O GeoGebra é um software educacional livre que permite manipular objetos matemáticos do plano, representando-os algébrica e geometricamente. Neste artigo recorremos a conceitos matemáticos, como matrizes de mudança de base e transformações lineares, a fim de simularmos a representação de objetos tridimensionais em GeoGebra e implementarmos um procedimento para a planificação de prismas regulares retos.
A Geometria é o ramo da matemática dedicado ao estudo de questões relacionadas com a posição relativa de objetos e suas propriedades, num determinado espaço. A introdução de referenciais cartesianos para o estudo de elementos geométricos, permite a tradução de problemas algébricos em problemas geométricos e vice-versa, facilitando a sua resolução. O seu estudo promove o raciocínio lógico e o pensamento dedutivo...
The notion of kernel of a finite monoid relative to a pseudovariety of groups can be used to define relative solvability of monoids in a similar way to the manner in which the notion of derived subgroup can be used to define solvable group. In this paper we study the solvability of certain inverse monoids relative to pseudovarieties of abelian groups.
Knowledge representation techniques as a way to describe the real world, based on mechanical, logical or other means, will be, always, a function of the systems ability to describe the existing world. Knowledge and belief are generally incomplete, contradictory, or error sensitive, being desirable to use formal tools to deal with the problems that arise from the use of incomplete, contradictory, ambiguous, impe...
We consider members of some well studied classes of finite transformation monoids and give descriptions of their abelian kernels relative to decidable pseudovarieties of abelian groups.
Let H be a pseudovariety of abelian groups corresponding to a recursive supernatural number. In this note we explain how a concrete implementation of an algorithm to compute the kernel of a finite monoid relative to H can be achieved. The case of the pseudovariety Ab of all finite abelian groups was already treated by the second author and plays an important role here, where we will be interested in the prope...
International Journal of Algebra and Computation, 15, nº 3 (2005), p. 547-570 ; The notion of Abelian kernel of a nite monoid extends the notion of derived subgroup of a nite group. In this line, an extension of the notion of solvable group to monoids is quite natural: they are the monoids such that the chain of Abelian kernels ends with the submonoid generated by the idempotents. We prove in this paper that...
Semigroup Forum vol. 68 (2004), p. 335–356 ; We compute the abelian kernels of some monoids of partial transformations. More precisely, the cases of the symmetric inverse monoid, monoids of order-preserving or order-reversing transformations and monoids of orientationpreserving or orientation-reversing transformations are treated.
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