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Can I define a function from a list of values?


I am doing numerical integration. If I define the resulting function as a list of values, I have to keep track of both the number of values and the distance between them. This also makes showing the domain on a plot more annoying. Could I instead define a function object from the list of values? In other words, I need an array whose index is not necessarily integer. And I need to be able to plot it over a range.