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

The CASC Workshops are normally held in flip within the Commonwealth of IndependentStates(CIS)andoutsideCIS(Germanyinparticular,but,attimes, additionally different nations with vigorous CA communities). the former CASC Wo- store was once held in Japan, and the twelfth workshop was once 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, particularly, with difficulties in such branches of typical technological know-how as arithmetic, informatics, physics, astronomy, biochemistry, and so on. It follows from the talks provided on the earlier CASC workshops that the tools and platforms of machine algebra will be utilized effectively in the entire above-listed branches of traditional sciences. as a result, the organizers of the twelfth CASC Workshop desire that the current workshop can assist the Armenian scientists to develop into much more conversant in the features of complicated desktop algebra equipment and platforms and to get involved with experts in desktop algebra from different nations. The eleven prior 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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**Example text**

X[k] . )T , and the matrices M1k (solution matrices) can be calculated according to the recurrence sequence of following formulas [8]: Mk ◦ X[l] = exp{LGk } ◦ X[l] = X[l] + ∞ + m 1 G⊕((j−1)(k−1)+l) X[m(k−1)+l] , (7) m m! m=1 j=1 where G⊕l = G⊕(l−1) ⊗E+E[l−1] ⊗G denotes the Kronecker sum of the lth order. The algebraical expressions similar to (7) are used for evaluation of aberration A Role of Symbolic Computations in Beam Physics 23 matrices up to an approximating order N . For this purpose a researcher has to realize one of the concatenation procedures.

T. S. The ﬁber cardinality is often not immediately available, as we may be unable to take inequations into account. However, we can use all information contained in the equations using reduction, if all equations are contained in ST . Thus we require (SQ )=

Math. 7(4), 649–679 (1954) 4. : Theory of emittance invariants. Lectures Notes Phys. 343, 94–121 (1989) 5. : Symbolic computation of approximate symmetries for ordinary diﬀerential equations. Mathematics and Computers in Simulation 57(3-5), 147–154 (2001) 6. : Dynamical Modeling of Control Systems for Particle Beams. In: SPbSU, Saint Petersburg (2004) (in Russian) 7. : The explicit form for Lie transformations. In: Proc. Fifth European Particle Accelerator Conference EPAC 1996. SITGES, Barcelona, Spain, pp.