def come_out_roll(dice, status):
d = dice()
if sum(d) in (7, 11):
return Just(("win", sum(d), [d]))
elif sum(d) in (2, 3, 12):
return Just(("lose", sum(d), [d]))
return Just(("point", sum(d), [d]))
def read_rest(file, data):
# file, data = file_data[0], file_data[1]
txt = file.readline().rstrip()
if txt:
row = float * List(*txt.split("\t"))
return Just(data + [list(row)]) >> read_rest(file)
return Just(data)
def come_out_roll(dice, status):
d = dice()
if sum(d) in (7, 11):
return Just(('win', sum(d), [d]))
elif sum(d) in (2, 3, 12):
return Just(('lose', sum(d), [d]))
else:
return Just(('point', sum(d), [d]))
def hasIdentity(self):
""" """
for x in range(self.ORDER):
if (self.isIdentity(self.__class__(x))):
if (self.__identity == Nothing):
self.__identity = Just(x)
return True
return False
def point_roll(dice, status):
prev, point, so_far = status
if prev != "point":
return Just(status)
d = dice()
if sum(d) == 7:
return Just(("craps", point, so_far + [d]))
elif sum(d) == point:
return Just(("win", point, so_far + [d]))
return Just(("point", point, so_far + [d])) >> point_roll(dice)
def anscombe():
"""
>>> d= anscombe()
>>> d[0]
[10.0, 8.04, 10.0, 9.14, 10.0, 7.46, 8.0, 6.58]
>>> d[-1]
[5.0, 5.68, 5.0, 4.74, 5.0, 5.73, 8.0, 6.89]
"""
with open("Anscombe.txt") as source:
data = Just([]) >> read_header(source) >> read_rest(source)
data = data.getValue()
return data
def point_roll(dice, status):
prev, point, so_far = status
if prev != 'point':
return Just(status)
d = dice()
if sum(d) == 7:
return Just(('craps', point, so_far+[d]))
elif sum(d) == point:
return Just(('win', point, so_far+[d]))
else:
return (
Just(('point', point, so_far+[d]))
>> point_roll(dice)
)
def _run_pip_install(directory: Path):
if _requires_pip_install(directory):
with ChangeDir(directory):
print(f'Running pip install in {directory}')
execute_shell_command(
'pip3 install -r requirements.txt -t . >> /dev/null')
return Just(directory)
def hasIdentity(self): """ """ for x in range(self.ORDER): if(self.isIdentity(self.__class__(x))): if(self.__identity == Nothing): self.__identity = Just(x) return True return False
def craps(dice):
"""
>>> def seven():
... return (3,4)
>>> craps( seven )
('win', 7, [(3, 4)])
>>> rolls= [(3,3), (2,2), (3,3)]
>>> def fixed():
... global rolls
... head, *tail = rolls
... rolls= tail
... return head
>>> craps( fixed )
('win', 6, [(3, 3), (2, 2), (3, 3)])
"""
outcome = (Just(("", 0, [])) >> come_out_roll(dice) >> point_roll(dice))
print(outcome.getValue())
def get_maybe(cls, *args):
try:
return Just(super().get(*args))
except super().DoesNotExist as e:
return Nothing
def _get_prefix(stack_data: StackData):
return Just(
stack_data.bucket_prefix) if stack_data.bucket_prefix else Just(
stack_data.stack_name)
def _create_dist_and_copy_files(directory: Path):
dist_path = _get_dist_path(directory)
copytree(directory, dist_path)
return Just(dist_path)
def _run_zip(directory: Path):
with ChangeDir(directory):
zip_name = f'{directory.parent.name}.zip'
execute_shell_command(f'zip -r {zip_name} . >> /dev/null')
return Just(directory)
def check_stack_requirements(stack_data: StackData):
# also: check whether bucket exists? does require boto3 dependency
return get_as_path('.') >> partial(_check_template_exists,
