def test_xreplace():
assert b21.xreplace({b2: b1}) == Basic(b1, b1)
assert b21.xreplace({b2: b21}) == Basic(b21, b1)
assert b3.xreplace({b2: b1}) == b2
assert Basic(b1, b2).xreplace({b1: b2, b2: b1}) == Basic(b2, b1)
assert Atom(b1).xreplace({b1: b2}) == Atom(b1)
assert Atom(b1).xreplace({Atom(b1): b2}) == b2
pytest.raises(TypeError, b1.xreplace)
pytest.raises(TypeError, lambda: b1.xreplace([b1, b2]))
def test_sympyissue_6079():
# since x + 2.0 == x + 2 we can't do a simple equality test
assert _aresame((x + 2.0).subs({2: 3}), x + 2.0)
assert _aresame((x + 2.0).subs({2.0: 3}), x + 3)
assert not _aresame(x + 2, x + 2.0)
assert not _aresame(Basic(cos, 1), Basic(cos, 1.))
assert _aresame(cos, cos)
assert not _aresame(1, Integer(1))
assert not _aresame(x, symbols('x', positive=True))
def test_matches_basic():
instances = [Basic(b1, b1, b2), Basic(b1, b2, b1), Basic(b2, b1, b1),
Basic(b1, b2), Basic(b2, b1), b2, b1]
for i, b_i in enumerate(instances):
for j, b_j in enumerate(instances):
if i == j:
assert b_j.match(b_i) == {}
else:
assert b_j.match(b_i) is None
assert b1.match(b1) == {}
def test_equality():
instances = [b1, b2, b3, b21, Basic(b1, b1, b1), Basic]
for i, b_i in enumerate(instances):
for j, b_j in enumerate(instances):
assert (b_i == b_j) == (i == j)
assert (b_i != b_j) == (i != j)
assert Basic() != []
assert not(Basic() == [])
assert Basic() != 0
assert not(Basic() == 0)
def test_equality():
# pylint: disable=unneeded-not
instances = [b1, b2, b3, b21, Basic(b1, b1, b1), Basic]
for i, b_i in enumerate(instances):
for j, b_j in enumerate(instances):
assert (b_i == b_j) == (i == j)
assert (b_i != b_j) == (i != j)
assert Basic()
assert Basic() != 0
assert not Basic() == 0
def test_gcd_terms():
f = 2*(x + 1)*(x + 4)/(5*x**2 + 5) + (2*x + 2)*(x + 5)/(x**2 + 1)/5 + \
(2*x + 2)*(x + 6)/(5*x**2 + 5)
assert _gcd_terms(f) == (Rational(6, 5) * ((1 + x) / (1 + x**2)), 5 + x, 1)
assert _gcd_terms(Add.make_args(f)) == \
(Rational(6, 5)*((1 + x)/(1 + x**2)), 5 + x, 1)
newf = Rational(6, 5) * ((1 + x) * (5 + x) / (1 + x**2))
assert gcd_terms(f) == newf
args = Add.make_args(f)
# non-Basic sequences of terms treated as terms of Add
assert gcd_terms(list(args)) == newf
assert gcd_terms(tuple(args)) == newf
assert gcd_terms(set(args)) == newf
# but a Basic sequence is treated as a container
assert gcd_terms(Tuple(*args)) != newf
assert gcd_terms(Basic(Tuple(1, 3*y + 3*x*y), Tuple(1, 3))) == \
Basic((1, 3*y*(x + 1)), (1, 3))
# but we shouldn't change keys of a dictionary or some may be lost
assert gcd_terms(Dict((x*(1 + y), 2), (x + x*y, y + x*y))) == \
Dict({x*(y + 1): 2, x + x*y: y*(1 + x)})
assert gcd_terms((2 * x + 2)**3 +
(2 * x + 2)**2) == 4 * (x + 1)**2 * (2 * x + 3)
assert gcd_terms(0) == 0
assert gcd_terms(1) == 1
assert gcd_terms(x) == x
assert gcd_terms(2 + 2 * x) == Mul(2, 1 + x, evaluate=False)
arg = x * (2 * x + 4 * y)
garg = 2 * x * (x + 2 * y)
assert gcd_terms(arg) == garg
assert gcd_terms(sin(arg)) == sin(garg)
# issue sympy/sympy#6139-like
alpha, alpha1, alpha2, alpha3 = symbols('alpha:4')
a = alpha**2 - alpha * x**2 + alpha + x**3 - x * (alpha + 1)
rep = {
alpha: (1 + sqrt(5)) / 2 + alpha1 * x + alpha2 * x**2 + alpha3 * x**3
}
s = (a / (x - alpha)).subs(rep).series(x, 0, 1)
assert simplify(collect(s, x)) == -sqrt(5) / 2 - Rational(3, 2) + O(x)
# issue sympy/sympy#5917
assert _gcd_terms([Integer(0), Integer(0)]) == (0, 0, 1)
assert _gcd_terms([2 * x + 4]) == (2, x + 2, 1)
eq = x / (x + 1 / x)
assert gcd_terms(eq, fraction=False) == eq
def test_Singleton():
global instantiated
instantiated = 0
