2011. 11. 21.آ  of convex lattice polytopes ... prehensive Grobner Bases and Minimal Comprehensive...

download 2011. 11. 21.آ  of convex lattice polytopes ... prehensive Grobner Bases and Minimal Comprehensive Grobner

If you can't read please download the document

  • date post

    23-Sep-2020
  • Category

    Documents

  • view

    0
  • download

    0

Embed Size (px)

Transcript of 2011. 11. 21.آ  of convex lattice polytopes ... prehensive Grobner Bases and Minimal Comprehensive...

  • Contents

    ¬ÆF§L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

    ��wÁ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

    �wÁ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

    973�wÁ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

  • .

  • 111ooo333���IIIOOOÅÅÅêêêÆÆƬ¬¬§§§SSS

    555µ¤k¬Æ^êÑ3Æâ�6¥%�¢�“pì6YË[”

    11���25FFF§§§(((ÏÏÏÊÊÊ

    8:00-22:00 5þ��

    11���26FFF§§§(((ÏÏÏ888

    8:30-9:00 m4ª!ÜK

    9:00-10:00 ��w

    ̱

  • 16:30-16:50 Aè¼ê5¯K�ïÄ(J A Greedy Algorithm for Feed rate Plan- ning of CNC Machines long Curved Tool Path with Confined Jerk

    (4R�) (�S²)

    16:50-17:00 � �

    17:00-17:20 èÚÙ�¼ê ê\ó¥�ã3\\Ý�åe ��ÖÚ¢cÇ{

    ("NÆ) (Üák)

    17:00-17:40 TBA ý°Ä�AÛ�.{z

    (�À¶) (o²)

    18:00-20:00 CM2011 ��

    11���27FFF§§§(((ÏÏÏFFF

    8:30-9:30 ��w

    ̱

  • 14:00-15:00 ©¬7: ÎÒ-êO ©¬8: OÅêÆA^

    ̱

  • 10:40-10:50 � �

    10:50-11:10 Termination of Zeilberger-style algorithms: the mixed differential-q-shift and shift-q- shift cases

    Some new upper bounds for Heilbronn Problems of eight points in Squares and Triangles found by numeric-symbolic computation

    (�«!GI¹) (Q�Y!û)

    11:10-11:30 U?�©-�©A��{ Determination and Parametrization of ra- tional developable surfaces (ongoing)

    (o©x§±â§ö) (�á]!Ç=À)

    11:30-13:00 Ì ê

    14:00-15:00 ©¬13: ¢ê ©¬14: OÅêÆ�A^

    ̱

  • ������wwwÁÁÁ

    Primary Decomposition of Polynomial Ideals

    pXö Clemson University, {I

    The primary decomposition theorem, established by Lasker (1905) and Noether (1921), is a milestone in commutative algebra. It traces back to antiques in number theory in terms of integer and polynomial factorization and is a key witness to the development of modern algebra. Algorithms for computing primary decomposition have been studied extensively since 1920s and some of them are implemented in major computer algebra systems (e.g. Maple, Magma and Mathematica). However, efficient computation of primary decomposition is still a major challenge today even for intermediate size of polynomial systems (note that it is NP hard in general). In this talk, I shall give a brief survey of the basic ideas for computing primary decomposition, including a recent algorithm of the speaker with Daqing Wan and Mingsheng Wang on 0-dimensional ideals over finite fields.

    §§§¦¦¦)))êêêèèè©©©ÛÛÛ

    �[ ¥�ïÄ)�

    è{´d´u^M¢y�ê$|Ü���lÑXÚ"? è{�ÑÑ£©!êi\¶�¤nØþþL«Ñ\£²©! E¤Ú��ê§|§&EØM©

  • MacMahon©©©

    ©©©ÛÛÛ333���½½½êêêeee���õõõªªª{{{

    "Iü ÄÑÆ

    5¿ã§|�K�ê)´ê|ÜÆ�­Vg§3OA Û¥q¡knàõ/S�:"ÙOê¯K´êÆ¥�Ä�¯ K§3éõêÆïÄ¥Ók~­�/ §Ï ��\ïÄ"ê| ܧMacMahon© ©Û®¤?n5¿ã§|�K�ê) �5{"õ«{�Jѧ^±)û«¢S¯K§�éu� .OÑ� ´¶¯K"OAÛ�­?дBarvinokJÑ� 3�½êe�õªm{§dLoera�uÐ�LattE^¢y" ,T{´õªm{§�3éõ¢S¯K¥�Ly¿Øn"Ï Lk�(Üü+¥�`D{g§·òí2Barvinok�(J§¢ yMacMahon© ©Û3·�^e�õªm{§0�¯­ ½�·^u�.O�MacMahon© ©Û{"

    6

  • ���wwwÁÁÁ

    An algorithm for decision of the existence of nonclassical symmetry

    °

    An algorithm which uses differential characteristic set algorithm for the decision of the existence of nonclassical symmetry of partial differential equa- tions is proposed. The algorithm partially gives answer for an open problem proposed by P.A. Clarkson on nonclassical symmetry of partial differential equations. As applications of our algorithm, several examples of determining the nonclassical symmetries of some evolution equations are presented.

