       Re: Generation of polynomials

• To: mathgroup at smc.vnet.net
• Subject: [mg113042] Re: Generation of polynomials
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Tue, 12 Oct 2010 04:24:24 -0400 (EDT)

```"Simplest" is arguable. Performance is measurable.

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

f[n_] := (Expand[
Normal[Series[
Product[Sum[(q*t)^i, {i, 0, n}], {q, {x, y}}], {t, 0, n}]]]) /.
t -> 1

Table[poly[i], {i, 1, 100}]; // Timing

{1.51514,Null}

Table[f[i], {i, 1, 100}]; // Timing

{4.94317,Null}

Andrzej Kozlowski

On 11 Oct 2010, at 11:16, Richard Fateman wrote:

>
>
> f[n_] := (Expand[Normal[
>     Series[Product[Sum[(q*t)^i, {i, 0, n}], {q , {x, y}}], {t, 0,
>       n}]]]) /. t -> 1
>
>
> from which one can generate polynomials e.g. f,f,f.
>
> Now this does not generate the same display as given since Mathematica
> has a different ordering of terms in mind.
>
> Sometimes the simplest way to produce a mathematical expression is to do
> mathematics, not hacking lists, tables, etc.
>
>
>

```

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