|
Документ взят из кэша поисковой машины. Адрес
оригинального документа
: http://theory.sinp.msu.ru/pipermail/computer_algebra/2004-March/000069.html
Дата изменения: Sun Apr 11 07:28:02 2004 Дата индексирования: Tue Oct 2 07:56:35 2012 Кодировка: |
This is a multi-part message in MIME format.
------=_NextPart_000_005C_01C4081D.856E5210
Content-Type: text/plain;
charset="koi8-r"
Content-Transfer-Encoding: quoted-printable
Dear Colleagues,
The next meeting of Computer Algebra seminar will take place on =
Wednsday, March 17, at 16:20 (room 782, building VMK, Moscow State
University).
AGENDA:
A.Ovchinnicov, MSU, Faculty of Mechanics and Mathematics
The Problem How to Compute a Characteristic Set of a Radical =
Differential Ideal
The problem of computation of a characteristic set in Kolchin's sense of =
a radical differential ideal is discussed. In particular, in the case of =
orderly rankings and differential ideals satisfying special conditions =
an algorithm for computation of a characteristic set is presented. =
Moreover, possible generalizations of this technique are also to be =
discussed.
Alexey Zobnin, MSU, Faculty of Mechanics and Mathematics
Standard Bases of Ideals in Differential Polynomial Rings
We consider standard bases (also known as differential Groebner bases by =
Carra Ferro and Ollivier) in a ring of ordinary differential polynomials =
in one indeterminate. They are a generalization of polynomial Groebner =
bases to differential algebra.
It was supposed that even the ideal [x^2] does not have finite standard =
bases. But we establish a link between these bases and Levi's process of =
reduction and construct a class of orderings such that the ideals [x^p] =
admit finite standard bases of only one element {x^p}.
Also we study various properties of admissible orderings on differential =
monomials. We bring up the following problem: whether there is a =
finitely generated differential ideal that does not admit a finite =
standard basis w.r.t. any ordering.
S. Polyakov, MSU, Faculty of Computational Mathematics & Cybernetics
Additive Decomposition of the Rational Functions
The problems of additive decomposition of the rational functions are =
considered. These problems consist in decomposing the rational function =
into the sum of two rational functions such that the first one is the =
difference of some rational function and the second one is minimal in =
some sence. The algorithm for solving one of these problems is =
presented.
------=_NextPart_000_005C_01C4081D.856E5210
Content-Type: text/html;
charset="koi8-r"
Content-Transfer-Encoding: quoted-printable
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=3DContent-Type content=3D"text/html; charset=3Dkoi8-r">
<META content=3D"MSHTML 6.00.2600.0" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT size=3D2><FONT size=3D3> Dear=20
Colleagues,<BR><BR> The next meeting of Computer =
Algebra=20
seminar will take place on Wednsday, March 17, at 16:20 (room 782, =
building VMK,=20
Moscow State<BR>University).<BR><BR> =20
AGENDA:<BR><BR>A.Ovchinnicov, MSU, Faculty of Mechanics and=20
Mathematics<BR><BR>The Problem How to Compute a Characteristic Set of a =
Radical=20
Differential Ideal<BR><BR>The problem of computation of a characteristic =
set in=20
Kolchin's sense of a radical differential ideal is discussed. In =
particular, in=20
the case of orderly rankings and differential ideals satisfying special=20
conditions an algorithm for computation of a characteristic set is =
presented.=20
Moreover, possible generalizations of this technique are also to be=20
discussed.<BR><BR>Alexey Zobnin, MSU, Faculty of Mechanics and=20
Mathematics<BR><BR>Standard Bases of Ideals in Differential Polynomial=20
Rings<BR><BR>We consider standard bases (also known as differential =
Groebner=20
bases by Carra Ferro and Ollivier) in a ring of ordinary differential=20
polynomials in one indeterminate. They are a generalization of =
polynomial=20
Groebner bases to differential algebra.<BR>It was supposed that even the =
ideal=20
[x^2] does not have finite standard bases. But we establish a link =
between these=20
bases and Levi's process of reduction and construct a class of orderings =
such=20
that the ideals [x^p] admit finite standard bases of only one element=20
{x^p}.<BR>Also we study various properties of admissible orderings on=20
differential monomials. We bring up the following problem: whether there =
is a=20
finitely generated differential ideal that does not admit a finite =
standard=20
basis w.r.t. any ordering.<BR><BR>S. Polyakov, MSU, Faculty of =
Computational=20
Mathematics & Cybernetics<BR></FONT></FONT></DIV>
<DIV><FONT size=3D2><FONT size=3D3>Additive Decomposition of the =
Rational=20
Functions<BR><BR>The problems of additive decomposition of the rational=20
functions are considered. These problems consist in decomposing the =
rational=20
function into the sum of two rational functions such that the first one =
is the=20
difference of some rational function and the second one is minimal in =
some=20
sence. The algorithm for solving one of these problems is=20
presented.</FONT><BR></DIV></FONT></BODY></HTML>
------=_NextPart_000_005C_01C4081D.856E5210--