def asfrac(A, limit=None):
if isinstance(A, (np.ndarray, float, int, long)):
return f.frac(A, 1, limit)
elif isinstance(A, f.frac):
return f.frac(A.a, A.b, limit)
elif isinstance(A, p.Poly):
return p.asfrac(A, limit)
raise NotImplementedError
def asfrac(A, limit=None):
if isinstance(A, (np.ndarray, float, int, long)):
return f.frac(A, 1, limit)
elif isinstance(A, f.frac):
return f.frac(A.a, A.b, limit)
elif isinstance(A, p.Poly):
return p.asfrac(A, limit)
raise NotImplementedError
def asfrac(P, limit=None):
B = P.A.copy()
for key in P.keys:
B[key] = f.frac(B[key], 1, limit)
out = Poly(B, P.dim, P.shape, f.frac)
return out
def asfrac(P, limit=None):
B = P.A.copy()
for key in P.keys:
B[key] = f.frac(B[key], 1, limit)
out = Poly(B, P.dim, P.shape, f.frac)
return out
def around(A, decimals=0):
"""
Evenly round to the given number of decimals.
Parameters
----------
A : p.Poly, f.frac, array_like
Input data.
decimals : int, optional
Number of decimal places to round to (default: 0). If
decimals is negative, it specifies the number of positions to
the left of the decimal point.
Returns
-------
Q : p.Poly, f.frac, array_like
Same type as A.
Examples
--------
>>> P = cp.prange(3)*2**-np.arange(0, 6, 2, float)
>>> print P
[1.0, 0.25q0, 0.0625q0^2]
>>> print cp.around(P)
[1.0, 0.0, 0.0]
>>> print cp.around(P, 2)
[1.0, 0.25q0, 0.06q0^2]
"""
if isinstance(A, (np.ndarray, float, int, long)):
return np.around(A, decimals)
elif isinstance(A, f.frac):
if decimals >= 0:
a = (A.a * 10**decimals) // A.b
return f.frac(a, 10**decimals)
a = A.a // (A.b * 10**-decimals)
return f.frac(a * 10**-decimals)
elif isinstance(A, p.Poly):
B = A.A.copy()
for key in A.keys:
B[key] = around(B[key], decimals)
return p.Poly(B, A.dim, A.shape, A.dtype)
raise NotImplementedError
def around(A, decimals=0):
"""
Evenly round to the given number of decimals.
Parameters
----------
A : p.Poly, f.frac, array_like
Input data.
decimals : int, optional
Number of decimal places to round to (default: 0). If
decimals is negative, it specifies the number of positions to
the left of the decimal point.
Returns
-------
Q : p.Poly, f.frac, array_like
Same type as A.
Examples
--------
>>> P = cp.prange(3)*2**-np.arange(0, 6, 2, float)
>>> print P
[1.0, 0.25q0, 0.0625q0^2]
>>> print cp.around(P)
[1.0, 0.0, 0.0]
>>> print cp.around(P, 2)
[1.0, 0.25q0, 0.06q0^2]
"""
if isinstance(A, (np.ndarray, float, int, long)):
return np.around(A, decimals)
elif isinstance(A, f.frac):
if decimals>=0:
a = (A.a*10**decimals)//A.b
return f.frac(a, 10**decimals)
a = A.a//(A.b*10**-decimals)
return f.frac(a*10**-decimals)
elif isinstance(A, p.Poly):
B = A.A.copy()
for key in A.keys:
B[key] = around(B[key], decimals)
return p.Poly(B, A.dim, A.shape, A.dtype)
raise NotImplementedError
def call(P, args):
"""
Evaluate a polynomial along specified axes.
Parameters
----------
P : Poly
Input polynomial.
args : array_like, masked
Argument to be evalutated.
Masked values keeps the variable intact.
Returns
-------
Q : Poly, np.array
If masked values are used the Poly is returned. Else an
numpy array matching the polynomial's shape is returned.
