• To: mathgroup at smc.vnet.net
• Subject: [mg96942] Re: About Reduce and Mod
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Fri, 27 Feb 2009 06:17:36 -0500 (EST)

```On 2/26/09 at 7:59 AM, olfa.mraihi at yahoo.fr (olfa) wrote:

>I have this input:   Reduce[{Mod[x, 5] ==
>Mod[xP, 5], 0 <= xP < 5}, {xP}, Backsubstitution -> True]

>Mathematicas gives me this output:0 <= Re[Mod[x, 5]] < 5 &&
>Im[Mod[x, 5]] == 0 && xP == Mod[x, 5] 1)but why there is 0 <=
>Re[Mod[x, 5]] < 5 && Im[Mod[x, 5]] == 0 as part of the output ?

Mathematica by default assumes all variables can take on complex
values. The output is specifying the conditions on a complex
variable needed to make the equality hold.

>2) and how could I eliminate it (by adding something in reduce for
>example) because all that I want is only this output xP == Mod[x, 5]?

In[4]:= Assuming[Element[{x, xP}, Reals],
Refine[
Reduce[{Mod[x, 5] == Mod[xP, 5], Mod[xP, 5], 0 <= xP < 5},
{xP}, Backsubstitution -> True]]]

Out[4]= xP == x mod 5

```

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