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Date: Sat, 2 Jul 2016 22:56:15 -0400
Subject: [PATCH] books/bookvolbib Axiom Citations in the Literature
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Goal: Axiom Literate Programming
\index{Delliere, Stephane}
\begin{chunk}{axiom.bib}
@techreport{Dell00a,
author = "Delliere, Stephane",
title = {A first course to $D_7$ with examples},
institution = "Universite de Limoges",
year = "2000",
type = "technical report",
number = "2000-17",
paper = "Dell00a.pdf",
url = http://www.unilim.fr/laco/rapports/2000/R2000_17.pdf,
keywords = "axiomref"
}
\end{chunk}
\index{Watt, Stephen M.}
\begin{chunk}{axiom.bib}
@misc{Watt00,
author = "Watt, Stephen M.",
title = "Aldor: The language and recent directions",
year = "2000",
institution = "University of Western Ontario",
url = "http://www.aldor.org/docs/reports/sa2000/aldortalk-sa2000.pdf",
keywords = "axiomref",
paper = "Watt00.pdf"
}
\end{chunk}
\index{Watt, Stephen M.}
\begin{chunk}{axiom.bib}
@misc{Watt00a,
author = "Watt, Stephen M.",
title = "Aldor: An Introduction to the Language",
year = "2000",
institution = "University of Western Ontario",
url = "http://www.aldor.org/docs/reports/ukqcd-2000/intro1-ukqcd00.pdf",
keywords = "axiomref",
paper = "Watt00a.pdf"
}
\end{chunk}
\index{Koepf, Wolfram}
\begin{chunk}{axiom.bib}
@article{Koep96,
author = "Koepf, Wolfram",
title = "Closed form Laurent-Puiseux series of algebraic functions",
journal = "Appl. Algebra Eng. Commun. Comput.",
volume = "7",
number = "1",
pages = "21-26",
year = "1996",
keywords = "axiomref",
abstract =
"Let $y$ be an algebraic function defined by a polynomial equation
$P(x,y)=0$ whose coefficients are polynomials in $x$ over a field $K$
which may be one of the fields $\mathbb{Q}$, $\mathbb{R}$, or
$\mathbb{C}$. D. V. and G. V. Chudnovsky [J. Complexity 2, 271-294
(1986; Zbl 0629.68038); ibid. 3, 1-25 (1987; Zbl 0656.34003)] describe
a pair of algorithms to calculate the coefficients in the
Laurent-Puiseux developments of the branches of $y$: The first
algorithm returns a linear differential equation
\[q_n(x)y^{(n)} + y_{n-1}(x)y^{(n-1)}+\cdots+q_1(x)y^{'}+q_0(x)y=0\]
which is satisfied by all branches of $y$ and whose coefficients are
polynomials in $x$ over $K$, the other uses this differential equation
to get a linear recurrence relation for the Puiseux coefficients. The
author used this algorithms (the second in a simpler version) to
calculate the recurrence relation; if this relation contains only two
terms, an algorithm found by the author returns an explicit formula
for the Puiseux coefficients [J. Symb. Comp. 13, 581-603 (1992; Zbl
0758.30026)]. In this paper, the author gives examples to illustrate
his algorithms and to show that for many algebraic functions defined
by polynomials of low degree a closed form of their Puiseux
coefficients may be calculated. He points out that on the other side
the complexity of the resulting recurrence equation may be extremely
high even for an algebraic function defined by a sparse polynomial of
low degree."
}
\end{chunk}
\index{Norman, Arthur C.}
\begin{chunk}{axiom.bib}
@InProceedings{Norm96,
author = "Norman, Arthur C.",
title = "Memory tracing of algebraic calculations",
booktitle = "Proc. 1996 ISSAC",
series = "ISSAC 1996",
year = "1996",
publisher = "ACM Press",
location = "New York, NY",
pages = "113-119",
keywords = "axiomref",
url = "http://opus.bath.ac.uk/16452/1/NormanFitch96a.ps",
paper = "Norm96.pdf",
abstract =
"We present a software tool which allows us to visualize details of the
use of memory during the execution of an algebra system. We apply this
to gain a better understanding of the behaviour of REDUCE, and hence
to make proposals for ways in which the execution can be improved. The
same tool will soon be used in the performance engineering of a
version of axiom."
}
\end{chunk}
\index{O'Keefe, Christine M.}
\index{Storme, Leo}
\begin{chunk}{axiom.bib}
@article{OKee96,
author = "O'Keefe, Christine M. and Storme, Leo",
title = {Arcs in PG(n,q) fixed by A_5 and A_6},
journal = "J. Geom.",
volume = "55",
number = "1-2",
pages = "123-138",
year = "1996",
keywords = "axiomref",
abstract =
"A $k$-arc in a projective space is a set of points, no three of which
are collinear. The author determines the $k$ arcs in $PG(n,q)$ which
are fixed by primitive groups isomorphic to $A_5$ or $A_6$. The best
known examples are $q+1$ arcs: in general these are normal rational
curves and are conics in $PG(2,q)$ and twisted cubics in $PG(3,q)$.
The other cases turn out to be 6-arcs or 10-arcs."
}
\end{chunk}
\index{Tuomela, Jukka}
\begin{chunk}{axiom.bib}
@article{Tuom96,
author = "Tuomela, Jukka",
title = "On the construction of arbitrary order schemes for the many
dimensional wave equation",
journal = "BIT",
volume = "36",
number = "1",
pages = "158-165",
year = "1996",
keywords = "axiomref",
abstract =
"The paper is devoted to a problem which was of an interest in the
beginning of the theory of difference methods. The elementary
constructed explicit high-order approximations for the wave equation
(on the simplest cubic grid in space) assume that the solution is very
smooth and that no boundary conditions are given. Stability is also
understood in the simplest way (in $L_2$)."
}
\end{chunk}
\index{Arnault, F.}
\begin{chunk}{axiom.bib}
@article{Arna95a,
author = "Arnault, F.",
title = "Rabin-Miller primality test: Composite numbers which pass it",
journal = "Mathematics of Computation",
volume = "64",
number = "209",
pages = "355-361",
year = "1995",
keywords = "axiomref",
url =
"https://www.jointmathematicsmeetings.org/mcom/1995-64-209/S0025-5718-1995-1260124-2/S0025-5718-1995-1260124-2.pdf",
paper = "Arna95a.pdf",
abstract =
"The Rabin-Miller primality test is a probabilistic test which can be
found in several algebraic computing systems (such as Pari, Maple,
ScratchPad) because it is very easy to implement and, with a
reasonable amount of computing, indicates whether a number is
composite or ``probably prime'' with a very low probability of error. In
this paper, we compute composite numbers which are strong pseudoprimes
to several chosen bases. Because these bases are those used by the
ScratchPad implementation of the test, we obtain, by a method which
differs from a recent one by G. Jaeschke [ibid. 61, 915-926 (1993; Zbl
0802.11001)], composite numbers which are found to be ``probably prime''
by this test."
}
\end{chunk}
\index{Atkinson, M. D.}
\index{Linton, S. A.}
\index{Walker, L. A.}
\begin{chunk}{axiom.bib}
@article{Atki95,
author = "Atkinson, M. D. and Linton, S. A. and Walker, L. A.",
title = "Priority queues and multisets",
journal = "J. Comb",
volume = "2",
pages = "385-402",
year = "1995",
keywords = "axiomref",
url =
"http://www.combinatorics.org/ojs/index.php/eljc/article/download/v2i1r24.pdf",
paper = "Atki95.pdf",
abstract =
"A priority queue, a container data structure equipped with the
operations insert and delete-minimum, can re-order its input in
various ways, depending both on the input and on the sequence of
operations used. If a given input $\sigma$ can produce a particular
output $\tau$ then $(\sigma,\tau)$ is said to be an allowable pair. It
is shown that allowable pairs on a fixed multiset are in one-to-one
correspondence with certain $k$-way trees and, consequently, the
allowable pairs can be enumerated. Algorithms are presented for
determining the number of allowable pairs with a fixed input
component, or with a fixed output component. Finally, generating
functions are used to study the maximum number of output components
with a fixed input component, and a symmetry result is derived."
