       • To: mathgroup at smc.vnet.net
• From: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>
• Date: Fri, 17 Apr 2009 04:27:59 -0400 (EDT)
• References: <gs6pfe\$h1o\$1@smc.vnet.net>

```Combine both Reduces:

Reduce[{Element[{i, j}, Integers], i <= iP, j >= jP, j + i == jP + =
iP,
Element[{n, iP}, Integers], Not[(iP < n)],
Exists[{iPP}, (iPP < n) && iP == iPP + 1]}, {iP, jP},
Backsubstitution -> True]

Cheers -- Sjoerd

On Apr 16, 10:15 am, olfa <olfa.mra... at yahoo.fr> wrote:
> Hi Mathematica community,
> I have to solve this system:
> Reduce[{Element[{i, j}, Integers], i <= iP, j >= jP,
>   1*j + 1*i == 1*jP + 1*iP,
>   Reduce[{Element[{N, iP}, Integers], Not[(iP < N)],
>     Exists[{iPP}, (iPP < N) && iP == iPP + 1]}]}, {iP, jP},
>  Backsubstitution -> True]
>
> the output should be:( i | j | N | iP) are Integers && i <= N && iP ==
=
> N &&
>  jP == i + j - N
> but mathematica gave me this output:
> (C | C | C | C) are Integers && C >= 0 &&
>  C >= 0 && C >= 0 && C >= 0 && i == C - C - C[=
3] &&
>  iP == C - C + C && N == C - C + C &&
>  jP == j - C - C
>
> which is not understandable at all! and I dont want the output to be
> like that.
>
> I have observed that when I remove i from Element[{i, j}, Integers]
> mathematica give me the output I want and which is :iP == N &&  jP =
==
> i + j - N
>
> So how can I have this same output without removing i from Element[{i,
> j}, Integers]?
>
> Thank you very much in advance.

```

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