Getting comfortable with objects.

The function form for a subscripted variable  ,  and the summation object    can be used to construct a power series function.
For example, the coefficients for the exponential series are reciprocals of factorials.

They can be used together to make a familiar polynomial approximation to .

Our use of the function for a subscripted variable precludes some awkward subscripts in the list of data points which we want to label with the starting subscript zero, for example for  .

Note that the "points" require a data structure that is a list of "pairs" of numbers. The mathematics we use uses individual values such as .  

The abscissas and ordinates are extracted with the assistance of the "Transpose" operator

Using the selection operation for matrices we can get the    out of the "list" with the command

That's o.k. but you need to add one to the "matrix subscript" to get the desired "abscissa."  To make things nicer we used a function for a subscripted variable.

Compare this with the commands for working with "matrix subscripts."  Notice the difference in the range: 0,1,2,3,4 for the subscripted variable and 1,2,3,4,5 for the "table" which is stored in a "list."

The product object   is probably new to you.  It can be used to construct a polynomial with known roots.

(c) John H. Mathews 2004