Martin Schonert et al., GAP { Groups, Algorithms, and Programming, Lehrstuhl D fur Mathematik, Rheinisch Westfalische Technische Hochschule, Aachen, Germany, fth ed., 1995, Home page: http://www.gap-system.org.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a further upper bound. MC C (MC1 C ) uses CLIQUE to determine a clique in Step 1, and FCP C (COLOR) to determine upper bounds in Step 2. MCD (MC1D ) uses FCPD (DSATUR) for these purposes. 4. Computational results See [19] for a complete description of the implementation of our algorithms in GAP [17] on a Sun Sparcstation 10. We now compare the performance of algorithms MC C ,MC D , MC1 C and MC1D with existing algorithms for the maximum clique problem. By BXB we refer to a combination of the algorithms of [2, 6] the most e#cient known algorithms for the maximum clique problem. BXB uses FCPD ....

M. Sch#onert et al., GAP-Groups, Algorithms and Programming, Lehrstuhl D f# ur Mathematik, Rheinisch Westf#alische Technische Hochschule, Aachen, Germany, 1995.

....followed by the computation of an expression for the closure, under the pro nite group topology, of its commutative image. We use the modi cation proposed here to compute directly this expression, obtaining this way an algorithm that works much better in practice. The implementation in GAP [14, 18] of the original algorithm allowed computations of some examples, but only of monoids of small order. Bigger examples were handled as the algorithm was improved. The ability to compute the Abelian kernels of some monoids led the author and V. H. Fernandes to the results of [6] After a section of ....

....being implemented in GAP [18] by the author. It uses algorithms to produce normal forms of matrices that, as observed earlier, are already implemented in GAP. Of course, we are also using the facilities already available in GAP to work with semigroups. The implementation process began, using GAP3 [14] and the package Monoid [9] when the author was visiting the LIAFA at the University of Paris 7. During this phase we used monoids of injective partial transformations, which were being studied by V. H. Fernandes, to do some tests. The computation of several examples gave the necessary intuition ....

Schonert, M., et al., GAP { Groups, Algorithms, and Programming, Lehrstuhl D fur Mathematik, Rheinisch Westfalische Technische Hochschule, Aachen, Germany, fth edition, 1995. 16 MANUEL DELGADO

....Several contemporary computer programs for group theoretical calculations can be used to nd the orbits of vectors as outlined above. Davies and Royle [7] for example, use Cayley, an algebra system that has been further developed into Magma [6] Other algebra systems that can be used include GAP [23]. The eciency of this approach depends on the value of the codimension r, and it is practical when r is small, that is, when k is large. In this sense, it complements the previously discussed approach. 4 Determining Equivalence of Codes To nd out whether codes are equivalent or not, we can ....

M. Schonert et al., GAP | Groups, Algorithms, and Programming, 5th ed., Lehrstuhl D fur Mathematik, Rheinisch Westfalische Technische Hochschule, Aachen (1995).

....application for generating and manipulating coset tables. It can be used interactively, or can take its input from a script le. It is reasonably robust and comprehensive, but no attempt has been made to make it industrial strength or to give it any of the features of, say, Magma [2] or GAP [14]. Most of its features have been added in response to user requests, and it is assumed that the user is competent . One of the primary goals in developing ACE was to demonstrate how to correctly use ACE Levels 0 1; some care is taken to ensure that the user cannot generate invalid tables. A ....

M. Schonert et al. GAP { Groups, Algorithms and Programming. Lehrstuhl D fur Mathematik, Rheinisch-Westfalische Technische Hochschule, Aachen, 1995. 47

....If jAj is larger than m 6 then Theorems 6.1, 6.2 imply that such multisets are rare. Therefore, on most inputs, Algorithm MULT will nd an exterior square root if one exists. 7 Testing The author has implemented Algorithm MULT in the programming language GAP, version 3. 4 (see [6]) The test runs were performed on an Silicon Graphics R4000 Indigo. As GAP version 3.4 is not compilable, it does not run particularly fast. For this reason, we have restricted our testing to multisets of size n 120 (in fact, we have used n 2 f10; 45; 105g) However, for compilable programming ....

Martin Sch onert and others, GAP { Groups, Algorithms, and Programming. Lehrstuhl D fur Mathematik, Rheinisch Westfalische Technische Hochschule, Aachen, Germany, 5th edn., (1995). 23

.... a session manager, the mathematical knowledge base MBase, a user model, a pedagogical module, and deduction and computation support systems such as the proof planner of mega [12] with a user interface that is more tailored to educational needs, and the computer algebra systems Maple [4] and gap [15]. At the clients side a web server and browser reside. The presentation planner requests and processes information from MBase, from the user model, and from pedagogical module in order to generate an individual document. Some information about the actions of the user, such as learned concepts or ....

Martin Schonert et al. GAP { Groups, Algorithms, and Programming. Lehrstuhl D fur Mathematik, Rheinisch Westfalische Technische Hochschule, Aachen, Germany, 1995.

