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Generation of polynomials

• To: mathgroup at smc.vnet.net
• Subject: [mg112983] Generation of polynomials
• From: "pier.mail at gmail.com" <pier.mail at gmail.com>
• Date: Sat, 9 Oct 2010 06:34:42 -0400 (EDT)

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