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)
- Reply-to: hanlonr at cox.net
- 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 > > From: carlos at colorado.edu 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? > >