def test_s_input():
expr = Basic(1, 2)
a, b = map(ExprWild, 'ab')
pattern = Basic(a, b)
assert list(unify(expr, pattern, {})) == [{a: 1, b: 2}]
assert list(unify(expr, pattern, {a: 5})) == []
def test_bottom_up_once():
bottom_rl = bottom_up_once(rl)
assert bottom_rl(Basic(1, 2, Basic(3, 4))) == \
Basic(1, 2, Basic2(3, 4))
def test_construct():
expr = Compound(Basic, (1, 2, 3))
expected = Basic(1, 2, 3)
assert construct(expr) == expected
def test_unify_variables():
assert list(unify(Basic(1, 2), Basic(1, x), {}, variables=(x, ))) == [{
x: 2
}]
def _test_global_traversal(trav):
x, y, z = symbols('x,y,z')
zero_all_symbols = trav(zero_symbols)
assert zero_all_symbols(Basic(x, y, Basic(x, z))) == \
Basic(0, 0, Basic(0, 0))
def test_zero_ints():
expr = Basic(2, Basic(5, 3), 8)
expected = set([Basic(0, Basic(0, 0), 0)])
brl = canon(posdec)
assert set(brl(expr)) == expected
def test_18778():
raises(TypeError, lambda: is_le(Basic(), Basic()))
raises(TypeError, lambda: is_gt(Basic(), Basic()))
raises(TypeError, lambda: is_ge(Basic(), Basic()))
raises(TypeError, lambda: is_lt(Basic(), Basic()))
def test_arguments():
"""Functions accepting `Point` objects in `geometry`
should also accept tuples and lists and
automatically convert them to points."""
singles2d = ((1, 2), [1, 2], Point(1, 2))
singles2d2 = ((1, 3), [1, 3], Point(1, 3))
doubles2d = cartes(singles2d, singles2d2)
p2d = Point2D(1, 2)
singles3d = ((1, 2, 3), [1, 2, 3], Point(1, 2, 3))
doubles3d = subsets(singles3d, 2)
p3d = Point3D(1, 2, 3)
singles4d = ((1, 2, 3, 4), [1, 2, 3, 4], Point(1, 2, 3, 4))
doubles4d = subsets(singles4d, 2)
p4d = Point(1, 2, 3, 4)
# test 2D
test_single = [
'distance', 'is_scalar_multiple', 'taxicab_distance', 'midpoint',
'intersection', 'dot', 'equals', '__add__', '__sub__'
]
test_double = ['is_concyclic', 'is_collinear']
for p in singles2d:
Point2D(p)
for func in test_single:
for p in singles2d:
getattr(p2d, func)(p)
for func in test_double:
for p in doubles2d:
getattr(p2d, func)(*p)
# test 3D
test_double = ['is_collinear']
for p in singles3d:
Point3D(p)
for func in test_single:
for p in singles3d:
getattr(p3d, func)(p)
for func in test_double:
for p in doubles3d:
getattr(p3d, func)(*p)
# test 4D
test_double = ['is_collinear']
for p in singles4d:
Point(p)
for func in test_single:
for p in singles4d:
getattr(p4d, func)(p)
for func in test_double:
for p in doubles4d:
getattr(p4d, func)(*p)
# test evaluate=False for ops
x = Symbol('x')
a = Point(0, 1)
assert a + (0.1, x) == Point(0.1, 1 + x, evaluate=False)
a = Point(0, 1)
assert a / 10.0 == Point(0, 0.1, evaluate=False)
a = Point(0, 1)
assert a * 10.0 == Point(0.0, 10.0, evaluate=False)
# test evaluate=False when changing dimensions
u = Point(.1, .2, evaluate=False)
u4 = Point(u, dim=4, on_morph='ignore')
assert u4.args == (.1, .2, 0, 0)
assert all(i.is_Float for i in u4.args[:2])
# and even when *not* changing dimensions
assert all(i.is_Float for i in Point(u).args)
# never raise error if creating an origin
assert Point(dim=3, on_morph='error')
# raise error with unmatched dimension
raises(ValueError, lambda: Point(1, 1, dim=3, on_morph='error'))
# test unknown on_morph
raises(ValueError, lambda: Point(1, 1, dim=3, on_morph='unknown'))
# test invalid expressions
raises(TypeError, lambda: Point(Basic(), Basic()))
def test_simple_variables():
rl = rewriterule(Basic(x, 1), Basic(x, 2), variables=(x, ))
assert list(rl(Basic(3, 1))) == [Basic(3, 2)]
rl = rewriterule(x**2, x**3, variables=(x, ))
assert list(rl(y**2)) == [y**3]
def test_top_down_big_tree():
expr = Basic(1, Basic(2), Basic(3, Basic(4), 5))
expected = Basic(2, Basic(3), Basic(4, Basic(5), 6))
brl = top_down(inc)
assert set(brl(expr)) == set([expected])
def test_top_down_easy():
expr = Basic(1, 2)
expected = Basic(2, 3)
brl = top_down(inc)
assert set(brl(expr)) == set([expected])
def test_count_ops_visual():
ADD, MUL, POW, SIN, COS, EXP, AND, D, G = symbols(
'Add Mul Pow sin cos exp And Derivative Integral'.upper())
DIV, SUB, NEG = symbols('DIV SUB NEG')
def count(val):
return count_ops(val, visual=True)