stack_data) >> Just(stack_data)
def check_requirements(lambda_dir):
return Just(
lambda_dir
) >> _check_root_dir >> _check_dir_has_sub_dirs >> _check_dirs_contain_python
from pymonad import Just, List, Nothing, curry
@curry
def add(x, y):
return x + y
def add10(x):
return add * Just(10) & x
print(add10(List(1, 2, 3, 4, 5, 6)))
print(add10(Just(33)))
def craps():
return (
Just(('', 0, [])) >> come_out_roll(dice)
>> point_roll(dice)
)
"""
fp_task4
just_nothing_list
"""
from pymonad import Just, List, Nothing, curry
@curry
def add(x, y):
return x + y
@curry
def add10(x):
return add() * Just(10) & x
print(add10(List(12, 56, 0, 3)))
print(add10(Just(8)))
print(add10()(Nothing))
"""
fp_task5
"""
from pymonad import List, Just, Nothing, Maybe
# посадка птиц на левую сторону
to_left = lambda num: lambda x: Nothing if abs(
(x[0] + num) - x[1]) > 4 else Just((x[0] + num, x[1]))
# посадка птиц на правую сторону
to_right = lambda num: lambda x: Nothing if abs(
(x[1] + num) - x[0]) > 4 else Just((x[0], x[1] + num))
# банановая кожура
banana = lambda x: Nothing
# отображение результата
def show(Maybe):
if Maybe == Nothing:
return print("Will Fall")
else:
falled, pole = Maybe.getValue()
return print(
"Will not Fall, birds on l.side:{}, birds on r.side:{}".format(
falled, pole))
begin = lambda: Just((0, 0))
def get_as_path(value):
return Just(Path(value))
class Magma(metaclass=MagmaMeta):
"""
Magma is an abstract base class used to represent the algebraic structure known as a magma,
which is simply a set, and a binary operator (* by default) that maps two values in the set to another
value in the set.
The Magma class used the static constant CAYLEY_TABLE to define how the binary operator works,
CAYLEY_TABLE is a two dimensional array that represents the result of the binary operator.
By convention, the row number corresponds to the value on the left side of the binary operator,
and the column number corresponds to the value on the right. e.a. for a*b=c, a is the row number,
c is the column number, and c is the result of the operation.
The row and column numbers are also 0-indexed, e.a. the 1st column is actually, the 0th column,
the 2nd column is actually the 1st column...
*****BASIC USAGE*****:
To create a new magma class with a Cayley table, use the following syntax:
class DihedralD3(magpy.Magma):
CAYLEY_TABLE == [[0,1,2,3,4,5],
[1,0,4,5,2,3],
[2,5,0,4,3,1],
[3,4,5,0,1,2],
[4,3,1,2,5,0],
[5,2,3,1,0,4]]
To instantiate a magma class, use this syntax:
d = DihedralD3(2)
Finally, to use the binary operator of the magma, simply use "*"
d * d
Currently the binary operator may be either + or * depending on user preference. To
change the binary operator you want to use, call the method setMagmaOperator() on
any object in the magma class in question. Pass the method "add" to set the operation
to + class wide, and "mult" to set the operation as * class wide.
Using the declared class and object from above:
d.setMagmaOperator("add")
d + d
Note: Internally, & is used as the representation of the magma operator, this allows
all of the methods using the magma operator to work regardless of whether + or * is
being used at the magma operation.
