Re: Eliminate works but Solve does not?

• To: mathgroup at smc.vnet.net
• Subject: [mg121541] Re: Eliminate works but Solve does not?
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Mon, 19 Sep 2011 07:04:44 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201109180811.EAA06330@smc.vnet.net>

```This has no solution:

Solve[{x[3]^2 + y[3]^2 == L[3]^2, x[1]^2 + y[1]^2 == L[1]^2,
x[1] + x[2] == 2, y[1] == -2 + y[3], x[4]^2 + y[4]^2 == L[3]^2,
x[2]^2 + y[2]^2 == L[1]^2, x[2] + x[4] == 1.6875`,
y[2] == -2 + y[4], y[4] == 0.15625` + y[3]}, {L[1], L[3]}]

{}

because, implicitly, it requires (for instance) that

x[1]^2 + y[1]^2 == Sqrt[x[2]^2 + y[2]^2]

based on two different equations involving L[1]. The x variables are
constrained and so, for general (unconstrained) x values, there are no L
variables to solve the system.

Your Eliminate statement, on the other hand, solves for x variables in
terms of L variables. In that situation, there ARE solutions.

Here's a third try:

Eliminate[{x[3]^2 + y[3]^2 == L[3]^2, x[1]^2 + y[1]^2 == L[1]^2,
x[1] + x[2] == 2, y[1] == -2 + y[3], x[4]^2 + y[4]^2 == L[3]^2,
x[2]^2 + y[2]^2 == L[1]^2, x[2] + x[4] == 1.6875`,
y[2] == -2 + y[4], y[4] == 0.15625` + y[3]}, {L[1], L[3]}]

4096. x[1] == 3431. + 320. y[4] && 4096. x[2] == 4761. - 320. y[4] &&
1.67772*10^7 x[3]^2 ==
4.2172*10^6 + 6.61952*10^6 y[4] + 102400. y[4]^2 &&
4096. x[4] == 2151. + 320. y[4] && 32. y[1] == -69. + 32. y[4] &&
y[2] == -2. + y[4] && 32. y[3] == -5. + 32. y[4]

in which the constraints on x (which made the first try impossible) are

Bobby

On Sun, 18 Sep 2011 03:11:06 -0500, RobertB <robert.c.baruch at gmail.com>
wrote:

> I have a physical problem where I have a system of 9 equations in 10
> unknowns. I am trying to determine the relationship between 2
> unknowns. Here is the system:
>
> Subscript[y, 3]^2 + Subscript[x, 3]^2 == Subscript[L, 3]^2 &&
>
>  Subscript[y, 1]^2 + Subscript[x, 1]^2 == Subscript[L, 1]^2 &&
>
>  Subscript[x, 1] + Subscript[x, 3] == 2 &&
>
>  Subscript[y, 1] == Subscript[y, 3] - 2 &&
>
>  Subscript[y, 4]^2 + Subscript[x, 4]^2 == Subscript[L, 3]^2 &&
>
>  Subscript[y, 2]^2 + Subscript[x, 2]^2 == Subscript[L, 1]^2 &&
>
>  Subscript[x, 2] + Subscript[x, 4] == 1.6875 &&
>
>  Subscript[y, 2] == Subscript[y, 4] - 2 &&
>
>  Subscript[y, 4] == Subscript[y, 3] + (0.3125/2)
>
> Now, when I use Solve[..., {Subscript[L, 1], Subscript[L, 3]}], the
>
> However, when I use Eliminate[..., {Subscript[x, 1], Subscript[x, 2],
> Subscript[x, 3], Subscript[x, 4], Subscript[y, 1], Subscript[y, 2],
> Subscript[y, 3], Subscript[y, 4]}], I get a proper answer, that is, a
> function of L_1 and L_3 = another function of L_1 and L_3.
>
> Even if I add a condition, such as Subscript[L, 1] == 1 to the system,
> and Solve (or even NSolve) for Subscript[L, 3], I get { } even though
> I know that a solution exists.
>
> Can anyone explain why Solve/NSolve doesn't seem to do anything?
>
> Thanks!
>

--
DrMajorBob at yahoo.com

```

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