View source for CoCoA:Interpolate

  <command>
    <title>Interpolate</title>
    <short_description>interpolating polynomial</short_description>

    <description>
This function returns a multivariate polynomial which takes given
values at a given set of points.
<par/>
NOTE:
<par/>
 * the current ring must have at least as many indeterminates as the
   dimension of the space in which the points lie;
<par/>
 * the base field for the space in which the points lie is taken to be
   the coefficient ring, which should be a field;
<par/>
 * 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;
<par/>
 * 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 Q[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
-------------------------------
  [Eval(F,P) | P In Points] = Values;  -- check
TRUE
-------------------------------
</example>
    </description>

    <syntax>
Interpolate(Points:LIST,Values:LIST):POLY

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.
</syntax>

    <type>list</type>
    <type>points</type>
    <type>polynomial</type>

    <key>interpolate</key>
  </command>