Re: Re: Reduce in Ver 6

• To: mathgroup at smc.vnet.net
• Subject: [mg85558] Re: [mg85502] Re: Reduce in Ver 6
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Wed, 13 Feb 2008 07:25:21 -0500 (EST)

```Another approach is to use ReplaceRepeated when using the rules.

equ = {a + b + c == 3, a^2 + b^2 + c^2 < 10, a^3 + b^3 + c^3 == 15,
a^4 + b^4 + c^4 == 35};

sol = {ToRules[Reduce[equ, {a, b, c}]]};

a^5 + b^5 + c^5 //. sol // Simplify

{83,83,83,83,83,83}

Bob Hanlon

---- Dana DeLouis <dana.del at gmail.com> wrote:
> > Use the Backsubstitution -> True setting for Reduce[]
>
> Darn!  Yep!  Right there in help under Reduce.
> Thank you very much.  I think I've been confusing this with the
> "VerifySolutions" option under Solve.  I now understand my mistake.  Can't
> believe I've missed this all this time.
> Thanks again.
>
> equ = {a + b + c == 3, a^2 + b^2 + c^2 < 10,
> a^3 + b^3 + c^3 == 15, a^4 + b^4 + c^4 == 35};
>
> sol = {ToRules[Reduce[equ, {a, b, c},
>        Backsubstitution -> True]]};
>
> Simplify[a^5 + b^5 + c^5 /. sol]
> {83, 83, 83, 83, 83, 83}
>
> --
> Dana DeLouis
>
> <snip>
>
> >> I use Reduce, but 'c is returned as a function of a & b.
> >> What I would like is for c to replace a & b with the appropriate values.
> >>
> >> r = {ToRules[Reduce[equ, {a, b, c}]]}
> >>
> >> {{a -> 1, b -> 1 - Sqrt[2], c -> 3 - a - b},
>
>
> > Use the Backsubstitution -> True setting for Reduce[]
> >
> > Szabolcs
>
>
>
>
>

```

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