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separators for affine points
SeparatorsOfPoints(Points:LIST):LIST
where Points is a list of lists of coefficients representing a set of
distinct points in affine space.

This function computes separators for the points: that is, for each
point a polynomial is determined whose value is 1 at that point and 0
at all the others. The separators yielded are reduced with respect to
the reduced Groebner basis which would be found by
IdealOfPoints
.
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;
* the separators are in the same order as the points (i.e. the first
separator is the one corresponding the first point, 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:
S := SeparatorsOfPoints(Pts);
Foreach Element In S Do
PrintLn Element;
EndForeach;
For separators of points in projective space, see
SeparatorsOfProjectivePoints
.
Use R ::= QQ[x,y];
Points := [[1, 2], [3, 4], [5, 6]];
S := SeparatorsOfPoints(Points);  compute the separators
S;
[1/8y^2  5/4y + 3, 1/4y^2 + 2y  3, 1/8y^2  3/4y + 1]

[[Eval(F, P)  P In Points]  F In S];  verify separators
[[1, 0, 0], [0, 1, 0], [0, 0, 1]]

