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For instance, $f=x^2y^2+1$ is an element of $\mathbb{C}[x,y]$, I want to extract the coefficient of $x^2$, which is $y^2$. However "f.coefficient(x,2)" only works for symbolic expressions, are there similar functions for ring elements?

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    By the way, there http://ask.sagemath.org/ for sage. In case you have more specific questions in the future.2012-06-30

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Simply use f.coefficient(x^2), as in this example:

sage: R. = CC[] sage: f = x^2 *  y^2 + 1 sage: f.coefficient(x^2) y^2