       • To: mathgroup at smc.vnet.net
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Wed, 8 Sep 2010 00:57:56 -0400 (EDT)

```On 7 Sep 2010, at 08:02, olfa wrote:

> On 5 sep, 11:28, Andrzej Kozlowski <a... at mimuw.edu.pl> wrote:
>> On 4 Sep 2010, at 10:00, olfa wrote:
>>
>>> Hi Mathematica Community,
>>
>>> Is Mathematica able to detect(recognize) implication between equations?
>>
>>> Thank you.
>>
>> Your question is not clear enough to answer with much confidence but at least Mathematica can do things like these:
>>
>> Assuming[x^2 + y^2 ======== 1, Refine[x^4 + 2 x^2 y^2 + y^4 ======
> ==== 1]]
>>
>> True
>>
>> or
>>
>> Assuming[x^2 + y^2 ======== 1, Refine[x ======== 0 || x^2 + y^2 ==
> ======== 1]]
>>
>> True
>>
>> etc.
>>
>> Andrzej Kozlowski
>
> With this example I will try to clarify my question:
> x,xP,y,yP,t,tP are variables. y and yP are integer variables. Having
> this disjunction of conjunctions  :
> (y+Floor[Log[2,x]]====yP+Floor[Log[2,xP]] && t====tP && y====yP) || (t/
> 2^(y)====tP/2^(yP) && y+Log[2,x]====yP+Log[2,xP])
>
> is Mathematica able to detect (to recognize) that there is
> implications in this system?
>
>
>
>

No. It is only able to recognise implications between (essentially) polynomial systems.

Andrzej Kozlowski

```

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