Re: polynomial long division using Series[] and changing
- To: mathgroup at smc.vnet.net
- Subject: [mg112405] Re: polynomial long division using Series[] and changing
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Tue, 14 Sep 2010 05:14:36 -0400 (EDT)
Convert to TraditionalForm num = 2 + z; den = z^2 + 2*z + 1; r = Normal[Series[num/den, {z, 0, 4}]] // TraditionalForm 6 z^4-5 z^3+4 z^2-3 z+2 Or go to menu Preferences | Evaluation | Format type of new output cells: and select TraditionalForm Bob Hanlon ---- "Nasser M. Abbasi" <nma at 12000.org> wrote: ============= Mathematica experts: I need a way to tell Mathematica to reverse the default ordering it uses for polynomial. The problem: I have 2 uni-variants polynomials num(z) and den(z), I can do the polynomial num(z)/den(z) long division using the Series command Series[num/den,{z,0,n}] Where n is the maximum number of terms I want to see in the long division. This is a small example --------------- num = 2 + z; den = z^2 + 2*z + 1; Normal[Series[num/den, {z, 0, 4}]] 2 - 3*z + 4*z^2 - 5*z^3 + 6*z^4 ---------------- But due to Mathematica default ordering of polynomial, which is from low to high degree, the above is long division done as follows, when done by hand: +---------- 1+ 2*z + z^2 | 2 + z ---------------+ What I want is to do the long division as follows +---------- z^2 + 2*z + 1 | z + 2 ---------------+ Which, when done by hand, would result in : z^-1 - z^-3 + 2 z^-4 +.... The reason, is that I am using long division to find the inverse Z transform of H(z) = num(z)/den(z), and this is a causal discrete system, hence I need the result of the long division to come out in negative powers of z. Once the result comes out in negative powers of z, then I can read the impulse response h(n) from the corresponding coefficients of z's. Notice that Z transform is H(z)= Sum[ h(n) * z^(-n) ,{n,0,Infinity}]. So, I need the long division to happen as in the second form above. i.e. I need the ordering of the polynomials to be from large degree to low degree (reverse what the default is). I did not know how to tell Mathematica Series command to do the division num/den using this ordering. I read this http://reference.wolfram.com/mathematica/tutorial/PolynomialOrderings.html But it is hard for me to understand how to use the above information in the context of what I am trying to do. Is there any easy way to change this ordering so that Series[] will return the answer that I wanted? Is there Some option or may be some global setting I need to set? thanks --Nasser