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surrealnumber.py
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surrealnumber.py
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import operator
import functools
import itertools
from fractions import Fraction
from math import log
class SurrealNumber(object):
'''A class that represents a surreal number. Right now we will focus on
surreal numbers that were born on a finite day.
Attributes:
left: (list) a list of the surreal numbers that are possible moves for
left.
right: (list) a list fo the surreal numbers that are a possible move for
right.
value: is an attribute which is computed from the left and right lists.
Start with support for numbers, nimbers, and switches.
'''
def __init__(self, **kwargs):
# try:
# setattr(self, '_value', kwargs.pop('value'))
# except:
# pass
try:
setattr(self, '_left', kwargs.pop('left'))
except:
pass
try:
setattr(self, '_right', kwargs.pop('right'))
except:
pass
for key, value in kwargs.items():
setattr(self, key, value)
@property
def value(self):
if not self.is_number():
raise TypeError("Only numbers have a value")
#self.simplify()
if len(self.left) == 0 and len(self.right) == 0:
return 0
elif len(self.left) == 1 and len(self.right) == 0:
try:
n = self.left[0].value
except Exception as e:
print(e)
return None
if n >= 0:
return int(n) + 1
if n < 0:
return 0
if len(self.right) == 1 and len(self.left) == 0:
try:
n = self.right[0].value
except Exception as e:
print(e)
return None
if n <= 0:
return int(n) - 1
if n > 0:
return 0
if len(self.right) == 1 and len(self.left) == 1:
try:
r = self.right[0].value
l = self.left[0].value
except Exception as e:
print(e)
return None
if l < r:
if r > 0 and l < 0:
return 0
if r < 0 and l < 0:
sign = -1
r = -1 * l
r = -1 * r
else:
sign = 1
if (r - l) > 1:
return int(l) + 1
else:
current = 1
denom = 2 ** (current)
step = Fraction(1, denom)
#guess =int(left)+power
guess = int(l) + step
while (l >= guess):
#print guess
if int(guess + step) >= int(r):
current += 1
denom = 2 ** (current)
step = Fraction(1, denom)
guess = int(l) + step
else:
guess = guess + step
return sign * guess
@property
def nim_value(self):
if not self.is_nimber():
raise TypeError("Only nimbers have a nim_value")
n=0
while (SurrealNumber.nimber(n) in self.right):
n+=1
#print(n)
return n
@property
def left(self):
return self._left
@property
def right(self):
return self._right
@property
def options(self):
return (self.left, self.right)
def __add__(self, other):
if isinstance(other, SurrealNumber):
if self.is_nimber() and other.is_nimber():
return SurrealNumber.nimber(self.nim_value^other.nim_value)
my_left = self.left
other_left = other.left
new_left = [self + n for n in other_left] + [other + n for n in
my_left]
#print(new_left)
my_right = self.right
other_right = other.right
new_right = [self + n for n in other_right] + [other + n for n in
my_right]
#print(new_right)
n = SurrealNumber(left=new_left, right=new_right)
#n.simplify()
return n
else:
raise TypeError(
'Must add surreal numbers to other surreal numbers.')
def __mul__(self, other):
if isinstance(other, SurrealNumber):
my_left = self.left
other_left = other.left
my_right = self.right
other_right = other.right
new_left = [n[0] * other + self * n[1] - n[0] * n[1] for n in
itertools.product(my_left, other_left)] + \
[n[0] * other + self * n[1] - n[0] * n[1] for n in
itertools.product(my_right, other_right)]
new_right = [n[0] * other + self * n[1] - n[0] * n[1] for n in
itertools.product(my_left, other_right)] + \
[n[0] * other + self * n[1] - n[0] * n[1] for n in
itertools.product(my_left, other_left)]
n = SurrealNumber(left=new_left, right=new_right)
n.simplify()
return n
else:
raise TypeError(
'Must multiply surreal numbers to other surreal numbers.')
def simplify(self):
for n in self.left:
n = n.simplify()
for n in self.right:
n = n.simplify()
oldright=list(self.right)
oldleft=list(self.left)
self.remove_dominated_options()
self.remove_reversible_options()
while((not oldleft==self.left) and (not oldright==self.right)):
self.remove_dominated_options()
self.remove_reversible_options()
oldright=list(self.right)
oldleft=list(self.left)
def remove_dominated_options(self):
x=self.dominated_right_option()
while x:
self._right=[n for n in self.right if n!=x]
x=self.dominated_right_option()
x=self.dominated_left_option()
while x:
self._right=[n for n in self.left if n!=x]
x=self.dominated_left_option()
def dominated_right_option(self):
testlist=itertools.combinations(self.right,2)
for a,b in testlist:
if a<=b:
return b
return None
def dominated_left_option(self):
testlist=itertools.combinations(self.right,2)
for a,b in testlist:
if a<=b:
return a
return None
def remove_reversible_options(self):
left_remove = []
left_new = []
right_remove = []
right_new = []
for n in self.right:
for j in n.left:
if j >= self:
#j is a reversible right option.