"""
## options ##
usegreek = False
use_eabc = False
usecustomcharset = False
__magma_operator = 'mult'
## Charsets ##
#
# Used in the display of individual values of magmas, and the display of a
# magma's CAYLEY_TABLE. Customizable with the charset options.
#
customcharset = []
greek = ['α','β','γ','δ','ε','ζ','η','θ','ι','κ','λ','μ','ν','ξ','ο','π','ρ','σ','τ','υ','φ','χ','ψ','ω']
eabc = ['e','a','b','c','d','f','g','h','i','j','k','l','m','n','o','p','q','r','s','t','u','v','w','x','y','z']
### Constant Static Variables ###
#
# These must be given values (other than the default) in subclasses of Magma in order
# for those subclasses to be valid. These values are CONSTANTS for subclasses of Magma,
# and should not be modified after the class has been instantiated.
#
CAYLEY_TABLE = []
SET = set([])
ORDER = 0
#
__identity = Nothing
def __init__(self,n):
if self.__class__.__name__ == 'Magma':
raise NotImplementedError("Magma is an abstract base class, it must be instantiated before use. See help(Magma) for more information.")
if(n in self.SET):
self.n = n
else:
raise Exception("Invalid argument.")
def magmaOp(self,x):
new = self.__class__(self.CAYLEY_TABLE[self.n][x.n])
if(self.usegreek == True or x.usegreek == True):
new.usegreek = True
return new
def setMagmaOperator(self,op):
if op == "mult":
self.__class__.__magma_operator = "mult"
elif op == "add":
self.__class__.__magma_operator = "add"
else:
print("Please use either \"mult\" or \"add\" for the magma operator (default is mult).")
def __and__(x,y):
""" Used as an internal symbol for representation of the magma operator. """
return x.magmaOp(y)
def __add__(x,y):
if(x.__class__.__magma_operator == "add"):
return x.__and__(y)
def __mul__(x,y):
if(x.__class__.__magma_operator == "mult"):
return x.__and__(y)
def __eq__(x,y): # ==
if x.n == y.n:
return True
else:
return False
def __repr__(self):
if not self.usegreek:
return str(self.n)
elif self.usegreek:
return self.greek[self.n]
else:
return "error"
def isCommutative(self):
""" Checks to see if x + y = y + x for all x and y in the magma. """
for _x in range(self.ORDER):
for _y in range(self.ORDER):
x = self.__class__(_x)
y = self.__class__(_y)
if(x & y == y & x):
pass
else:
return False
return True
def isAssociative(self):
""" """
for _x in range(self.ORDER):
for _y in range(self.ORDER):
for _z in range(self.ORDER):
x = self.__class__(_x)
y = self.__class__(_y)
z = self.__class__(_z)
if( (x & y) & z == x & (y & z) ):
pass
else:
return False
return True
def hasIdentity(self):
""" """
for x in range(self.ORDER):
if(self.isIdentity(self.__class__(x))):
if(self.__identity == Nothing):
self.__identity = Just(x)
return True
return False
def isIdentity(self,e):
""" """
for _x in range(self.ORDER):
x = self.__class__(_x)
if(not x & e == x):
return False
return True
def hasInverse(self,x):
""" """
if(self.__identity == Nothing):
return False
else:
for _y in range(self.ORDER):
y = self.__class__(_y)
e = self.__class__(self.__identity.getValue())
if(x & y == e):
return True
return False
def isInvertable(self):
""" """
for _x in range(self.ORDER):
x = self.__class__(_x)
if(not self.hasInverse(x)):
return False
return True
def isMonoid(self):
""" """
if(self.hasIdentity() and self.isAssociative()):
return True
else:
return False
def isGroup(self):
""" """
if(self.isMonoid() and self.isInvertable()):
return True
else:
return False
def isAbeleanGroup(self):
""" """
if(self.isGroup() and self.isCommutative()):
return True
else:
return False
def isLoop(self):
""" """
if(self.hasIdentity() and self.isInvertable()):
return True
else:
return False
def isMoufangLoop(self):
""" """
for _x in range(self.ORDER):
for _y in range(self.ORDER):
for _z in range(self.ORDER):
if not z(x(zy)) == ((z&x)&z)&y:
return False
if not x&(z&(y&z)) == ((x&z)&y)&z:
return False
if not (z&x)&(y&z) == (z&(x&y))&z:
return False
if not (z&x)&(y&z) == z&((x&y)&z):
return False
return True
def isSelfDistributive(self):
""" Returns true if all of the elements of the magma satisfy the self distributive property. """
for _x in range(self.ORDER):
for _y in range(self.ORDER):
for _z in range(self.ORDER):
x = self.__class__(_x)
y = self.__class__(_y)
z = self.__class__(_z)
if(not x & (y & z) == (x & y) & (x & z) ):
return False
return True
def __rackProperty__(self):
""" for all a, b, there exists exactly one c such that a * c = b """
count = 0 # number of c
for _a in range(self.ORDER):
for _b in range(self.ORDER):
for _c in range(self.ORDER):
a = self.__class__(_a)
b = self.__class__(_b)
c = self.__class__(_c)
if (a & c == b):
count = count + 1
if (count > 1):
return False
if(count == 1):
return True
else:
return False
def isRack(self):
""" """
if(self.isSelfDistributive() and self.__rackProperty__()):
return True
else:
return False
def isQuandle(self):
""" """
if(self.isRack() and self.isIdempotent()):
return True
else:
return False
def isIdempotent(self):
""" Tests to see if mag obeys the indepotent property for all x.