"""
args = list(args)
# expand args to match dim
if len(args)<P.dim:
args = args + [np.nan]*(P.dim-len(args))
elif len(args)>P.dim:
raise ValueError, "too many arguments"
# Find and perform substitutions, if any
x0,x1 = [],[]
for i in xrange(len(args)):
if isinstance(args[i], Poly):
x0.append(Poly({tuple(np.eye(P.dim)[i]):np.array(1)}))
x1.append(args[i])
args[i] = np.nan
if x0:
P = call(P, args)
return substitute(P, x0, x1)
# Create masks
masks = np.zeros(len(args), dtype=bool)
for i in xrange(len(args)):
if np.ma.is_masked(args[i]) \
or np.any(args[i]!=args[i]):
masks[i] = True
args[i] = 0
shape = np.array(args[np.argmax([np.prod(np.array(arg).shape)\
for arg in args])]).shape
args = np.array([np.ones(shape, dtype=int)*arg \
for arg in args])
A = {}
for key in P.keys:
key_ = np.array(key)*(1-masks)
val = np.outer(P.A[key], np.prod((args.T**key_).T, \
axis=0))
val = np.reshape(val, P.shape + tuple(shape))
val = np.where(val!=val, 0, val)
mkey = tuple(np.array(key)*(masks))
if not mkey in A:
A[mkey] = val
else:
A[mkey] = A[mkey] + val
if P.dtype==f.frac:
A[mkey] = f.frac(A[mkey])
out = Poly(A, P.dim, None, None)
if out.keys and not np.sum(out.keys):
out = out.A[out.keys[0]]
elif not out.keys:
out = np.zeros(out.shape, dtype=out.dtype)
return out
def __init__(self, A=None, dim=None, shape=None,
dtype=None, V=0):
"""
Parameters
----------
A : array_like, dict, Poly
The polynomial coefficient Tensor.
Where A[(i,j,k)] corresponds to a_{ijk} x^i y^j z^k
(A[i][j][k] for list and tuple)
dim : int
the dimensionality of the polynomial.
Automatically set if A contains a value.
shape : tuple
the number of polynomials represented.
Automatically set if A contains a value.
dtype : type
The type of the polynomial coefficients
"""
if V: print "\nConstruct poly out of:\n", A
if isinstance(A, Poly):
dtype_ = A.dtype
shape_ = A.shape
dim_ = A.dim
A = A.A.copy()
elif isinstance(A, np.ndarray):
dtype_ = A.dtype
shape_ = A.shape
dim_ = 1
A = {(0,):A}
elif isinstance(A, (int, long, float)):
dtype_ = type(A)
shape_ = ()
dim_ = 1
A = {(0,):np.array(A)}
elif isinstance(A, dict):
A = A.copy()
if not A:
dtype_ = int
dim_ = 1
shape_ = ()
else:
key = A.keys()[0]
shape_ = np.array(A[key]).shape
dim_ = len(key)
dtype_ = dtyping(A[key])
elif isinstance(A, f.frac):
dtype_ = f.frac
shape_ = A.shape
dim_ = 1
if isinstance(A.a, int):
A = f.frac(np.array(A.a), np.array(A.b))
A = {(0,): A}
elif isinstance(A, (np.ndarray, list, tuple)):
A = [Poly(a) for a in A]
shape_ = (len(A),) + A[0].shape
dtype_ = dtyping(*[_.dtype for _ in A])
dims = np.array([a.dim for a in A])
dim_ = np.max(dims)
if dim_!=np.min(dims):
A = [setdim(a, dim_) for a in A]
d = {}
for i in xrange(len(A)): # i over list of polys
if V: print "Adding:", A[i], "(%d)" % i
for key in A[i].A: # key over exponents in each poly
if not d.has_key(key):
if V: print "creating key", key
if dtype_==f.frac:
d[key] = f.frac(np.zeros(shape_))
else:
d[key] = np.zeros(shape_, dtype=dtype_)
d[key][i] = A[i].A[key]
if V: print "update", key, d[key]
if V: print "creating master dict:\n", d
A = d
else:
raise TypeError, \
"Poly arg: 'A' is not a valid type " + repr(A)
if dtype is None:
dtype = dtype_
if dtype==int:
