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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
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