[Edu-sig] Algebra + Python

[Kirby Urner]

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