Could this be extended to a symbolic math implementation? At least, could you implement compose, add, subtract, multiply, and divide methods so that f.compose(g) f.add(g) would work? -- Seth David Schoen <schoen@loyalty.org> | And do not say, I will study when I Temp. http://www.loyalty.org/~schoen/ | have leisure; for perhaps you will down: http://www.loyalty.org/ (CAF) | not have leisure. -- Pirke Avot 2:5 ============ Sure. Compose was already implied in Brent's class, since f(10) returns a number, and therefore so does g(f(10)) and g(f(10)). Using operator overriding, we can actually use + - and * for addition, subtraction and multiplication (I haven't done divide): Definition and Representation:
f = Poly([1,2,3]) f x**2 + 2*x + 3 g = Poly([2,3,4,5]) g 2*x**3 + 3*x**2 + 4*x + 5
Negation:
-f -x**2 - 2*x - 3
Subtraction:
f-g -2*x**3 - 2*x**2 - 2*x - 2
Evaluation:
g(10) 2345 f(10) 123
Composition:
f(g(10)) 5503718 g(f(10)) 3767618
Multiplication:
f*g 2*x**5 + 7*x**4 + 16*x**3 + 22*x**2 + 22*x + 15 g*f 2*x**5 + 7*x**4 + 16*x**3 + 22*x**2 + 22*x + 15
Evaluation and Multiplication:
x = -1 eval(str(g*f)) 4 h=g*f h(-1) 4
Negation and Multiplication:
-f*g -2*x**5 - 7*x**4 - 16*x**3 - 22*x**2 - 22*x - 15
Derivative:
h 2*x**5 + 7*x**4 + 16*x**3 + 22*x**2 + 22*x + 15 h.deriv() 10*x**4 + 28*x**3 + 48*x**2 + 44*x + 22
I'm pretty sure all of the above is correct. I've put the code I have so far at: http://www.inetarena.com/~pdx4d/ocn/polynomial.py (Python source) http://www.inetarena.com/~pdx4d/ocn/polynomial.html (colorized HTML) Maybe we can improve/streamline the implementation somewhat -- and I wouldn't be surprised if someone, somewhere has implemented something very similar already. The hardest part was getting the algebraic strings to look pretty. Kirby