[Edu-sig] Algebra + Python

[Kirby Urner]

> OK, I implemented __pow__, compose, __rmul__, __rsub__, and __radd__.
> The implementation of __pow__ does not take advantage of the binomial
> theorem or its higher-order generalizations, mostly because I don't
> know the higher-order generalizations.

Great.  I'd done a __pow__ earlier, but I like yours better.
I also make sure the exponent is non-negative, as we're not
promising to handle that kind of algebra here.

> I also did the type check thing so that integer constants are
> automatically converted to polynomials where appropriate.  That means
> it would be possible to implement __neg__ as "return self * -1".

This is good -- I've incorporated it.

> (This version gets rid of list comprehensions, +=, and -=, so it will
> run under 1.5.2.)
> 
> http://www.loyalty.org/~schoen/polynomial.py

My most recent at:
http://www.inetarena.com/~pdx4d/ocn/python/polynomial.html
or same w/ .py extension for cut and paste source.

Note that for commutative ops like __add__ and __mul__, you can 
just go __radd__ = __add__ and __rmul__ = __mul__ to create 
equivalent definitions.  Only subtraction needs to be handled 
differently, because arg order matters.

Also, once your enhancements are added, you really don't need a 
separate compose method (which is very cool).  Just pass a 
polynomial as your "value of x" in the already-defined call 
method:

 >>> from polynomial import *
 >>> f = Poly([1,-3,2])
 >>> g = Poly([1,3,0])
 >>> f
 x**2 - 3*x + 2
 >>> g
 x**2 + 3*x
 >>> f(g)  # <--- symbolic composition
 x**4 + 6*x**3 + 6*x**2 - 9*x + 2
 >>> g(f)  # <--- symbolic composition
 x**4 - 6*x**3 + 16*x**2 - 21*x + 10
 >>> f(g(10))  # <--- or you can do numeric evaluation
 16512
 >>> g(f(10))
 5400

I've put your name in lights in my program's marquee.

Kirby