[Edu-sig] more from my classroom

[kirby urner]

Here's some more code from the night class I'm teaching, invisibly in the
sense it's all virtual, but in real time, different from my usual
asynchronous gig based on evaluating student work.

About twenty login and we have our private session, company tech support
listening in for Q/A.  Complementary synchronous work, with students off
the hook but welcome and often eager to dive in (I don't see their desktops
usually, though they're free to share).  The code below started out as a
Lab where I just suggested using trial by division (I described the
approach) in the context of an iterator.

We're just at that point where "iterator" (versus iterable) is coming
together with these new grammatical constructs, these new underscore
names.  We're also tackling decorators and context managers around this
same time.

# -*- coding: utf-8 -*-
"""
Created on Tue Dec  8 17:39:27 2015

@author: Kirby Urner, 4Dsolutions.net
(copyleft)  MIT License, 2015

Two models of iterator that do the same thing.  All primes
found so far will be a list of all primes <= n without any
missing.  Algorithm:  trial by division.
"""

def next_prime():
    """
    creates an iterator that spits out successive prime numbers
    """
    so_far = [2]
    yield 2
    n = 2
    while True:
        n += 1
        for divisor in so_far:
            if divmod(n, divisor)[1] == 0:  # goes evenly
                break
            if divisor ** 2 > n:
                yield n
                so_far.append(n)
                break


class Primes:
    """
    creates an iterator that spits out successive prime numbers
    """

    def __init__(self):
        self.so_far = [2]
        self.n = 2

    def __iter__(self):
        return self

    def __next__(self):
        if self.n == 2:
            self.n += 1
            return 2
        while True:
            for divisor in self.so_far:
                if divmod(self.n, divisor)[1] == 0:  # goes evenly
                    break
                if divisor ** 2 > self.n:
                    self.so_far.append(self.n)
                    self.n += 1
                    return self.so_far[-1]
            self.n += 1


There's a license on it not because I think I'm being all that original
i.e. these is not genius math or anything.  I've been told people are more
comfortable sharing if there's at least some explicit attention to sharing
rights.  The point for purposes of my class was to show two ways to write
an iterator, using function generator syntax or a class with the __next__,
__iter__ protocol.  The latter is a refactoring of the former, or vice
versa.

However, putting on my "used to be a high school math teacher" hat, I
really like this naive ramping up into Primeville.  As an algorithm it
sputters if your goal is working with uber-primes ala RSA or whatever, but
this is not about dissing algorithms its about learning what "algorithm"
means.  Also the difference between prime and composite.  I found myself
bringing up the Fundamental Theorem of Arithmetic again, just like the old
days (I haven't been a full time high school math teach since the early
1980s, spent a lot more years coding in FoxPro :-D).


>>> g = next_prime()

>>> [next(g) for _ in range(20)]
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71]

>>> g = Primes()

>>> [next(g) for _ in range(20)]
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71]

Other news from my angle...

We're enjoying lots of action on python-cuba (a workgroup) -- some planning
conference coming up on the 12th.  Public archive, check it out.

https://mail.python.org/mailman/listinfo/python-cuba

Also I'm sometimes chiming in on the Chipy listserv, one of my favorites.
Portland's is quiet by contrast (I'm in Portland -- born in Chicago though).

Kirby
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