Expression comparison in Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg48028] Expression comparison in Mathematica
- From: David Dalton <dalton at nfld.com>
- Date: Fri, 7 May 2004 04:29:45 -0400 (EDT)
- Organization: Memorial University of Newfoundland
- Sender: owner-wri-mathgroup at wolfram.com
I have three expressions obtained by different methods (partly by math on paper, partly by Mathematica) that should be the same, all three for the general anisotropic elasticity matrix with 21 independent components, and all three reduce to the correct expression for isotropy when the isotropic elasticity matrix is inserted, so they all pass that test. However the expressions are not the same in the anisotropic case and I would like to know good methods of comparing them and seeing how they differ with Mathematica in order to trace my possible typo(s). Of course I will also review my paper math and Mathematica coding again. Expression1 is actually a ratio of two polynomials, NUM/DEN . So lets say I want to compare Expression1 and Expression2. Some things I have tried (or am trying now) are FullSimplify[Expression1-Expression2] (which should ideally be zero) FullSimplify[Expression1/Expression2] (which should ideally be one) and FullSimplify[PolynomialRemainder[Expression1*DEN,Expression2*DEN,f1]] (where they are actually polynomials in f1, f2, f3 so I would repeat that for f2 and f3) (the remainder should ideally be zero) So what do you think of that, and can you recommend any other methods of comparing two expressions that should be identical, including in the case where one is fairly long and perhaps not being reduced as well as it could by FullSimplify , or maybe that is not true? I also asked this of support at wolfram.com (though I was mainly e-mailing to complain about a couple of little other things) on Monday afternoon and they haven't gotten back to me yet so perhaps they don't have any suggestions. (But the automatic reply said usual turnaround is three days so I guess it can sometimes be a little longer.) I'm leaving the office now and heading home and leaving some Mathematica running and the results should be ready when I come in in mid-morning. David