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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