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Showing 1 to 20 of 46 for “"computer algebra"”.
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Finite Geometry and Computer Algebra, with Applications
The interaction between geometry and algebra is a diverse and fruitful area to explore. Of particular interest is the area of groups and geometry. In this work we will examine various aspects of this interplay, in particular looking at geometric canonical forms of figures in various projective …
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A computer algebra package for polynomial sequence recognition
The software package developed in the thesis research implements functions for the intelligent guessing of polynomial sequence formulas based on user-defined expected sequence factors of the input coefficients. We present a specialized hybrid approach to finding exact representations for polynomial …
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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 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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Applications of computer algebra to the theory of electron energy loss
… recurrence relation and solved it exactly, using computer algebra (REDUCE and MATHEMATICA) as an essential guide. For all the problems listed above, we have obtained <i>closed form</i> solutions for the dispersion relations of surface and interface plasmons and for the angle-resolved energy-loss …
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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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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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Predicate dispatching in the Common Lisp Object
… 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 be well suited for both users and programmers.
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Fast Algorithms, Modular Methods, Parallel Approaches and Software Engineering for Solving Polynomial Systems Symbolically
… Its implementation also brings to the Maple computer algebra system a unique capacity for automatic case discussion and recombination. A high-level categorical parallel framework is developed, written in the Al- DOR language, to support high-performance computer algebra on symmetric multi …
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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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Theorem proving with the real numbers
… relevant for attempts to inject more rigour into computer algebra systems. Our work is conducted in a version of the HOL theorem prover. We describe the rigorous definitional construction of the real numbers, using a new version of Cantor's method, and the formalization of a significant portion of …
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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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An Analysis of Improvements to Buchberger's Algorithm for Groebner Basis Computation
… of the memory constraint issues occurring in computer algebra.
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Embodied mathematics by interactive sketching
… and an interactive sketch interface to combine computer algebra algorithms with layers of sketched, visually interpretable compositions.
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On Groebner Bases of (Non)commutative Free Algebras
… by Buchberger. It has been implemented in many computer algebra systems. In a paper in 1999, Faugere developed a modification of Buchberger’s algorithm. His algorithm uses row reduction of matrices to perform several steps of the algorithm at once. The goal for the project will be to develop a …
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Performance Engineering of Modular Symbols
… commonly used to compute modular forms. Existing computer algebra systems such as Sage and Magma include implementations of modular symbols. Our implementation applies the principles of performance engineering to this computational number theory problem, and MFSplit is at least 3 times faster than …
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