}
\end{chunk}
\index{Colin, Antoine}
\begin{chunk}{axiom.bib}
@InProceedings{Coli95,
author = "Colin, Antoine",
title = "Formal computation of Galois groups with relative resolvants",
booktitle = "Proc. AAECC-11",
series = "AAECC-11",
year = "1995",
publisher = "Springer-Verlag",
location = "Paris, France",
pages = "169-182",
keywords = "axiomref",
abstract =
"Let $k$ be a field and $f \in k[x]$ be a polynomial of degree $n$. The
permutation action of $G$ on the roots $\{\alpha_i\}_{i=1}^n$ of $f$
can be determined by an algorithm suggested by R. Stauduhar
[Math. Comput. 27, 981-996 (1973; Zbl 0282.12004)] that approximates $G$
via successive steps in a chain of subgroups
$S_n=H_0 > H_1 > \ldots > H_k=G$. In each step $H_{i-1} > H_i$
it checks as a test for $G \le H_i$ whether a relative invariant $k_i
\in k[x_1,\ldots,x_n]$ yields a value under the specialization
$\varphi : g(x_1,\ldots,x_n) \mapsto g(\alpha_1,\ldots,\alpha_n)$. In
implementations this evaluation has been done using $p$-adic
[H. Darmon and D. Ford, Commun. Algebra 17, No. 12, 2941-2943 (1989;
Zbl 0693.12010)] or numerical (R. Stauduhar [ibid.]; Y. Eichenlaub and
M. Olivier [preprint]) approximation of the roots.
The paper under review presents a new approach which avoids all
approximations: If $G \le H_i$ and $H_i$ is maximal in $H_{i-1}$ the
invariant $h_i$ is a primitive element of the invariant field
$k_i=k(x_1,\ldots,x_n)^{H_i}$ as an extension of
$k_{i-1}=K(x_1,\ldots,x_n)^{H_{i-1}}$.
The author develops an algorithm to express the specialized values
$\varphi(g)$ of elements $g \in k_i$ in terms of $k_{i-1}$ and the
specialization $\varphi(h_i)$.
This algorithm then is applied to the relative resolvent polynomial
\[s_i = \prod_a{(y-a(x_1,\ldots,x_n))}\]
where $a$ runs through the images of $h_i$ under $H_{i-1}.
It has $y$-coefficients which are in $k_{i-1}$.
The algorithm then permits to express the coefficients of the
specialization $r_i(y)=\varphi(s_i) \in k[y]$ recursively in the
(already known) specializations $\varphi(h_i)$ for $j \le i-1$,
using the coefficients of $f$ (as $S_n$-invariants in the roots)
as a seed. A root of $r_i(y)$ in the base field then proves that $G$
is contained in (a conjugate of) $H_i$, and this value of the root can
be used as specialized $\varphi(h_{i+1})$ in the next step of the
algorithm. Special care is given to the case when denominators of
elements in $k(x_1,\ldots,x_n)$ evaluate to zero after specialization.
The paper closes with a short discussion of applicability. An
implementation using AXIOM and GAP is in process but has not yet been
completed."
}
\end{chunk}
\index{Landau, Susan}
\begin{chunk}{axiom.bib}
@article{Land93,
author = "Landau, Susan",
title = "How to Tangle with a Nested Radical",
institution = "University of Massachusetts",
journal = "The Mathematical Intelligencer",
year = "1993",
paper = "Land93.pdf"
}
\end{chunk}
\index{Crouch, Peter E.}
\index{Lamnabhi-Lagarrigue, Francoise}
\index{Pinchon, Didier}
\begin{chunk}{axiom.bib}
@article{Crou95,
author = "Crouch, Peter E. and Lamnabhi-Lagarrigue, Francoise and
Pinchon, Didier",
title = "Some realizations of algorithms for nonlinear input-output systems",
journal = "Int. J. Control",
volume = "62",
number = "4",
pages = "941-960",
year = "1995",
keywords = "axiomref",
abstract =
"The first two authors previously developed an algorithm for
constructing a parametrization of the observation space of a nonlinear
control system directly from the differential equation representation
of the input-output behaviour. This paper extends the previous
algorithm by including settings where a set of implicit input-output
differential equations is given as well as more general state-space
representations in which the controls enter nonlinearly. Various
state-space realizations, including bilinear, polynomial and nilpotent
approximating realizations are discussed. The final section of the
paper sketches the implementation of the algorithm using the symbolic
manipulation package AXIOM to find the realizations mentioned above in
feasible cases."
}
\end{chunk}
\index{Fleischer, J.}
\index{Grabmeier, J.}
\index{Hehl, F.W.}
\index{Kuchlin, W.}
\begin{chunk}{axiom.bib}
@book{Flei94,
author = "Fleischer, J. and Grabmeier, J. and Hehl, F.W. and
Kuchlin, W. (eds)",
title = "Proc. Conf. Computer Algebra in Science and Engineering",
booktitle = "Computer Algebra in Science and Engineering",
year = "1994",
location = "Bielefeld, Germany",
publisher = "World Scientific, River Edge, NJ",
abstract =
"Systems and tools of computer algebra (Like AXIOM, Derive, FORM,
Mathematica, Maple, Mupad, REDUCE, Macsyma…) let us manipulate
extremely complex algebraic formulae symbolically on a
computer. Contrary to numerics these computations are exact and there
is no loss of accuracy. After decades of research and development,
these tools are now becoming as indispensable in Science and
Engineering as traditional number crunching already is.
The ZiF'94 workshop is amongst the first devoted specifically to
applications of computer algebra (CA) in Science and Engineering. The
book documents the state of the art in this area and serves as an
important reference for future work."
}
\end{chunk}
---
books/bookvolbib.pamphlet | 429 +++++++++++++++++++++++++++++++-
changelog | 2 +
patch | 542 ++++++++++++++++++++--------------------
src/axiom-website/patches.html | 2 +
4 files changed, 698 insertions(+), 277 deletions(-)
diff --git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index c3af887..636f585 100644
--- a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ -5960,6 +5960,19 @@ J. Symbolic COmputations 36 pp 855-889
\end{chunk}
+\index{Landau, Susan}
+\begin{chunk}{axiom.bib}
+@article{Land93,
+ author = "Landau, Susan",
+ title = "How to Tangle with a Nested Radical",
+ institution = "University of Massachusetts",
+ journal = "The Mathematical Intelligencer",
+ year = "1993",
+ paper = "Land93.pdf"
+}
+
+\end{chunk}
+
\section{Integration} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\index{Kaltofen, Erich}
@@ -11309,6 +11322,68 @@ J. Symbolic Computation 5, 237-259 (1988)
\end{chunk}
+\index{Arnault, Francois}
+\begin{chunk}{axiom.bib}
+@article{Arna95a,
+ author = "Arnault, Francois",
+ title = "Rabin-Miller primality test: Composite numbers which pass it",
+ journal = "Mathematics of Computation",
+ volume = "64",
+ number = "209",
+ pages = "355-361",
+ year = "1995",
+ keywords = "axiomref",
+ url =
+"https://www.jointmathematicsmeetings.org/mcom/1995-64-209/S0025-5718-1995-1260124-2/S0025-5718-1995-1260124-2.pdf",
+ paper = "Arna95a.pdf",
+ abstract =
+ "The Rabin-Miller primality test is a probabilistic test which can be
+ found in several algebraic computing systems (such as Pari, Maple,
+ ScratchPad) because it is very easy to implement and, with a
+ reasonable amount of computing, indicates whether a number is
+ composite or ``probably prime'' with a very low probability of error. In
+ this paper, we compute composite numbers which are strong pseudoprimes
+ to several chosen bases. Because these bases are those used by the
+ ScratchPad implementation of the test, we obtain, by a method which
+ differs from a recent one by G. Jaeschke [ibid. 61, 915-926 (1993; Zbl
+ 0802.11001)], composite numbers which are found to be ``probably prime''
+ by this test."