assert count(7) is S.Zero
assert count(S(7)) is S.Zero
assert count(-1) == NEG
assert count(-2) == NEG
assert count(S(2) / 3) == DIV
assert count(pi / 3) == DIV
assert count(-pi / 3) == DIV + NEG
assert count(I - 1) == SUB
assert count(1 - I) == SUB
assert count(1 - 2 * I) == SUB + MUL
assert count(x) is S.Zero
assert count(-x) == NEG
assert count(-2 * x / 3) == NEG + DIV + MUL
assert count(1 / x) == DIV
assert count(1 / (x * y)) == DIV + MUL
assert count(-1 / x) == NEG + DIV
assert count(-2 / x) == NEG + DIV
assert count(x / y) == DIV
assert count(-x / y) == NEG + DIV
assert count(x**2) == POW
assert count(-x**2) == POW + NEG
assert count(-2 * x**2) == POW + MUL + NEG
assert count(x + pi / 3) == ADD + DIV
assert count(x + S(1) / 3) == ADD + DIV
assert count(x + y) == ADD
assert count(x - y) == SUB
assert count(y - x) == SUB
assert count(-1 / (x - y)) == DIV + NEG + SUB
assert count(-1 / (y - x)) == DIV + NEG + SUB
assert count(1 + x**y) == ADD + POW
assert count(1 + x + y) == 2 * ADD
assert count(1 + x + y + z) == 3 * ADD
assert count(1 + x**y + 2 * x * y + y**2) == 3 * ADD + 2 * POW + 2 * MUL
assert count(2 * z + y + x + 1) == 3 * ADD + MUL
assert count(2 * z + y**17 + x + 1) == 3 * ADD + MUL + POW
assert count(2 * z + y**17 + x + sin(x)) == 3 * ADD + POW + MUL + SIN
assert count(2 * z + y**17 + x +
sin(x**2)) == 3 * ADD + MUL + 2 * POW + SIN
assert count(2 * z + y**17 + x + sin(x**2) +
exp(cos(x))) == 4 * ADD + MUL + 2 * POW + EXP + COS + SIN
assert count(Derivative(x, x)) == D
assert count(Integral(x, x) + 2 * x / (1 + x)) == G + DIV + MUL + 2 * ADD
assert count(Basic()) is S.Zero
assert count({x + 1: sin(x)}) == ADD + SIN
assert count([x + 1, sin(x) + y, None]) == ADD + SIN + ADD
assert count({x + 1: sin(x), y: cos(x) + 1}) == SIN + COS + 2 * ADD
assert count({}) is S.Zero
assert count([x + 1, sin(x) * y, None]) == SIN + ADD + MUL
assert count([]) is S.Zero
assert count(And(x, y, z)) == 2 * AND
assert count(Basic(x, x + y)) == ADD
# is this right or should we count the Eq, too...like an Add?
assert count(Eq(x + y, S(2))) == ADD
def test_sympy__core__basic__Basic():
from sympy.core.basic import Basic
assert _test_args(Basic())
def test_deconstruct():
expr = Basic(1, 2, 3)
expected = Compound(Basic, (1, 2, 3))
assert deconstruct(expr) == expected
def test_purestr():
assert purestr(Symbol('x')) == "Symbol(x)"
assert purestr(Basic(1, 2)) == "Basic(1, 2)"
def test_flatten():
assert flatten(Basic(1, 2, Basic(3, 4))) == Basic(1, 2, 3, 4)
def test_print_basic():
