By S. A. Abramov, M. A. Barkatou, D. E. Khmelnov (auth.), Vladimir P. Gerdt, Ernst W. Mayr, Evgenii V. Vorozhtsov (eds.)

This booklet constitutes the refereed lawsuits of the eleventh foreign Workshop on machine Algebra in clinical Computing, CASC 2009, held in Kobe, Japan, in September 2009.

The 28 revised complete papers offered including 2 invited lectures have been conscientiously reviewed and chosen from various submissions. the themes addressed are all simple components of medical computing as they enjoy the program of machine algebra tools and software program. The papers conceal computing device algebra tools and algorithms, program of symbolic and algebraic manipulation, and CA tools and effects for the numerical integration of the partial differential equations of the mathematical physics.

**Read or Download Computer Algebra in Scientific Computing: 11th International Workshop, CASC 2009, Kobe, Japan, September 13-17, 2009. Proceedings PDF**

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**Extra resources for Computer Algebra in Scientific Computing: 11th International Workshop, CASC 2009, Kobe, Japan, September 13-17, 2009. Proceedings**

**Example text**

De Abstract. Closure systems and closure operations play an important role in both mathematics and computer science. In addition there are a number of concepts which have been proven to be isomorphic to closure systems and we refer to all such concepts as closure objects. In this work we develop relation-algebraic specifications to recognize several classes of closure objects, compute the complete lattices they constitute and transform any of these closure objects into another. All specifications are algorithmic and can directly be translated into the programming language of the computer algebra system RelView, which is a special purpose tool for computing with relations.

If the sets X and Y of R’s type [X ↔ Y ] are ﬁnite and of size m and n, respectively, we may consider R as a Boolean matrix with m rows and n columns. Since the Boolean matrix interpretation is well suited for many purposes and is also used by the computer algebra system RelView as one of its possibilities to depict relations, we often use matrix terminology and matrix Computing and Visualizing Closure Objects 31 notation. Especially we speak about the rows, columns and entries of a relation and write Rx,y instead of x, y ∈ R or x R y.

Problem 4. Let us assign the unperturbed motion in the following form: ϕ = 0 , θ = 0 , ψ = 0 , α1 = αo1 , α2 = αo2 , α3 = αo3 , ϕ˙ = 0 , θ˙ = 0 , ψ˙ = 0 , α˙1 = 0 , α˙2 = 0 , α˙3 = 0 , φ˙1 = h1 , φ˙2 = h2 , φ˙3 = h3 . V. Banshchikov Here h1 , h2 , h3 are constant values for angular rates of proper rotations of the rotors; αo1 , αo2 , αo3 are constant values of the angles of the gyrodine’s frames. The given unperturbed motion is substituted into nonlinear equations of motion constructed at the previous step.