+}
+
+\end{chunk}
+
+\index{Atkinson, M. D.}
+\index{Linton, S. A.}
+\index{Walker, L. A.}
+\begin{chunk}{axiom.bib}
+@article{Atki95,
+ author = "Atkinson, M. D. and Linton, S. A. and Walker, L. A.",
+ title = "Priority queues and multisets",
+ journal = "J. Comb",
+ volume = "2",
+ pages = "385-402",
+ year = "1995",
+ keywords = "axiomref",
+ url =
+"http://www.combinatorics.org/ojs/index.php/eljc/article/download/v2i1r24.pdf",
+ paper = "Atki95.pdf",
+ abstract =
+ "A priority queue, a container data structure equipped with the
+ operations insert and delete-minimum, can re-order its input in
+ various ways, depending both on the input and on the sequence of
+ operations used. If a given input $\sigma$ can produce a particular
+ output $\tau$ then $(\sigma,\tau)$ is said to be an allowable pair. It
+ is shown that allowable pairs on a fixed multiset are in one-to-one
+ correspondence with certain $k$-way trees and, consequently, the
+ allowable pairs can be enumerated. Algorithms are presented for
+ determining the number of allowable pairs with a fixed input
+ component, or with a fixed output component. Finally, generating
+ functions are used to study the maximum number of output components
+ with a fixed input component, and a symmetry result is derived."
+}
+
+\end{chunk}
+
\index{Augot, D.}
\index{Charpin, P.}
\index{Sendrier, N.}
@@ -12587,6 +12662,63 @@ Proc. Natl. Acad. Sci. USA Vol 86
\index{Colin, Antoine}
\begin{chunk}{axiom.bib}
+@InProceedings{Coli95,
+ author = "Colin, Antoine",
+ title = "Formal computation of Galois groups with relative resolvants",
+ booktitle = "Proc. AAECC-11",
+ series = "AAECC-11",
+ year = "1995",
+ publisher = "Springer-Verlag",
+ location = "Paris, France",
+ pages = "169-182",
+ keywords = "axiomref",
+ abstract =
+ "Let $k$ be a field and $f \in k[x]$ be a polynomial of degree $n$. The
+ permutation action of $G$ on the roots $\{\alpha_i\}_{i=1}^n$ of $f$
+ can be determined by an algorithm suggested by R. Stauduhar
+ [Math. Comput. 27, 981-996 (1973; Zbl 0282.12004)] that approximates $G$
+ via successive steps in a chain of subgroups
+ $S_n=H_0 > H_1 > \ldots > H_k=G$. In each step $H_{i-1} > H_i$
+ it checks as a test for $G \le H_i$ whether a relative invariant $k_i
+ \in k[x_1,\ldots,x_n]$ yields a value under the specialization
+ $\varphi : g(x_1,\ldots,x_n) \mapsto g(\alpha_1,\ldots,\alpha_n)$. In
+ implementations this evaluation has been done using $p$-adic
+ [H. Darmon and D. Ford, Commun. Algebra 17, No. 12, 2941-2943 (1989;
+ Zbl 0693.12010)] or numerical (R. Stauduhar [ibid.]; Y. Eichenlaub and
+ M. Olivier [preprint]) approximation of the roots.
+
+ The paper under review presents a new approach which avoids all
+ approximations: If $G \le H_i$ and $H_i$ is maximal in $H_{i-1}$ the
+ invariant $h_i$ is a primitive element of the invariant field
+ $k_i=k(x_1,\ldots,x_n)^{H_i}$ as an extension of
+ $k_{i-1}=K(x_1,\ldots,x_n)^{H_{i-1}}$.
+ The author develops an algorithm to express the specialized values
+ $\varphi(g)$ of elements $g \in k_i$ in terms of $k_{i-1}$ and the
+ specialization $\varphi(h_i)$.
+
+ This algorithm then is applied to the relative resolvent polynomial
+ \[s_i = \prod_a{(y-a(x_1,\ldots,x_n))}\]
+ where $a$ runs through the images of $h_i$ under $H_{i-1}.
+ It has $y$-coefficients which are in $k_{i-1}$.
+ The algorithm then permits to express the coefficients of the
+ specialization $r_i(y)=\varphi(s_i) \in k[y]$ recursively in the
+ (already known) specializations $\varphi(h_i)$ for $j \le i-1$,
+ using the coefficients of $f$ (as $S_n$-invariants in the roots)
+ as a seed. A root of $r_i(y)$ in the base field then proves that $G$
+ is contained in (a conjugate of) $H_i$, and this value of the root can
+ be used as specialized $\varphi(h_{i+1})$ in the next step of the
+ algorithm. Special care is given to the case when denominators of
+ elements in $k(x_1,\ldots,x_n)$ evaluate to zero after specialization.
+
+ The paper closes with a short discussion of applicability. An
+ implementation using AXIOM and GAP is in process but has not yet been
+ completed."
+}
+
+\end{chunk}
+
+\index{Colin, Antoine}
+\begin{chunk}{axiom.bib}
@article{Coli97,
author = "Colin, Antoine",
title = "Solving a system of algebraic equations with symmetries",
@@ -12864,6 +12996,37 @@ Coding Theory and Applications Proceedings. Springer-Verlag, Berlin, Germany
\end{chunk}
+\index{Crouch, Peter E.}
+\index{Lamnabhi-Lagarrigue, Francoise}
+\index{Pinchon, Didier}
+\begin{chunk}{axiom.bib}
+@article{Crou95,
+ author = "Crouch, Peter E. and Lamnabhi-Lagarrigue, Francoise and
+ Pinchon, Didier",
+ title = "Some realizations of algorithms for nonlinear input-output systems",
+ journal = "Int. J. Control",
+ volume = "62",
+ number = "4",
+ pages = "941-960",
+ year = "1995",
+ keywords = "axiomref",
+ abstract =
+ "The first two authors previously developed an algorithm for
+ constructing a parametrization of the observation space of a nonlinear
+ control system directly from the differential equation representation
+ of the input-output behaviour. This paper extends the previous
+ algorithm by including settings where a set of implicit input-output
+ differential equations is given as well as more general state-space
+ representations in which the controls enter nonlinearly. Various
+ state-space realizations, including bilinear, polynomial and nilpotent
+ approximating realizations are discussed. The final section of the
+ paper sketches the implementation of the algorithm using the symbolic
+ manipulation package AXIOM to find the realizations mentioned above in
+ feasible cases."
+}
+
+\end{chunk}
+
\index{Cuypers, Hans}
\index{Hendriks, Maxim}
\index{Knopper, Jan Willem}
@@ -13485,6 +13648,22 @@ May 1984
\index{Delliere, Stephane}
\begin{chunk}{axiom.bib}
+@techreport{Dell00a,
+ author = "Delliere, Stephane",
+ title = {A first course to $D_7$ with examples},
+ institution = "Universite de Limoges",
+ year = "2000",
+ type = "technical report",
+ number = "2000-17",
+ paper = "Dell00a.pdf",
+ url = http://www.unilim.fr/laco/rapports/2000/R2000_17.pdf,
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Delliere, Stephane}
+\begin{chunk}{axiom.bib}
@article{Dell01,
author = "Delliere, Stephane",
title = "On the links between triangular sets and dynamic constructable
@@ -13878,6 +14057,19 @@ Grant citation GR/L48256 Nov 1, 1997-Feb 28, 2001
\end{chunk}
+\index{Dunstan, Martin}
+\begin{chunk}{axiom.bib}
+@misc{Duns99b,
+ author = "Dunstan, Martin",
+ title = "An Introduction to Aldor and its Type System",
+ year = "1999",
+ url = "http://www.aldor.org/docs/reports/cfc99/aldor-cfc99.pdf",
+ paper = "Duns99b.pdf",
+ comment = "slides"
+}
+
+\end{chunk}
+
\index{Adams, Andrew A.}
\index{Dunstan, Martin}
\index{Gottlieben, Hanne}
@@ -13928,12 +14120,14 @@ Madrid Spain, NAG conference (private copy of paper)
\begin{chunk}{axiom.bib}
@article{Duva95,
author = "Duval, D.",
- title = "Evaluation dynamique et cl\^oture alg\'ebrique en Axiom",
+ title = "Dynamic evaluation and algebraic closure in Axiom",
+ comment = "Evaluation dynamique et cl\^oture alg\'ebrique en Axiom",
journal = "Journal of Pure and Applied Algebra",
volume = "99",
year = "1995",
pages = "267--295.",
keywords = "axiomref",
+ paper = "Duva95.pdf",
abstract =
"Dynamic evaluation allows to compute with algebraic numbers without
factorizing polynomials. It also allows to manipulate parameters in a
@@ -14305,6 +14499,36 @@ Germany / Heildelberg, Germany / London, UK / etc., 1993. ISBN 0-387-57272-4
\end{chunk}
+\index{Fleischer, J.}
+\index{Grabmeier, J.}
+\index{Hehl, F.W.}
+\index{Kuchlin, W.}
+\begin{chunk}{axiom.bib}
+@book{Flei94,
+ author = "Fleischer, J. and Grabmeier, J. and Hehl, F.W. and
+ Kuchlin, W. (eds)",
+ title = "Proc. Conf. Computer Algebra in Science and Engineering",
+ booktitle = "Computer Algebra in Science and Engineering",
+ year = "1994",
+ location = "Bielefeld, Germany",
+ publisher = "World Scientific, River Edge, NJ",
+ abstract =
+ "Systems and tools of computer algebra (Like AXIOM, Derive, FORM,
+ Mathematica, Maple, Mupad, REDUCE, Macsyma…) let us manipulate
+ extremely complex algebraic formulae symbolically on a
+ computer. Contrary to numerics these computations are exact and there
+ is no loss of accuracy. After decades of research and development,
+ these tools are now becoming as indispensable in Science and
+ Engineering as traditional number crunching already is.