expr = Basic(1, 2)
assert mpp.doprint(expr) == '<mrow><mi>basic</mi><mfenced><mn>1</mn><mn>2</mn></mfenced></mrow>'
assert mp.doprint(expr) == '<basic><cn>1</cn><cn>2</cn></basic>'
def test_unpack():
assert unpack(Basic(2)) == 2
assert unpack(Basic(2, 3)) == Basic(2, 3)
def test_split5():
expr = Basic(2, Basic(5, 3), 8)
expected = set([Basic(0, Basic(0, 0), 10), Basic(0, Basic(10, 0), 10)])
brl = canon(branch5)
assert set(brl(expr)) == expected
def test_sort():
assert sort(str)(Basic(3, 1, 2)) == Basic(1, 2, 3)
def test_count_ops_visual():
ADD, MUL, POW, SIN, COS, EXP, AND, D, G = symbols(
'Add Mul Pow sin cos exp And Derivative Integral'.upper())
DIV, SUB, NEG = symbols('DIV SUB NEG')
NOT, OR, AND, XOR, IMPLIES, EQUIVALENT, ITE, BASIC, TUPLE = symbols(
'Not Or And Xor Implies Equivalent ITE Basic Tuple'.upper())
def count(val):
return count_ops(val, visual=True)
assert count(7) is S.Zero
assert count(S(7)) is S.Zero
assert count(-1) == NEG
assert count(-2) == NEG
assert count(S(2) / 3) == DIV
assert count(pi / 3) == DIV
assert count(-pi / 3) == DIV + NEG
assert count(I - 1) == SUB
assert count(1 - I) == SUB
assert count(1 - 2 * I) == SUB + MUL
assert count(x) is S.Zero
assert count(-x) == NEG
assert count(-2 * x / 3) == NEG + DIV + MUL
assert count(1 / x) == DIV
assert count(1 / (x * y)) == DIV + MUL
assert count(-1 / x) == NEG + DIV
assert count(-2 / x) == NEG + DIV
assert count(x / y) == DIV
assert count(-x / y) == NEG + DIV
assert count(x**2) == POW
assert count(-x**2) == POW + NEG
assert count(-2 * x**2) == POW + MUL + NEG
assert count(x + pi / 3) == ADD + DIV
assert count(x + S(1) / 3) == ADD + DIV
assert count(x + y) == ADD
assert count(x - y) == SUB
assert count(y - x) == SUB
assert count(-1 / (x - y)) == DIV + NEG + SUB
assert count(-1 / (y - x)) == DIV + NEG + SUB
assert count(1 + x**y) == ADD + POW
assert count(1 + x + y) == 2 * ADD
assert count(1 + x + y + z) == 3 * ADD
assert count(1 + x**y + 2 * x * y + y**2) == 3 * ADD + 2 * POW + 2 * MUL
assert count(2 * z + y + x + 1) == 3 * ADD + MUL
assert count(2 * z + y**17 + x + 1) == 3 * ADD + MUL + POW
assert count(2 * z + y**17 + x + sin(x)) == 3 * ADD + POW + MUL + SIN
assert count(2 * z + y**17 + x +
sin(x**2)) == 3 * ADD + MUL + 2 * POW + SIN
assert count(2 * z + y**17 + x + sin(x**2) +
exp(cos(x))) == 4 * ADD + MUL + 2 * POW + EXP + COS + SIN
assert count(Derivative(x, x)) == D
assert count(Integral(x, x) + 2 * x / (1 + x)) == G + DIV + MUL + 2 * ADD
assert count(Basic()) is S.Zero
assert count({x + 1: sin(x)}) == ADD + SIN
