Titlebook: Computer Mathematics; 9th Asian Symposium Ruyong Feng,Wen-shin Lee,Yosuke Sato Conference proceedings 2014 Springer-Verlag Berlin Heidelbe

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https://doi.org/10.1007/978-3-662-36253-2In this paper we define the Popov and weak Popov forms of matrices over Poincaré–Birkhoff–Witt (PBW) extensions, and exhibit effective algorithms to find them. As applications we give general methods to calculate the ranks of such matrices, and a method to transfer a system of differential equations into a first order equation.

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Factorization of MotionsWe define . as polynomials with coefficients in the dual quaternions and study their factorizations. The motion polynomials correspond to motions in 3D space, and factoring into linear factors means to compose the motion into translations and rotations.

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Computing Popov Forms of Matrices Over PBW ExtensionsIn this paper we define the Popov and weak Popov forms of matrices over Poincaré–Birkhoff–Witt (PBW) extensions, and exhibit effective algorithms to find them. As applications we give general methods to calculate the ranks of such matrices, and a method to transfer a system of differential equations into a first order equation.

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,Station?re Umstr?mung von K?rpern,d at the Tenth Asian Symposium on Computer Mathematics (ASCM) in Beijing, China, on October 26, 2012 on the complexity theoretic hardness of many problems that the discipline of symbolic computation tackles.

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