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MathGroup Archive 2000

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

Out[1]=
-Sqrt[2]

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

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

In[3]:=
Experimental`Infimum[x, E^x < 2, x]

Out[3]=
Experimental`Infimum::nrtpi:
    x
   E  < 2 is not a logical formula consisting of polynomial equations and
inequalities in {x}
     with rational number coefficients.
Out[3]=
                         x
Experimental`Infimum[x, E  < 2, x]


In[4]:=
Experimental`Infimum[E^x, 1 < x < 2, x]


Experimental`Infimum::npoly:
    x
   E  is not a polynomial with rational number coefficients.
Out[4]=
                      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[1]:=
>>> Developer`ContextFreeForm[aaa`x+bbb`y+z]
>>> 
>>> Out[1]=
>>> x+y+z
>>> 
>>> 
>>> In[2]:=
>>> Experimental`Infimum[11+6 x-10 x^2-5 x^3+2 x^4+x^5,-2<x<2,x]//InputForm
>>> 
>>> Out[2]=
>>> Root[-69847 - 171468*#1 - 129054*#1^2 - 24692*#1^3 + 3125*#1^4 & , 1]
>>> 
>>> --------------------
>>> Regards,
>>> Ted Ersek
>>> 
>>> Download Mathematica tips, tricks from
>>> http://www.verbeia.com/mathematica/tips/Tricks.html
>>> 
>> 
>> 
> 
> 



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