assert count([x + 1, sin(x) + y, None]) == ADD + SIN + ADD
assert count({x + 1: sin(x), y: cos(x) + 1}) == SIN + COS + 2 * ADD
assert count({}) is S.Zero
assert count([x + 1, sin(x) * y, None]) == SIN + ADD + MUL
assert count([]) is S.Zero
assert count(Basic()) == 0
assert count(Basic(Basic(), Basic(x, x + y))) == ADD + 2 * BASIC
assert count(Basic(x, x + y)) == ADD + BASIC
assert count(Or(x, y)) == OR
assert count(And(x, y)) == AND
assert count(And(x**y, z)) == AND + POW
assert count(Or(x, Or(y, And(z, a)))) == AND + OR
assert count(Nor(x, y)) == NOT + OR
assert count(Nand(x, y)) == NOT + AND
assert count(Xor(x, y)) == XOR
assert count(Implies(x, y)) == IMPLIES
assert count(Equivalent(x, y)) == EQUIVALENT
assert count(ITE(x, y, z)) == ITE
assert count([Or(x, y), And(x, y), Basic(x + y)]) == ADD + AND + BASIC + OR
assert count(Basic(Tuple(x))) == BASIC + TUPLE
#It checks that TUPLE is counted as an operation.
assert count(Eq(x + y, S(2))) == ADD
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 test_s_input():
expr = Basic(1, 2)
a, b = map(Symbol, 'ab')
pattern = Basic(a, b)
assert list(unify(expr, pattern, {}, (a, b))) == [{a: 1, b: 2}]
assert list(unify(expr, pattern, {a: 5}, (a, b))) == []
def test_sort_variable():
vsort = Derivative._sort_variable_count
def vsort0(*v, **kw):
reverse = kw.get('reverse', False)
return [
i[0]
for i in vsort([(i, 0) for i in (reversed(v) if reverse else v)])
]
for R in range(2):
assert vsort0(y, x, reverse=R) == [x, y]
assert vsort0(f(x), x, reverse=R) == [x, f(x)]
assert vsort0(f(y), f(x), reverse=R) == [f(x), f(y)]
assert vsort0(g(x), f(y), reverse=R) == [f(y), g(x)]
assert vsort0(f(x, y), f(x), reverse=R) == [f(x), f(x, y)]
fx = f(x).diff(x)
assert vsort0(fx, y, reverse=R) == [y, fx]
fy = f(y).diff(y)
assert vsort0(fy, fx, reverse=R) == [fx, fy]
fxx = fx.diff(x)
assert vsort0(fxx, fx, reverse=R) == [fx, fxx]
assert vsort0(Basic(x), f(x), reverse=R) == [f(x), Basic(x)]
assert vsort0(Basic(y), Basic(x), reverse=R) == [Basic(x), Basic(y)]
assert vsort0(Basic(y, z), Basic(x),
reverse=R) == [Basic(x), Basic(y, z)]
assert vsort0(fx, x, reverse=R) == [x, fx] if R else [fx, x]
assert vsort0(Basic(x), x, reverse=R) == [x, Basic(x)
] if R else [Basic(x), x]
assert vsort0(Basic(f(x)), f(x), reverse=R) == [
f(x), Basic(f(x))
] if R else [Basic(f(x)), f(x)]
assert vsort0(Basic(x, z), Basic(x), reverse=R) == [
Basic(x), Basic(x, z)
] if R else [Basic(x, z), Basic(x)]
assert vsort([]) == []
assert _aresame(vsort([(x, 1)]), [Tuple(x, 1)])
