/changelog
+++ b/changelog
@@ 1,3 +1,5 @@
+20160626 tpd src/axiomwebsite/patches.html 20160625.02.tpd.patch
+20160626 tpd books/bookvol10.3 Add Riob92, Emir04 domain RECLOS RealClosure
20160626 tpd src/axiomwebsite/patches.html 20160625.01.tpd.patch
20160626 tpd books/bookvolbib Axiom Citations in the Literature
20160625 tpd src/axiomwebsite/patches.html 20160625.08.tpd.patch
diff git a/patch b/patch
index ce40e2a..6873230 100644
 a/patch
+++ b/patch
@@ 1,254 +1,4 @@
books/bookvolbib Axiom Citations in the Literature
+books/bookvol10.3 Add Riob92, Emir04 domain RECLOS RealClosure
Goal: Axiom Literate Programming
\index{Gottlieben, Hanne}
\index{Kelsey, Tom}
\index{Martin, Ursula}
\begin{chunk}{axiom.bib}
@article{Gott05,
 author = "Gottliebsen, Hanne and Kelsey, Tom and Martin, Ursula",
 title = "Hidden verification for computational mathematics",
 journal = "Journal of Symbolic Computation",
 volume = "39",
 number = "5",
 pages = "539567",
 year = "2005",
 url = "http://www.sciencedirect.com/science/article/pii/S0747717105000295",
 paper = "Gott05.pdf",
 keywords = "axiomref",
 abstract =
 "We present hidden verification as a means to make the power of
 computational logic available to users of computer algebra systems
 while shielding them from its complexity. We have implemented in PVS a
 library of facts about elementary and transcendental function, and
 automatic procedures to attempt proofs of continuity, convergence and
 differentiability for functions in this class. These are called
 directly from Maple by a simple pipelined interface. Hence we are
 able to support the analysis of differential equations in Maple by
 direct calls to PVS for: result refinement and verification, discharge
 of verification conditions, harnesses to ensure more reliable
 differential equation solvers, and verifiable lookup tables."
}

\end{chunk}

\index{Kaplan, Michael}
\begin{chunk}{axiom.bib}
@book{Kapl05,
 author = "Kaplan, Michael",
 title = "Computer Algebra",
 publisher = "Springer, Berlin, Germany",
 year = "2005",
 isbn = "3540213791",
 keywords = "axiomref",
 comment = "German Language"
}

\end{chunk}

\index{Oancea, Cosmin E.}
\index{Watt, Stephen M.}
\begin{chunk}{axiom.bib}
@InProceedings{Oanc05,
 author = "Oancea, Cosmin E. and Watt, Stephen M.",
 title = "Domains and expressions: an interface between two approaches to
 computer algebra",
 booktitle = "Proc. 2005 ISSAC",
 series = "ISSAC 2005",
 year = "2005",
 isbn = "1595930957",
 location = "Beijing, China",
 pages = "261268",
 keywords = "axiomref",
 paper = "Oanc05.pdf",
 url = "http://www.csd.uwo.ca/~watt/pub/reprints/2005issacalma.pdf",
 abstract =
 "This paper describes a method to use compiled, strongly typed Aldor
 domains in the interpreted, expressionoriented Maple
 environment. This represents a nontraditional approach to structuring
 computer algebra software: using an efficient, compiled language,
 designed for writing large complex mathematical libraries, together
 with a toplevel system based on userinterface priorities and ease of
 scripting.

 We examine what is required to use Aldor libraries to extend Maple in
 an effective and natural way. Since the computational models of Maple
 and Aldor differ significantly, new runtime code must implement a
 nontrivial semantic correspondence. Our solution allows Aldor
 functions to run tightly coupled to the Maple environment, able to
 directly and efficiently manipulate Maple data objects. We call the
 overall system Alma."
}

\end{chunk}

\index{Brunelli, J.C.}
\begin{chunk}{axiom.bib}
\article{Brun04,
 author = "Brunelli, J.C.",
 title = "PSEUDO: applications of streams and lazy evaluation to integrable
 models",
 journal = "Comput. Phys. Commun.",
 volume = "163",
 number = "1",
 pages = "2240",
 year = "2004",
 keywords = "axiomref",
 url =
 paper =
 abstract =
 "Procedures to manipulate pseudodifferential operators in MAPLE are
 implemented in the program PSEUDO to perform calculations with
 integrable models. We use lazy evaluation and streams to represent and
 operate with pseudodifferential operators. No order of truncation is
 needed since terms are produced on demand. We give a series of
 concrete examples."
}

