       Re: Solving on mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg88521] Re: Solving on mathematica
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Wed, 7 May 2008 07:08:47 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <fvpctc\$mkh\$1@smc.vnet.net>

```Chris wrote:

> How would i go about solving this equaiton on mathematica
>
> (Xi -Ux)^2 + (Yi - Uy)^2 + (Zi - Uz) = (Ri - Cb)
> i = 1,2,3,4
>
> where we need to find Ux, Uy, Uz, Cb tried a few things and they dont work.
>
> NSolve[ (Xi - U)^2 + (Yi - V)^2 + (Zi - W)^2 == (Ri - B)^2, {U, V, W,
>   B}, { i = 1, 2, 3, 4} ]
>
> any ideas?

Below, we assume that the Xi, Yi, etc., are some kind of indexed
variables or arrays that hold some values.

(* First, we generate some random data. *)
Do[{X[i], Y[i], Z[i], R[i]} = RandomInteger[{-5, 5}, 4], {i, 4}]

(* Then, we build the system of equations. *)
eqns = Table[(X[i] - U)^2 + (Y[i] - V)^2 + (Z[i] - W)^2 == (R[i] -
B)^2, {i, 1, 4}]

(* Now we solve it. *)
sols = NSolve[eqns, {U, V, W, B}]

(* Finally, we check the results. *)
eqns /. sols

Out= {(3 - U)^2 + (2 - V)^2 + (-3 - W)^2 == (-4 -
B)^2, (5 - U)^2 + (1 - V)^2 + (-5 - W)^2 == (-2 -
B)^2, (5 - U)^2 + (5 - V)^2 + (4 - W)^2 == (-3 -
B)^2, (4 - U)^2 + (-2 - V)^2 + (1 - W)^2 == (-3 - B)^2}

Out= {{U -> 41.8099, V -> -1.64395, W -> -2.60076,
B -> 34.9827}, {U -> 4.23504, V -> 2.48516, W -> 0.289612,
B -> -7.54715}}

Out= {{True, True, True, True}, {True, True, True, True}}

Regards,
-- Jean-Marc

```

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