This program is written in Python. It was written and tested against the latest stable version, 3.5, but it should work fine with any version >= 3.2.
To run the program, simply pass the engine.py file to your Python 3 interpreter, e.g. python3 engine.py. The specific interpreter alias is machine-dependent, and you'll need to know what it is for your machine.
Follow the in-console prompts.
Example:
$ python3 engine.py
Difference Engine Simulator (degree = 8)
f(x): x^2 + 3x + 4
number of cranks: 3
Δ0: x^2 + 3x + 4
Δ1: 2x + 3
Δ2: 2
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
2 1 0 0 0 0 0 0
2 0 2 0 0 0 0 0
As you've noticed from the basic usage section, you do not need to compute the difference functions by hand to calculate the initial values -- you can just type in the polynomial f(x) function by hand. The parser supports any single-variable polynomial with no negative terms.
Valid input examples:
f(x): 8x^4 + x^2 + 2x + 19 f(x): 8t^4 + t^2 + 2t + 19 -> you need not use x, but they'll be treated as such f(x): 8x4 + x2 + 2x + 19 -> carets may be omitted f(x): x^18 -> only useful if you've increased the degree cap, see below f(x): 100000
Invalid input examples:
f(x): hello -> only polynomials are supported f(x): cos(x) -> only polynomials are supported f(x): -10x^2 -> negative terms not supported f(x): x^2 - 1 -> negative terms not supported
The engine supports arbitrary polynomials up to any degree. By default, it only supports up to 8th-degree polynomials, as per the writeup. However, you can set this limit to any integer you want, by passing that number as a command-line argument.
Example:
$ python3 engine.py 15
Difference Engine Simulator (degree = 15)
f(x): 8x4 + x2 + 2x + 19
number of cranks: 10
Δ0: 8x^4 + x^2 + 2x + 19
Δ1: 32x^3 + 48x^2 + 34x + 11
Δ2: 96x^2 + 192x + 114
Δ3: 192x + 288
Δ4: 192
0 7 1 2 0 0 0 0 0 0 0 0 0 0 0
1 1 6 2 1 0 0 0 0 0 0 0 0 0 0
3 5 3 0 9 0 0 0 0 0 0 0 0 0 0
9 1 4 8 2 0 0 0 0 0 0 0 0 0 0