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interpolating polynomial
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.
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***** 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:
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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