Re: Simplifying polynomial and rounding problems

*To*: mathgroup at smc.vnet.net*Subject*: [mg82838] Re: Simplifying polynomial and rounding problems*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Thu, 1 Nov 2007 05:09:58 -0500 (EST)*Organization*: The Open University, Milton Keynes, UK*References*: <fg9onv$mea$1@smc.vnet.net>

Isaac Martinez G. wrote: > I am having problems with Mathematica precision/accuracy (or whatever you call it) > I have the following expression > A1=1.0000000000000002-0.6721560269293043s^2 - 0.32784397307069685s^4 > Now when I factorize: > There are a couple of (-1+s)(1+s) factors or something very close to 1. Like 0.999999999999999997+s > I want to elliminate those factors but due to the fact that it is not really 1, but 0.999999999999999997 Mathematica does not always cancel those factors neither with A1/((-1.+s)(1.+s)) nor A1/((-1+s)(1+s)). > How can I avoid the problem of 1 versus 0.999999999999999997 > I am doing directional coupler design and I do need to elliminate some factors from an ABCD matrix where 5 to 6 decimal places is just fine in the last step. > I have tried > Factor[] > Cancel[] > FactorList[] > but I always have this problem and it screws up my program. > Sorry, I am new to Mathematica All those functions are designed to work with *symbolic* expressions or *exact* arithmetic, so you may want to use *Rationalize* before attempting any simplifications. For instance, In[1]:= A1 = 1.0000000000000002 - 0.6721560269293043 s^2 - 0.32784397307069685 s^4 Out[1]= 1.- 0.672156 s^2 - 0.327844 s^4 In[2]:= Factor@A1 Out[2]= -0.327844 (-1. + s) (1.+ s) (3.05023+ s^2) In[3]:= Rationalize[#, 10^(-6)] & /@ % Out[3]= -(219/668) (-1 + s) (1 + s) (3947/1294 + s^2) In[4]:= %/((-1 + s) (1 + s)) Out[4]= -(219/668) (3947/1294 + s^2) Regards, -- Jean-Marc