func1 = asint
if shape is None:
shape = shape_
elif np.any(np.array(shape)!=shape_):
ones = np.ones(shape, dtype=int)
func1 = lambda x: asint(x*ones)
elif dtype==f.frac:
func1 = f.frac
if shape is None:
shape = shape_
elif np.any(np.array(shape)!=shape_):
ones = np.ones(shape, dtype=int)
func1 = lambda x: f.frac(x*ones)
else:
func1 = lambda x:np.array(x, dtype=dtype)
if shape is None:
shape = shape_
elif np.any(np.array(shape)!=shape_):
ones = np.ones(shape, dtype=int)
func1 = lambda x: 1.*x*ones
func2 = lambda x:x
if dim is None:
dim = dim_
elif dim<dim_:
func2 = lambda x:x[:dim]
elif dim>dim_:
func2 = lambda x:x + (0,)*(dim-dim_)
d = {}
for key, val in A.items():
d[func2(key)] = func1(val)
A = d
if isinstance(shape, int):
shape = (shape,)
# Remove empty elements
for key in A.keys()[:]:
if np.all(A[key]==0):
del A[key]
# assert non-empty container
if not A:
if dtype==float:
dt = float
else:
dt = int
A = {(0,)*dim: np.zeros(shape, dtype=dt)}
self.keys = A.keys()
self.dim = dim
self.shape = shape
self.dtype = dtype
self.A = A
if V: print "result", A
from fraction import frac
x = frac(*map(int, input().split("/"))) # "3/5"のように入力された分数を読み取る
denominators = [] # 分母をこのリストに入れる
# TODO
print("= 1/", end="")
print(*denominators, sep=" + 1/")
def call(P, args):
"""
Evaluate a polynomial along specified axes.
Parameters
----------
P : Poly
Input polynomial.
args : array_like, masked
Argument to be evalutated.
Masked values keeps the variable intact.
Returns
-------
Q : Poly, np.array
If masked values are used the Poly is returned. Else an
numpy array matching the polynomial's shape is returned.
"""
args = list(args)
# expand args to match dim
if len(args) < P.dim:
args = args + [np.nan] * (P.dim - len(args))
elif len(args) > P.dim:
raise ValueError, "too many arguments"
# Find and perform substitutions, if any
x0, x1 = [], []
for i in xrange(len(args)):
if isinstance(args[i], Poly):
x0.append(Poly({tuple(np.eye(P.dim)[i]): np.array(1)}))
x1.append(args[i])
args[i] = np.nan
if x0:
P = call(P, args)
return substitute(P, x0, x1)
# Create masks
masks = np.zeros(len(args), dtype=bool)
for i in xrange(len(args)):
if np.ma.is_masked(args[i]) \
or np.any(args[i]!=args[i]):
masks[i] = True
args[i] = 0
shape = np.array(args[np.argmax([np.prod(np.array(arg).shape)\
for arg in args])]).shape
args = np.array([np.ones(shape, dtype=int)*arg \
for arg in args])
A = {}
for key in P.keys:
key_ = np.array(key) * (1 - masks)
val = np.outer(P.A[key], np.prod((args.T**key_).T, \
axis=0))
val = np.reshape(val, P.shape + tuple(shape))
val = np.where(val != val, 0, val)
mkey = tuple(np.array(key) * (masks))
if not mkey in A:
A[mkey] = val
else:
A[mkey] = A[mkey] + val
if P.dtype == f.frac:
A[mkey] = f.frac(A[mkey])
out = Poly(A, P.dim, None, None)
if out.keys and not np.sum(out.keys):
out = out.A[out.keys[0]]
elif not out.keys:
out = np.zeros(out.shape, dtype=out.dtype)
return out
def __init__(self, A=None, dim=None, shape=None, dtype=None, V=0):
"""
Parameters
----------
A : array_like, dict, Poly
The polynomial coefficient Tensor.
Where A[(i,j,k)] corresponds to a_{ijk} x^i y^j z^k
(A[i][j][k] for list and tuple)
dim : int
the dimensionality of the polynomial.
