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Given a field $F$ and $A = F^3$. we define $L$ to be the line that goes through the points: $(8,1,-1)$, $(5,0,-1)$. My object is to find two polynomials $q(X_1,X_2,X_3)$, $p(X_1,X_2,X_3)$ in $F[X_1,X_2,X_3]$ of degree $\leq 1$ such that $L$ is the set of zeros of $p$ and $q$.

thanks. benny

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    You basically are looking for the equation of a line in three-dimensional space (as an intersection of two planes).2012-01-15
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    joel, do you mean I am looking for the intersection of the planes: 8X1+X2-X3=0 and 5X1-X3=0?2012-01-15

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