#print("found one")
right_remove.append(n)
right_new += j.right
for n in self.left:
for j in n.right:
if j <= self:
#j is a reversible left option
#print("found one")
left_remove.append(n)
left_new += j.left
self._right = [n for n in self.right if
n not in right_remove]
for n in right_new:
if n not in self.right:
self._right.append(n)
self._left = [n for n in self.left if n not in left_remove]
for n in left_new:
if n not in self.left:
self._left.append(n)
def is_number(self):
test = itertools.product(self.right, self.left)
for a,b in test:
if not a<b:
return False
return True
def is_nimber(self):
if self.right != self.left:
return False
for n in self.right:
if not n.is_nimber():
return False
return True
def __repr__(self):
if self.is_nimber():
try:
return str('*'+str(self.nim_value))
except:
pass
if self.is_number():
try:
return str(self.value)
except:
pass
ans = '{'
for i in self.left:
ans += ' ' + str(i) + ','
if len(self.left) > 0:
ans = ans[:-1]
ans += ' |'
for i in self.right:
ans += ' ' + str(i) + ','
if len(self.right) > 0:
ans = ans[:-1]
return ans + ' }'
def __str__(self):
if self.is_number():
try:
return str(self.value)
except:
pass
if self.is_nimber():
try:
return str('*'+str(self.nim_value))
except:
pass
return self.__repr__()
def __lt__(self, other):
return not other.__ge__(self)
def __gt__(self, other):
return not other.__le__(self)
def __le__(self, other):
for n in self.left:
if other <= n:
return False
for n in other.right:
if n <= self:
return False
return True
def __ge__(self, other):
for n in self.right:
if n <= other:
return False
for n in other.left:
if self <= n:
return False
return True
def __eq__(self, other):
self.simplify()
other.simplify()
return (self.left == other.left) and (self.right == other.right)
def __neg__(self):
new_left = [-n for n in self.right]
new_right = [-n for n in self.left]
return SurrealNumber(left=new_left, right=new_right)
@classmethod
def integer(cls, n):
if not isinstance(n, int):
raise TypeError("Function requires an integer")
if n == 0:
return cls(left=[], right=[])
elif n > 0:
return cls(left=[cls.integer(n - 1)], right=[])
else:
return cls(left=[], right=[cls.integer(n + 1)])
@classmethod
def nimber(cls, n):
if not isinstance(n, int):
raise TypeError("Function requires an integer")
options = []
for i in range(n):
options.append(SurrealNumber.nimber(i))
return cls(left=options, right=options)
@classmethod
def ups(cls, n):
if not isinstance(n, int):
raise TypeError("Function requires an integer")
zero=cls.integer(0)
ans=cls.integer(0)
up=cls(left=[zero], right=[cls.nimber(1)])
for i in range(n):
ans=ans+up
ans.simplify()
return ans
@classmethod
def fraction(cls, f):
if not isinstance(f, Fraction):
raise TypeError("Function requires an fraction")
denominator = f.denominator
power = int(log(denominator, 2))
if 2 ** power != denominator:
raise TypeError(
"Function requires a dydatic fraction (power of 2 denominator)")
leftvalue = Fraction(f.numerator - 1, f.denominator)
if leftvalue.denominator == 1:
leftvalue = int(leftvalue)
rightvalue = Fraction(f.numerator - 1, f.denominator)
if rightvalue.denominator == 1:
rightvalue = int(rightvalue)
leftnum = cls.simplified_form(leftvalue)
rightnum = cls.simplified_form(rightvalue)
return cls(left=[leftnum], right=[rightnum])
def main():
zero2 = SurrealNumber(value=0)
zero = SurrealNumber(left=[], right=[])
print(zero.is_number())
print(zero.value)
#zero.simplify()
one = SurrealNumber(left=[zero], right=[])
neg_one = SurrealNumber(left=[], right=[zero])
star = SurrealNumber(left=[zero], right=[zero])
switch = SurrealNumber(left=[one], right=[neg_one])
print("zero = " + str(zero))
print("one = " + str(one))
print(one.left[0] == zero)
print(zero >= one)
print(star)
print(star.is_number())
print(neg_one)
print(switch)
two = one + one
two.simplify()
print(two.left)
print(two + two + two)
print("one plus one")
print(str(one + one))
print(two + star + switch)
print(star + star)
if __name__ == '__main__':
main()