       Re: Re: Undocumented Features In 4.0

• To: mathgroup at smc.vnet.net
• Subject: [mg24969] Re: [mg24953] Re: [mg24938] Undocumented Features In 4.0
• From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
• Date: Mon, 28 Aug 2000 08:27:26 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Experimental`Infimum[p,q,v], where p is a polynomial in v, q is a  logical
formula consisting of polynomial equations and inequalities  with rational
number coefficients in  v, and v is a list of variables,  gives the infimum
of p, subject to the conditions determined by q. An important limitation is
that it will deal only with algebraic functions.

Here are a few simple examples:

In:=
Experimental`Infimum[x, x^2 < 2, x]

Out=
-Sqrt

In:=
Experimental`Infimum[y, y^2 < x && x < 9, {x, y}]
Out=
-3

Of course, (unlike FindMinimum), it will not work with transcendental
functions:

In:=
Experimental`Infimum[x, E^x < 2, x]

Out=
Experimental`Infimum::nrtpi:
x
E  < 2 is not a logical formula consisting of polynomial equations and
inequalities in {x}
with rational number coefficients.
Out=
x
Experimental`Infimum[x, E  < 2, x]

In:=
Experimental`Infimum[E^x, 1 < x < 2, x]

Experimental`Infimum::npoly:
x
E  is not a polynomial with rational number coefficients.
Out=
x
Experimental`Infimum[E , 1 < x < 2, x]

In fact, you can always obtain the information returned by
Experimental`Infimum by using the Algebra`InequalitySolve` package, but it
is much easier to use Experimental`Infimum, so I assume it will in some
future version become a standard Mathematica function.

--
Andrzej Kozlowski
Toyama International University, JAPAN

For Mathematica related links and resources try:
<http://www.sstreams.com/Mathematica/>

on 8/25/00 6:02 AM, Matt Herman at Henayni at hotmail.com wrote:

> Hi,
>
> Infimum (used in the analysis sense) is just the maximum of lower bounds for
> a function (or a set).
> Perhaps this is an exact value for findminimum?
>
> Matt
>
> ----- Original Message -----
> From: "Ersek, Ted R" <ErsekTR at navair.navy.mil>
To: mathgroup at smc.vnet.net
> To: mathgroup at smc.vnet.net
> Subject: [mg24969] [mg24953] [mg24938] Undocumented Features In 4.0
>
>
>> I was poking around the Wolfram Research FAQ web pages and went to
>> http://support.wolfram.com/Kernel/Symbols/Developer/index.html
>> and
>> http://support.wolfram.com/Kernel/Symbols/Experimental/index.html
>>
>> There I found what looks like lists of all symbols in the Experimental and
>> Developer contexts.  Several of the symbols listed there aren't documented
>> in the Help Browser, but I was able to figure out how to use two of them.
>> Below I demonstrate two of these undocumented features.  I couldn't figure
>> out any of the other undocumented symbols listed at the above URLs.  If
> you
>> can figure them out please let me know.
>>
>>
>>> In:=
>>> Developer`ContextFreeForm[aaa`x+bbb`y+z]
>>>
>>> Out=
>>> x+y+z
>>>
>>>
>>> In:=
>>> Experimental`Infimum[11+6 x-10 x^2-5 x^3+2 x^4+x^5,-2<x<2,x]//InputForm
>>>
>>> Out=
>>> Root[-69847 - 171468*#1 - 129054*#1^2 - 24692*#1^3 + 3125*#1^4 & , 1]
>>>
>>> --------------------
>>> Regards,
>>> Ted Ersek
>>>
>>> http://www.verbeia.com/mathematica/tips/Tricks.html
>>>
>>
>>
>
>

```

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