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Showing 1 to 14 of 14 for “"Computer Algebra systems"”.
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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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Theorem proving with the real numbers
… of floating point hardware and hybrid systems. It also allows the formalization of many more branches of classical mathematics, which is particularly relevant for attempts to inject more rigour into computer algebra systems. Our work is conducted in a version of the HOL theorem prover. …
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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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Component Groups of Stabilizers in Algebraic Groups: Computational Methods and Applications
… of nilpotent elements in complex semisimple Lie algebras have been a relevant topic of research over the last century. The works of Alekseevskii (1979) and Sommers (1998) contributed significantly to the determination of such groups for exceptional Lie algebras, while Jantzen (2004) provided …
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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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Analysis and Implementation of Algorithms for Noncommutative Algebra
A fundamental task of algebraists is to classify algebraic structures. For example, the classification of finite groups has been widely studied and has benefited from the use of computational tools. Advances in computer power have allowed researchers to attack problems never possible before. In …
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Symbolic Evaluations Inspired by Ramanujan's Series for 1/pi
… research being conducted, up-to-date versions of Computer Algebra Systems such as Mathematica and Maple could not evaluate our introduced series, such as $$ \sum _{n=1}^{\infty } \frac{ \binom{2 n}{n}^2 H_n}{32^n (n + 1)} = 8-\frac{2 \Gamma^2 \left(\frac{1} {4}\right)}{\pi ^{3/2}}-\frac{4 \pi …
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Rethinking teaching strategies : a framework and demonstration through augmenting Maple
… multiple teaching strategies, and • the use of Computer Algebra Systems (CAS) in teaching problem solving in university mathematics. As a result, the SIMTA (Styles Implemented by Methods Tactics Actions) theoretical framework has been developed to support and sustain teaching strategies in the …
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Gestión mecanizada del conocimiento matemático en topología algebraica
… Mathematical Knowledge Management to Algebraic Topology. Mathematical Knowledge Management is a branch of Computer Science whose main goal consists in developing integral assistants for Mathematics including computation, deduction and powerful user interfaces able to make the daily …