       Re: Replacement gyrations

• To: mathgroup at smc.vnet.net
• Subject: [mg55912] Re: [mg55872] Replacement gyrations
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Sat, 9 Apr 2005 03:56:55 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```\$Version

5.1 for Mac OS X (January 27, 2005)

Wsol={{W11->(A2*x21+A1*
x32)/(L86^2*(-(x32*y21)+x21*y32)),W12->(A2*y21+
A1*y32)/(-(L86^2*x32*y21)+L86^2*x21*y32),W21->(A2*x21+
A1*x32)/(L75^2*(-(x32*y21)+x21*
y32)),W22->(A2*y21+A1*y32)/(-
(L75^2*x32*y21)+L75^2*x21*y32)}};

FullSimplify works

Wsol = Wsol//FullSimplify

{{W11 -> (A2*x21 + A1*x32)/(L86^2*(x21*y32 - x32*y21)),
W12 -> -((A2*y21 + A1*y32)/(L86^2*(x32*y21 - x21*y32))),
W21 -> (A2*x21 + A1*x32)/(L75^2*(x21*y32 - x32*y21)),
W22 -> -((A2*y21 + A1*y32)/(L75^2*(x32*y21 - x21*y32)))}}

Wsol/.(-(x32*y21)+x21*y32)->2*A123

{{W11 -> (A2*x21 + A1*x32)/(2*A123*L86^2),
W12 -> -((A2*y21 + A1*y32)/(L86^2*(x32*y21 - x21*y32))),
W21 -> (A2*x21 + A1*x32)/(2*A123*L75^2),
W22 -> -((A2*y21 + A1*y32)/(L75^2*(x32*y21 - x21*y32)))}}

This is only partially successful since some terms have a -1 factor.  Instead,
use a substitution rule like

Wsol /. x21*y32->2*A123+x32*y21

{{W11 -> (A2*x21 + A1*x32)/(2*A123*L86^2),
W12 -> (A2*y21 + A1*y32)/(2*A123*L86^2),
W21 -> (A2*x21 + A1*x32)/(2*A123*L75^2),
W22 -> (A2*y21 + A1*y32)/(2*A123*L75^2)}}

Bob Hanlon

>
To: mathgroup at smc.vnet.net
> Date: 2005/04/08 Fri AM 01:37:00 EDT
> To: mathgroup at smc.vnet.net
> Subject: [mg55912] [mg55872] Replacement gyrations
>
> A Solve for 4 variables W11,W12,W21,W22 produces, after Simplify
>
>  Wsol={{W11 -> (A2*x21 + A1*x32)/(L86^2*(-(x32*y21) + x21*y32)),
>         W12 -> (A2*y21 + A1*y32)/(-(L86^2*x32*y21) + L86^2*x21*y32),
>         W21 -> (A2*x21 + A1*x32)/(L75^2*(-(x32*y21) + x21*y32)),
>         W22 -> (A2*y21 + A1*y32)/(-(L75^2*x32*y21) + L75^2*x21*y32)}}
>
> Question 1: why do L86^2 and L75^2  come out as a factor in two
> expression denominators and not in the others?  Seems a random event.
>
> This uncertainty inhibits the action of further replacement rules such
> as
>             (-(x32*y21) + x21*y32) -> 2*A123
>
> which works on W11 and W21 only.
>
> Question 2: I tried Collect [Wsol,{L86,L75}] to try to force grouping
> of L86^2 and L75^2, but it has no effect.
> Do I need to say Wsol=Wsol*L86^2*L75^2, Simplify, replace and finally
> Wsol=Wsol/L86^2*L75^2 ? Or fool around with Numerator and
Denominator?
>
>

```

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