By Mohamed Barakat (auth.), Victor G. Ganzha, Ernst W. Mayr, Evgenii V. Vorozhtsov (eds.)
The ebook covers numerous issues of desktop algebra tools, algorithms and software program utilized to medical computing. a major subject awarded within the e-book, that may be of curiosity to researchers and engineers, is the applying of machine algebra ways to the advance of recent effective analytic and numerical solvers, either for traditional and partial differential equations. a particular characteristic of the e-book is an extreme use of complex software program platforms like Mathematica, Maple and so on. for the answer of difficulties as defined above and for the commercial program of machine algebra for simulation. The booklet could be necessary for researchers and engineers who practice complex desktop algebra equipment for the answer in their problems.
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Additional info for Computer Algebra in Scientific Computing CASC 2001: Proceedings of the Fourth International Workshop on Computer Algebra in Scientific Computing, Konstanz, Sept. 22-26, 2001
1 Introduction Differential equations are of central importance in all applied sciences. Whenever a continuous process is modelled mathematically, chances are high that the model is built upon them. Thus it is not surprising that almost any computer algebra system provides functions for analysing differential equations. Within MuPAD, this is largely the task of the library DETools. 0). We describe briefly the main components of the library in its current state: a fairly general package for Lie symmetry analysis and a algebraicgeometric completion package for overdetermined systems.
The main difficulty is still to find out the strata where P has to assume minima, and, of course, the construction of the function P which assumes the minima on the 'right' strata. , in the determination of minima of Higgs potentials. Acknowledgements The author is very grateful to Johannes Zimmer from technical university munich for showing me the connection of shape memory alloys to invariant theory and for the numerous useful discussions. References 1. , The Geometry of Spontaneous Symmetry Breaking.
Our new algorithm avoids these using some algebraic concepts. An open question is its relative efficiency compared with approaches based on differential forms . 1 The Algorithm The general framework for our algorithm is the Cartan-Kuranishi completion in formal theory. A system of differential equations of order q is interpreted as a fibred submanifold Rq of a jet bundle J q £. Two natural operations are prolongation to higher order jet bundles and projection to lower order bundles which may produce integrability conditions.
Computer Algebra in Scientific Computing CASC 2001: Proceedings of the Fourth International Workshop on Computer Algebra in Scientific Computing, Konstanz, Sept. 22-26, 2001 by Mohamed Barakat (auth.), Victor G. Ganzha, Ernst W. Mayr, Evgenii V. Vorozhtsov (eds.)