(n,d) = rationalInterpolation(pts, vals, numBasis, denBasis)
(n,d) = rationalInterpolation(pts, vals, numDenBasis)
Given a list of points $pts = \{p_1,\dots,p_k\}$ and values $vals = \{v_1,\dots,v_k\}$, attempts to find a rational function $f = g/h$, such that $f(p_i) = v_i$. The polynomials $g$ and $h$ have monomial support numBasis and denBasis respectively.
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The output corresponds to the function $x / (x^2 + y^2)$. If no fitting rational function is found, the method returns an error.
The method rationalInterpolation(List,List,Ring) can be used to choose monomial supports automatically.
The method uses the first point to remove the rational functions whose numerator and denominator would both evaluate to 0 on the point. Because of this, the first entry of val should be non-zero.
The object rationalInterpolation is a method function with options.