class MyNewSingleton(Basic, metaclass=Singleton):
def __new__(cls):
global instantiated
instantiated += 1
return Basic.__new__(cls)
assert instantiated == 0
MyNewSingleton() # force instantiation
assert instantiated == 1
assert MyNewSingleton() is not Basic()
assert MyNewSingleton() is MyNewSingleton()
assert S.MyNewSingleton is MyNewSingleton()
assert instantiated == 1
class MySingletonSub(MyNewSingleton):
pass
assert instantiated == 1
MySingletonSub()
assert instantiated == 2
assert MySingletonSub() is not MyNewSingleton()
assert MySingletonSub() is MySingletonSub()
def __new__(cls, mat):
if not mat.is_Matrix:
raise TypeError("input to Trace, %s, is not a matrix" % str(mat))
if not mat.is_square:
raise ShapeError("Trace of a non-square matrix")
return Basic.__new__(cls, mat)
def __new__(cls, mat):
mat = sympify(mat)
if not mat.is_Matrix:
raise TypeError("Input to Determinant, %s, not a matrix" % str(mat))
if not mat.is_square:
raise ShapeError("Det of a non-square matrix")
return Basic.__new__(cls, mat)
def test_styleof():
styles = [(Basic, {
'color': 'blue',
'shape': 'ellipse'
}), (Expr, {
'color': 'black'
})]
assert styleof(Basic(1), styles) == {'color': 'blue', 'shape': 'ellipse'}
assert styleof(x + 1, styles) == {'color': 'black', 'shape': 'ellipse'}
def _new(cls, *args, **kwargs):
shape, flat_list = cls._handle_ndarray_creation_inputs(*args, **kwargs)
shape = Tuple(*map(_sympify, shape))
flat_list = flatten(flat_list)
flat_list = Tuple(*flat_list)
self = Basic.__new__(cls, flat_list, shape, **kwargs)
self._shape = shape
self._array = tuple(flat_list)
self._rank = len(shape)
self._loop_size = functools.reduce(lambda x, y: x * y,
shape) if shape else 0
return self
def __new__(cls, parent, rowslice, colslice):
rowslice = normalize(rowslice, parent.shape[0])
colslice = normalize(colslice, parent.shape[1])
if not (len(rowslice) == len(colslice) == 3):
raise IndexError()
if ((0 > rowslice[0]) is S.true
or (parent.shape[0] < rowslice[1]) is S.true
or (0 > colslice[0]) is S.true
or (parent.shape[1] < colslice[1]) is S.true):
raise IndexError()
if isinstance(parent, MatrixSlice):
return mat_slice_of_slice(parent, rowslice, colslice)
return Basic.__new__(cls, parent, Tuple(*rowslice), Tuple(*colslice))
def __new__(cls, domain, condition):
if condition is True:
return domain
cond = rv_subs(condition)
# Check that we aren't passed a condition like die1 == z
# where 'z' is a symbol that we don't know about
# We will never be able to test this equality through iteration
if not cond.free_symbols.issubset(domain.free_symbols):
raise ValueError(
'Condition "%s" contains foreign symbols \n%s.\n' %
(condition, tuple(cond.free_symbols - domain.free_symbols)) +
"Will be unable to iterate using this condition")
return Basic.__new__(cls, domain, cond)
def test_Idx_construction():
i, a = symbols('i a', integer=True)
assert Idx(i) != Idx(i, 1)
assert Idx(i, a) == Idx(i, (0, a - 1))
assert Idx(i, oo) == Idx(i, (0, oo))
pytest.raises(TypeError, lambda: Idx(x))
pytest.raises(TypeError, lambda: Idx(0.5))
pytest.raises(TypeError, lambda: Idx(i, x))
pytest.raises(TypeError, lambda: Idx(i, 0.5))
pytest.raises(TypeError, lambda: Idx(i, (x, 5)))
pytest.raises(TypeError, lambda: Idx(i, (2, x)))
pytest.raises(TypeError, lambda: Idx(i, (2, 3.5)))
pytest.raises(ValueError, lambda: Idx(i, (1, 2, 3)))
pytest.raises(TypeError, lambda: Idx(i, Basic()))
def test_sympyissue_6100():
assert x**1.0 != x
assert x != x**1.0
assert true != x**1.0
assert x**1.0 is not True
assert x is not True
assert x * y != (x * y)**1.0
assert (x**1.0)**1.0 != x
assert (x**1.0)**2.0 == x**2
b = Basic()