∀xϵmag(x * x = x) """
for row in self.CAYLEY_TABLE:
for _x in row:
x = self.__class__(_x)
if(x & x == x):
pass
else:
return False
return True
def isSzasz(self):
""" A Szasz magma has exactly one nonassociative ordered triple of members of the magma. """
pass
def isParamedial(self):
""" """
for _x in range(self.ORDER):
for _y in range(self.ORDER):
for _a in range(self.ORDER):
for _b in range(self.ORDER):
x = self.__class__(_x)
y = self.__class__(_y)
a = self.__class__(_a)
b = self.__class__(_b)
if(not (a&x)&(y&b) == (b&x)&(y&a)):
return False
return True
def isFlexible(self):
""" X*(Y*X) = (X*Y)*X """
for _x in range(self.ORDER):
for _y in range(self.ORDER):
x = self.__class__(_x)
y = self.__class__(_y)
if(not x&(y&x) == (x&y)&x):
return False
return True
def isJordan(self):
""" ((XX)Y)X = (XX)(YX) """
for _x in range(self.ORDER):
for _y in range(self.ORDER):
x = self.__class__(_x)
y = self.__class__(_y)
if(not ((x&x)&y)&x == (x&x)&(y&x) ):
return False
return True
def isAntiCommutative(self):
""" """
pass
def isAlternative(self):
""" (X*X)*Y = X*(X*Y) and X*(Y*Y) = (X*Y)*Y """
for _x in range(self.ORDER):
for _y in range(self.ORDER):
x = self.__class__(_x)
y = self.__class__(_y)
if not (x&x)&y == x&(x&y) and x&(y&y) == (x&y)&y:
return False
return True
def isExtra(self):
""" ((XY)Z)X = X(Y(ZX)) """
for _x in range(self.ORDER):
for _y in range(self.ORDER):
for _z in range(self.ORDER):
x = self.__class__(_x)
y = self.__class__(_y)
z = self.__class__(_z)
if( ((x&y)&z)&x == x&(y&(z&x)) ):
return False
return True
def isLeftBol(self):
""" Y(Z(YX)) = (Y(ZY))X """
for _x in range(self.ORDER):
for _y in range(self.ORDER):
for _z in range(self.ORDER):
x = self.__class__(_x)
y = self.__class__(_y)
z = self.__class__(_z)
if(not y&(z&(y&x)) == (y&(z&y))&x):
return False
return True
def isRightBol(self):
""" ((XY)Z)Y = X((YZ)Y) """
for _x in range(self.ORDER):
for _y in range(self.ORDER):
for _z in range(self.ORDER):
x = self.__class__(_x)
y = self.__class__(_y)
z = self.__class__(_z)
if(not ((x&y)&z)&y == x&((y&z)&y) ):
return False
return True
def isQuasidihedral(self):
""" Returns true if the magma is quasidihedral, that is:
* It is a non-abelian group
* It has an order of 2^n """
if(self.isGroup() and \
not self.isCommutative() and \
log(self.ORDER,2).is_integer() ):
return True
else:
return False
def isBand(self):
""" """
if(self.isAssociative() and self.isIdempotent()):
return True
else:
return False
def isRightInvoulntary():
""" (XY)Y = X """
for _x in range(self.ORDER):
for _y in range(self.ORDER):
x = self.__class__(_x)
y = self.__class__(_y)
if(not (x&y)&y == x):
return False
def isKei(self):
""" """
if(self.isQuandle() and self.isRightInvoulntary()):
return True
else:
return False
def isSteiner(self):
""" """
for _x in range(self.ORDER):
for _y in range(self.ORDER):
x = self.__class__(_x)
y = self.__class__(_x)
if(not (x&(x&y) == y and self.isCommutative())):
return False
return True
def isSquag(self):
