### 5.1.155 vandermonde

Syntax:
vandermonde ( ideal_expression, ideal_expression, int_expression )
Type:
poly
Purpose:
vandermonde(p,v,d) computes the (unique) polynomial of degree d with prescribed values v[1],...,v[N] at the points p p, N=(d+1), the number of ring variables.

The returned polynomial is , where the coefficients are the solution of the (transposed) Vandermonde system of linear equations

Note:
the ground field has to be the field of rational numbers. Moreover, ncols(p)==, the number of variables in the basering, and all the given generators have to be numbers different from 0,1 or -1. Finally, ncols(v)==(d+1), and all given generators have to be numbers.
Example:
 ring r=0,(x,y),dp; // determine f with deg(f)=2 and with given values v of f // at 9 points: (2,3)^0=(1,1),...,(2,3)^8=(2^8,3^8) // valuation point: (2,3) ideal p=2,3; ideal v=1,2,3,4,5,6,7,8,9; poly ip=vandermonde(p,v,2); ip[1..5]; // the 5 first terms of ip: ==> -1/9797760x2y2-595/85536x2y+55/396576xy2+935/384x2-1309/3240xy // compute value of ip at the point 2^8,3^8, result must be 9 subst(subst(ip,x,2^8),y,3^8); ==> 9 

User manual for Singular version 4-0-3, 2016, generated by texi2html.