assert Pow(b, 1.0, evaluate=False) != b
# if the following gets distributed as a Mul (x**1.0*y**1.0 then
# __eq__ methods could be added to Symbol and Pow to detect the
# power-of-1.0 case.
assert isinstance((x * y)**1.0, Pow)
def test_subs():
assert b21.subs({b2: b1}) == Basic(b1, b1)
assert b21.subs({b2: b21}) == Basic(b21, b1)
assert b3.subs({b2: b1}) == b2
assert b21.subs([(b2, b1), (b1, b2)]) == Basic(b2, b2)
assert b21.subs({b1: b2, b2: b1}) == Basic(b2, b2)
pytest.raises(ValueError, lambda: b21.subs('bad arg'))
pytest.raises(ValueError, lambda: b21.subs(b1, b2, b3))
assert b21.subs(collections.ChainMap({b1: b2}, {b2: b1})) == Basic(b2, b2)
assert b21.subs(collections.OrderedDict([(b2, b1), (b1, b2)])) == Basic(b2, b2)
def __new__(cls, *domains):
symbols = sumsets([domain.symbols for domain in domains])
# Flatten any product of products
domains2 = []
for domain in domains:
if not domain.is_ProductDomain:
domains2.append(domain)
else:
domains2.extend(domain.domains)
domains2 = FiniteSet(*domains2)
if all(domain.is_Finite for domain in domains2):
from diofant.stats.frv import ProductFiniteDomain
cls = ProductFiniteDomain
if all(domain.is_Continuous for domain in domains2):
from diofant.stats.crv import ProductContinuousDomain
cls = ProductContinuousDomain
return Basic.__new__(cls, *domains2)
def test_preorder_traversal():
expr = Basic(b21, b3)
assert list(
preorder_traversal(expr)) == [expr, b21, b2, b1, b1, b3, b2, b1]
assert list(preorder_traversal(('abc', ('d', 'ef')))) == [
('abc', ('d', 'ef')), 'abc', ('d', 'ef'), 'd', 'ef']
result = []
pt = preorder_traversal(expr)
for i in pt:
result.append(i)
if i == b2:
pt.skip()
assert result == [expr, b21, b2, b1, b3, b2]
expr = z + w*(x + y)
assert list(preorder_traversal([expr], keys=default_sort_key)) == \
[[w*(x + y) + z], w*(x + y) + z, z, w*(x + y), w, x + y, x, y]
assert list(preorder_traversal((x + y)*z, keys=True)) == \
[z*(x + y), z, x + y, x, y]
def __new__(cls, *spaces):
rs_space_dict = {}
for space in spaces:
for value in space.values:
rs_space_dict[value] = space
symbols = FiniteSet(*[val.symbol for val in rs_space_dict.keys()])
# Overlapping symbols
if len(symbols) < sum(len(space.symbols) for space in spaces):
raise ValueError("Overlapping Random Variables")
if all(space.is_Finite for space in spaces):
from diofant.stats.frv import ProductFinitePSpace
cls = ProductFinitePSpace
if all(space.is_Continuous for space in spaces):
from diofant.stats.crv import ProductContinuousPSpace
cls = ProductContinuousPSpace
obj = Basic.__new__(cls, *FiniteSet(*spaces))
return obj
def test_unpack():
assert unpack(Basic(2)) == 2
assert unpack(Basic(2, 3)) == Basic(2, 3)
def test_flatten():
assert flatten(Basic(1, 2, Basic(3, 4))) == Basic(1, 2, 3, 4)
def __new__(cls, rows, cols, lamda):
rows, cols = sympify(rows), sympify(cols)
return Basic.__new__(cls, rows, cols, lamda)
def __new__(cls):
global instantiated
instantiated += 1
return Basic.__new__(cls)
"""This tests the basic submodule with (ideally) no reference to subclasses."""
import collections
import pytest
from diofant import (Add, Atom, Basic, Function, I, Integral, Lambda, cos,
default_sort_key, exp, gamma, preorder_traversal, sin)
from diofant.abc import w, x, y, z
from diofant.core.singleton import S
from diofant.core.singleton import SingletonWithManagedProperties as Singleton
__all__ = ()
b1 = Basic()
b2 = Basic(b1)
b3 = Basic(b2)
b21 = Basic(b2, b1)
def test_structure():
assert b21.args == (b2, b1)
assert b21.func(*b21.args) == b21
assert bool(b1)
def test_equality():
# pylint: disable=unneeded-not
instances = [b1, b2, b3, b21, Basic(b1, b1, b1), Basic]
for i, b_i in enumerate(instances):
for j, b_j in enumerate(instances):
def __new__(cls, name, antisym, **kwargs):
obj = Basic.__new__(cls, name, antisym, **kwargs)
obj.name = name
obj.antisym = antisym
return obj
def test_sort():
assert sort(str)(Basic(3, 1, 2)) == Basic(1, 2, 3)
def test_rm_id():
rmzeros = rm_id(lambda x: x == 0)
assert rmzeros(Basic(0, 1)) == Basic(1)
assert rmzeros(Basic(0, 0)) == Basic(0)
assert rmzeros(Basic(2, 1)) == Basic(2, 1)
def __new__(cls, *args):
args = list(map(sympify, args))
return Basic.__new__(cls, *args)
def __new__(cls, density):
density = Dict(density)
return Basic.__new__(cls, density)
def __new__(cls, symbol, set):
if not isinstance(set, FiniteSet):
set = FiniteSet(*set)
return Basic.__new__(cls, symbol, set)