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Re: How can I get better solution for this...?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg120047] Re: How can I get better solution for this...?
*From*: DrMajorBob <btreat1 at austin.rr.com>
*Date*: Thu, 7 Jul 2011 07:29:07 -0400 (EDT)
*References*: <201107060939.FAA29377@smc.vnet.net>
*Reply-to*: drmajorbob at yahoo.com
Ah yes... I misread your post in the heat of the moment.
The first three equations determine sy, gx, and gy in terms of p00, p01,
p11, and sx:
soln = Quiet@
Solve[{sx^2 (1 + gx gy)^2 + sx^2 gy^2 == p00,
sx sy gx (1 + gx gy) + sx sy gy == p01,
sy^2 (1 + gx^2) == p11}, {sx, sy, gx, gy}];
soln[[All, All, 1]]
{{sy, gx, gy}, {sy, gx, gy}, {sy, gx, gy}, {sy, gx, gy}}
giving four solutions. If the fourth equation is also true, each of these
solutions determines a value for d:
Solve[sx sy == d, d] /. soln
(four solutions)
Hence, your four equations have no solution with d free to vary.
Solve[{sx^2 (1 + gx gy)^2 + sx^2 gy^2 == p00,
sx sy gx (1 + gx gy) + sx sy gy == p01, sy^2 (1 + gx^2) == p11,
sx sy == d}, {gx}]
{}
Bobby
On Wed, 06 Jul 2011 11:50:17 -0500, Siddharth Srivastava
<siddys at gmail.com> wrote:
> Hi Bobby,
> Thanks. I actually wanted sx, sy, gx and gy in terms of the P coeff.
> The
> solution
> you gave is just the equation that I wanted to solve!
> #
>
> On Wed, Jul 6, 2011 at 9:18 AM, DrMajorBob <btreat1 at austin.rr.com> wrote:
>
>> Solve[{sx^2 (1 + gx gy)^2 + sx^2 gy^2 == p00,
>> sx sy gx (1 + gx gy) + sx sy gy == p01, sy^2 (1 + gx^2) == p11,
>> sx sy == d}, {p00, p01, p11, d}]
>>
>> {{p00 -> sx^2 + 2 gx gy sx^2 + gy^2 sx^2 + gx^2 gy^2 sx^2,
>> p01 -> gx sx sy + gy sx sy + gx^2 gy sx sy, p11 -> (1 + gx^2) sy^2,
>> d -> sx sy}}
>>
>> Bobby
>>
>> On Wed, 06 Jul 2011 04:39:55 -0500, sid <siddys at gmail.com> wrote:
>>
>> Hi all,
>>> I am trying to solve the following for {sx,sy,gx,gy}
>>>
>>> sx^2 (1 + gx gy)^2 + sx^2 gy^2 = P00 ........(1)
>>> sx sy gx (1 + gx gy) + sx sy gy = P01 .......(2)
>>> sy^2 ( 1 + gx^2) = P11 ..............................**.(3)
>>> sx sy = D ..............................**..................(4)
>>>
>>> in terms of P00,P01,P11, and D.
>>>
>>> When I use Solve[] , I get a huge output containing the P terms up
>>> till the order of 16 (i.e P00^16 etc..), which
>>> I know is not correct. I do not think I am specifying the problem
>>> correctly, and being a non-expert in Mathematica, would appreciate
>>> some help. Specifically
>>> 1) should I specify the simultaneous equation using && operator? I
>>> have tried it, and I get different (but huge) output
>>> 2) can I break the problem into parts? how?
>>> Thanks,
>>> s.
>>>
>>>
>>
>> --
>> DrMajorBob at yahoo.com
>>
--
DrMajorBob at yahoo.com
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