+
+ The ZiF'94 workshop is amongst the first devoted specifically to
+ applications of computer algebra (CA) in Science and Engineering. The
+ book documents the state of the art in this area and serves as an
+ important reference for future work."
+}
+
+\end{chunk}
+
\index{Fogus, Michael}
\begin{chunk}{ignore}
\bibitem[Fogus 11]{Fog11} Fogus, Michael
@@ -16081,6 +16305,45 @@ University of St Andrews, 6th April 2000
\index{Koepf, Wolfram}
\begin{chunk}{axiom.bib}
+@article{Koep96,
+ author = "Koepf, Wolfram",
+ title = "Closed form Laurent-Puiseux series of algebraic functions",
+ journal = "Appl. Algebra Eng. Commun. Comput.",
+ volume = "7",
+ number = "1",
+ pages = "21-26",
+ year = "1996",
+ keywords = "axiomref",
+ abstract =
+ "Let $y$ be an algebraic function defined by a polynomial equation
+ $P(x,y)=0$ whose coefficients are polynomials in $x$ over a field $K$
+ which may be one of the fields $\mathbb{Q}$, $\mathbb{R}$, or
+ $\mathbb{C}$. D. V. and G. V. Chudnovsky [J. Complexity 2, 271-294
+ (1986; Zbl 0629.68038); ibid. 3, 1-25 (1987; Zbl 0656.34003)] describe
+ a pair of algorithms to calculate the coefficients in the
+ Laurent-Puiseux developments of the branches of $y$: The first
+ algorithm returns a linear differential equation
+ \[q_n(x)y^{(n)} + y_{n-1}(x)y^{(n-1)}+\cdots+q_1(x)y^{'}+q_0(x)y=0\]
+ which is satisfied by all branches of $y$ and whose coefficients are
+ polynomials in $x$ over $K$, the other uses this differential equation
+ to get a linear recurrence relation for the Puiseux coefficients. The
+ author used this algorithms (the second in a simpler version) to
+ calculate the recurrence relation; if this relation contains only two
+ terms, an algorithm found by the author returns an explicit formula
+ for the Puiseux coefficients [J. Symb. Comp. 13, 581-603 (1992; Zbl
+ 0758.30026)]. In this paper, the author gives examples to illustrate
+ his algorithms and to show that for many algebraic functions defined
+ by polynomials of low degree a closed form of their Puiseux
+ coefficients may be calculated. He points out that on the other side
+ the complexity of the resulting recurrence equation may be extremely
+ high even for an algebraic function defined by a sparse polynomial of
+ low degree."
+}
+
+\end{chunk}
+
+\index{Koepf, Wolfram}
+\begin{chunk}{axiom.bib}
@InProceedings{Koep99,
author = "Koepf, Wolfram",
title = "Orthogonal polnomials and computer algebra",
@@ -17688,6 +17951,31 @@ IBM T.J. Watson Research RC4998
\end{chunk}
+\index{Norman, Arthur C.}
+\begin{chunk}{axiom.bib}
+@InProceedings{Norm96,
+ author = "Norman, Arthur C.",
+ title = "Memory tracing of algebraic calculations",
+ booktitle = "Proc. 1996 ISSAC",
+ series = "ISSAC 1996",
+ year = "1996",
+ publisher = "ACM Press",
+ location = "New York, NY",
+ pages = "113-119",
+ keywords = "axiomref",
+ url = "http://opus.bath.ac.uk/16452/1/NormanFitch96a.ps",
+ paper = "Norm96.pdf",
+ abstract =
+ "We present a software tool which allows us to visualize details of the
+ use of memory during the execution of an algebra system. We apply this
+ to gain a better understanding of the behaviour of REDUCE, and hence
+ to make proposals for ways in which the execution can be improved. The
+ same tool will soon be used in the performance engineering of a
+ version of axiom."
+}
+
+\end{chunk}
+
\index{Nguyen, Minh Van}
\begin{chunk}{axiom.bib}
@phdthesis{Nguy09,
@@ -17765,6 +18053,29 @@ IBM T.J. Watson Research RC4998
\end{chunk}
+\index{O'Keefe, Christine M.}
+\index{Storme, Leo}
+\begin{chunk}{axiom.bib}
+@article{OKee96,
+ author = "O'Keefe, Christine M. and Storme, Leo",
+ title = {Arcs in PG(n,q) fixed by A_5 and A_6},
+ journal = "J. Geom.",
+ volume = "55",
+ number = "1-2",
+ pages = "123-138",
+ year = "1996",
+ keywords = "axiomref",
+ abstract =
+ "A $k$-arc in a projective space is a set of points, no three of which
+ are collinear. The author determines the $k$ arcs in $PG(n,q)$ which
+ are fixed by primitive groups isomorphic to $A_5$ or $A_6$. The best
+ known examples are $q+1$ arcs: in general these are normal rational
+ curves and are conics in $PG(2,q)$ and twisted cubics in $PG(3,q)$.
+ The other cases turn out to be 6-arcs or 10-arcs."
+}
+
+\end{chunk}
+
\index{Ollivier, F.}
\begin{chunk}{ignore}
\bibitem[Ollivier 89]{Oll89} Ollivier, F.
@@ -18985,6 +19296,29 @@ IBM Manual, March 1988
\end{chunk}
+\index{Tuomela, Jukka}
+\begin{chunk}{axiom.bib}
+@article{Tuom96,
+ author = "Tuomela, Jukka",
+ title = "On the construction of arbitrary order schemes for the many
+ dimensional wave equation",
+ journal = "BIT",
+ volume = "36",
+ number = "1",
+ pages = "158-165",
+ year = "1996",
+ keywords = "axiomref",
+ abstract =
+ "The paper is devoted to a problem which was of an interest in the
+ beginning of the theory of difference methods. The elementary
+ constructed explicit high-order approximations for the wave equation
+ (on the simplest cubic grid in space) assume that the solution is very
+ smooth and that no boundary conditions are given. Stability is also
+ understood in the simplest way (in $L_2$)."
+}
+
+\end{chunk}
+
\subsection{U} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{chunk}{axiom.bib}
@@ -19256,6 +19590,9 @@ Version 1.0.0 O($\epsilon{}^1$) June 8, 1994
\index{Broadbery, Peter A.}
\index{Dooley, Sam}
\index{Iglio, Pietro}
+\index{Morrison, Scott C.}
+\index{Steinbach, Jonathan M.}
+\index{Sutor, Robert S.}
\begin{chunk}{axiom.bib}
@techreport{Watt94,
author = "Watt, Stephen M. and Broadbery, Peter A. and Dooley, Samuel S.
