Download Computer Algebra in Scientific Computing: 17th International by Vladimir P. Gerdt, Wolfram Koepf, Werner M. Seiler, Evgenii PDF

By Vladimir P. Gerdt, Wolfram Koepf, Werner M. Seiler, Evgenii V. Vorozhtsov

This booklet constitutes the lawsuits of the 17th overseas Workshop on machine Algebra in medical Computing, CASC 2015, held in Aachen, Germany, in September 2015.

The 35 complete papers awarded during this quantity have been rigorously reviewed and chosen from forty two submissions. They care for the continued growth either in theoretical machine algebra and its increasing functions. New and nearer interactions are fostered through combining the realm of laptop algebra tools and platforms and the appliance of the instruments of laptop algebra for the answer of difficulties in medical computing.

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Additional info for Computer Algebra in Scientific Computing: 17th International Workshop, CASC 2015, Aachen, Germany, September 14-18, 2015, Proceedings

Example text

Finally ρp is the reduction associated with the reduction path p satisfying ρp vm (xμ hγ ) = qp v hβ (8) for some polynomial qp ∈ P. A key point for applying this construction in the context of involutive bases is that any Janet basis has initially linear syzygies. Thus given a Janet basis we have two resolutions available: (1) and the one obtained by Sk¨oldberg’s construction. The main result of this section will be that the two are isomorphic. Lemma 10. Let H = {h1 , . . , hs } be the Janet basis of the polynomial submodule U ⊆ P t .

3. 5 GB. A * marks when we run out of time and ** marks when we run out of memory. A bold line indicates that the given example is δ-singular, i. e. that no Pommaret basis exists for it in the used coordinates. As benchmarks, we took a number of standard examples given in [16]. As most of these ideals are not homogeneous, we homogenised them by adding a new smallest variable. Furthermore, we always chose = /101 as base field. Singular and Macaulay2 apply the command res for computing a free resolution at first.

Hs } ⊂ P t is a finite set with s elements and ≺ an arbitrary term order on P t , then the Schreyer order ≺H is the term order induced on the free module P s by setting xμ eα ≺H xν eβ , if lt (xμ hα ) ≺ lt (xν hβ ) or if these leading terms are equal and β < α. The Schreyer order ≺H depends on the ordering of H. For the involutive version of the Schreyer Theorem, we assume that H is a Janet basis and order its elements in a suitable manner. We associate a directed graph with H. Its vertices are given by the elements in H.

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