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I was wondering how to write $x$ as an algebraic combination of $\{x+xy,y+xy,x^2,y^2\}$, with the coefficients $\in \mathbb Q[x,y]$.

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    I think that the kind of combination that you want is called an _algebraic_ combination.2012-02-05
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    I've revised my answer to include a solution to this new, edited problem. See my post below.2012-02-05
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    @alex.jordan Thanks.2012-02-05

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