# CoCoA:Interpolate

From ApCoCoAWiki

## Interpolate

interpolating polynomial

### Description

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 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 -------------------------------

### 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.

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