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-rw-r--r--systems/doc/metapost/source-manual/mpman-app-numbersystems.tex4
1 files changed, 2 insertions, 2 deletions
diff --git a/systems/doc/metapost/source-manual/mpman-app-numbersystems.tex b/systems/doc/metapost/source-manual/mpman-app-numbersystems.tex
index 7e82e29c87..d3d1c2dc1f 100644
--- a/systems/doc/metapost/source-manual/mpman-app-numbersystems.tex
+++ b/systems/doc/metapost/source-manual/mpman-app-numbersystems.tex
@@ -60,7 +60,7 @@ and are usually orders of magnitude slower than in \texttt{double} mode.
The \index{interval?interval number system}\texttt{interval} number
system MPFI~\cite{lib:mpfi}, introduced in version \texttt{2.10}, is built on the top of the MPFR library
-and an interval quantity \texttt{[}\textit{number}\texttt{,}\textit{number}\texttt{]} is entered as
+and an interval quantity \texttt{[}\textit{number}\texttt{,}\textit{number}\texttt{]} is created with
\begin{center}\index{interval\_set?\texttt{interval\_set}}\label{Dintervalset}\texttt{w := interval\_set(}\textit{number}\texttt{,}\textit{number}\texttt{);}\end{center}
An interval is a set, the left extrema being
\begin{center}\index{interval\_get\_left\_endpoint?\texttt{interval\_get\_left\_endpoint}}\label{Dintervalleft}\texttt{l := interval\_get\_left\_endpoint(}\textit{interval}\texttt{);}\end{center}
@@ -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,