I have an ideal $I$ generated by multivariate polynomials $f,g$ over $GF(2)$. Suppose another polynomial $h$ is in $I$. So there are two polynomials $h_1$ and $h_2$ such that $h=h_1 f +h_2 g$. How to find $h_1, h_2$?

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I have an ideal $I$ generated by multivariate polynomials $f,g$ over $GF(2)$. Suppose another polynomial $h$ is in $I$. So there are two polynomials $h_1$ and $h_2$ such that $h=h_1 f +h_2 g$. How to find $h_1, h_2$?

I have an ideal $I$ generated by multivariate polynomials $f,g$ over ~~$GF(2)$. ~~BooleanPolynomialRing.
Suppose another polynomial $h$ is in $I$. So there are two polynomials
$h_1$ and $h_2$ such that $h=h_1 f +h_2 g$. How to find $h_1, ~~h_2$? ~~h_2$?

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