@@ -19266,8 +19603,7 @@ Version 1.0.0 O($\epsilon{}^1$) June 8, 1994
type = "technical report",
number = "RC19529 (85075)",
paper = "Watt94.pdf",
- url =
- "http://axiom-wiki.newsynthesis.org/public/refs/axiom-aldor-a-sharp.pdf",
+ url = "http://www.aldor.org/docs/reports/i94acomp/i94acomp.pdf",
keywords = "axiomref",
abstract =
"The $A^{#}$ compiler allows users of computer algebra to develop
@@ -19348,6 +19684,48 @@ IBM T. J. Watson Research Center (2001)
\end{chunk}
+\index{Watt, Stephen M.}
+\begin{chunk}{axiom.bib}
+@misc{Watt00,
+ author = "Watt, Stephen M.",
+ title = "Aldor: The language and recent directions",
+ year = "2000",
+ institution = "University of Western Ontario",
+ url = "http://www.aldor.org/docs/reports/sa2000/aldortalk-sa2000.pdf",
+ keywords = "axiomref",
+ paper = "Watt00.pdf"
+}
+
+\end{chunk}
+
+\index{Watt, Stephen M.}
+\begin{chunk}{axiom.bib}
+@misc{Watt00a,
+ author = "Watt, Stephen M.",
+ title = "Aldor: An Introduction to the Language",
+ year = "2000",
+ institution = "University of Western Ontario",
+ url = "http://www.aldor.org/docs/reports/ukqcd-2000/intro1-ukqcd00.pdf",
+ keywords = "axiomref",
+ paper = "Watt00a.pdf"
+}
+
+\end{chunk}
+
+\index{Watt, Stephen M.}
+\begin{chunk}{axiom.bib}
+@misc{Watt00b,
+ author = "Watt, Stephen M.",
+ title = "Aldor: Interfaces",
+ year = "2000",
+ institution = "University of Western Ontario",
+ url = "http://www.aldor.org/docs/reports/ukqcd-2000/intro2-ukqcd00.pdf",
+ keywords = "axiomref",
+ paper = "Watt00b.pdf"
+}
+
+\end{chunk}
+
\index{Weber, Andreas}
\begin{chunk}{axiom.bib}
@phdthesis{Webe93b,
@@ -19657,7 +20035,33 @@ LCCN QA76.7.S54 v22:7 SIGPLAN Notices, vol 22, no 7 (July 1987)
title = "Polynomial Algorithms in Computer Algebra",
year = "1996",
publisher = "Springer-Verlag",
- isbn = "3-211-82759-5"
+ isbn = "3-211-82759-5",
+ abstract =
+ "This book surveys algorithms and results of Computer Algebra that are
+ concerned with polynomials. It introduces algorithms from the bottom
+ up, starting from very basic problems in computation over the
+ integers, and finally leading to, e.g. advanced topics in
+ factorization, solution of polynomial equations and constructive
+ algebraic geometry. It is not based on a particular computer algebra
+ program system.
+
+ After two introductory chapters, the book contains six chapters with
+ the following respective topics: computation by homomorphic images,
+ gcd computation, factorization and decomposition of polynomials,
+ linear systems and Hankel systems, Gröbner bases. The last three
+ chapters are concerned with applications of polynomial algorithms to
+ higher level problems in computer algebra. In particular, a decision
+ algorithm in the elementary theory of real closed fields, a
+ description of Gosper’s algorithm for solving summation problems, and
+ an algorithm for deciding whether an algebraic curve can be
+ parametrized by rational functions (and if so for computing such a
+ parametrization) is given. Along the way, the complexity of many of
+ the algorithms is investigated. Each chapter ends with rich
+ bibliographical notes.
+
+ The book was originally developed from course material. It can easily
+ be used as a textbook on the topic. Most subsections contain
+ exercises. Solutions of some of the exercises are provided."
}
\end{chunk}
@@ -21539,9 +21943,24 @@ Grove, IL, USA and Oxford, UK, 1992
title = "Effective construction of algebraic geometry codes",
journal = "IEEE Transaction on Information Theory",
volume = "41",
+ number = "6",
month = "November",
year = "1995",
- pages = "1615--1628"
+ pages = "1615--1628",
+ paper = "Hach95.pdf",
+ url = "https://hal.inria.fr/inria-00074404/file/RR-2267.pdf",
+ keywords = "axiomref",
+ abstract =
+ "We intend to show that algebraic geometry codes (AG-codes, introduced
+ by Goppa in 1977 [5]) can be constructed easily using blowing-up
+ theory. This work is based on a paper by Le Brigand and Risler. Given
+ a plane curve, we desingularize the curve by means of blowing-up, and
+ then using the desingularisation trees and the monoidal
+ transformations associated to the blowing-up morphisms, we compute the
+ adjoint divisor of the curve. Finally we show how to use the algorithm
+ of Brill-Noether to compute a basis of the vector space associated to
+ a divisor of the curve. Two examples of constructions of AG-codes are
+ given at the end."
}
\end{chunk}
diff --git a/changelog b/changelog
index e47a477..4894c0c 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,5 @@
+20160702 tpd src/axiom-website/patches.html 20160702.03.tpd.patch
+20160702 tpd books/bookvolbib Axiom Citations in the Literature
20160702 tpd src/axiom-website/patches.html 20160702.02.tpd.patch
20160702 tpd books/bookvolbib Axiom Citations in the Literature
20160702 tpd src/axiom-website/patches.html 20160702.01.tpd.patch
diff --git a/patch b/patch
index 5dac759..82c5f42 100644
--- a/patch
+++ b/patch
@@ -2,351 +2,349 @@ books/bookvolbib Axiom Citations in the Literature
Goal: Axiom Literate Programming
-\index{Fateman, Richard J.}
+\index{Delliere, Stephane}
\begin{chunk}{axiom.bib}
-@misc{Fate99,
- author = "Fateman, Richard J.",
- title = "Symbolic mathematics system evaluators",
- year = "1999",
- keywords = "axiomref",
- url = "http://people.eecs.berkeley.edu/~fateman/papers/evalnew.pdf",
- paper = "Fate99.pdf",
- abstract =
- "``Evaluation'' of expressions and programs in a computer algebra
- system is central to every system, but inevitably fails to provide
- complete satisfaction. Here we explain the conflicting requirements,
- describe some solutions from current systems, and propose alternatives
- that might be preferable sometimes. We give examples primarily from
- Axiom, Macsyma, Maple, Mathematica, with passing metion of a few other
- systems."
-}
+@techreport{Dell00a,
+ author = "Delliere, Stephane",
+ title = {A first course to $D_7$ with examples},
+ institution = "Universite de Limoges",
+ year = "2000",
+ type = "technical report",
+ number = "2000-17",
+ paper = "Dell00a.pdf",
+ url = http://www.unilim.fr/laco/rapports/2000/R2000_17.pdf,
+ keywords = "axiomref"
+}
\end{chunk}
-\index{G{\'o}mez-D{\'\i}az, Teresa}
+\index{Watt, Stephen M.}
\begin{chunk}{axiom.bib}
-@phdthesis{Gome92,
- author = "Gomez-Dias, Teresa",
- title = {Quelques applications de l`\'evaluation dynamique},
- school = "L'Universite de Limoges",
- year = "1992",
- month = "March",
- paper = "Gome92.pdf"
+@misc{Watt00,
+ author = "Watt, Stephen M.",
+ title = "Aldor: The language and recent directions",
+ year = "2000",
+ institution = "University of Western Ontario",
+ url = "http://www.aldor.org/docs/reports/sa2000/aldortalk-sa2000.pdf",
+ keywords = "axiomref",
+ paper = "Watt00.pdf"
}
\end{chunk}
-\index{G{\'o}mez-D{\'\i}az, Teresa}
+\index{Watt, Stephen M.}
\begin{chunk}{axiom.bib}
-@article{Gome96,
- author = "Gomez-Diaz, Theresa",
- title = "Examples of using dynamic constructible closure",
- journal = "Math. Comput. Simul.",
- volume = "42",
- number = "4-6",
- pages = "375-383",
- year = "1996",
+@misc{Watt00a,
+ author = "Watt, Stephen M.",
+ title = "Aldor: An Introduction to the Language",
+ year = "2000",
+ institution = "University of Western Ontario",
+ url = "http://www.aldor.org/docs/reports/ukqcd-2000/intro1-ukqcd00.pdf",
keywords = "axiomref",
- abstract =
- "We present here some examples of using the ``Dynamic Constructible
- Closure'' program, which performs automatic case distinctions in
- computations involving parameters over a base field ``K''. This
- program is an application of the ``Dynamic Evaluation'' principle
- which generalizes tradional evaluation and was first used to deal with
- algebraic numbers."
