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

This e-book constitutes the refereed complaints of the eleventh overseas Workshop on laptop Algebra in clinical Computing, CASC 2009, held in Kobe, Japan, in September 2009.

The 28 revised complete papers awarded including 2 invited lectures have been conscientiously reviewed and chosen from various submissions. the themes addressed are all simple parts of clinical computing as they enjoy the program of laptop algebra equipment and software program. The papers hide machine algebra equipment 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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LNCS, vol. 1382, pp. 318–321. Springer, Heidelberg (1998) 3. : Solving algorithmic problems on orders and lattices by relation algebra and relView. V. ) CASC 2006. LNCS, vol. 4194, pp. 49–63. Springer, Heidelberg (2006) 4. : Implementation of relational algebra using binary decision diagrams. In: de Swart, H. ) RelMiCS 2001. LNCS, vol. 2561, pp. 241–257. Springer, Heidelberg (2002) 5. : RelView – An OBDD-based Computer Algebra system for relations. V. ) CASC 2005. LNCS, vol. 3718, pp. 40–51. Springer, Heidelberg (2005) 6.

The kinetic energy T (q˙ , q) for the system of bodies as a quadratic form with respect to generalized velocities q˙ , and the force function U (q ) of the approximate Newtonian ﬁeld of gravitation have been obtained. Here q is the vector of generalized coordinates. Problem 3. Nonlinear equations of motion in the Lagrange 2nd kind form have been constructed. It has been determined that the three generalized coordinates φ1 , φ2 , φ3 are cyclic, while the rest six coordinates are positional. The formulas used in Problems 1 − 3 can be found, for example, in [4] or at the URL-address of [5].

Hence, Aumann’s contacts are exactly the dependency relations in the sense of [6]. In the following theorem, we present relation-algebraic versions of the two axioms given in [6]. 41. Let M : X ↔ 2X be a membership-relation. Then a relation D : X ↔ 2X is a dependency relation iﬀ the following formulae hold: M⊆D D MT D ⊆ D Proof. We only show how the second inclusion can be obtained from a ﬁrst-order formalization of the sexond axiom of [6]: ∀ x ∈ X, Y, Z ∈ 2X : Dx,Y ∧ (∀ y ∈ Y : Dy,Z ) → Dx,Z ⇔ ∀ x ∈ X, Y, Z ∈ 2X : Dx,Y ∧ ¬(∃ y ∈ X : y ∈ Y ∧ D y,Z ) → Dx,Z ⇔ ∀ x ∈ X, Y, Z ∈ 2X : Dx,Y ∧ MT D Y,Z → Dx,Z ⇔ ∀ x ∈ X, Z ∈ 2X : (∃ Y ∈ 2X : Dx,Y ∧ MT D Y,Z ) → Dx,Z ⇔ ∀ x ∈ X, Z ∈ 2X : (D MT D )x,Z → Dx,Z ⇔ D MT D ⊆ D Computing and Visualizing Closure Objects 43 In [1] a one-to-one correspondence between the set O(2X ) of all closure operations of (2X , ⊆) and the set D(X) of all contacts of type [X ↔ 2X ] is established, which is also mentioned in [6] for dependency relations.