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Commit 637a4d0e authored by Luigi Scarso's avatar Luigi Scarso
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Fixed manual for interval arithmetic (thanks to Pétiard François)

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......@@ -68,7 +68,7 @@ and the right extrema
\begin{center}\index{interval\_get\_right\_endpoint?\texttt{interval\_get\_right\_endpoint}}\label{Dintervalright}\texttt{r := interval\_get\_right\_endpoint(}\textit{interval}\texttt{);}\end{center}
and it's always $l\leq r$\,; a number \texttt{x} is always seen as the interval \texttt{[x,x]}, i.e. a set with one element.
At first glance, interval arithmetic can be confusing: if $w$ is an interval,
$w*w$ is the set $\left\{ x*x: x\in w\right\}$, but $f(w)=w^2$ is the set $\left\{f(x): x\in w\right\} = \left\{x^2: x\in w\right\}$:
$w*w$ is the set $\left\{ x*y: x\in w, y\in w\right\}$, but $f(w)=w^2$ is the set $\left\{f(x): x\in w\right\} = \left\{x^2: x\in w\right\}$:
if $w=[-1,1]$ then $w*w=[-1,1]$ and $w^2=[0,1]$. On the other hand, it's easy to verify that $w*w*w = w^3$ always. For this reason,
given that currently the
implementation of the MetaPost functions in MPFI mimics those of MPFR and they are not adapted to the interval arithmetic,
......
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