By Sergey Abrahamyan, Melsik Kyureghyan (auth.), Vladimir P. Gerdt, Wolfram Koepf, Ernst W. Mayr, Evgenii V. Vorozhtsov (eds.)
This ebook constitutes the refereed lawsuits of the thirteenth overseas Workshop on computing device Algebra in clinical Computing, CASC 2011, held in Kassel, Germany, in September 2011. The 26 complete papers incorporated within the e-book have been conscientiously reviewed and chosen from various submissions. The articles are prepared in topical sections at the improvement of item orientated machine algebra software program for the modeling of algebraic buildings as typed gadgets; matrix algorithms; the research by means of desktop algebra; the advance of symbolic-numerical algorithms; and the appliance of symbolic computations in utilized difficulties of physics, mechanics, social technological know-how, and engineering.
Read Online or Download Computer Algebra in Scientific Computing: 13th International Workshop, CASC 2011, Kassel, Germany, September 5-9, 2011. Proceedings PDF
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Extra info for Computer Algebra in Scientific Computing: 13th International Workshop, CASC 2011, Kassel, Germany, September 5-9, 2011. Proceedings
An } where a1 < · · · < an ; furthermore, we denote a0 = −∞, an+1 = ∞. Then, our goal is to prove that for t ∈ (ai , ai+1 ), where i = 0, . . , n, all the surfaces of the family can be described by the same simplicial complex; hence, that the shape of the family is invariant along (ai , ai+1 ). Now the key of this proof is the notion of delineability. The reader may see  for further reading on this notion, or revise Section 3 in , for a brief review on it. Here we will simply recall the following formal deﬁnition: Definition 1.
2! 2 The above described approach gives us the new LEGO objects – the matrices R1k (for usual ODE’s) or M1k (for Hamiltonian diﬀerential equations) up to necessary truncation order. The corresponding symbolic computation can be evaluated up to necessary order of truncation (now some formulae up to ﬁfth order for several types of control elements, such as dipoles, quadrupoles, and so on are calculated). 4 Auxiliary LEGO Objects In the previous sections, we have described the basic classes of LEGO objects and their mathematical presentation in the matrix formalism.
In: Koepf, W. ) ISSAC 2010 Proceedings, pp. 45–52. ACM Press, New York (2010) 7. : An algorithm computing the regular formal solutions of a system of linear diﬀerential equations. J. Symbolic Computation 28, 569–588 (1999) 8. : On the equivalence problem of linear diﬀerential systems and its application for factoring completely reducible systems. In: Gloor, O. ) ISSAC 1998 Proceedings, pp. 268–275. ACM Press, New York (1998) 9. : Computing super-irreducible forms of systems of linear diﬀerential equations via Moser-reduction: A new approach.