       Re: Solving equations and inequalities with Reduce - how?

• To: mathgroup at smc.vnet.net
• Subject: [mg87710] Re: [mg87655] Solving equations and inequalities with Reduce - how?
• From: "W_Craig Carter" <ccarter at mit.edu>
• Date: Wed, 16 Apr 2008 05:00:33 -0400 (EDT)
• References: <200804150950.FAA24909@smc.vnet.net>

```Hello Marc,
Your initial example worked fine for me:

Reduce[200000 a + 20000 b + 2000 c + 200 d + 20 e + 2 f ==
100000 c + 10000 d + 1000 e + 100 f + 10 a + b, {a, b, c, d, e, f},
Modulus -> 9]

resulted in
a == C && b == C && c == C && d == C && e == C &&
f == 8 C + 8 C + 8 C + 8 C + 8 C

and not
20000 a

Craig
On Tue, Apr 15, 2008 at 5:50 AM, Marc Heusser
<marc.heusser at byeheusser.commercialspammers.invalid> wrote:
> I tried to solve equations with Reduce and somehow did not quite
>  formulate it right, so Reduce complains with
>  "Reduce::ivar: 1 is not a valid variable".
>
>  This is what I tried:
>
>  Wanted: A six digit number satisfying the following conditions:
>  The first digit is not zero.
>  If you take the first two digits and move them to the end of the number,
>  the resulting number must be twice the original number.
>
>  In:=Reduce[200000a +20000 b +2000 c+200 d+20 e  +       2 f
>  \[Equal]100000c +10000 d +1000 e+100 f+10 a  + b ,  {a,b,c,d,e,f},
>  Modulus\[Rule]9]
>
>  I did solve the problem through exhaustive search:
>
>  In:=Timing[Select[Range[10^6],    FractionalPart[#/10000] 1000000 +
>  IntegerPart[#/10000]\[Equal] 2  #&]]
>  Out={34.2848 Second,{142857,285714,428571}}
>
>  but would like to understand how to use Reduce (or another function) to
>  solve such a set of equations.
>
>  TIA
>
>  Marc
>
>  --
>  remove bye and from mercial to get valid e-mail
>  <http://www.heusser.com>
>
>

--
W. Craig Carter

```

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