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problem with reduce

• To: mathgroup at smc.vnet.net
• Subject: [mg100347] problem with reduce
• From: olfa <olfa.mraihi at yahoo.fr>
• Date: Mon, 1 Jun 2009 07:11:15 -0400 (EDT)

Hi mathematica community,
I have to solve this example
In[88]:= Reduce[Exists[{C[1], C[2]},
  Element[{C[1], C[2]}, Integers] && C[1] >= 0 && C[2] >= 0 &&
   i == 1 + C[1] && N == 1 + C[1] + C[2] && iP == 1 + C[1] + C[2] &&
   jP == j - C[2]], {iP, jP}, Backsubstitution -> True]

During evaluation of In[88]:= Reduce::nsmet: This system cannot be
solved with the methods available to \
Reduce. >>

I have observed that when I remove Element[{C[1], C[2]}, Integers] && C
[1] >= 0 && C[2] >= 0 like that:
In[89]:= Reduce[
 Exists[{C[1], C[2]},
  i == 1 + C[1] && N == 1 + C[1] + C[2] && iP == 1 + C[1] + C[2] &&
   jP == j - C[2]], {iP, jP}, Backsubstitution -> True]

it gives me an output which is:

Out[89]= iP == N && jP == i + j - N


I need to keep the information that Element[{C[1], C[2]}, Integers] &&
C[1] >= 0 && C[2] >= 0  but reduce tells me that it cannot solve this
system. why and how to deal with this problem?
thank you.

• Follow-Ups:
  • Re: problem with reduce
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>