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>*Reply-to*: drmajorbob at yahoo.com

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 made explicit. 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 > answer is { }. > > 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

**References**:**Eliminate works but Solve does not?***From:*RobertB <robert.c.baruch@gmail.com>