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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