""" A squag is an idempotent Steiner magma. """
if(self.isSteiner() and self.isIdempotent()):
return True
else:
return False
def isDiassociative(self):
""" Returns true if each submagma of the magma m generated by two elements is associative. """
pass
def isMedial(self):
""" Returns true if the agma satisfies the medial law (x*y)*(u*v) = (x*u)*(y*v). """
for _x in range(self.ORDER):
for _y in range(self.ORDER):
for _u in range(self.ORDER):
for _v in range(self.ORDER):
x = self.__class__(_x)
y = self.__class__(_y)
u = self.__class__(_u)
v = self.__class__(_v)
if(not (x&y)&(u&v) == (x&u)&(y&v)):
return False
return True
def IsSubMagma(self,magma):
""" Determines if magma is a submagma of the magma object """
pass
def isZeropotent(self):
""" (X*X)*Y = (Y*Y)*X = X*X """
for _x in range(self.ORDER):
for _y in range(self.ORDER):
x = self.__class__(_x)
y = self.__class__(_y)
if not (x&x)&y == (y&y)&x and (x&x)&y == x&x:
return False
return True
def isLeftSemimedial(self):
""" """
pass
def isRightSemimedial(self):
""" """
pass
def isSemimedial(self):
""" """
pass
def nucleus(self):
""" """
pass
def evaluate(self,expr):
""" Evaluates a string of symbols and letters or numbers representing the operator and symbols of the magma.
(NOT YET IMPLEMENTED) """
if(self.usegreek):
# Tokenize with () first?
pass # Tokenize with ' ' and '*' or '+'.
# make into list
elif(self.usecustomcharset):
pass #tokenize
else:
pass
class Magma(metaclass=MagmaMeta):
"""
Magma is an abstract base class used to represent the algebraic structure known as a magma,
which is simply a set, and a binary operator (* by default) that maps two values in the set to another
value in the set.
The Magma class used the static constant CAYLEY_TABLE to define how the binary operator works,
CAYLEY_TABLE is a two dimensional array that represents the result of the binary operator.
By convention, the row number corresponds to the value on the left side of the binary operator,
and the column number corresponds to the value on the right. e.a. for a*b=c, a is the row number,
c is the column number, and c is the result of the operation.
The row and column numbers are also 0-indexed, e.a. the 1st column is actually, the 0th column,
the 2nd column is actually the 1st column...
*****BASIC USAGE*****:
To create a new magma class with a Cayley table, use the following syntax:
class DihedralD3(magpy.Magma):
CAYLEY_TABLE == [[0,1,2,3,4,5],
[1,0,4,5,2,3],
[2,5,0,4,3,1],
[3,4,5,0,1,2],
[4,3,1,2,5,0],
[5,2,3,1,0,4]]
To instantiate a magma class, use this syntax:
d = DihedralD3(2)
Finally, to use the binary operator of the magma, simply use "*"
d * d
Currently the binary operator may be either + or * depending on user preference. To
change the binary operator you want to use, call the method setMagmaOperator() on
any object in the magma class in question. Pass the method "add" to set the operation
to + class wide, and "mult" to set the operation as * class wide.