Automatically set if A contains a value.
shape : tuple
the number of polynomials represented.
Automatically set if A contains a value.
dtype : type
The type of the polynomial coefficients
"""
if V: print "\nConstruct poly out of:\n", A
if isinstance(A, Poly):
dtype_ = A.dtype
shape_ = A.shape
dim_ = A.dim
A = A.A.copy()
elif isinstance(A, np.ndarray):
dtype_ = A.dtype
shape_ = A.shape
dim_ = 1
A = {(0, ): A}
elif isinstance(A, (int, long, float)):
dtype_ = type(A)
shape_ = ()
dim_ = 1
A = {(0, ): np.array(A)}
elif isinstance(A, dict):
A = A.copy()
if not A:
dtype_ = int
dim_ = 1
shape_ = ()
else:
key = A.keys()[0]
shape_ = np.array(A[key]).shape
dim_ = len(key)
dtype_ = dtyping(A[key])
elif isinstance(A, f.frac):
dtype_ = f.frac
shape_ = A.shape
dim_ = 1
if isinstance(A.a, int):
A = f.frac(np.array(A.a), np.array(A.b))
A = {(0, ): A}
elif isinstance(A, (np.ndarray, list, tuple)):
A = [Poly(a) for a in A]
shape_ = (len(A), ) + A[0].shape
dtype_ = dtyping(*[_.dtype for _ in A])
dims = np.array([a.dim for a in A])
dim_ = np.max(dims)
if dim_ != np.min(dims):
A = [setdim(a, dim_) for a in A]
d = {}
for i in xrange(len(A)): # i over list of polys
if V: print "Adding:", A[i], "(%d)" % i
for key in A[i].A: # key over exponents in each poly
if not d.has_key(key):
if V: print "creating key", key
if dtype_ == f.frac:
d[key] = f.frac(np.zeros(shape_))
else:
d[key] = np.zeros(shape_, dtype=dtype_)
d[key][i] = A[i].A[key]
if V: print "update", key, d[key]
if V: print "creating master dict:\n", d
A = d
else:
raise TypeError, \
"Poly arg: 'A' is not a valid type " + repr(A)
if dtype is None:
dtype = dtype_
if dtype in (int, long):
func1 = asint
if shape is None:
shape = shape_
elif np.any(np.array(shape) != shape_):
ones = np.ones(shape, dtype=int)
func1 = lambda x: asint(x * ones)
elif dtype == f.frac:
func1 = f.frac
if shape is None:
shape = shape_
elif np.any(np.array(shape) != shape_):
ones = np.ones(shape, dtype=int)
func1 = lambda x: f.frac(x * ones)
else:
func1 = lambda x: np.array(x, dtype=dtype)
if shape is None:
shape = shape_
elif np.any(np.array(shape) != shape_):
ones = np.ones(shape, dtype=int)
func1 = lambda x: 1. * x * ones
func2 = lambda x: x
if dim is None:
dim = dim_
elif dim < dim_:
func2 = lambda x: x[:dim]
elif dim > dim_:
func2 = lambda x: x + (0, ) * (dim - dim_)
d = {}
for key, val in A.items():
d[func2(key)] = func1(val)
A = d
if isinstance(shape, int):
shape = (shape, )
# Remove empty elements
for key in A.keys()[:]:
if np.all(A[key] == 0):
del A[key]
# assert non-empty container
if not A:
if dtype == float:
dt = float
else:
dt = int
A = {(0, ) * dim: np.zeros(shape, dtype=dt)}
self.keys = A.keys()
self.dim = dim
self.shape = shape
self.dtype = dtype
self.A = A
if V: print "result", A
from fraction import frac
x = frac(*map(int, input().split("/"))) # "3/5"のように入力された分数を読み取ってfracクラスを作る
denominators = [] # 分母をこのリストに入れる
while x.bunsi != 1:
t = x.bunbo // x.bunsi + 1
denominators.append(t)
x = x - frac(1, t)
denominators.append(x.bunbo)
print("= 1/", end="")
print(*denominators, sep=" + 1/")