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Reduce in Ver 6

• To: mathgroup at smc.vnet.net
• Subject: [mg85464] Reduce in Ver 6
• From: "Dana DeLouis" <dana.del at gmail.com>
• Date: Mon, 11 Feb 2008 06:13:16 -0500 (EST)

Hi.  I was wondering if anyone knows of a more efficient way to do this.
This issue came up in ver 6.0 with these equations:

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
}

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},
 {a -> 1, b -> 1 + Sqrt[2], c -> 3 - a - b},
 {a -> 1 - Sqrt[2], b -> 1, c -> 3 - a - b},
 {a -> 1 - Sqrt[2], b -> 1 + Sqrt[2], c -> 3 - a - b},
 {a -> 1 + Sqrt[2], b -> 1, c -> 3 - a - b},
 {a -> 1 + Sqrt[2], b -> 1 - Sqrt[2], c -> 3 - a - b}}

My workaround is rather tough, especially if this was much larger.

convert = {a -> aa_, b -> bb_, c -> cc_} ->
          {a -> aa, b -> bb, c -> 3 - aa - bb};

new = r /. convert

{{a -> 1, b -> 1 - Sqrt[2], c -> 1 + Sqrt[2]},
 {a -> 1, b -> 1 + Sqrt[2], c -> 1 - Sqrt[2]},
 {a -> 1 - Sqrt[2], b -> 1, c -> 1 + Sqrt[2]},

Etc..

Any help is much appreciated.  I hope I'm not overlooking something obvious.

Dana
ddelouis at gmail.com

• Follow-Ups:
  • Re: Reduce in Ver 6
    • From: Carl Woll <carlw@wolfram.com>