Using the declared class and object from above:
d.setMagmaOperator("add")
d + d
Note: Internally, & is used as the representation of the magma operator, this allows
all of the methods using the magma operator to work regardless of whether + or * is
being used at the magma operation.
"""
## options ##
usegreek = False
use_eabc = False
usecustomcharset = False
__magma_operator = 'mult'
## Charsets ##
#
# Used in the display of individual values of magmas, and the display of a
# magma's CAYLEY_TABLE. Customizable with the charset options.
#
customcharset = []
greek = [
'α', 'β', 'γ', 'δ', 'ε', 'ζ', 'η', 'θ', 'ι', 'κ', 'λ', 'μ', 'ν', 'ξ',
'ο', 'π', 'ρ', 'σ', 'τ', 'υ', 'φ', 'χ', 'ψ', 'ω'
]
eabc = [
'e', 'a', 'b', 'c', 'd', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n',
'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z'
]
### Constant Static Variables ###
#
# These must be given values (other than the default) in subclasses of Magma in order
# for those subclasses to be valid. These values are CONSTANTS for subclasses of Magma,
# and should not be modified after the class has been instantiated.
#
CAYLEY_TABLE = []
SET = set([])
ORDER = 0
#
__identity = Nothing
def __init__(self, n):
if self.__class__.__name__ == 'Magma':
raise NotImplementedError(
"Magma is an abstract base class, it must be instantiated before use. See help(Magma) for more information."
)
if (n in self.SET):
self.n = n
else:
raise Exception("Invalid argument.")
def magmaOp(self, x):
new = self.__class__(self.CAYLEY_TABLE[self.n][x.n])
if (self.usegreek == True or x.usegreek == True):
new.usegreek = True
return new
def setMagmaOperator(self, op):
if op == "mult":
self.__class__.__magma_operator = "mult"
elif op == "add":
self.__class__.__magma_operator = "add"
else:
print(
"Please use either \"mult\" or \"add\" for the magma operator (default is mult)."
)
def __and__(x, y):
""" Used as an internal symbol for representation of the magma operator. """
return x.magmaOp(y)
def __add__(x, y):
if (x.__class__.__magma_operator == "add"):
return x.__and__(y)
def __mul__(x, y):
if (x.__class__.__magma_operator == "mult"):
return x.__and__(y)
def __eq__(x, y): # ==
if x.n == y.n:
return True
else:
return False
def __repr__(self):
if not self.usegreek:
return str(self.n)
elif self.usegreek:
return self.greek[self.n]
else:
return "error"
def isCommutative(self):
""" Checks to see if x + y = y + x for all x and y in the magma. """
for _x in range(self.ORDER):
for _y in range(self.ORDER):
x = self.__class__(_x)
y = self.__class__(_y)
if (x & y == y & x):
pass
else:
return False
return True
def isAssociative(self):
""" """
for _x in range(self.ORDER):
for _y in range(self.ORDER):
for _z in range(self.ORDER):
x = self.__class__(_x)
y = self.__class__(_y)
z = self.__class__(_z)
if ((x & y) & z == x & (y & z)):
pass
else:
return False
return True
def hasIdentity(self):
""" """
for x in range(self.ORDER):
if (self.isIdentity(self.__class__(x))):
if (self.__identity == Nothing):
self.__identity = Just(x)
return True
return False
def isIdentity(self, e):
""" """
for _x in range(self.ORDER):
x = self.__class__(_x)
if (not x & e == x):
return False
return True
def hasInverse(self, x):
""" """
if (self.__identity == Nothing):
return False
else:
for _y in range(self.ORDER):
y = self.__class__(_y)
e = self.__class__(self.__identity.getValue())