+ paper = "Watt00a.pdf"
}
\end{chunk}
-\index{Green, Edward L.}
+\index{Koepf, Wolfram}
\begin{chunk}{axiom.bib}
-@book{Gree01,
- author = "Green, Edward L.",
- title = "Symbolic Computation: Solving Equations in Algebra, Geometry, and
- Engineering",
- booktitle = "Proc. AMS-IMS-SIAM Joint Summer Research Conference on Symbolic
- Computation",
- volume = "232",
- publisher = "American Mathematical Society",
- year = "2001",
+@article{Koep96,
+ author = "Koepf, Wolfram",
+ title = "Closed form Laurent-Puiseux series of algebraic functions",
+ journal = "Appl. Algebra Eng. Commun. Comput.",
+ volume = "7",
+ number = "1",
+ pages = "21-26",
+ year = "1996",
keywords = "axiomref",
abstract =
- "This volume contains papers related to the research conference,
- ``Symbolic Computation: Solving Equations in Algebra, Analysis, and
- Engineering,'' held at Mount Holyoke College (MA). It provides a broad
- range of active research areas in symbolic computation as it applies
- to the solution of polynomial systems. The conference brought together
- pure and applied mathematicians, computer scientists, and engineers,
- who use symbolic computation to solve systems of equations or who
- develop the theoretical background and tools needed for this
- purpose. Within this general framework, the conference focused on
- several themes: systems of polynomials, systems of differential
- equations, noncommutative systems, and applications."
+ "Let $y$ be an algebraic function defined by a polynomial equation
+ $P(x,y)=0$ whose coefficients are polynomials in $x$ over a field $K$
+ which may be one of the fields $\mathbb{Q}$, $\mathbb{R}$, or
+ $\mathbb{C}$. D. V. and G. V. Chudnovsky [J. Complexity 2, 271-294
+ (1986; Zbl 0629.68038); ibid. 3, 1-25 (1987; Zbl 0656.34003)] describe
+ a pair of algorithms to calculate the coefficients in the
+ Laurent-Puiseux developments of the branches of $y$: The first
+ algorithm returns a linear differential equation
+ \[q_n(x)y^{(n)} + y_{n-1}(x)y^{(n-1)}+\cdots+q_1(x)y^{'}+q_0(x)y=0\]
+ which is satisfied by all branches of $y$ and whose coefficients are
+ polynomials in $x$ over $K$, the other uses this differential equation
+ to get a linear recurrence relation for the Puiseux coefficients. The
+ author used this algorithms (the second in a simpler version) to
+ calculate the recurrence relation; if this relation contains only two
+ terms, an algorithm found by the author returns an explicit formula
+ for the Puiseux coefficients [J. Symb. Comp. 13, 581-603 (1992; Zbl
+ 0758.30026)]. In this paper, the author gives examples to illustrate
+ his algorithms and to show that for many algebraic functions defined
+ by polynomials of low degree a closed form of their Puiseux
+ coefficients may be calculated. He points out that on the other side
+ the complexity of the resulting recurrence equation may be extremely
+ high even for an algebraic function defined by a sparse polynomial of
+ low degree."
}
\end{chunk}
-\index{Dragan, Laurentiu}
-\index{Watt, Stephen}
+\index{Norman, Arthur C.}
\begin{chunk}{axiom.bib}
-@InProceedings{Drag10,
- author = "Dragan, Laurentiu and Watt, Stephen",
- title = "Type Specialization in Aldor",
- booktitle = "Computer algebra in scientific computing",
- series = "CASC 2010",
- year = "2010",
- location = "Tsakhadzor, Armenia",
- pages = "73-84",
+@InProceedings{Norm96,
+ author = "Norman, Arthur C.",
+ title = "Memory tracing of algebraic calculations",
+ booktitle = "Proc. 1996 ISSAC",
+ series = "ISSAC 1996",
+ year = "1996",
+ publisher = "ACM Press",
+ location = "New York, NY",
+ pages = "113-119",
keywords = "axiomref",
- url = "http://www.csd.uwo.ca/~watt/pub/reprints/2010-casc-specdom.pdf",
- paper = "Drag10.pdf",
+ url = "http://opus.bath.ac.uk/16452/1/NormanFitch96a.ps",
+ paper = "Norm96.pdf",
abstract =
- "Computer algebra in scientific computation squarely faces the dilemma
- of natural mathematical expression versus efficiency. While
- higher-order programming constructs and parametric polymorphism
- provide a natural and expressive language for mathematical
- abstractions, they can come at a considerable cost. We investigate how
- deeply nested type constructions may be optimized to achieve
- performance similar to that of hand-tuned code written in lower-level
- languages."
+ "We present a software tool which allows us to visualize details of the
+ use of memory during the execution of an algebra system. We apply this
+ to gain a better understanding of the behaviour of REDUCE, and hence
+ to make proposals for ways in which the execution can be improved. The
+ same tool will soon be used in the performance engineering of a
+ version of axiom."
}
\end{chunk}
-\index{Delliere, Stephane}
-\index{Wang, Dongming}
+\index{O'Keefe, Christine M.}
+\index{Storme, Leo}
\begin{chunk}{axiom.bib}
-@techreport{Dell00,
- author = "Delliere, Stephane and Wang, Dongming",
- title = "simple systems and dynamic constructible closure",
- institution = "Universite de Limoges",
- year = "2000",
- type = "technical report",
- number = "2000-16",
- paper = "Dell00.pdf",
- url = "http://www.unilim.fr/laco/rapports/2000/R2000\_16.pdf",
+@article{OKee96,
+ author = "O'Keefe, Christine M. and Storme, Leo",
+ title = {Arcs in PG(n,q) fixed by A_5 and A_6},
+ journal = "J. Geom.",
+ volume = "55",
+ number = "1-2",
+ pages = "123-138",
+ year = "1996",
keywords = "axiomref",
abstract =
- "Dynamic evaluation is a general method for computing with parameters
- [6, 9]. In 1994, T. Gomez-Diaz implemented the dynamic constructible
- closure in the scientific computation system Axiom [17]: by simulating
- dynamic evaluation, it offers the possibility to compute with
- parameters in a very large way [13]. The outputs of a calculs with
- T. Gomez-Diaz programs are represented by a finite collection of
- constructible triangular systems defined in [12, definition
- p.106]. Though there are numerous applications of these programs
- (notably polynomial system solving with parameters [11], automatic
- geometric theorem proving [14, 15], computation of Jordan forms with
- parameters [16]), nobody gives theorical interest to this kind of
- triangular systems. The main reason of this phenomenon is that they
- are definied in [12] within the dynamic evaluation context. On the
- opposite, most notions of triangular systems (J.F. Ritt-W.T. Wu
- characteristic sets [24, 28], M. Kalkbrener regular chains [18],
- D. Lazard triangular sets [20], M. Moreno Maza regular sets [22],
- D.M. Wang simple systems [26, 27]) are defined in terms of commutative
- algebra. This problem is at the origin of the work done in [7] where
- we give a relevant algebraic model of T. Gomez-Diaz systems within
- commutative algebra terminology. This allows us to relate them to many
- concepts of triangular systems [7]. Thus, we give interest to the
- connections with D. Lazard triangular sets in [8]. In a way, this
- paper is the continuation of this previous work. This time, we study
- relationships between T. Gomez-Diaz systems and D.M. Wang simple
- systems. The paper is structured as follows. We have collected in
- section 2 some needed notations. In section 3, we give all the
- terminology related to our algebraic model of T. Gomez-Diaz
- systems. Thus, we define the notion of weak constructible triangular
- systems and introduce the properties of normalization and
- squarefreeness. Section 4 is more detailed. First of all, we study a
- weaker form of normalization called $L$-normalization. Then we give
- many properties of constructible triangular systems verifying this new
- notion. We obtain an algebraic and geometric framework which permits,
- in section 5, to explore the connections between T. Gomez-Diaz systems
- and D.M. Wang simple systems. In particular, this last section will
- demonstrate well the importance of our $L$-normalization
- property. Indeed, we show that simple systems and squarefree
- $L$-normalized constructible triangular systems are equivalent."
+ "A $k$-arc in a projective space is a set of points, no three of which
+ are collinear. The author determines the $k$ arcs in $PG(n,q)$ which
+ are fixed by primitive groups isomorphic to $A_5$ or $A_6$. The best
+ known examples are $q+1$ arcs: in general these are normal rational
+ curves and are conics in $PG(2,q)$ and twisted cubics in $PG(3,q)$.
