Applied numerical linear algebra
Applied numerical linear algebra
Algorithms for trigonometric curves (simplification, implicitization, parameterization)
Journal of Symbolic Computation
Modern computer algebra
Analysis of PSLQ, an integer relation finding algorithm
Mathematics of Computation
Towards factoring bivariate approximate polynomials
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Polynomial Factorization by Root Approximation
EUROSAM '84 Proceedings of the International Symposium on Symbolic and Algebraic Computation
Numerical Implicitization of Parametric Hypersurfaces with Linear Algebra
AISC '00 Revised Papers from the International Conference on Artificial Intelligence and Symbolic Computation
Implicitization of Rational Parametric Curves and Surfaces
AAECC-8 Proceedings of the 8th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
A geometric-numeric algorithm for absolute factorization of multivariate polynomials
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
The Mathematica Book
The midpoint locus of a triangle in a corner
ADG'10 Proceedings of the 8th international conference on Automated Deduction in Geometry
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A few years ago S-H Kim investigated some problems at the boundary of number theory, optimization, and geometry. One question regarded an optimal packing of certain “triangular oval” planar curves and another looked at some related transformations of ℝ2 to ℝ2. These were investigated primarily using tools from calculus but it turns out that computational algebra methods may instead be employed to particular advantage. Moreover, generalizations that are beyond the reach of such methods are still amenable to hybrid approaches using numeric and symbolic methods in tandem. We introduce some of the specific problems and generalizations, and show by detailed example how such techniques may be implemented and deployed.