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Division algorithm in one variable

asked 2020-09-06 12:59:38 -0500

Hit gravatar image

Hi! I'm trying to implement the division algorithm 'by hand' (yes, I know the existence of f.maxima_methods().divide(g))

So far I've came up with this:

def div(f,g):
q==0; r==f;
while r != 0 and g.lt().divides(r.lt()):
q==q+r.lt()/g.lt()
r==r-(r.lt()/g.lt())*g
return q,r

but I'm getting an error on the "while" line. I'm following Ideals, Varieties and Algorithms by Cox (page 39 of the book), and they insert a "do" at the end of the while line, but I'm getting an "invalid syntax" error there. I'm pretty inexperienced with coding, and even more with Python/Sage (I've only taken a numerical methods course with Fortran).

I've gotten this "far" reading the book + documentation. Any ideas on how to proceed here?

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answered 2020-09-06 19:33:14 -0500

slelievre gravatar image

In Python (the programming language Sage uses),

  • assignment uses =, while == is to test equality
  • indentation is syntax, and in particular
  • the content of a while loop is everything that is indented after :.

So your code might want to look something like that instead:

def div(f, g):
    q = 0
    r = f
    while r != 0 and g.lt().divides(r.lt()):
        q = q + r.lt() // g.lt()
        r = r - (r.lt() // g.lt()) * g
    return q, r

Then you can use the function as follows.

Define a polynomial ring and two polynomials:

sage: R.<x> = QQ[]
sage: f = x^5 + x^3 + 2
sage: g = x^2 + 1

Apply the function:

sage: div(f, g)
(x^3, 2)
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Comments

Hi! After playing and reading for a while after posting the question I managed to make it look similar to yours, but still wasn't compiling correctly. Now I see why

Thanks a ton, mate!!

Hit gravatar imageHit ( 2020-09-06 22:51:37 -0500 )edit

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Asked: 2020-09-06 12:59:38 -0500

Seen: 57 times

Last updated: Sep 06