\end{chunk}

\index{Emiris, Ioannis Z.}
\index{Tsigaridas, Elias P.}
\begin{chunk}{axiom.bib}
@InProceedings{Emir04,
 author = "Emiris, Ioannis Z. and Tsigaridas, Elias P.",
 title = "Comparing real algebraic numbers of small degree",
 booktitle = "12th annual European symposium",
 series = "ESA 2004",
 year = "2004",
 isbn = "3540230254",
 location = "Bergen, Norway",
 pages = "652663",
 keywords = "axiomref",
 paper = "Emir04.pdf",
 url = "http://wwwpolsys.lip6.fr/~elias/files//etesa04.pdf",
 comment = "\newline\refto{domain RECLOS RealClosure}",
 abstract =
 "We study polynomials of degree up to 4 over the rationals or a
 computable real subfield. Our motivation comes from the need to
 evaluate predicates in nonlinear computational geometry efficiently
 and exactly. We show a new method to compare real algebraic numbers by
 precomputing generalized Sturm sequences, thus avoiding iterative
 methods; the method, moreover handles all degenerate cases. Our first
 contribution is the determination of rational isolating points, as
 functions of the coefficients, between any pair of real roots. Our
 second contribution is to exploit invariants and Bezoutian
 subexpressions in writing the sequences, in order to reduce bit
 complexity. The degree of the tested quantities in the input
 coefficients is optimal for degree up to 3, and for degree 4 in
 certain cases. Our methods readily apply to real solving of pairs of
 quadratic equations, and to sign determination of polynomials over
 algebraic numbers of degree up to 4. Our third contribution is an
 implementation in a new module of library SYNAPS v2.1. It improves
 significantly upon the efficiency of certain publicly available
 implementations: Riobooâ€™s approach on AXIOM, the package of
 GuibasKaravelasRussel, and CORE v1.6, MAPLE v9, and SYNAPS
 v2.0. Some existing limited tests had shown that it is faster than
 commercial library LEDA v4.5 for quadratic algebraic numbers."
}

\end{chunk}

\index{Rioboo, Renaud}
\begin{chunk}{axiom.bib}
@InProceedings{Riob92,
 author = "Rioboo, Renaud",
 title = "Real algebraic closure of an ordered field,
 Implementation in Axiom",
 booktitle = "Proc. ISSAC 92",
 series = "ISSAC 92",
 year = "1992",
 isbn = "9783540751861",
 location = "Berkeley, California",
 pages = "206215",
 isbn = "0897914899 (soft), 0897914902 (hard)",
 paper = "Riob92.pdf",
 keywords = "axiomref",
 comment = "\newline\refto{domain RECLOS RealClosure}",
 abstract = "
 Real algebraic numbers appear in many Computer Algebra problems. For
 instance the determination of a cylindrical algebraic decomposition
 for an euclidean space requires computing with real algebraic numbers.
 This paper describes an implementation for computations with the real
 roots of a polynomial. This process is designed to be recursively
 used, so the resulting domain of computation is the set of all real
 algebraic numbers. An implementation for the real algebraic closure
 has been done in Axiom (previously called Scratchpad)."
}

\end{chunk}

\index{Hivert, Florent}
\index{Thiery, Nicolas M.}
\begin{chunk}{axiom.bib}
@article{Hive04,
 author = "Hivert, Florent and Thiery, Nicolas M.",
 title = "MuPADCombinat, an opensource package for research in
 algebraic combinatorics",
 journal = "Seminaire Lotharingien de Combinatoire",
 volume = "51",
 number = "B51z",
 year = "2004",
 keywords = "axiomref",
 url = "http://www.emis.de/journals/SLC/wpapers/s51thiery.pdf",
 paper = "Hive04.pdf",
 abstract =
 "In this article we give an overview of the MuPADCombinat opensource
 algebraic combinatorics package for the computer algebra system MuPAD
 2.0.0 and higher. This includes our motivations for developing yet
 another combinatorial software, a tutorial introduction with lots of
 examples, as well as notes on the general design. The material
 presented here is also available as a part of the MuPADCombinat
 handbook; further details and references on the algorithms used can be
 found there. The package and the handbook are available from the web
 page, together with download and installation instructions, mailing
 lists, etc."
}

\end{chunk}

\index{Hemmecke, Ralf}
\index{Rubey, Martin}
\begin{chunk}{axiom.bib}
@misc{RISC06,
 title = "AXIOM Workshop 2006",
 url = "http://axiomwiki.newsynthesis.org/WorkShopRISC2006",
 year = "2006",
 location = "Hagenberg, Austria",
 keywords = "axiomref",
 abstract =
 "Axiom is a computer algebra system with a long tradition. It recently
 became free software.

 The workshop aims at a cooperation of Axiom developers with developers
 of packages written for other Computer Algebra Systems or developers
 of standalone packages. Furthermore, the workshop wants to make the
 potential of Axiom and Aldor more widely known in order to attract new
 users and new developers."
}

\end{chunk}

\index{Hemmecke, Ralf}
\index{Rubey, Martin}
\begin{chunk}{axiom.bib}
@misc{RISC07,
 title = "AXIOM Workshop 2007",
 url = "http://axiomwiki.newsynthesis.org/WorkShopRISC2007",
 year = "2007",
 location = "Hagenberg, Austria",
 keywords = "axiomref",
 abstract =
 "The workshop aims at a cooperation of Axiom developers with deelopers
 of packages written for other Computer Algebra Systems, and
 mathematicians that would like to use a computer algebra system to
 perform experiments.

 One goal of the workshop is to learn about the mathematical theory,
 the design of packages written for other CAS and to make those
 functionalities available in Axiom."
}

\end{chunk}

diff git a/src/axiomwebsite/patches.html b/src/axiomwebsite/patches.html
index df99a83..d098014 100644
 a/src/axiomwebsite/patches.html
+++ b/src/axiomwebsite/patches.html
@@ 5394,6 +5394,8 @@ books/bookvolbib Axiom Citations in the Literature
books/bookvol10.4 add Rube06, Hebi10 GUESS references
20160626.01.tpd.patch
books/bookvolbib Axiom Citations in the Literature
+20160626.02.tpd.patch
+books/bookvol10.3 Add Riob92, Emir04 domain RECLOS RealClosure

1.7.5.4