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I'm trying to factorise a 20-term polynomial of the 4th degree with four variables. Ideally, I'd like to do it by hand, but I get the idea that this is pretty improbable. Can anyone point me to some helpful resources on this subject?

Thanks

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    Over what field?2011-02-05
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    In mathematics, one should avoid saying *complex* if one just means *complicated*.2011-02-05
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    Rahul, noted. Qiaochu, as in real, complex, rational, etc?2011-02-05

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Try Wolfram Alpha.

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    Thanks. That seems to work great for slightly less complicated polynomials, but only accepts about half of the polynomial I enter. I'll try downloading a trial version of Mathematica, as that seems to be the engine much of Wolfram Alpha is based on.2011-02-05
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My vote goes to Sage, a free (in two senses) incredible piece of software. Also available to try online without installation.

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    Sage looks a very interesting FOSS alternative to Mathematica. I would up-vote, but unfortunately don't have enough reputation yet.2011-02-05
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    I use it an awful lot nowadays; to my mind it's a rather impressive alternative (all the more for being free) to things like Mathematica, Maple, and Matlab. I've also had great luck getting questions/concerns answered/addressed by the awesome Sage community.2011-02-06