Problem defining assumptions on a set of variables

• To: mathgroup at smc.vnet.net
• Subject: [mg58012] Problem defining assumptions on a set of variables
• From: "Koffijberg, H." <H.Koffijberg at umcutrecht.nl>
• Date: Thu, 16 Jun 2005 05:36:38 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```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]

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  ]

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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