       Re: Why this cannot be solved

• To: mathgroup at smc.vnet.net
• Subject: [mg116272] Re: Why this cannot be solved
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Wed, 9 Feb 2011 02:10:48 -0500 (EST)

```olfa wrote:
> On 4 f=E9v, 07:43, "Sjoerd C. de Vries" <sjoerd.c.devr... at gmail.com>
> wrote:
>> I'm not sure what you're trying to do here, aP is a function name, not
>> a variable. You can't solve for that. Also aP == a is not an algebraic
>> equation as both aP and a are heads not variables.
>>
>> Cheers -- Sjoerd
>>
>>  On Feb 3, 11:32 am, olfa <olfa.mra... at yahoo.fr> wrote:
>>
>>
>>
>>> Hi Mathematica community,
>>> System 1)
>>> Reduce[Max[e, s + a[i]] == Max[c, d + aP[iP]] && d == s - a[n]
>>> +Sum[a[j],{j,i,n}] &&
>>>    aP == a && iP == n, {aP, iP, d, c}, Reals]
>>> this gives:
>>> Reduce::nsmet: This system cannot be solved with the methods available
>>> to Reduce.
>>> System 2)
>>> Reduce[Max[e, s + a[i]] == Max[c, d + aP[iP]] && d == s - a[n]
>>> +Sum[a[j],{j,i,n}] , { d, c}, Reals]
>>> this gives solutions.
>>> the only difference between them is the variables aP and iP and their
>>> respective equations.
>>> What I didn't understand is why the first system cannot be solved
>>> although I have given values for iP and aP inside of it?
>>> thank you.- Masquer le texte des messages pr=E9c=E9dents -
>> - Afficher le texte des messages pr=E9c=E9dents -
>
> if aP == a is not an algebraic equation as both aP and a are heads not
> variableshere why this example works:
> Reduce[x + Sum[a[index], {index, k, n}] ==
>    xP + Sum[aP[index], {index, kP, n}] && aP == a, {aP, xP},
>  Backsubstitution -> True]?
> Thank you.
>

By itself aP==a is of course algebraic. What was meant, I'm fairly
certain, is that these are not algebraic variables due to the very
visible aP[iP], a[i], and a[n]. So in creating these variables aP and a
you are introducing, in effect, functional dependencies.

The key difference in your new example is that the Sum[...] terms do not
evaluate, hence effectively encapsulate everything inside them. So
aP[index] and a[index] are not visible as  "variables" in any way.

This is substantially the same as was explained previously in regard to
Table.

http://forums.wolfram.com/mathgroup/archive/2011/Jan/msg00915.html

Daniel Lichtblau
Wolfram Research

```

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