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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[1],f[2],f[3].
> 
> 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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