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Monique Teillaud 2007-09-03 11:21:34 +00:00
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39
Algebraic_kernel_d/doc_tex/Algebraic_kernel_d_ref/open.tex
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@ -1,6 +1,26 @@
\section{Questions and Remarks}
\section{Notes}
\begin{itemize}
\item CA\_2 and CPA\_2 require squarefree and coprime input!
\item Events at infinity are only important for a single curve. Since
inf doesn't play a role in CPA\_2 we discuss it for the sake of
simplicity as a special case in CA\_2 only.
\item AlgebraicReal\_1 - refine: with relative precision is enough. \\
Moreover, you can use 'refine() until' for absolute prec.
\item SquareFreeFactorization is not returning an additional constant
factor. This prevents us from providing an extra interface for
algebraic coefficients.
\item Is Derivative and XCriticalPoints/YCriticalPoints are not
redundant. We decided to keep them both because it is possible that
XCriticalPoints/YCriticalPoints use a different methodology, other
than residing to the Derivative functor. As Michael pointed out:
\emph{``I think we should keep it, since it is more abstract than
$solve(derivative(p),p)$. This would again move the {\em
AlgebraicKernel} towards a more abstract layer.''}
\end{itemize}
\section{Questions}
\begin{itemize}
\item problem is due to \ccc{AK_1}$<double>$.\\
@ -40,22 +60,3 @@
this traits class concept a refinement of RealEmbeddableTraits.
\end{itemize}
\section{Notes}
\begin{itemize}
\item CA\_2 and CPA\_2 require squarefree and coprime input!
\item Events at infinity are only important for a single curve. Since
inf doesn't play a role in CPA\_2 we discuss it for the sake of
simplicity as a special case in CA\_2 only.
\item AlgebraicReal\_1 - refine: with relative precision is enough. \\
Moreover, you can use 'refine() until' for absolute prec.
\item SquareFreeFactorization is not returning an additional constant
factor. This prevents us from providing an extra interface for
algebraic coefficients.
\item Is Derivative and XCriticalPoints/YCriticalPoints are not
redundant. We decided to keep them both because it is possible that
XCriticalPoints/YCriticalPoints use a different methodology, other
than residing to the Derivative functor. As Michael pointed out:
\emph{``I think we should keep it, since it is more abstract than
$solve(derivative(p),p)$. This would again move the {\em
AlgebraicKernel} towards a more abstract layer.''}
\end{itemize}