       Re: Generation of polynomials

• To: mathgroup at smc.vnet.net
• Subject: [mg113001] Re: Generation of polynomials
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Sun, 10 Oct 2010 06:42:50 -0400 (EDT)

```As usual with Mathematica there are a number of different ways. The first one that came to my mind is:

poly[m_] :==
FromCoefficientRules[
Thread[Flatten[Table[{i, n - i}, {n, 0, m}, {i, 0, n}], 1] ->
1], {x, y}]

Then:

Column[Table[poly[i], {i, 0, 4}]]
1
x+y+1
x^2+x y+x+y^2+y+1
x^3+x^2 y+x^2+x y^2+x y+x+y^3+y^2+y+1
x^4+x^3 y+x^3+x^2 y^2+x^2 y+x^2+x y^3+x y^2+x y+x+y^4+y^3+y^2+y+1

Andrzej Kozlowski

On 9 Oct 2010, at 12:34, pier.mail at gmail.com wrote:

> Hi!
> This is probably trivial, but I am a total novice with Mathematica...
> is it possible to generate all complete polynomials in x,y up to a
> certain degree, i.e
>
> 1
> 1+x+y
> 1+x+y+x^2+y^2+xy
> 1+x+y+x^2+y^2+xy+x^3+y^3+x^2y+y^2x
> 1+x+y+x^2+y^2+xy+x^3+y^3+x^2y+y^2x+x^4+y^4+x^3y+y^3x+x^2y^2
> ...
>
> Thanks,
> Pier
>
>
>
>

```

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