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Showing 1 to 17 of 17 for “"computer algebra system"”.
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The construction of DNA codes using a computer algebra system
… libraries and in microarray technologies. The computer algebra system Magma, which deals successfully with coding theory computation, is applied initially to the construction of DNA codes sat- isfying a GC-content constraint and a minimum Hamming distance constraint. The constraints are …
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Predicate dispatching in the Common Lisp Object
… mechanisms, to the Common Lisp Object System (CLOS). To demonstrate its utility, I used predicate dispatching to enhance Weyl, a computer algebra system which doubles as a CLOS library. My result is Dispatching-Enhanced Weyl (DEW), a computer algebra system that I have demonstrated to …
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Representations of Algebras: Some Computational Aspects
Let n ϵ Z≥1 and R be a finitely presented k-algebra over a computable field k. We describe algorithms for computably deciding representation-theoretic properties of R, following work by Letzter. Among these algorithms is an algorithm deciding whether an n-dimensional irreducible representation …
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Computational Algebraic Geometry Applied to Invariant Theory
Commutative algebra finds its roots in invariant theory and the connection is drawn from a modern standpoint. The Hilbert Basis Theorem and the Nullstellenstatz were considered lemmas for classical invariant theory. The Groebner basis is a modern tool used and is implemented with the computer …
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A study of homological invariants modulo an exact zero divisor
… algorithm for this construction, written for the computer algebra system Macaulay2. Given two R-modules, we then use a mapping cone construction to relate homology of the two modules over Q to homology over R, and we give applications of this construction to the study of several homological …
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Magpy: A Python Package for Magmas
… provers, finite counter-example generators, and computer algebra systems, most of which have a complicated installation process, unintuitive syntax, a lack of comprehensiveness for mathematical structures, or some combination of these. Computer algebra systems are indispensable tools due to their …
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Cylindrical Decomposition Under Application-Oriented Paradigms
… so far implemented methods, QE by cylindrical algebraic decomposition (CAD) is the most important complete method. The aim of this thesis is to develop CAD-based algorithms, which can solve more problems in practice and/or provide more interesting information as output. An algorithm that …
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Non-commutative Gröbner Bases and Applications
… were computed using the package gbmr of the computer algebra system ApCoCoA. The package was developed by the author. It contains dozens of functions for Gröbner basis computations and many concrete applications. The package gbmr and a collection of interesting examples are available at …
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Integration of Computer Algebra Systems and Machine Learning in the Authoring of the SANYMS Intelligent Tutoring System
<p>Computer-based feedback is an increasingly common tool in mathematics education. The feedback that such programs provide can range from indicating whether an answer was correct, to giving an answer or worked out solution or suggesting a similar practice problem. One type of computer-based …
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New methods for the integration of distributions of vector fields
… in the CinfStructures package for the computer algebra system Maple. A detailed description of the package has been included.
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Fast Algorithms, Modular Methods, Parallel Approaches and Software Engineering for Solving Polynomial Systems Symbolically
… most promising methods for solving non-linear systems of equations symbolically. We first adapt nearly optimal algorithms for polynomial arithmetic over fields to direct products of fields for polynomial multiplication, inversion and GCD compu tations. Then, by introducing the notion of …
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Towards justifying computer algebra algorithms in Isabelle/HOL
… grow, we are in need of certified algorithms in computer algebra to tackle problems over the real numbers. This is important because uncertified procedures can drastically increase the size of the trust base and under- mine the overall confidence established by interactive theorem provers, which …
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The Combinatorics of Involutive Bases: Theory, algorithms and applications
… and other related structures in commutative algebra. Our primary tool for exploring the connections between these algebraic objects and combinatorics is the use of involutive bases, along with other types of Gröbner bases that exhibit additional combinatorial properties. In particular, the …
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A Computational Approach to the Quillen-Suslin Theorem, Buchsbaum-Eisenbud Matrices, and Generic Hilbert-Burch Matrices
… domain, is free. We describe a package for the computer algebra system <italic>Macaulay2</italic> which we have developed to compute free generating sets for projective modules. We give special attention to the algorithms when R is the ring of integers and provide a constructive proof of a …
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Real root counting for parametric polynomial systems and applications.
Polynomial systems appear in many different fields of study. Many important problems can be reduced to solving systems of polynomial equations and usually the coefficients involve parameters. This thesis is devoted to finding practical ways to solve such problems from two fields, the studies of …
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Nonlinear dynamics of composite plates and other physical systems
The computer algebra system MACSYMA is used to derive the nonlinear expression for the Lagrangian and the nonlinear equations of motion of composite plates undergoing large deformations by using a higher-order shear-deformation theory. When computer algebra is not used, the derivation of these …
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Automatización e implementación de algunos problemas algebráicos y geométricos
… a otras tres dadas). 4. Aplicación de métodos algebraicos (método de las bases de Groebner y método de seudodivisiones de Wu) a la automatización de un criterio de no-ramificación de ideales primos en extensiones algebraicas y a la demostración automática de un teorema original de Geometría …