Re: Getting the small parts right or wrong. Order and Collect
- To: mathgroup at smc.vnet.net
- Subject: [mg63658] Re: Getting the small parts right or wrong. Order and Collect
- From: Bill Rowe <readnewsciv at earthlink.net>
- Date: Mon, 9 Jan 2006 04:48:39 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
On 1/8/06 at 3:32 AM, fateman at cs.berkeley.edu (Richard Fateman)
wrote:
>Putting the coefficients in an array is plausible, but Andrzej
>other solution, which is
>1 + Plus @@ Table[Coefficient[(1 + x + y)^3, x^i]*x^i, {i, 1, 3}]
>is wrong because it results in answers in the order 1, x^3, x^2, x.
More importantly, this solution omits the terms with y but not x. That is
In[7]:=
(1 + Plus@@Table[Coefficient[(1+x+y)^3, x^i] x^i, {i, 1, 3}]])//Simplify
Out[7]=x^3 + 3*(y + 1)*x^2 + 3*(y + 1)^2*x + 1
is clearly not (1+x+y)^3
>And of course picking out the coefficient of "1".
>Along those lines it is better to do ...
>Table[Coefficient[(1+x+y)^3,x,i] ,{i,0,3}] where i can also be 0.
>And the table keeps the coefficients from being randomly sorted.
And this will not work either since Coefficient will correctly point out x^0 which evaluates to 1 is not a valid variable.
To get a list of the coefficients you should use CoefficientList, i.e.,
In[13]:=CoefficientList[(1 + x + y)^3, x]
Out[13]=
{y^3 + 3*y^2 + 3*y + 1, 3*y^2 + 6*y + 3, 3*y + 3, 1}
which can be used with Table to generate the desired form, i.e.,
CoefficientList[(1 + x + y)^3, x].Table[x^n, {n,0,3}]
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