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Download Computer Algebra in Scientific Computing: 12th International by Sergey Abrahamyan (auth.), Vladimir P. Gerdt, Wolfram Koepf, PDF

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

The CASC Workshops are regularly held in flip within the Commonwealth of IndependentStates(CIS)andoutsideCIS(Germanyinparticular,but,attimes, additionally different nations with full of life CA communities). the former CASC Wo- store used to be held in Japan, and the twelfth workshop used to be held for the ?rst time in Armenia, that is one of many CIS republics. it may be famous that greater than 35 institutes and scienti?c facilities functionality in the nationwide Academy of S- ences of Armenia (further information about the constitution of the academy might 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 forth. It follows from the talks awarded on the earlier CASC workshops that the tools and structures of machine algebra will be utilized effectively in the entire above-listed branches of common sciences. as a result, the organizers of the twelfth CASC Workshop wish that the current workshop can help the Armenian scientists to develop into much more acquainted with the functions of complex desktop algebra equipment and platforms and to get involved with experts in machine algebra from different international locations. The eleven past 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

The second approach is based on the numerical solution of differential equations for aberration matrices (see (14)), which can be evaluated for arbitrary forms of fringe fields in the control elements. Here we lose not only the symbolic-specific flexibility, but possibility to keep corresponding solutions in data knowledge as LEGO-objects [12]. 2 Symplectification Procedures The both (above described) cases demand symplectic property for the restricted beam propagator MN . Several symplectic integration methods have been proposed in the literature (see, for example, [13]–[15]).

7], [Yap00, Chap. t. x, Thomas Decomposition of Algebraic and Differential Systems 37 and by PRSi (p, q, x), i < dq the regular polynomial of degree i in PRS(p, q, x) if it exists, or 0 otherwise. Furthermore, PRSdp (p, q, x) := p, PRSdq (p, q, x) := q and PRSi (p, q, x) := 0, dq < i < dp . Define resi (p, q, x) := init (PRSi (p, q, x)) for 0 < i < dp , whereas resdp (p, q, x) := 1 and res0 (p, q, x) := PRS0 (p, q, x). Note that res(p, q, x) := res0 (p, q, x) is the usual resultant. 10. Let S be a system and p1 , p2 ∈ R with ld(p1 ) = ld(p2 ) = x.

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.

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