+ The other cases turn out to be 6-arcs or 10-arcs."
}
\end{chunk}
-\index{Aubry, Phillippe}
+\index{Tuomela, Jukka}
\begin{chunk}{axiom.bib}
-@phdthesis{Aubr99b,
- author = "Aubry, Philippe",
- title = "Ensembles triangulaires de polynomes et resolution de systemes
- algebriques. Implantation en Axiom",
- school = "l'Universite de Paris VI",
- year = "1999",
- month = "January",
- paper = "Aubr99b.pdf",
- comment = "French"
+@article{Tuom96,
+ author = "Tuomela, Jukka",
+ title = "On the construction of arbitrary order schemes for the many
+ dimensional wave equation",
+ journal = "BIT",
+ volume = "36",
+ number = "1",
+ pages = "158-165",
+ year = "1996",
+ keywords = "axiomref",
+ abstract =
+ "The paper is devoted to a problem which was of an interest in the
+ beginning of the theory of difference methods. The elementary
+ constructed explicit high-order approximations for the wave equation
+ (on the simplest cubic grid in space) assume that the solution is very
+ smooth and that no boundary conditions are given. Stability is also
+ understood in the simplest way (in $L_2$)."
}
\end{chunk}
-\index{Duval, Dominique}
+\index{Arnault, F.}
\begin{chunk}{axiom.bib}
-@article{Duva94c,
- author = "Duval, Dominique",
- title = "Algebraic Numbers: An Example of Dynamic Evaluation",
- journal = "J. Symbolic Computation",
- volume = "18",
- pages = "429-445",
- year = "1994",
- url = "http://www.sciencedirect.com/science/article/pii/S0747717106000551",
- paper = "Duva94c.pdf",
+@article{Arna95a,
+ author = "Arnault, F.",
+ title = "Rabin-Miller primality test: Composite numbers which pass it",
+ journal = "Mathematics of Computation",
+ volume = "64",
+ number = "209",
+ pages = "355-361",
+ year = "1995",
keywords = "axiomref",
- abstract = "
- 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."
+ url =
+"https://www.jointmathematicsmeetings.org/mcom/1995-64-209/S0025-5718-1995-1260124-2/S0025-5718-1995-1260124-2.pdf",
+ paper = "Arna95a.pdf",
+ abstract =
+ "The Rabin-Miller primality test is a probabilistic test which can be
+ found in several algebraic computing systems (such as Pari, Maple,
+ ScratchPad) because it is very easy to implement and, with a
+ reasonable amount of computing, indicates whether a number is
+ composite or ``probably prime'' with a very low probability of error. In
+ this paper, we compute composite numbers which are strong pseudoprimes
+ to several chosen bases. Because these bases are those used by the
+ ScratchPad implementation of the test, we obtain, by a method which
+ differs from a recent one by G. Jaeschke [ibid. 61, 915-926 (1993; Zbl
+ 0802.11001)], composite numbers which are found to be ``probably prime''
+ by this test."
}
\end{chunk}
-\index{Hubert, Evelyne}
+\index{Atkinson, M. D.}
+\index{Linton, S. A.}
+\index{Walker, L. A.}
\begin{chunk}{axiom.bib}
-@InProceedings{Hube03,
- author = "Hubert, Evelyne",
- title = "Notes on Triangular Sets and Triangulation-Decomposition I:
- Polynomial Systems",
- booktitle = "Symbolic and Numerical Scientific Computing",
- series = "Lecture Notes in Computer Science 2630",
- year = "2003",
- pages = "1-39",
+@article{Atki95,
+ author = "Atkinson, M. D. and Linton, S. A. and Walker, L. A.",
+ title = "Priority queues and multisets",
+ journal = "J. Comb",
+ volume = "2",
+ pages = "385-402",
+ year = "1995",
keywords = "axiomref",
- paper = "Hube03.pdf",
- url = "http://www.cecm.sfu.ca/~rpearcea/sdmp/sdmp\_paper.pdf",
- abstract =
- "This is the first in a series of two tutorial articles devoted to
- triangulation- decomposition algorithms. The value of these notes
- resides in the uniform presen- tation of triangulation-decomposition
- of polynomial and differential radical ideals with detailed proofs of
- all the presented results.We emphasize the study of the mathematical
- objects manipulated by the algorithms and show their properties in
- independently of those. We also detail a selection of algorithms, one
- for each task. We address here polynomial systems and some of the
- material we develop here will be used in the second part, devoted to
- differential systems."
+ url =
+"http://www.combinatorics.org/ojs/index.php/eljc/article/download/v2i1r24.pdf",
+ paper = "Atki95.pdf",
+ abstract =
+ "A priority queue, a container data structure equipped with the
+ operations insert and delete-minimum, can re-order its input in
+ various ways, depending both on the input and on the sequence of
+ operations used. If a given input $\sigma$ can produce a particular
+ output $\tau$ then $(\sigma,\tau)$ is said to be an allowable pair. It
+ is shown that allowable pairs on a fixed multiset are in one-to-one
+ correspondence with certain $k$-way trees and, consequently, the
+ allowable pairs can be enumerated. Algorithms are presented for
+ determining the number of allowable pairs with a fixed input
+ component, or with a fixed output component. Finally, generating
+ functions are used to study the maximum number of output components
+ with a fixed input component, and a symmetry result is derived."
}
\end{chunk}
-\index{Hubert, Evelyne}
+\index{Colin, Antoine}
\begin{chunk}{axiom.bib}
-@InProceedings{Hube03a,
- author = "Hubert, Evelyne",
- title = "Notes on Triangular Sets and Triangulation-Decomposition II:
- Differential Systems",
- booktitle = "Symbolic and Numerical Scientific Computing",
- series = "Lecture Notes in Computer Science 2630",
- year = "2003",
- pages = "40-87",
+@InProceedings{Coli95,
+ author = "Colin, Antoine",
+ title = "Formal computation of Galois groups with relative resolvants",
+ booktitle = "Proc. AAECC-11",
+ series = "AAECC-11",
+ year = "1995",
+ publisher = "Springer-Verlag",
+ location = "Paris, France",
+ pages = "169-182",
keywords = "axiomref",
- paper = "Hube03a.pdf",
- url =
- "http://www-sop.inria.fr/members/Evelyne.Hubert/publications/sncsd.pdf",
- abstract =
- "This is the second in a series of two tutorial articles devoted to
- triangulation-decomposition algorithms. The value of these notes
- resides in the uniform presentation of triangulation-decomposition of
- polynomial and differential radical ideals with detailed proofs of all
- the presented results.We emphasize the study of the mathematical
- objects manipulated by the algorithms and show their properties
- independently of those. We also detail a selection of algorithms, one
- for each task. The present article deals with differential systems. It
- uses results presented in the first article on polynomial systems but
- can be read independently."
+ abstract =
+ "Let $k$ be a field and $f \in k[x]$ be a polynomial of degree $n$. The
+ permutation action of $G$ on the roots $\{\alpha_i\}_{i=1}^n$ of $f$
+ can be determined by an algorithm suggested by R. Stauduhar
+ [Math. Comput. 27, 981-996 (1973; Zbl 0282.12004)] that approximates $G$
+ via successive steps in a chain of subgroups
+ $S_n=H_0 > H_1 > \ldots > H_k=G$. In each step $H_{i-1} > H_i$
+ it checks as a test for $G \le H_i$ whether a relative invariant $k_i
+ \in k[x_1,\ldots,x_n]$ yields a value under the specialization
+ $\varphi : g(x_1,\ldots,x_n) \mapsto g(\alpha_1,\ldots,\alpha_n)$. In
+ implementations this evaluation has been done using $p$-adic
+ [H. Darmon and D. Ford, Commun. Algebra 17, No. 12, 2941-2943 (1989;
+ Zbl 0693.12010)] or numerical (R. Stauduhar [ibid.]; Y. Eichenlaub and
+ M. Olivier [preprint]) approximation of the roots.
