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MathGroup Archive 2006

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Re: Convert expression to polynomial

  • To: mathgroup at smc.vnet.net
  • Subject: [mg70412] Re: Convert expression to polynomial
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Mon, 16 Oct 2006 02:33:57 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <egsd96$cj7$1@smc.vnet.net>

Diana wrote:
> Math folks,
> 
> I am generating a list of partial sums which look like:
> 
> x = 1 + (-t + t^2)^(-1) + 1/((-t + t^2)^2*(-t + t^4)) +  1/((-t +
> t^2)^4*(-t + t^4)^2*(-t + t^8))
> 
> I then try to calculate the PolynomialQuotient[Numerator[x],
> Denominator[x], t], etc., and I get an error saying that x is not a
> polynomial function.
> 
> I tried to find the command to put everything over a common
> denominator, but was unable to find this. Can someone help?
> 
> Thanks,
> 
> Diana M.
> 

Hi Diana,

Use the built-in function Together [1].

In[1]:=
x = 1 + (-t + t^2)^(-1) +
    1/((-t + t^2)^2*(-t + t^4)) +
    1/((-t + t^2)^4*(-t + t^4)^2*(-t + t^8))

Out[1]=
        1               1
1 + ------- + -------------------- +
           2          2 2        4
     -t + t    (-t + t )  (-t + t )

                  1
   -------------------------------
          2 4        4 2        8
   (-t + t )  (-t + t )  (-t + t )

In[2]:=
Together[x]

Out[2]=
       4      5      6      7      8       9
(1 + t  - 2 t  + 2 t  - 5 t  + 9 t  - 10 t  +

         10       11       12       13       14
     12 t   - 16 t   + 17 t   - 14 t   + 14 t   -

         15       16       17       18       19
     16 t   + 14 t   - 13 t   + 15 t   - 15 t   +

         20      21      22      23    24
     12 t   - 9 t   + 7 t   - 4 t   + t  ) /

            7  7           2 2
   ((-1 + t)  t  (1 + t + t )

               2    3    4    5    6
     (1 + t + t  + t  + t  + t  + t ))

In[3]:=
PolynomialQuotient[Numerator[Together[x]],
   Denominator[Together[x]], t]

Out[3]=
1

Regards,
Jean-Marc

[1] http://documents.wolfram.com/mathematica/functions/Together


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