if (x & y == e):
return True
return False
def isInvertable(self):
""" """
for _x in range(self.ORDER):
x = self.__class__(_x)
if (not self.hasInverse(x)):
return False
return True
def isMonoid(self):
""" """
if (self.hasIdentity() and self.isAssociative()):
return True
else:
return False
def isGroup(self):
""" """
if (self.isMonoid() and self.isInvertable()):
return True
else:
return False
def isAbeleanGroup(self):
""" """
if (self.isGroup() and self.isCommutative()):
return True
else:
return False
def isLoop(self):
""" """
if (self.hasIdentity() and self.isInvertable()):
return True
else:
return False
def isMoufangLoop(self):
""" """
for _x in range(self.ORDER):
for _y in range(self.ORDER):
for _z in range(self.ORDER):
if not z(x(zy)) == ((z & x) & z) & y:
return False
if not x & (z & (y & z)) == ((x & z) & y) & z:
return False
if not (z & x) & (y & z) == (z & (x & y)) & z:
return False
if not (z & x) & (y & z) == z & ((x & y) & z):
return False
return True
def isSelfDistributive(self):
""" Returns true if all of the elements of the magma satisfy the self distributive property. """
for _x in range(self.ORDER):
for _y in range(self.ORDER):
for _z in range(self.ORDER):
x = self.__class__(_x)
y = self.__class__(_y)
z = self.__class__(_z)
if (not x & (y & z) == (x & y) & (x & z)):
return False
return True
def __rackProperty__(self):
""" for all a, b, there exists exactly one c such that a * c = b """
count = 0 # number of c
for _a in range(self.ORDER):
for _b in range(self.ORDER):
for _c in range(self.ORDER):
a = self.__class__(_a)
b = self.__class__(_b)
c = self.__class__(_c)
if (a & c == b):
count = count + 1
if (count > 1):
return False
if (count == 1):
return True
else:
return False
def isRack(self):
""" """
if (self.isSelfDistributive() and self.__rackProperty__()):
return True
else:
return False
def isQuandle(self):
""" """
if (self.isRack() and self.isIdempotent()):
return True
else:
return False
def isIdempotent(self):
""" Tests to see if mag obeys the indepotent property for all x.
∀xϵmag(x * x = x) """
for row in self.CAYLEY_TABLE:
for _x in row:
x = self.__class__(_x)
if (x & x == x):
pass
else:
return False
return True
def isSzasz(self):
""" A Szasz magma has exactly one nonassociative ordered triple of members of the magma. """
pass
def isParamedial(self):
""" """
for _x in range(self.ORDER):
for _y in range(self.ORDER):
for _a in range(self.ORDER):
for _b in range(self.ORDER):
x = self.__class__(_x)
y = self.__class__(_y)
a = self.__class__(_a)
b = self.__class__(_b)
if (not (a & x) & (y & b) == (b & x) & (y & a)):
return False
return True
def isFlexible(self):
""" X*(Y*X) = (X*Y)*X """
for _x in range(self.ORDER):
for _y in range(self.ORDER):
x = self.__class__(_x)
y = self.__class__(_y)
if (not x & (y & x) == (x & y) & x):
return False
return True
def isJordan(self):
""" ((XX)Y)X = (XX)(YX) """
for _x in range(self.ORDER):
for _y in range(self.ORDER):
x = self.__class__(_x)
y = self.__class__(_y)
if (not ((x & x) & y) & x == (x & x) & (y & x)):
return False
return True
def isAntiCommutative(self):
""" """
pass
def isAlternative(self):
""" (X*X)*Y = X*(X*Y) and X*(Y*Y) = (X*Y)*Y """
for _x in range(self.ORDER):
for _y in range(self.ORDER):
x = self.__class__(_x)
y = self.__class__(_y)
if not (x & x) & y == x & (x & y) and x & (y & y) == (x
& y) & y:
