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D.7.2.4 interpolate

Procedure from library solve.lib (see solve_lib).

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

Assume:
ground field K are the rational numbers,
p and v are lists consisting of elements of the ground field K, size(p)=n and size(v)=N=(d+1)^n where n=nvars(basering)

Compute:
polynomial f of degree d with prescribed values at certain points p1,..,pN derived from p;
more precisely: consider p as point in K^n and v as N elements in K, let pi=(p[1]^i,..,p[n]^i), i=1,..,N, then the procedure computes the polynomial f of degree d satisfying f(pi) = v[i]

Return:
polynomial f of degree d

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 2-0-0, February 2001, generated by texi2html.