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Showing 1 to 6 of 6 for “"computational algebra"”.
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Robust stability and contraction analysis of nonlinear systems via semidefinite optimization
… formulations can be solved numerically with computationally-effcient interior-point methods. Many of the first LMI-based stability formulations applied to linear systems and the class of nonlinear systems representable as an interconnection of a linear system with bounded uncertainty blocks. …
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An Algebraic Approach to Reverse Engineering with an Application to Biochemical Networks
… a discrete modeling approach, rooted in computational algebra, to reverse-engineer networks from experimental time series data. The algebraic method uses algorithmic tools, including Groebner-basis techniques, to build the set of all discrete models that fit time series data and to select …
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Formulae for symmetric powers and tensor products of modular representations of elementary abelian p-groups
… utilized the Magma calculator within the Magma computational algebra software as our primary methodology. Through the use of Magma’s calculator, we efficiently com-puted the tensor products and symmetric powers of modular representations of elementary abelian p-groups, providing precise outcomes …
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Algorithms for modeling and simulation of biological systems; applications to gene regulatory networks
… method for an exploration of the solution space. Computational algebra tools delimit the search space, enabling also a description of model complexity. The performance and robustness of the algorithm are explored via an artificial network of the segment polarity genes in the D. melanogaster. Once …
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Infinite Groebner Bases And Noncommutative Polly Cracker Cryptosystems
… ideal membership problem for a noncommutative algebra over a finite field. We show that this system, which is the noncommutative analogue of the Polly Cracker cryptosystem, is more secure than the commutative version. This is due to the fact that there are a number of ideals of noncommutative …
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On the Complexity of Computing Galois Groups of Differential Equations
… can be solved by integrals, exponentials and algebraic functions if and only if the connected component of its differential Galois group is solvable. Computing the differential Galois groups would help us determine the existence of the solutions expressed in terms of elementary functions …