By Sergey Abrahamyan (auth.), Vladimir P. Gerdt, Wolfram Koepf, Ernst W. Mayr, Evgenii V. Vorozhtsov (eds.)

ISBN-10: 3642152740

ISBN-13: 9783642152740

The CASC Workshops are often held in flip within the Commonwealth of IndependentStates(CIS)andoutsideCIS(Germanyinparticular,but,attimes, additionally different nations with energetic CA communities). the former CASC Wo- store was once held in Japan, and the twelfth workshop used to be held for the ?rst time in Armenia, that's one of many CIS republics. it's going to be famous that greater than 35 institutes and scienti?c facilities functionality in the nationwide Academy of S- ences of Armenia (further info about the constitution of the academy may be foundhttp://www. sci. am). those associations are involved, specifically, with difficulties in such branches of common technology as arithmetic, informatics, physics, astronomy, biochemistry, and so on. It follows from the talks provided on the past CASC workshops that the tools and structures of laptop algebra could be utilized effectively in all of the above-listed branches of normal sciences. hence, the organizers of the twelfth CASC Workshop wish that the current workshop can help the Armenian scientists to develop into much more conversant in the services of complex laptop algebra tools and structures and to get involved with experts in computing device algebra from different nations. The eleven previous CASC meetings, CASC 1998, CASC 1999, CASC 2000, CASC 2001, CASC 2002, CASC 2003, CASC 2004, CASC 2005, CASC 2006, CASC 2007, and CASC 2009 have been held, respectively, in St. Petersburg (R- sia), Munich (Germany), Samarkand (Uzbekistan), Konstanz (Germany), Yalta (Ukraine), Passau (Germany), St.

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**Additional info for Computer Algebra in Scientific Computing: 12th International Workshop, CASC 2010, Tsakhkadzor, Armenia, September 6-12, 2010. Proceedings**

**Sample text**

Fig. 1. The scheme of usage of computer algebra tools 2 Mathematical Background In this paper, dynamics of beam particles is presented in the form of an operator form using the Lie nonlinear transformation M (see, for example, [2]) ⎛ t ⎞ M(t|t0 ) = T exp ⎝ LF(τ ) dτ ⎠ , (1) t0 where LF(τ ) is a Lie operator associated with some vector function F(τ ) = F(τ ; X, U, B) deﬁning the motion equation for beam particles dX = F(t; X, U, B). dt (2) A Role of Symbolic Computations in Beam Physics 21 Here X ∈ X , U ∈ U, B ∈ B are the phase vector, the vector of control functions, and the vector of control parameters, respectively.

2. The total cycle of the computational experiment symplectic automatically, and following [8] one can evaluate these equations and write for matrix Q[2] = {qij } the following: ⎤ ⎡ q15 q16 q17 q18 q19 q110 q11 q12 q13 q14 ⎥ ⎢ ⎢ q21 q22 q23 q15 q25 q17 q27 q19 /2 2 q110 q210 ⎥ ⎥ ⎢ 12 Q =⎢ (17) ⎥. ⎢ q31 q32 q33 −2 q11 −2 q21 −q12 −q22 q14 /2 −q15 q25 /2 ⎥ ⎦ ⎣ q32 /2 2 q33 q43 −q12 −q22 q32 /2 2 q33 q43 −q12 −q22 Similar formulas can be obtained for any order of nonlinearities N and dimension of the phase vector X.

8 (InitSplit). Input: A system S, an equation or inequation q with ld(q) = x. Output: Two systems S1 and S2 , where (S1 ∪ {q}, S2 ) is a disjoint decomposition of S∪{q}. Moreover, φa (init(q)) = 0 holds for all a ∈ Sol(S1 ) and φa (init(q)) = 0 for all a ∈ Sol(S2 ). 1) we view a multivariate polynomial p as the univariate polynomial φ

### Computer Algebra in Scientific Computing: 12th International Workshop, CASC 2010, Tsakhkadzor, Armenia, September 6-12, 2010. Proceedings by Sergey Abrahamyan (auth.), Vladimir P. Gerdt, Wolfram Koepf, Ernst W. Mayr, Evgenii V. Vorozhtsov (eds.)

by Daniel

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