From 92ce168f6d19bfb30cce64ed1b655e75ad595006 Mon Sep 17 00:00:00 2001
From: Tim Daly
Date: Mon, 20 Jun 2016 23:12:51 -0400
Subject: [PATCH] books/bookvolbib add Ritt50, Hubb category
DifferentialVariableCategory
Goal: Axiom Literate Programming
Collect algebra references in the bibliography
\index{Ritt, Joseph Fels}
\begin{chunk}{axiom.bib}
@article{Ritt50,
author = "Ritt, Joseph Fels",
title = "Differential Algebra",
journal = "AMS Colloquium Publications",
volume = "33",
isbn = "978-0-8218-4638-4",
paper = "Ritt50.pdf",
comment = "\refto{category DVARCAT DifferentialVariableCategory}"
}
\end{chunk}
\index{Hubbard, John H.}
\index{Lundell, Benjamin}
\begin{chunk}{axiom.bib}
@misc{Hubb,
author = "Hubbard, John H. and Lundell, Benjamin",
title = "A First Look at Differential Algebra",
url = "http://www.math.cornell.edu/~hubbard/diffalg1.pdf",
paper = "Hubb.pdf",
comment = "\refto{category DVARCAT DifferentialVariableCategory}",
abstract =
"The object of the paper is to prove that the differential equation
\[u^{'}(t)=t-[u(t)]^2\]
has no solutions which can be written using elementary functions, or
anti-derivatives of elementary functions, or exponentials of such
anti-derivatives, or anti-derivative of those, etc. We should note
that Equation 1 can be solved using power series, integrals which
depend on a parameter, or Bessel functions of order $1/3$. However,
as we will see, none of these methods of solution are ``algebraic'' in
nature.
We aim to give a precise definition of ``algebraic'' by developing the
theory of {\sl differential algebra}, which is largely the work of
Ritt. Other contributors are Liouville, Picard, Vessoit, Kolchin,
Rosenlicht, ... The part of differential Galois theory which leads to
a proof of Abel's celebrated result that a general polynomial equation
of degree five or higher cannot be solved by radicals. In effort to
derive these two areas in parallel, we will also explain why the
polynomial equation
\[x^5-4x^2-2=0\]
has no solutions which can be written as radicals of solutions to
lower degree polyomial equations."
}
\end{chunk}
---
books/bookvol10.2.pamphlet | 2 +
books/bookvolbib.pamphlet | 47 +++++++++++++++++++++++++++--
changelog | 3 ++
patch | 64 +++++++++++++++++++++++++---------------
src/axiom-website/patches.html | 2 +
5 files changed, 91 insertions(+), 27 deletions(-)
diff --git a/books/bookvol10.2.pamphlet b/books/bookvol10.2.pamphlet
index 66473b5..7b50123 100644
--- a/books/bookvol10.2.pamphlet
+++ b/books/bookvol10.2.pamphlet
@@ -15637,6 +15637,8 @@ These exports come from \refto{RetractableTo}(S:OrderedSet):
\begin{verbatim}
\end{verbatim}
+See: Ritt \cite{Ritt50}, Hubbard and Lundell \cite{Hubb}
+\label{category DVARCAT DifferentialVariableCategory}
\begin{chunk}{category DVARCAT DifferentialVariableCategory}
)abbrev category DVARCAT DifferentialVariableCategory
++ Author: William Sit
diff --git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index f86ad7b..f95c3bd 100644
--- a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ -16209,6 +16209,41 @@ IEEE Comput. Soc. Press, pp. 678--687.
\end{chunk}
+\index{Hubbard, John H.}
+\index{Lundell, Benjamin}
+\begin{chunk}{axiom.bib}
+@misc{Hubb,
+ author = "Hubbard, John H. and Lundell, Benjamin",
+ title = "A First Look at Differential Algebra",
+ url = "http://www.math.cornell.edu/~hubbard/diffalg1.pdf",
+ paper = "Hubb.pdf",
+ comment = "\refto{category DVARCAT DifferentialVariableCategory}",
+ abstract =
+ "The object of the paper is to prove that the differential equation
+ \[u^{'}(t)=t-[u(t)]^2\]
+ has no solutions which can be written using elementary functions, or
+ anti-derivatives of elementary functions, or exponentials of such
+ anti-derivatives, or anti-derivative of those, etc. We should note
+ that Equation 1 can be solved using power series, integrals which
+ depend on a parameter, or Bessel functions of order $1/3$. However,
+ as we will see, none of these methods of solution are ``algebraic'' in
+ nature.
+
+ We aim to give a precise definition of ``algebraic'' by developing the
+ theory of {\sl differential algebra}, which is largely the work of
+ Ritt. Other contributors are Liouville, Picard, Vessoit, Kolchin,
+ Rosenlicht, ... The part of differential Galois theory which leads to
+ a proof of Abel's celebrated result that a general polynomial equation
+ of degree five or higher cannot be solved by radicals. In effort to
+ derive these two areas in parallel, we will also explain why the
+ polynomial equation
+ \[x^5-4x^2-2=0\]
+ has no solutions which can be written as radicals of solutions to
