Fwd: Replacing an expression by an expression

*To*: mathgroup at smc.vnet.net*Subject*: [mg55659] Fwd: [mg55625] Replacing an expression by an expression*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Fri, 1 Apr 2005 05:36:51 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Could you please remove my reply since the OP has apparently removed his post. Thank you. Andrzej Begin forwarded message: > From: Carlos Felippa <carlos at titan.colorado.edu> To: mathgroup at smc.vnet.net > Date: 31 March 2005 18:55:50 GMT+02:00 > To: Andrzej Kozlowski <akoz at mimuw.edu.pl> > Subject: [mg55659] Re: [mg55625] Replacing an expression by an expression > > I have removed that post. I realize now that > signs do matter. Pls do not reply & if you > have, pls remove. Thanks, CAF > > > on 3/31/05 8:28 AM, Andrzej Kozlowski at akoz at mimuw.edu.pl wrote: > >> *This message was transferred with a trial version of CommuniGate(tm) >> Pro* >> On 31 Mar 2005, at 08:24, carlos at colorado.edu wrote: >> >>> I have a 8 x 8 symbolic matrix B of complicated entries. >>> Several partial expressions, however, can be simplified. Sample: >>> >>> rep= {(J12*x14-J11*y14)*(J12*(x32+x43)-J11*(y32+y43)) -> A0*(A1-A0)}; >>> >>> The left expression appears verbatim in entry B[[1,1]], which is >>> >>> -(L21*(J12*x14-J11*y14)*(J12*(-x32-x43)+J11*(y32+y43)))/ >>> (16*A412*J*(J11^2+J12^2)) >>> >>> But when I say B=B/.rep, nothing happens. For a few entries I could >>> do >>> cut and paste by hand: >>> >>> -(L21* A0*(A1-A0) )/ >>> (16*A412*J*(J11^2+J12^2)) >>> >>> But it get tedious and error prone for 64. Any suggestions on how to >>> get Mathematica to do the replacement? >>> >> >> >> This is a common problem; the expressions that you are trying to match >> are semantically the same but not syntactically so (look carefully at >> the minus coefficients of x32 and x43). In this case there is a very >> simple solution >> >> In[1]:= >> v = -(L21*(J12*x14 - J11*y14)*(J12*(-x32 - x43) + >> J11*(y32 + y43)))/(16*A412*J*(J11^2 + J12^2)); >> >> In[2]:= >> rep = {(J12*x14 - J11*y14)*(J12*(x32 + x43) - >> J11*(y32 + y43)) -> A0*(A1 - A0)}; >> >> In[3]:= >> Simplify[v] /. Simplify[rep] >> >> Out[3]= >> (A0*(-A0 + A1)*L21)/(16*A412*J*(J11^2 + J12^2)) >> >> but this is not guaranteed to work always in such cases (Simplify may >> in fact rearrange the matching parts so that they no longer match). >> >> There is a more subtle way to do this, which should work in all >> polynomial and rational function cases, but it can be somewhat tricky. >> Instead of rule we define an ideal: >> >> b = {(J12*x14 - J11*y14)*(J12*(x32 + x43) - J11*(y32 + y43)) - A0*(A1 >> - >> A0)}; >> >> compute a Groebner basis: >> >> gg = GroebnerBasis[b]; >> >> and then use: >> >> >> Simplify[Last[PolynomialReduce[v, gg, >> Join[Variables[v], Variables[gg]]]]] >> >> >> (A0*(-A0 + A1)*L21)/(16*A412*J*(J11^2 + J12^2)) >> >> >> We were lucky here that the order of variables proved to be just >> right. >> In general we may have to try different variable orders. >> >> Actually, all of the above will be performed automatically by Simplify >> with assumptions >> >> Simplify[v, (J12*x14 - J11*y14)*(J12*(x32 + x43) - >> J11*(y32 + y43)) == A0*(A1 - A0)] >> >> >> (A0*(-A0 + A1)*L21)/(16*A412*J*(J11^2 + J12^2)) >> >> but again we were lucky that the default order of variables happened >> to >> be just right. The advantage of the first approach (using >> PolynomialReduce) is the tone can easier control the order of the >> variables. >> >> >> Andrzej Kozlowski >> Chiba, Japan >> http://www.akikoz.net/andrzej/index.html >> http://www.mimuw.edu.pl/~akoz/ >> > >