J.C. Faug`ere. R'esolution des syst`emes d"equations alg'ebriques. Universit'e Paris 6, 1994. Th`ese de Doctorat.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... some software modules of the Parsac framework [1,19] but it is completely sequential (no threads of control) Timings of some examples with different combinations of our algorithmic variations and implementation techniques can be found in [3] Reference timings are for version 4 of the GB system [13]. Lexico and Sugar refer to the respective options of GB; speedup is computed as Sugar (Grevlex Walk) GB Parsac S Speedup Lexico Sugar Grevlex Grevlex Walk arnborg7 186 s 112 s 0.23 s 0.32 s 0.4 s 156 caprasse 5288 s 3174 s 0.23 s 0.18 s 1.0 s 2645 cassou 1 h 1 h 59.0 s 28.0 s 0.6 s ....

J. C. Faug`ere. R'esolution des syst`emes d"equations alg'ebriques. PhD thesis, Universit'e Paris 6, Feb. 1994.

....since the time spent in swapping is difficult to measure: it is not reported by the Unix system call getrusage( and may vary at each execution. 13.2 Opportunistic Collection The idea of using a temporary area for allocating temporary objects in the Buchberger algorithm was suggested by Faug ere [23] who realised it through a manual allocator deallocator in his system. The CMM generalises this idea and automates the mechanism. One may question however whether other known techniques would work as well. For instance one may think that an incremental collector would provide similar benefits, ....

J. C. Faug`ere, `R'esolution des syst`emes d"equations alg'ebriques', PhD thesis, Universit'e Paris 6, (1994).

....above. We used the AXIOM computer algebra system ( JS92] We defined categories corresponding to the different properties of triangular sets, packages and domains for the common sub routines. Futhermore, AXIOM is connected with GB, the very powerful Grobner engine developed by J.C. Faug ere ([Fau94]) This allowed us the non trivial Grobner basis computations which are needed in order to satisfy the second requirement above. Our implementation of each method uses the same polynomial domain constructor. Thus, a method involving particular data structures like the dynamic sets and dynamic ....

....our current implementation of Wu s method does not solve Liu s example any more. This checking process ffl has been intensively tested for more than one year, ffl is based on simple and well known algorithms and ffl is implemented in a direct way in AXIOM as an over level of the GB software ([Fau94]) Thus it will be considered as certainly reliable. In our analysis of the computed solutions we also look for other informations than timings or correctness. Given a solution, we want to know if some of the computed triangular sets are inconsistent or if some quasi components are contained in ....

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J.C. Faug`ere. R'esolution des syst`emes d"equations alg'ebriques. Universit'e Paris 6, 1994. Th`ese de Doctorat.

....Maple As a conclusion we give the class of each systems: Mathematica Maple MAS Macaulay Reduce Alpi Axiom GB classe 4 4.5 4.5 Theta 5 6( 6 7 5 Chapter 2 Basic user s manual of the GB package 2. 1 Presentation This user s manuel is a short extract from the French documentation ( Fau, Fau94] of the Faug ere s GB package. Do not expect a lot from this : only the basic commands that one needs in order to compute Grobner basis are presented here. If you need more detailed informations. The present translation will be completed and improved. The purpose of the Faug ere s GB package is ....

J.C. Faug`ere. R'esolution des syst`emes d"equations alg'ebriques. PhD thesis, Universit'e Paris 6, Feb. 1994.

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