17.1.1  Lagrange polynomial

The lagrange command finds the Lagrange polynomial which interpolates given data.

• lagrange takes two mandatory arguments and one optional argument:
  • l₁ and l₂, two lists of the same size. These can be given as a matrix with two rows.

    The first list (resp. row) corresponds to the abscissa values x_k (k=1,…,n), and the second list (resp. row) corresponds to ordinate values y_k (k=1,…,n).

  • Optionally x, the name of a variable (by default x).
• lagrange(l₁,l₂  ⟨,x⟩) returns a polynomial expression P(x) of degree n−1 such that P(x_i)=y_i.

You can use the interp command as a synonym for lagrange.

Examples

or:

since x−1/2=0 for x=1 and x−1/2=1 for x=3.

Remark.

An attempted function definition such as 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 then the Lagrange polynomial would be computed each time f is called (indeed in a function definition, the second member of the assignment 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.