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>