+
+ The paper under review presents a new approach which avoids all
+ approximations: If $G \le H_i$ and $H_i$ is maximal in $H_{i-1}$ the
+ invariant $h_i$ is a primitive element of the invariant field
+ $k_i=k(x_1,\ldots,x_n)^{H_i}$ as an extension of
+ $k_{i-1}=K(x_1,\ldots,x_n)^{H_{i-1}}$.
+ The author develops an algorithm to express the specialized values
+ $\varphi(g)$ of elements $g \in k_i$ in terms of $k_{i-1}$ and the
+ specialization $\varphi(h_i)$.
+
+ This algorithm then is applied to the relative resolvent polynomial
+ \[s_i = \prod_a{(y-a(x_1,\ldots,x_n))}\]
+ where $a$ runs through the images of $h_i$ under $H_{i-1}.
+ It has $y$-coefficients which are in $k_{i-1}$.
+ The algorithm then permits to express the coefficients of the
+ specialization $r_i(y)=\varphi(s_i) \in k[y]$ recursively in the
+ (already known) specializations $\varphi(h_i)$ for $j \le i-1$,
+ using the coefficients of $f$ (as $S_n$-invariants in the roots)
+ as a seed. A root of $r_i(y)$ in the base field then proves that $G$
+ is contained in (a conjugate of) $H_i$, and this value of the root can
+ be used as specialized $\varphi(h_{i+1})$ in the next step of the
+ algorithm. Special care is given to the case when denominators of
+ elements in $k(x_1,\ldots,x_n)$ evaluate to zero after specialization.
+
+ The paper closes with a short discussion of applicability. An
+ implementation using AXIOM and GAP is in process but has not yet been
+ completed."
}
\end{chunk}
-\index{Philippe, M. Trebuchet}
+\index{Landau, Susan}
\begin{chunk}{axiom.bib}
-@phdthesis{Phil02,
- author = "Philippe, M. Trebuchet",
- title = "Toward a fast and numerically stable algebraic equation solving",
- comment = "Vers une resolution stable et rapide des equations algebriques",
- school = "l'Universite de Paris 6",
- year = "2002",
- month = "December",
- paper = "Phil02.pdf",
- abstract =
- "Polynomial systems can be found in many industrial applications. They
- are also in the heart of effective algebraic geometry. A fundamental
- tool for studying them is the Groebner bases. The knowledge of this
- paricular base of the ideal generated by the polynomials composing the
- system allows us to compute in $A=K[x_1,\ldots,x_n]/I$, the quotient
- algebra, and this is necessary when we try to solve. Nevertheless,
- Groebner bases computations rely heavily on the introduction of
- monomial ordering. This introduces a certain rigidity in the
- computation and thus numerical instability. We propose a new algorithm
- that tries to remedy that problem. It generalises Groebner bases
- computation and is much less numerically instable. To do this, we
- decrease the requirement of monomial ordering, and use a new normal
- form criterion. We then give an algorithm and prove its termination
- and correctness when the input polynomial system is
- 0-dimensional. After, we compare it with the previously known methods
- and show how it can be seen as a generalisation of them. Next, we
- detail how we implemented it in C++ using the Synaps library. We also
- describe the sparse matrix elimination algorithm we used in or
- program. Finally, we present some of the experiments we have done with
- our program in domains like computer vision, algorithmic geometry,
- robotics, or pharmacology."
+@article{Land93,
+ author = "Landau, Susan",
+ title = "How to Tangle with a Nested Radical",
+ institution = "University of Massachusetts",
+ journal = "The Mathematical Intelligencer",
+ year = "1993",
+ paper = "Land93.pdf"
}
\end{chunk}
-\index{Duval, Dominique}
+\index{Crouch, Peter E.}
+\index{Lamnabhi-Lagarrigue, Francoise}
+\index{Pinchon, Didier}
\begin{chunk}{axiom.bib}
-@article{Duva95,
- author = "Duval, D.",
- title = "Evaluation dynamique et cl\^oture alg\'ebrique en Axiom",
- journal = "Journal of Pure and Applied Algebra",
- volume = "99",
+@article{Crou95,
+ author = "Crouch, Peter E. and Lamnabhi-Lagarrigue, Francoise and
+ Pinchon, Didier",
+ title = "Some realizations of algorithms for nonlinear input-output systems",
+ journal = "Int. J. Control",
+ volume = "62",
+ number = "4",
+ pages = "941-960",
year = "1995",
- pages = "267--295.",
keywords = "axiomref",
- abstract =
- "Dynamic evaluation allows to compute with algebraic numbers without
- factorizing polynomials. It also allows to manipulate parameters in a
- flexible and user-friendly way. The aim of this paper is the
- following: Explain what is dynamic evaluation, with its basic notions
- of dynamic set and splitting. Present its application to computations
- involving algebraic numbers, which amounts to defining the dynamic
- algebraic closure of a field. Describe the Axiom program which
- implements this, and give a user guide for it (only this last point
- assumes some knowledge of Axiom) Dynamic evaluation is described here
- without any reference to sketch theory, however our presentation, less
- rigourous, may be considered as more accessible."
+ abstract =
+ "The first two authors previously developed an algorithm for
+ constructing a parametrization of the observation space of a nonlinear
+ control system directly from the differential equation representation
+ of the input-output behaviour. This paper extends the previous
+ algorithm by including settings where a set of implicit input-output
+ differential equations is given as well as more general state-space
+ representations in which the controls enter nonlinearly. Various
+ state-space realizations, including bilinear, polynomial and nilpotent
+ approximating realizations are discussed. The final section of the
+ paper sketches the implementation of the algorithm using the symbolic
+ manipulation package AXIOM to find the realizations mentioned above in
+ feasible cases."
}
\end{chunk}
-\index{Montes, Antonio}
+\index{Fleischer, J.}
+\index{Grabmeier, J.}
+\index{Hehl, F.W.}
+\index{Kuchlin, W.}
\begin{chunk}{axiom.bib}
-@misc{Mont07,
- author = "Montes, Antonio",
- title = "On the canonical discussion of polynomial systems with parameters",
- year = "2007",
- url = "http://arxiv.org/pdf/math/0601674.pdf",
- paper = "Mont07.pdf",
- keywords = "axiomref",
+@book{Flei94,
+ author = "Fleischer, J. and Grabmeier, J. and Hehl, F.W. and
+ Kuchlin, W. (eds)",
+ title = "Proc. Conf. Computer Algebra in Science and Engineering",
+ booktitle = "Computer Algebra in Science and Engineering",
+ year = "1994",
+ location = "Bielefeld, Germany",
+ publisher = "World Scientific, River Edge, NJ",
abstract =
- "Given a parametric polynomial ideal $I$, the algorithm DISPGB,
- introduced by the author in 2002, builds up a binary tree describing a
- dichotomic discussion of the different reduced Groebner bases
- depending on the values of the parameters, whose set of terminal
- vertices form a Comprehensive Groebner System (CGS). It is relevant
- to obtain CGS’s having further properties in order to make them more
- useful for the applications. In this paper the interest is focused on
- obtaining a canonical CGS. We define the objective, show the
- difficulties and formulate a natural conjecture. If the conjecture is
- true then such a canonical CGS will exist and can be computed. We also
- give an algorithm to transform our original CGS in this direction and
- show its utility in applications."
+ "Systems and tools of computer algebra (Like AXIOM, Derive, FORM,
+ Mathematica, Maple, Mupad, REDUCE, Macsyma…) let us manipulate
+ extremely complex algebraic formulae symbolically on a
+ computer. Contrary to numerics these computations are exact and there
+ is no loss of accuracy. After decades of research and development,
+ these tools are now becoming as indispensable in Science and
+ Engineering as traditional number crunching already is.
+
+ The ZiF'94 workshop is amongst the first devoted specifically to
+ applications of computer algebra (CA) in Science and Engineering. The
+ book documents the state of the art in this area and serves as an
+ important reference for future work."
}
\end{chunk}
diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html
index 2204973..8f5596a 100644
--- a/src/axiom-website/patches.html
+++ b/src/axiom-website/patches.html
@@ -5436,6 +5436,8 @@ books/axiom.bst Include new 'algebra' keyword for Spad refs

books/bookvolbib Axiom Citations in the Literature

20160702.02.tpd.patch
books/bookvolbib Axiom Citations in the Literature

+20160702.03.tpd.patch
+books/bookvolbib Axiom Citations in the Literature

--
1.7.5.4