+ lower degree polyomial equations."
+}
+
+\end{chunk}
+
\subsection{I} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{chunk}{ignore}
@@ -17552,10 +17587,16 @@ November 1996.
\end{chunk}
\index{Ritt, Joseph Fels}
-\begin{chunk}{ignore}
-\bibitem[Ritt 50]{Ritt50} Ritt, Joseph Fels
+\begin{chunk}{axiom.bib}
+@article{Ritt50,
+ author = "Ritt, Joseph Fels",
title = "Differential Algebra",
-AMS Colloquium Publications Volume 33 ISBN 978-0-8218-4638-4
+ journal = "AMS Colloquium Publications",
+ volume = "33",
+ isbn = "978-0-8218-4638-4",
+ paper = "Ritt50.pdf",
+ comment = "\refto{category DVARCAT DifferentialVariableCategory}"
+}
\end{chunk}
diff --git a/changelog b/changelog
index a9edeee..5ff8329 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,6 @@
+20160620 tpd src/axiom-website/patches.html 20160620.04.tpd.patch
+20160620 tpd books/bookvol10.2 add Ritt50, Hubb DifferentialVariableCategory
+20160620 tpd books/bookvolbib add Ritt50, Hubb DifferentialVariableCategory
20160620 tpd src/axiom-website/patches.html 20160620.03.tpd.patch
20160620 tpd books/bookvol10.2 add Jaco51, Jaco68 category MONAD Monad
20160620 tpd books/bookvolbib add Jaco51, Jaco68 category MONAD Monad
diff --git a/patch b/patch
index d1b1207..8e903b4 100644
--- a/patch
+++ b/patch
@@ -1,38 +1,54 @@
-books/bookvolbib add Jaco51, Jaco68 category MONAD Monad
+books/bookvolbib add Ritt50, Hubb category DifferentialVariableCategory
Goal: Axiom Literate Programming
Collect algebra references in the bibliography
-\index{Jacobson, Nathan}
+\index{Ritt, Joseph Fels}
\begin{chunk}{axiom.bib}
-@article{Jaco51,
- author = "Jacobson, Nathan",
- title = "General Representation Theory of Jordan Algebras",
- journal = "Trans. of the American Mathematical Society",
- volume = "70",
- number = "3",
- year = "1951",
- pages = "509-530",
- url = "http://www.math.uci.edu/~brusso/jacobson1951.pdf",
- paper = "Jaco51.pdf",
- comment = "\refto{category MONAD Monad}"
+@article{Ritt50,
+ author = "Ritt, Joseph Fels",
+ title = "Differential Algebra",
+ journal = "AMS Colloquium Publications",
+ volume = "33",
+ isbn = "978-0-8218-4638-4",
+ paper = "Ritt50.pdf",
+ comment = "\refto{category DVARCAT DifferentialVariableCategory}"
}
\end{chunk}
-\index{Jacobson, Nathan}
+\index{Hubbard, John H.}
+\index{Lundell, Benjamin}
\begin{chunk}{axiom.bib}
-@article{Jaco68,
- author = "Jacobson, Nathan",
- title = "Structure and Representations of Jordan Algebras",
- journal = "Bull. Amer. Math. Soc",
- volume = "79",
- number = "3",
- year = "1973",
- pages = "509-514",
- url = "http://projecteuclid.org/euclid.bams/1183534656",
- comment = "\refto{category MONAD Monad}"
+@misc{Hubb,
+ author = "Hubbard, John H. and Lundell, Benjamin",
+ title = "A First Look at Differential Algebra",
+ url = "http://www.math.cornell.edu/~hubbard/diffalg1.pdf",
+ paper = "Hubb.pdf",
+ comment = "\refto{category DVARCAT DifferentialVariableCategory}",
+ abstract =
+ "The object of the paper is to prove that the differential equation
+ \[u^{'}(t)=t-[u(t)]^2\]
+ has no solutions which can be written using elementary functions, or
+ anti-derivatives of elementary functions, or exponentials of such
+ anti-derivatives, or anti-derivative of those, etc. We should note
+ that Equation 1 can be solved using power series, integrals which
+ depend on a parameter, or Bessel functions of order $1/3$. However,
+ as we will see, none of these methods of solution are ``algebraic'' in
+ nature.
+
+ We aim to give a precise definition of ``algebraic'' by developing the
+ theory of {\sl differential algebra}, which is largely the work of
+ Ritt. Other contributors are Liouville, Picard, Vessoit, Kolchin,
+ Rosenlicht, ... The part of differential Galois theory which leads to
+ a proof of Abel's celebrated result that a general polynomial equation
+ of degree five or higher cannot be solved by radicals. In effort to
+ derive these two areas in parallel, we will also explain why the
+ polynomial equation
+ \[x^5-4x^2-2=0\]
+ has no solutions which can be written as radicals of solutions to
+ lower degree polyomial equations."
}
\end{chunk}
diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html
index 2e6c202..7550b73 100644
--- a/src/axiom-website/patches.html
+++ b/src/axiom-website/patches.html
@@ -5344,6 +5344,8 @@ books/bookvolbib add Saun79, Category GRMOD GradedModule

books/bookvolbib add Dele06, Bron96a category LORER LeftOreRing

20160620.03.tpd.patch
books/bookvolbib add Jaco51, Jaco68 category MONAD Monad

+20160620.04.tpd.patch
+books/bookvolbib add Ritt50, Hubb category DifferentialVariableCategory

--
1.7.5.4