       Re: why doesn't the range on this interval match the plot range?

• To: mathgroup at smc.vnet.net
• Subject: [mg66440] Re: [mg66394] why doesn't the range on this interval match the plot range?
• From: Bruce Miller <brucem at wolfram.com>
• Date: Fri, 12 May 2006 02:03:46 -0400 (EDT)
• References: <200605110615.CAA17227@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

On May 11, 2006, at 1:15 AM, Chris Chiasson wrote:
> Parabola[x_]=4x^2+53x+160
> BeginPoint=-8;
> EndPoint=-5;
> Plot[Parabola[x],{x,BeginPoint,EndPoint}]
> Parabola[Interval[{BeginPoint,EndPoint}]]
>
> --
> http://chris.chiasson.name/
>

Interval is not set up for multi-level arithmetic, since the
second level treats the Intervals as independent.
For example, in the Trace below note that Interval[{100,256}] is
reversed (-8 end and -5 ends switched) compared with the Interval
for the linear term.  (This is with version 5.2.)

In:=
ibe=Interval[{BeginPoint,EndPoint}]

Out=
Interval[{-8, -5}]

In:=
Parabola[ibe]

Out=
Interval[{-164, 151}]

In:=
Trace[ Parabola[ibe] ]

Out=
{{ibe, Interval[{-8, -5}]}, Parabola[Interval[{-8, -5}]],

2
160 + 53 Interval[{-8, -5}] + 4 Interval[{-8, -5}] ,

{53 Interval[{-8, -5}], Interval[{-424, -265}]},

2
{{Interval[{-8, -5}] , Interval[{25, 64}]},

4 Interval[{25, 64}], Interval[{100, 256}]},

160 + Interval[{-424, -265}] + Interval[{100, 256}],

Interval[{-164, 151}]}

I did not find a simple workaround.  I will ask about clarifying the
documentation on what arithmetic can be done with Interval[list].

Bruce Miller
Technical Support
Wolfram Research, Inc.
support at wolfram.com
http://support.wolfram.com/

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