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Re: Problem defining assumptions on a set of variables
*To*: mathgroup at smc.vnet.net
*Subject*: [mg58060] Re: Problem defining assumptions on a set of variables
*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
*Date*: Fri, 17 Jun 2005 05:19:23 -0400 (EDT)
*Organization*: The Open University, Milton Keynes, England
*References*: <d8riof$ihp$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Koffijberg, H. wrote:
> Hi all,
>
> I have encountered two problems using Mathematica v5.0 with parameters
> for which no value is defined but for which some assumptions are defined.
> I do not understand why each of the following statements return -1.
>
> Assuming[q\[Element]Reals&&q>0&&q<1, If[q > 3, 1, 0, -1]]
> Refine[If[q > 3, 1, 0, -1],q\[Element]Reals&&q>0&&q<1]
>
Hi Erik,
No problem here; Mathematica behaves has expected. As an example, let
examine your first statement:
In[1]:=
Assuming[q â?? Reals && q > 0 && q < 1,
If[q > 3, 1, 0, -1]]
Out[1]=
-1
Part of this statement is equivalent to the logical combination of the
following two inequalities
In[2]:=
0 < q < 1 && q > 3
Out[2]=
0 < q < 1 && q > 3
In this case, Mathematica returns the expression itself since it cannot
decide whether it is right or wrong: each inequality is true by itself
but when combined they become a contradictory or undecidable proposition
about q.
Your original statement does not assign any value or range of values to
q, so the test is inconclusive and the *If* statement returns -1.
A similar reasoning apply to the next statement
In[3]:=
Refine[If[q > 3, 1, 0, -1], 0 < q < 1]
Hope this helps,
/J.M.
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