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BretTyp = list[list[str]]

BLAU   = "B"
ORANGE = "O"
LEER = "X"
anfangBret: BretTyp = [[BLAU, BLAU, ORANGE, BLAU],
                      [ORANGE, ORANGE, BLAU, ORANGE],
                      [BLAU, BLAU, ORANGE, BLAU],
                      [BLAU, BLAU, BLAU, BLAU]]

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from random import uniform
from math import cos, sin, pi, acos
from sympy import Symbol, I, Matrix, factor, simplify, im, re, expand, true

EPSILON = 0.0001
MAX_ITERATIONS = 1000

a = Symbol('a', real=true)
b = Symbol('b', real=true)
c = Symbol('c', real=true)

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from sympy.abc import a,b
from sympy import Matrix, pprint
from itertools import product
from sympy.physics.quantum import TensorProduct

# A \otimes \rho_{d}
def orderedTensorProduct(d):
	dDegreeMonomials = monomialDegrees(d)
	xyz = monomialDegrees(1)
	retVal = []

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from sympy import Matrix
from sympy.abc import a,b
from sympy.physics.quantum import TensorProduct

A = Matrix([[a, -b, 0],
            [b,  a, 0],
	    [0,  0,  1]])

#Embedding into tensor space.
E = Matrix([[1, 0, 0, 0, 0, 0],

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def fact(n):
	if (n <= 0):
		return 0
	elif ( n < 3 ):
		return n 
	else:
		return fact(n-1) + fact(n-2)


def memoize(f):

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from sympy import *
from sympy.solvers import solve

x = Symbol('x', real=true)
y = Symbol('y', real=true)
x0 = Symbol('x0', real=true)
x1 = Symbol('x1', real=true)
x2 = Symbol('x2', real=true)
y0 = Symbol('y0', real=true)
y1 = Symbol('y1', real=true)

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from sympy import *

a = Symbol('a', real=true)
b = Symbol('b', real=true)
c = Symbol('c', real=true)
d = Symbol('d', real=true)

x = a + I*b
z = c + I*d

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	cost	cost / person
Yoesmite Park Fees	$30	$6
Groceries	$170	$34
lyft ride from SFO to SF	$46	$11*
	$246	$51

* the actually cost was $66, before applying a $20 free ride credit. And subsequently the $46 is divided across the group (excluding me).

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from random import uniform
from numpy import array
from math import pi

def MaxArc(N):
    cuts = [ uniform(0, 2*pi) for x in range(N) ]
    cuts.sort()
    other = [x for x in cuts]
    other.insert(0, other.pop())
    cuts[0]+=2*pi

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from random import uniform 
"""
Monte Carlo approximation of PI

Sample run:
    person@pc-1 ~/> python pi_day.py 
    approximation of PI: 3.1427
"""

def generatePoints():