We prove a variation of the classical Cayley-Bacharach theorem for points on an n-dimensional box \choose  . A consequence of this theorem is that a function can be approximated on vertices of the box using other vertices to higher degrees than expected. This approximation is useful for various biological applications such as predicting the effect of a treatment with drug combinations and computing values of fitness landscape.
The vector space of all polynomial functions of degree k on a box of dimension n is of dimension n\choose k . A consequence of this fact is that a function can be approximated on vertices of the box using other vertices to higher degrees than expected. This approximation is useful for various biological applications such as predicting the effect of a treatment with drug combinations and computing values of fitness landscape.
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We prove a variation of the classical Cayley-Bacharach theorem for points on an n-dimensional box
The vector space of all polynomial functions of degree k on a box of dimension n is of dimension
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