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Re: Problem defining assumptions on a set of variables

Hi Erik,
see below,

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]
Assuming has no effect on "If[..]" only on functions like: Simplify,.. 
see manual. Therefore, "If" does his job without knowning about the 
assumptions, decides that q is not defined and returns -1.

> I would expect to get 0 as return value. What am I missing here ?
> In addition I would like to define a fairly large matrix (e.g. 100x100)
> in which each entry consists of a variable of unknown value. Something like:
> [ p11   p12   p13,   p14,   ... , p1100    ]
> [ p21   p22   p23,   p24,   ... , p2100    ]
>  ...
> [ p1001 p1002 p1003, p1004, ... , p100100  ]
Array is made for this job. E.g.
You assigne a value to an element by e.g.:

> with pij the variable on row i column j. Any ideas on how to define such
> a matrix without defining any values for the pij but with the added assumption
> that 0 <= pij <= 1 for all the pij's ? 
> I want to use this matrix for computations in which I will provide values
> for some of the variables and not provide values for the remaining variables
> so that the result is expressed in terms of the undefined variables. However
> the sets of defined / undefined variables will not be fixed so I'm looking for
> a flexible solution.
> Any help will be greatly appreciated.
> Erik Koffijberg.

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