A symbolic expression of one variable.
+ SETUP::
+
+ sage: from mjo.interpolation import lagrange_coefficient
+
TESTS::
sage: xs = [ -pi/2, -pi/6, 0, pi/6, pi/2 ]
A symbolic expression (polynomial) interpolating each (xs[k], ys[k]).
+ SETUP::
+
+ sage: from mjo.interpolation import lagrange_polynomial
+
TESTS::
sage: xs = [ -pi/2, -pi/6, 0, pi/6, pi/2 ]
A polynomial in ``x`` which interpolates ``f`` at ``xs``.
+ SETUP::
+
+ sage: from mjo.interpolation import lagrange_interpolate
+
EXAMPLES:
We're exact on polynomials of degree `n` if we use `n+1` points::
Assuming some function `f`, compute the coefficients of the
divided difference f[xs[0], ..., xs[n]].
- TESTS:
+ SETUP::
+
+ sage: from mjo.interpolation import divided_difference_coefficients
+
+ TESTS::
sage: divided_difference_coefficients([0])
[1]
The (possibly symbolic) divided difference function.
+ SETUP::
+
+ sage: from mjo.interpolation import divided_difference
+
TESTS::
sage: xs = [0]
A symbolic expression.
- TESTS:
+ SETUP::
+
+ sage: from mjo.interpolation import lagrange_polynomial, newton_polynomial
+
+ TESTS::
sage: xs = [ -pi/2, -pi/6, 0, pi/6, pi/2 ]
sage: ys = map(sin, xs)
A symbolic expression.
- TESTS:
+ SETUP::
+
+ sage: from mjo.interpolation import hermite_interpolant
+
+ TESTS::
sage: xs = [ 0, pi/6, pi/2 ]
sage: ys = map(sin, xs)