    On the Structure of Multivariate Mixed q-Hypergeometric Terms

    �«1, GI¹2, ¾X]2, x§2 1Department of Mathematics, North Carolina State University

    2Key Lab of Math.-Mech., Chinese Academy of Sciences schen21@ncsu.edu(Shaoshi Chen), ryfeng@amss.ac.cn(Ruyong Feng),

    fuguofeng@mmrc.iss.ac.cn(Guofeng Fu), jinkang@mmrc.iss.ac.cn(Jin Kang)

    Hypergeometric terms and their q-analogue have played an important role in the study of special functions. In combinatorics, a large class of enu- merative problems are encoded by sums or identities of those terms. In the early 1990’s, Zeilberger formulated a method, namely creative telescoping, which has become a powerful tool for automatically proving many combina- torial identities involving integrals or sums of hyperexponential functions, hypergeometric terms and their q-analogue [2, 6, 8].

    One of the challenging problems related to Zeilberger’s method is the termination problem. For bivariate hypergeometric terms, Abramov [1] ob- tained a termination criterion for Zeilberger’s algorithm. Later, Abramov’s criterion was extended to the cases of bivariate q-hypergeometric terms [5] and mixed hyperexponential-hypergeometric functions [3]. All of those re- sults were based on structure theorems of the bivariate inputs. In order to prove a conjecture by Wilf and Zeilberger [6], Chen and Li presented a structure theorem for multivariate hyperexponential-hypergeometric func- tions in [5]. Recently, a more general structure theorem has been derived

    7

  • in [4], where the functions may involve several q-variables. In this pa- per, we will present a refined version of the structure theorem for mixed q-hypergeometric terms.

    References

    [1] S. A. Abramov. When does Zeilberger’s algorithm succeed? Adv. in Appl. Math., 30(3):424–441, 2003.

    [2] G. Almkvist and D. Zeilberger. The method of differentiating under the integral sign. J. Symbolic Comput., 10:571–591, 1990.

    [3] S. Chen, F. Chyzak, R. Feng, and Z. Li. The existence of telescopers for hyperexponential-hypergeometric functions, 2010. MM-Res. Preprints (2010) No. 29, 239-267.

    [4] S. Chen, R. Feng, G. Fu, and Z. Li. On the Structure of Compatible Ra- tional Functions. In ISSAC ’11: Proceedings of the 2011 International Symposium on Symbolic and Algebraic Computation.

    [5] S. Chen and Z. Li. A multiplicative form of multivariate hyperexponential-hypergeometric functions, 2010. MM-Res. Preprints (2010) No. 29, 25-35.

    [6] W. Y. C. Chen, Q.-H. Hou, and Y.-P. Mu. Applicability of the q- analogue of Zeilberger’s algorithm. J. Symbolic Comput., 39(2):155– 170, 2005.

    [7] H. S. Wilf and D. Zeilberger. An algorithmic proof theory for hypergeo- metric (ordinary and “q”) multisum/integral identities. Invent. Math., 108(3):575–633, 1992.

    [8] D. Zeilberger. The method of creative telescoping. J. Symbolic Comput., 11(3):195–204, 1991.

    Termination of Zeilberger-style algorithms: the mixed differential-q-shift and shift-q-shift cases

    �«1, GI¹2 1Department of Mathematics, North Carolina State University

    2Key Lab of Math.-Mech., Chinese Academy of Sciences schen21@ncsu.edu fuguofeng@mmrc.iss.ac.cn

    8

  • Creative telescoping introduced by Zeilberger [7, 8] is an important tool for algorithmic integration and summation of special functions. Several results of the last two decades are fundamental for deciding the termination of algorithms based on it. Wilf and Zeilberger have shown that telescopers always exist for proper hypergeometric functions [6]. In the bivariate discrete case, Abramov has proved that a hypergeometric function can be written as a sum of a hypergeometric-summable function and a proper one if it has a telescoper [1]. Similar results have (more recently) been obtained in the q- shift case by B. Chen et al [5]. In the bivariate continuous-discrete case, the similar result has been given by S. Chen et al [3]. We consider the bivariate differential-q-shift case and shift-q-shift case, where q is not a root of unity.

    We present two criteria on the termination of Zeilberger’s algorithm in the mixed cases. The first is for the differential and q-shift case; the second is for the shift and q-shift case. The criteria describe necessary and sufficient conditions on the existence of telescopers for the hyperexponetial- hypergeometric solutions in the above mixed cases.

    Let k be a field of characteristic zero and k(t, y) be the field of rational functions in t and y over k. For every f ∈ k(t, y), we define

    Dt(f) = ∂f

    ∂t and Sy(f(t, y)) = f(t, qy),

    where q is not a root of unity in k. We denote by k(t, y)〈Dt, Sy〉 the ring of differential-q-shift operators with rational function coefficients in k(t, y). A first order differential-q-shift system

    Dt(z) = a z, Sy(z) = b z, with a, b ∈ k(t, y) (1)

    is said to be compatible if b 6= 0 and Dt(b)/b = Sy(a) − a. According to Theorem 2 in [2], there always exists a simple differential-q-difference extension A such that the compa