assert vsort([(x, y), (x, z)]) == [(x, y + z)]
assert vsort([(y, 1), (x, 1 + y)]) == [(x, 1 + y), (y, 1)]
# coverage complete; legacy tests below
assert vsort([(x, 3), (y, 2), (z, 1)]) == [(x, 3), (y, 2), (z, 1)]
assert vsort([(h(x), 1), (g(x), 1), (f(x), 1)]) == [(f(x), 1), (g(x), 1),
(h(x), 1)]
assert vsort([(z, 1), (y, 2), (x, 3), (h(x), 1), (g(x), 1),
(f(x), 1)]) == [(x, 3), (y, 2), (z, 1), (f(x), 1), (g(x), 1),
(h(x), 1)]
assert vsort([(x, 1), (f(x), 1), (y, 1), (f(y), 1)]) == [(x, 1), (y, 1),
(f(x), 1),
(f(y), 1)]
assert vsort([(y, 1), (x, 2), (g(x), 1), (f(x), 1), (z, 1), (h(x), 1),
(y, 2), (x, 1)]) == [(x, 3), (y, 3), (z, 1), (f(x), 1),
(g(x), 1), (h(x), 1)]
assert vsort([(z, 1), (y, 1), (f(x), 1), (x, 1), (f(x), 1),
(g(x), 1)]) == [(x, 1), (y, 1), (z, 1), (f(x), 2), (g(x), 1)]
assert vsort([(z, 1), (y, 2), (f(x), 1), (x, 2), (f(x), 2), (g(x), 1),
(z, 2), (z, 1), (y, 1), (x, 1)]) == [(x, 3), (y, 3), (z, 4),
(f(x), 3), (g(x), 1)]
assert vsort(((y, 2), (x, 1), (y, 1), (x, 1))) == [(x, 2), (y, 3)]
assert isinstance(vsort([(x, 3), (y, 2), (z, 1)])[0], Tuple)
assert vsort([(x, 1), (f(x), 1), (x, 1)]) == [(x, 2), (f(x), 1)]
assert vsort([(y, 2), (x, 3), (z, 1)]) == [(x, 3), (y, 2), (z, 1)]
assert vsort([(h(y), 1), (g(x), 1), (f(x), 1)]) == [(f(x), 1), (g(x), 1),
(h(y), 1)]
assert vsort([(x, 1), (y, 1), (x, 1)]) == [(x, 2), (y, 1)]
assert vsort([(f(x), 1), (f(y), 1), (f(x), 1)]) == [(f(x), 2), (f(y), 1)]
dfx = f(x).diff(x)
self = [(dfx, 1), (x, 1)]
assert vsort(self) == self
assert vsort([(dfx, 1), (y, 1), (f(x), 1), (x, 1), (f(y), 1),
(x, 1)]) == [(y, 1), (f(x), 1), (f(y), 1), (dfx, 1), (x, 2)]
dfy = f(y).diff(y)
assert vsort([(dfy, 1), (dfx, 1)]) == [(dfx, 1), (dfy, 1)]
d2fx = dfx.diff(x)
assert vsort([(d2fx, 1), (dfx, 1)]) == [(dfx, 1), (d2fx, 1)]
def test_top_down_once():
top_rl = top_down_once(rl)
assert top_rl(Basic(1, 2, Basic(3, 4))) == \
Basic2(1, 2, Basic(3, 4))
def prop(self):
return Basic()
def test_sall():
zero_onelevel = sall(zero_symbols)
assert zero_onelevel(Basic(x, y, Basic(x, z))) == \
Basic(0, 0, Basic(x, z))
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 test_nested():
expr = Basic(1, Basic(2), 3)
cmpd = Compound(Basic, (1, Compound(Basic, (2,)), 3))
assert deconstruct(expr) == cmpd
assert construct(cmpd) == expr
def test_unify():
expr = Basic(1, 2, 3)
a, b, c = map(ExprWild, 'abc')
pattern = Basic(a, b, c)
assert list(unify(expr, pattern, {})) == [{a: 1, b: 2, c: 3}]
assert list(unify(expr, pattern)) == [{a: 1, b: 2, c: 3}]
