Re: problem in solving inconsistent system of equations

• To: mathgroup at smc.vnet.net
• Subject: [mg127630] Re: problem in solving inconsistent system of equations
• From: Andrzej Kozlowski <akozlowski at gmail.com>
• Date: Wed, 8 Aug 2012 03:18:05 -0400 (EDT)
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• References: <20120807070146.E18726764@smc.vnet.net>

```On 7 Aug 2012, at 09:01, awaisysf <awaisysf at yahoo.com> wrote:

> Reduce[a^2 + a + b*c + 1 == 0 && e^2 + f*g + 1 == 0 &&
>  k^2 + k + l*m + 1 == 0 && s^2 + t*u + 1 == 0 &&
>  2*a*k + k + b*m + c*l + a + 1 == 0 && 2*a*s + s + b*u + c*t == 0 &&
>  2*k*e + e + f*m + g*l == 0 && 2*e*s + f*u + g*t == 0 &&
>  e (-1 - k) - g l + c (f (-1 - k) + e l) + b (g k - e m) +
>    a (-e - g l + f m) == 1, {a, b, c, e, f, g, k, l, m, s, t, u},
> Modulus -> 37]
>
> but when i solve this through Mathematica it gives this error
> "
> Reduce::munsp: Reduce was unable to solve the system. Increasing the value of SystemOption MaxModularPoints may help."
>
> actually there are many solution who satisfied this system of questions by the above mention command i need only one or first few solutions please help to modified this code . thanks
>

Well, let's do what Reduce suggests:

SetSystemOptions[ReduceOptions -> MaxModularPoints -> 10^7];

Now lets try FindInstance rather than Reduce since Reduce tries to find all solutions and right now I am interested in just one.

FindInstance[a^2+a+b*c+1==0&&e^2+f*g+1==0&&k^2+k+l*m+1==0&&s^2+t*u+1==0&&2*a*k+k+b*m+c*l+a+1==0&&2*a*s+s+b*u+c*t==0&&2*k*e+e+f*m+g*l==0&&2*e*s+f*u+g*t==0&&e (-1-k)-g l+c (f (-1-k)+e l)+b(g k-e m)+a (-e-g l+f m)==1,{a,b,c,e,f,g,k,l,m,s,t,u},Modulus->37]
{}

The answer {} means that Mathematica claims that there are no solutions. Any evidence that you are right and Mathematics is wrong?

Andrzej Kozlowski

```

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