....are almost simple (see also [M, 6.1] The proof of [M, 6. 1] shows that the only possible maximal overgroups are isomorphic to PSU(3; q 3 ) 3, or to PSL(2; 19) for q = 2 (also see the main theorem in [As] In fact, there is no subgroup isomorphic to PSL(2; 19) see [JLPW] one can also use GAP [Sc] and character restriction arguments to show this, as was pointed out to us by Malle) In the case PSU(3; q 3 ) 3 the overgroup is shown to be unique exactly as in [We] Finally, consider E 7 (q) q 3. If q = 3, then, by [LM, x6] T is contained in a unique maximal subgroup as listed. If q = 2 ....

M. Schonert et al., GAP, Groups, Algorithms and Programming. Lehrstuhl D fur Mathematik, Rheinisch-Westfalische Technische Hochschule, Aachen, Germany, 4th edition, 1995.

....Ab of all nite abelian groups. A counterexample is obtained after computing the abelian kernels of the monoids POI n and POPI n . In order to nd a general form for these abelian kernels, we have worked out several examples. The computations were made when the rst author was implementing in GAP [22] the algorithm Delgado and Fernandes 3 presented in [8] The implementation makes use of the GAP package MONOID [18] This paper is divided as follows: Section 1 is devoted to general preliminaries and in Section 2 we present background results on the monoids POI n and POPI n which will be used ....

Schonert, M., et al., GAP { Groups, Algorithms, and Programming, Lehrstuhl D fur Mathematik, Rheinisch Westfalische Technische Hochschule, Aachen, Germany, fth edition, 1995.

....and present my research schedule. 5.1 Initial Work To gain practical experience with Wedderburn decomposition, I have implemented a number of the algorithms from the literature. In all cases, the algorithms implemented are for algebras over nite elds and have been implemented in GAP [28] version 3.4.4, a freely available computer algebra system. For the Jacobson radical, I implemented the algorithms of Friedl and R onyai [16] and Eberly [11] For nding the central primitive idempotents, I implemented the algorithm of 27 Davis [8] I used the technique in Section 4.2.6 to ....

....and experiment on Wedderburn decomposition algorithms. Wedderburn decomposition plays a central role in Hopf, a non commutative algebra system being developed at Virginia Tech. I will implement existing and new algorithms for Wedderburn decomposition to support Hopf, which is being built in GAP [28], a freely available computer algebra system that runs on a wide variety of platforms including Unix and any (suciently powerful) MSDOS based machines. For Gr obner basis computations, I will use Opal by Keller [24] for noncommutative algebras and Groebner by Windsteiger and Buchberger [3] for ....

Martin Schonert et al. GAP | Groups, Algorithms, and Programming. Lehrstuhl D fur Mathematik, Rheinisch Westfalische Technische Hochschule, Aachen, Germany, fth edition, 1995.

....Massey products. This will be pursued elsewhere. Acknowledgment. We wish to thank Sergey Yuzvinsky for valuable discussions regarding the material in Section 5, and the referee for carefully reading the manuscript. The computations for this work were done with the help of the packages GAP 3.4. 4 ([30]) Macaulay 2 ( 14] and Mathematica 3.0. Contents 0. Introduction 1 1. Cohomology ring and second nilpotent quotient 3 2. Generators and relators 7 3. Resonance varieties 9 4. Prime index normal subgroups 12 5. Complex arrangements 15 6. Real arrangements 18 References 21 1. Cohomology ring and ....

M. Schonert et al., GAP { Groups, Algorithms, and Programming, Lehrstuhl D fur Mathematik, Rheinisch Westfalische Technische Hochschule, Aachen, Germany, fth edition, 1995; available at http://www-math.math.rwth-aachen.de/gap/gap.html.

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Martin Schnert et.al., GAP { Groups, Algorithms, and Programming, Lehrstuhl D fur Mathematik, Rheinisch Westfalische Technische Hochschule, Aachen, Germany, fth edition, 1995.

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Martin Schonert et al., GAP { Groups, Algorithms, and Programming, Lehrstuhl D fur Mathematik, Rheinisch Westfalische Technische Hochschule, Aachen, Germany, fth ed., 1995, Home page: http://www.gap-system.org.

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M. Sch onert et al., GAP | Groups, Algorithms and Programming. Rheinisch Westfalische Technische Hochschule, Aachen, Germany, 1995.

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M. Sch onert et al., GAP | Groups, Algorithms and Programming. Rheinisch Westfalische Technische Hochschule, Aachen, Germany, 1995.

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M. Sch onert et al., GAP | Groups, Algorithms and Programming. Rheinisch Westfalische Technische Hochschule, Aachen, Germany, 1995.

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M. Sch onert et al., GAP | Groups, Algorithms and Programming. Rheinisch Westfalische Technische Hochschule, Aachen, Germany, 1995.

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Martin Schonert et al. GAP { Groups, Algorithms, and Programming. Lehrstuhl D fur Mathematik, Rheinisch Westfalische Technische Hochschule, Aachen, Germany, third edition, 1993. EUCLIDICITY CRITERIA 49

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Martin Schonert et al. GAP { Groups, Algorithms, and Programming. Lehrstuhl D fur Mathematik, Rheinisch Westfalische Technische Hochschule, Aachen, Germany, 1995. 6

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Martin Schonert et al., GAP { Groups, Algorithms, and Programming, Lehrstuhl D fur Mathematik, Rheinisch Westfalische Technische Hochschule, Aachen, Germany, fth ed., 1995.

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