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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--