mirror of https://github.com/CGAL/cgal
added references for Polynomial manual
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@ -49446,6 +49446,15 @@ library."
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, update = "93.09 tamassia"
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, update = "93.09 tamassia"
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}
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}
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@Article{d-osa-00,
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author = {Lionel Ducos},
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title = {Optimizations of the Subresultant Algorithm},
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journal = {Journal of Pure and Applied Algebra},
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year = 2000,
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volume = 145,
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pages = {149--163}
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}
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@book{dh-pcsa-73
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@book{dh-pcsa-73
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, author = "R. O. Duda and P. E. Hart"
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, author = "R. O. Duda and P. E. Hart"
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, title = "Pattern Classification and Scene Analysis"
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, title = "Pattern Classification and Scene Analysis"
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@ -87793,6 +87802,14 @@ the R*-tree."
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, update = "99.11 bibrelex"
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, update = "99.11 bibrelex"
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}
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}
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@Article{k-dfcosubm-09,
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author = {Michael Kerber},
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title = {Division-Free Computation of Subresultants Using Bezout Matrices},
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journal = {International Journal of Computer Mathematics},
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year = 2009,
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note = {in print; a technical report with the same name appeared as MPI-I-2006-1-006, Saabr\"ucken, Germany}
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}
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@book{k-hdsl-1877
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@book{k-hdsl-1877
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, author = "Alfred Bray Kempe"
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, author = "Alfred Bray Kempe"
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, title = "How to Draw a Straight Line; a Lecture on Linkages"
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, title = "How to Draw a Straight Line; a Lecture on Linkages"
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@ -151743,3 +151760,4 @@ amplification and suppression of local contrast. Contains C code."
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, publisher = "Cambridge University Press"
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, publisher = "Cambridge University Press"
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, year = 1999
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, year = 1999
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}
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}
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@ -817,11 +817,11 @@ The computation method depends on the algebraic category of
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\ccc{PolynomialTraits_d::Coefficient_type}.
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\ccc{PolynomialTraits_d::Coefficient_type}.
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if it models \ccc{CGAL::IntegralDomain},
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if it models \ccc{CGAL::IntegralDomain},
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the subresultants are computed
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the subresultants are computed
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by a pseudo-division approach~\cite{ducos-optimizations}.
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by a pseudo-division approach~\cite{d-osa-00}.
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If they only model a
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If they only model a
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\ccc{CGAL::IntegralDomainWithoutDivision}, the subresultants
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\ccc{CGAL::IntegralDomainWithoutDivision}, the subresultants
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are computed by evaluating the determinants directly, avoiding divisions
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are computed by evaluating the determinants directly, avoiding divisions
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completely~\cite{kerber-division}.
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completely~\cite{k-dfcosubm-09}.
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\ccOperations
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\ccOperations
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\ccFunction{template<typename Polynomial_traits_d,typename OutputIterator>
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\ccFunction{template<typename Polynomial_traits_d,typename OutputIterator>
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