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 >>> >> >> > >