Re: Re: about Implication

*To*: mathgroup at smc.vnet.net*Subject*: [mg101613] Re: [mg101585] Re: [mg101527] about Implication*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Fri, 10 Jul 2009 23:25:38 -0400 (EDT)*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst*References*: <200907090558.BAA17362@smc.vnet.net> <200907101049.GAA15808@smc.vnet.net>*Reply-to*: murray at math.umass.edu

Interesting (?) observation: Whereas the Documentation Center page "Experimental/guide/ExperimentalPackage" lists only 6 functions, including ImpliesQ, evaluating ?Experimental`* gives a list of 49 functions. Andrzej Kozlowski wrote: > I think ImpliesQ uses CylindricalDecomposition and quantifier > elimination to test the implication between two statements involving > polynomial expressions in the same variables. Thus everything it can > do can also be done with Reduce. Let's take trivial example: > > Experimental`ImpliesQ[x>3,x>2] > > During evaluation of In[9]:= Experimental`ImpliesQ::obs: > Experimental`ImpliesQ has been superseded by Refine, and is now > obsolete. It will not be included in Mathematica version 8. >> > > True > > > This could be done with Reduce: > > Reduce[Not[x > 2] && x > 3] > False > > However, Reduce will attempt to use many more methods than InpliesQ > and therefore will tend to be slower. But, as we can see, Mathematica > 7 itself tells you the answer to your question (how come you did not > see it?): use Refine. So, the above examples can be done as follows: > > Refine[Not[x > 2], x > 3] > False > > > Actually, the above example belongs to ImpliesRealQ, a more > specialized version of ImpliesQ. The following is an example that > won't be done by ImpliesRealQ: > > In[3]:= Experimental`ImpliesQ[Element[x, Reals], Element[x, Complexes]] > During evaluation of In[3]:= > Experimental`ImpliesQ::obs:Experimental`ImpliesQ has been superseded > by Refine, and is now obsolete. It will not be included in Mathematica > version 8. >> > Out[3]= True > > So ImpliesRealQ is also obsolete and indeed Refine is an equally > efficient way to do this example: > > Refine[Element[x, Complexes], Element[x, Reals]] > True > > Of course Simplify will also work but, just as Reduce, it is less > efficient. > > Andrzej Kozlowski > > > On 9 Jul 2009, at 14:58, olfa wrote: > >> Hi mathematica community, >> when trying to use the function ImpliesQ (that tests if exp1 implies >> exp2 or not) mathematica show me a message telling that this function >> becomes obsolete and will disappear in mathematica8, could you tell me >> why? and by which function it is replaced. >> NB:Implies doesnt do the same thing as ImpliesQ. >> thank you. >> > > -- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305

**References**:**about Implication***From:*olfa <olfa.mraihi@yahoo.fr>

**Re: about Implication***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>

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**Re: about Implication**

**Re: about Implication**