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Interpolate

interpolating polynomial

Syntax
Interpolate(Points: LIST, Values: LIST): RINGELEM

where Points is a list of lists of coefficients representing a set of
distinct points and Values is a list of the same size containing
numbers from the coefficient ring.

Description
***** NOT YET IMPLEMENTED *****

This function returns a multivariate polynomial which takes given values at a given set of points.

NOTE:

* the current ring must have at least as many indeterminates as the dimension of the space in which the points lie;

* the base field for the space in which the points lie is taken to be the coefficient ring, which should be a field;

* in the polynomials returned, the first coordinate in the space is taken to correspond to the first indeterminate, the second to the second, and so on;

* if the number of points is large, say 100 or more, the returned value can be very large. To avoid possible problems when printing such values as a single item we recommend printing out the elements one at a time as in this example:

Example
  X := Interpolate(Pts, Vals);
  foreach element in X do
    println element;
  endforeach;

  Use QQ[x,y];
  Points := [[1/2, 2], [3/4, 4], [5, 6/11], [-1/2, -2]];
  Values := [1/2,1/3,1/5,-1/2];
  F := Interpolate(Points, Values);
  F;
-46849/834000y^2 - 1547/52125x + 13418/52125y + 46849/208500
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  [Eval(F, P) | P in Points] = Values;  -- check
True
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