Seth David Schoen writes:
Kirby Urner writes:
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?
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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)).
I was interested in having a polynomial returned explicitly, not just making a function that would have the same effect as composition. You could say I was hoping for a closed form.
To implement that, I guess you'd want an exponentiation operator for polynomials (implement __pow__).
[...]
I quickly noticed that you can't multiply a Poly by an integer, or add or subtract an integer. I think one approach would be to throw an
if type(other)==type(3): other = Poly([other])
at the start of __add__ and __mul__. That worked for me, so that I could multiply a Poly by an integer or add or subtract an integer.
You also might want to define __rmul__, __rsub__, and __radd__ in terms of __mul__, __sub__, and __add__ (polynomial multiplication and addition being commutative).
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. 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 version gets rid of list comprehensions, +=, and -=, so it will run under 1.5.2.) http://www.loyalty.org/~schoen/polynomial.py
q = Poly([1,1]) q x + 1 q ** 2 x**2 + 2*x + 1 q ** 3 x**3 + 3*x**2 + 3*x + 1 q - 1 x 1 - q -x q * 2 2*x + 2 2 * q 2*x + 2
It seems that it would be helpful to store the coefficients in reverse order. Then you could do for exponent in range(len(self.coeffs)): coeff = self.coeffs[exponent] # Some code that uses exponent and coeff goes here rather than counting down. -- 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