Converting a symbolic expression into a numeric function

As we have seen the numerical evaluation of a symbolic expression is done in three steps, first we do some symbolic computations and then we substitute values by numbers and do an evaluation to a floating point number by evalf.

The reason for symbolic computations is often that one wants to make parameter studies. This requires that the parameter is modified within a given parameter range. This requires that an symbolic expression is eventually turned into a numeric function.

A study on the parameter dependency of polynomial coefficients

We demonstrate a symbolic/ numeric parameter study by an interpolation example to introduce the SymPy command lambdify. Let us consider the task to interpolate the data x = [0, t, 1] and y = [0, 1,-1]. Here, t is a free parameter, which we will vary over the interval [-0.4, 1.4]. The quadratic interpolation polynomial has coefficients depending on this parameter:

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Using SymPy and the monomial approach...