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NoetherianOperators :: rationalInterpolation(List,List,Ring)

rationalInterpolation(List,List,Ring) -- numerically interpolate rational functions

Synopsis

Description

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 method first tries to find polynomials $g,h$ of degree 0; if this fails, it tries to find $g,h$ of degree 1 and so on. This procedure stops when there are not enough points to compute the next degree, in which case an error will be thrown.

i1 : R = CC[x]

o1 = R

o1 : PolynomialRing
i2 : pts = {point{{0}},point{{1}},point{{2}}, point{{3}}, point{{4}}}

o2 = {{0}, {1}, {2}, {3}, {4}}

o2 : List
i3 : vals = {-1, 1/2, 1, 5/4, 7/5}

          1     5  7
o3 = {-1, -, 1, -, -}
          2     4  5

o3 : List
i4 : rationalInterpolation(pts, vals, R)
-- warning: experimental computation over inexact field begun
--          results not reliable (one warning given per session)

o4 = (2x - 1, 1x + 1)

o4 : Sequence

See also