       Re: Replacement gyrations

• To: mathgroup at smc.vnet.net
• Subject: [mg55897] Re: [mg55872] Replacement gyrations
• From: "David Park" <djmp at earthlink.net>
• Date: Sat, 9 Apr 2005 03:55:47 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```When all else fails you can do 'surgery' on expressions.

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)}};

temp = MapAt[Factor, Wsol, {{1, 2, 2, 2}, {1, 4, 2, 2}}]
temp = MapAt[Minus, %, {{1, 2, 2, 1}, {1, 2, 2, 4, 1}}]
Wsol2 = MapAt[Minus, %, {{1, 4, 2, 1}, {1, 4, 2, 4, 1}}]

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

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

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

First I applied Factor to the specific part that I wanted factored. Then, in
the last two commands, I switched the signs of two factors. To find the
positions I often 'fish' for them with the Part command. For example,

Part[temp, 1, 4, 2, 4, 1]
x32 y21 - x21 y32

David Park

To: mathgroup at smc.vnet.net

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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