return False
return True
def isExtra(self):
""" ((XY)Z)X = X(Y(ZX)) """
for _x in range(self.ORDER):
for _y in range(self.ORDER):
for _z in range(self.ORDER):
x = self.__class__(_x)
y = self.__class__(_y)
z = self.__class__(_z)
if (((x & y) & z) & x == x & (y & (z & x))):
return False
return True
def isLeftBol(self):
""" Y(Z(YX)) = (Y(ZY))X """
for _x in range(self.ORDER):
for _y in range(self.ORDER):
for _z in range(self.ORDER):
x = self.__class__(_x)
y = self.__class__(_y)
z = self.__class__(_z)
if (not y & (z & (y & x)) == (y & (z & y)) & x):
return False
return True
def isRightBol(self):
""" ((XY)Z)Y = X((YZ)Y) """
for _x in range(self.ORDER):
for _y in range(self.ORDER):
for _z in range(self.ORDER):
x = self.__class__(_x)
y = self.__class__(_y)
z = self.__class__(_z)
if (not ((x & y) & z) & y == x & ((y & z) & y)):
return False
return True
def isQuasidihedral(self):
""" Returns true if the magma is quasidihedral, that is:
* It is a non-abelian group
* It has an order of 2^n """
if(self.isGroup() and \
not self.isCommutative() and \
log(self.ORDER,2).is_integer() ):
return True
else:
return False
def isBand(self):
""" """
if (self.isAssociative() and self.isIdempotent()):
return True
else:
return False
def isRightInvoulntary():
""" (XY)Y = X """
for _x in range(self.ORDER):
for _y in range(self.ORDER):
x = self.__class__(_x)
y = self.__class__(_y)
if (not (x & y) & y == x):
return False
def isKei(self):
""" """
if (self.isQuandle() and self.isRightInvoulntary()):
return True
else:
return False
def isSteiner(self):
""" """
for _x in range(self.ORDER):
for _y in range(self.ORDER):
x = self.__class__(_x)
y = self.__class__(_x)
if (not (x & (x & y) == y and self.isCommutative())):
return False
return True
def isSquag(self):
""" A squag is an idempotent Steiner magma. """
if (self.isSteiner() and self.isIdempotent()):
return True
else:
return False
def isDiassociative(self):
""" Returns true if each submagma of the magma m generated by two elements is associative. """
pass
def isMedial(self):
""" Returns true if the agma satisfies the medial law (x*y)*(u*v) = (x*u)*(y*v). """
for _x in range(self.ORDER):
for _y in range(self.ORDER):
for _u in range(self.ORDER):
for _v in range(self.ORDER):
x = self.__class__(_x)
y = self.__class__(_y)
u = self.__class__(_u)
v = self.__class__(_v)
if (not (x & y) & (u & v) == (x & u) & (y & v)):
return False
return True
def IsSubMagma(self, magma):
""" Determines if magma is a submagma of the magma object """
pass
def isZeropotent(self):
""" (X*X)*Y = (Y*Y)*X = X*X """
for _x in range(self.ORDER):
for _y in range(self.ORDER):
x = self.__class__(_x)
y = self.__class__(_y)
if not (x & x) & y == (y & y) & x and (x & x) & y == x & x:
return False
return True
def isLeftSemimedial(self):
""" """
pass
def isRightSemimedial(self):
""" """
pass
def isSemimedial(self):
""" """
pass
def nucleus(self):
""" """
pass
def evaluate(self, expr):
""" Evaluates a string of symbols and letters or numbers representing the operator and symbols of the magma.
(NOT YET IMPLEMENTED) """
if (self.usegreek):
# Tokenize with () first?
pass # Tokenize with ' ' and '*' or '+'.
# make into list
elif (self.usecustomcharset):
pass #tokenize
else:
pass
def add10(x):
return add * Just(10) & x
def read_header(file):
_ = file.readline()
_ = file.readline()
_ = file.readline()
return Just([])