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TeXLive
metapost
Commits
637a4d0e
Commit
637a4d0e
authored
1 year ago
by
Luigi Scarso
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Fixed manual for interval arithmetic (thanks to Pétiard François)
parent
8c392bd6
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manual/mpman-app-numbersystems.tex
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manual/mpman-app-numbersystems.tex
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637a4d0e
...
...
@@ -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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