• 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>

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 Experimental`ImpliesQ has been superseded by Refine, and is now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 Experimental`ImpliesQ::obs:Experimental`ImpliesQ has been superseded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

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