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D.7.2.5 interpolate

Procedure from library solve.lib (see solve_lib).

Usage:
interpolate(p,v,d); p,v=ideals of numbers, d=integer

Assume:
 
         ground field K are the rational numbers,
         p and v consists of elements of the ground field K
         with the following number of elements:
         size(p) = n and size(v)=N=(d+1)^n with n equals
         the number of variables,
         p is considered as point in K^n and with
         pi=(p[1]^i,..,p[n]^i), i=1,..,N the returned
         polynomial f satisfies f(pi) = v[i]
         (p[j] != -1,0,1);

Return:
 
         the unique polynomial f of degree n*d with prescribed
         values v at certain points p1,..,pN derived from p;

Note:
mainly useful when n=1, i.e. f is satisfying
 
         f(p^(i-1)) = v[i], i=1..d+1

Example:
 
LIB "solve.lib";
ring r1 = 0,(x),lp;
// determine f with deg(f) = 4 and
// v = values of f at points 3^0, 3^1, 3^2, 3^3, 3^4
ideal v=16,0,11376,1046880,85949136;
interpolate( 3, v, 4 );
==> 2x4-22x2+36


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            User manual for Singular version 2-0-2, August 2001, generated by texi2html.