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The maximum Shannon entropy on a system with six outcomes, uniformly distributed (a fair die), is log(6). In the prog1.py program above we evaluate the Shannon entropy for a loaded die: (1/10.1/10,1/10,1/10,1/10,1/2). Notice in the code, however, that I use “1.0” not “1”. This is because if the expression only involves integers the mathematics will be done as integer operations (returning an integer, thus truncation of some sort). An expression that is mixed, some integer terms, some floating point (with a decimal), will be evaluated as a floating point number. So, to force recognition of the numbers as floating point the “1” value in the terms is entered as “1.0”. Further tests are left to the Exercises (ssss1).

A basic review of getting a linux system running, with it is standard Python installed, is described in the Appendix, along with a discussion of how to install added Python modules (added code blocks with very useful, pre‐built, data structures, and subroutines), particularly “numpy,” which is indicated as a module to be imported (accessed) by the program by the first Python command: “import numpy as np.” (We will see in the Appendix that the first line is not a Python command but a shell directive as to what program to use to process the commands that follow, and this is the mechanism whereby a system level call on the Python script can be done.)