lagrange takes as argument two lists of size n (resp a
matrix with two rows and n columns) and the name of a variable
var (by default x).
The first list (resp row) corresponds to the abscissa values xk (k=1..n),
and the second list (resp row) corresponds to ordinate values yk
(k=1..n).
lagrange returns a polynomial expression P
with respect to var of degree
n-1, such that P(xi)=yi.
Input :
or :
Output :
since x−1/2=0 for x=1, and x−1/2=1 for x=3.
Input :
Output :
Warning
f:=lagrange([1,2],[3,4],y) does not return a function
but an expression with respect to y.
To define f as a function, input
Avoid f(x):=lagrange([1,2],[3,4],x) since
the Lagrange polynomial would be computed each time f is called
(indeed in a function definition, the second member of the affectation
is not evaluated).
Note also that
g(x):=lagrange([1,2],[3,4]) would not work
since the default argument of lagrange
would be global, hence not the same as the local
variable used for the definition of g.