mirror of https://github.com/CGAL/cgal
46 lines
1.6 KiB
TeX
46 lines
1.6 KiB
TeX
\section{Polynomial Data}
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Polynonomials form fundamenatal mathematical objects, especially
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in algebraic computation geometry. Several algorithms need to be implemented
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when defining curves and surfaces as zero sets of polynomials. Several
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problems can also be reduced to the univariate case, i.e., using elimination
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theory. As problems real root isolation, or gcd computations can be
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analysed using these data sets.
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\subsection{Random}
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Univariate random polynomials are provided in two sets. Both sets contain
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polynomials of degree up to 8, but with huge coefficients.
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The coefficient of this set are integral with bitlengths varying from
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200 to 2000.
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\ccBenchmarkInstance{Polynomial/Polynomial_1/Integer/random/}
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The coefficient of this sets are square-root extensions (all adjoinded
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by the same root). Their bitlengths vary from 100 to 1000 bits.
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\ccBenchmarkInstance{Polynomial/Polynomial_1/Sqrt_extension/random/}
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\subsection{Resultants}
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The following instances collect univariate polynomials
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of different size (number of polynomials, bitsize) that appear
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when computing intersections of quadrics using resultants.
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\ccBenchmarkInstance{Polynomial/Polynomial_1/Sqrt_extension/quadric_resultants/}
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\subsection{Pairs of Bivariate Polynomials}
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Concerning bivariate polynomials we list instances of various pairs.
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\begin{itemize}
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\item \ccBenchmarkInstance{Polynomial/Polynomial_2_pair/ci.bff}
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\item \ccBenchmarkInstance{Polynomial/Polynomial_2_pair/di.bff}
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\item \ccBenchmarkInstance{Polynomial/Polynomial_2_pair/mi.bff}
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\item \ccBenchmarkInstance{Polynomial/Polynomial_2_pair/ri.bff}
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\item \ccBenchmarkInstance{Polynomial/Polynomial_2_pair/wi.bff}
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\end{itemize}
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%labels
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