Dennis Sweeney sweeneyde

## monoid_homology.py
"""
Monoid Homology Calculator
written by Dennis Sweeney

Given a monoid M, we can produce a topological space (cw complex) BM,
whose n-cells are n-tuples of non-identity elements of M.
This program computes the integral homology of the space BM.

The problem of deciding whether two words are equal is not computable,
so we restrict to nice classes of monoid presentations. In particular,

## smith.py
class Matrix:
    def __init__(self, arr, n=None):
        if isinstance(arr, Matrix):
            self.arr = [list(row) for row in arr.arr]
            self.m = arr.m
            self.n = arr.n
        else:
            self.arr = [list(row) for row in arr]
            self.m = len(arr)
            if not arr:

## dragonturtle.py
from turtle import *
def turns():
    s = []
    while True:
        yield 90
        fold = [-x for x in reversed(s)]
        yield from fold
        s += [90] + fold
hideturtle()
speed(0)

## make_change.py
"""
Find the number of nonnegative integer solutions (x_1, ..., x_n)
to the equation a_1*x_1 + ...+ a_k*x_k = n,
where each a_i and n are positive integers.

Example: to find the number of ways to make $10.00 out of
1-, 5-, 10-, and 25-cent coins:

    >>> change(1000, (1, 5, 10, 25))
    142511

## lazier_product.py
class LazyProductObject:
    # Assume there are n >= 1 iterators, with repeat = r.
    #   len(pools) == n and len(indices) == len(result) == n*r
    # pools[0:num_incomplete_pools] are lists of items that will still
    # get added to from iterators, while pools[num_incomplete_pools:n]
    # are finished and don not need to be re-modified.
    # If repeat >= 2:
    #   then the pools will fill up as we iterate the first time
    #   over all possible result[(n-1)*r:n*r]
    # If repeat == 1:

## lots_of_benches.py
needles = ['H', 'F', 'C', 'E', 'D', 'G', 'A', 'B', 'L', 'U', 'AA', 'BA', 'AB', 'IB', 'EA', 'AD', 'AQ', 'BS', 'SA', 'AK', 'HA', 'GI', 'AP', 'FP', 'IN', 'FG', 'DQN', 'ABJ', 'GKC', 'AAD', 'IDM', 'BAB', 'JAB', 'CBD', 'AEC', 'CDB', 'AXA', 'BTG', 'RBC', 'VAC', 'YCB', 'AAZ', 'KAG', 'BHA', 'BFC', 'BAD', 'DCHU', 'BCIC', 'AASX', 'AAUU', 'AEDF', 'AAAA', 'HAQB', 'CBCA', 'AAUA', 'IBDA', 'BAKJ', 'AACC', 'BBEC', 'AABG', 'CAJC', 'EOCA', 'BAPL', 'ACAP', 'ADFL', 'HBCL', 'LABVF', 'EHRIR', 'AADSH', 'CCIBL', 'MEAKB', 'RIABB', 'BFHBA', 'GDAAN', 'AALCH', 'TABAH', 'RDAAH', 'BNAZA', 'BBCMB', 'AALGN', 'AAPWK', 'BYABD', 'MGBCK', 'XFFCH', 'ABAAX', 'BACDB', 'AVAAHA', 'DMPAXA', 'ACOSQF', 'ADNCBN', 'BLCDXA', 'AAHPGA', 'AFCBAD', 'CFTUBF', 'BDQAEB', 'AAABCC', 'LTHEEG', 'YJTCIA', 'BDAFBI', 'BBFBAG', 'FAAEBA', 'DBRBKI', 'EFHFIH', 'BHACAO', 'AAGDVD', 'PBDLOA', 'LPACABC', 'ATAJEEN', 'GBMXAAM', 'AALMCBY', 'AMABEQA', 'FFDAOCR', 'AABCDTC', 'LAAPAFA', 'EBHADDA', 'FWABCAM', 'DBJOIAF', 'IADNCAB', 'ABCDBAT', 'EAAAAIC', 'BCARAAT', 'TIGOEAC', 'ABACJKG',
	"""
	Monoid Homology Calculator
	written by Dennis Sweeney

	Given a monoid M, we can produce a topological space (cw complex) BM,
	whose n-cells are n-tuples of non-identity elements of M.
	This program computes the integral homology of the space BM.

	The problem of deciding whether two words are equal is not computable,
	so we restrict to nice classes of monoid presentations. In particular,
	class Matrix:
	def __init__(self, arr, n=None):
	if isinstance(arr, Matrix):
	self.arr = [list(row) for row in arr.arr]
	self.m = arr.m
	self.n = arr.n
	else:
	self.arr = [list(row) for row in arr]
	self.m = len(arr)
	if not arr:
	from turtle import *
	def turns():
	s = []
	while True:
	yield 90
	fold = [-x for x in reversed(s)]
	yield from fold
	s += [90] + fold
	hideturtle()
	speed(0)
	"""
	Find the number of nonnegative integer solutions (x_1, ..., x_n)
	to the equation a_1x_1 + ...+ a_kx_k = n,
	where each a_i and n are positive integers.

	Example: to find the number of ways to make $10.00 out of
	1-, 5-, 10-, and 25-cent coins:

	>>> change(1000, (1, 5, 10, 25))
	142511
	class LazyProductObject:
	# Assume there are n >= 1 iterators, with repeat = r.
	# len(pools) == n and len(indices) == len(result) == n*r
	# pools[0:num_incomplete_pools] are lists of items that will still
	# get added to from iterators, while pools[num_incomplete_pools:n]
	# are finished and don not need to be re-modified.
	# If repeat >= 2:
	# then the pools will fill up as we iterate the first time
	# over all possible result[(n-1)r:nr]
	# If repeat == 1: