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## Lagrange's polynomial : lagrange interp

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 :
lagrange([[1,3],[0,1]])
or :
lagrange([1,3],[0,1])
Output :
(x-1)/2
since = 0 for x = 1, and = 1 for x = 3.
Input :
lagrange([1,3],[0,1],y)
Output :
(y-1)/2
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
f:=unapply(lagrange([1,2],[3,4],x),x)
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.

suivant: Natural splines: spline monter: Polynomials précédent: Random list : ranm   Table des matières   Index
giac documentation written by Renée De Graeve and Bernard Parisse