def test_list():
assert sstr([x]) == "[x]"
assert str([x]) == "[Symbol('x')]"
assert sstr([x**2, x*y + 1]) == "[x**2, x*y + 1]"
assert str([x**2, x*y + 1]) == "[Pow(Symbol('x'), Integer(2)), Add(Mul(Symbol('x'), Symbol('y')), Integer(1))]"
assert sstr([x**2, [y + x]]) == "[x**2, [x + y]]"
assert str([x**2, [y + x]]) == "[Pow(Symbol('x'), Integer(2)), [Add(Symbol('x'), Symbol('y'))]]"
def test_Differential():
tp = TensorProduct(R2.dx, R2.dy)
assert sstr(LieDerivative(R2.e_x, tp)) == 'LieDerivative(e_x, TensorProduct(dx, dy))'
g = Function('g')
s_field = g(R2.x, R2.y)
assert sstr(Differential(s_field)) == 'd(g(x, y))'
def test_Dict():
assert str(Dict({1: 1 + x})) == sstr({1: 1 + x}) == "{1: x + 1}"
assert str(Dict({
1: x**2,
2: y * x
})) in ("{1: x**2, 2: x*y}", "{2: x*y, 1: x**2}")
assert sstr(Dict({1: x**2, 2: y * x})) == "{1: x**2, 2: x*y}"
def test_set():
assert sstr(set()) == 'set()'
assert sstr(frozenset()) == 'frozenset()'
assert sstr({1, 2, 3}) == '{1, 2, 3}'
assert sstr(frozenset({1, 2, 3})) == 'frozenset({1, 2, 3})'
assert sstr({1, x, x**2, x**3, x**4}) == '{1, x, x**2, x**3, x**4}'
def test_sstrrepr():
assert sstr('abc') == 'abc'
assert sstrrepr('abc') == "'abc'"
e = ['a', 'b', 'c', x]
assert sstr(e) == "[a, b, c, x]"
assert sstrrepr(e) == "['a', 'b', 'c', x]"
def test_sstrrepr():
assert sstr('abc') == 'abc'
assert sstrrepr('abc') == "'abc'"
e = ['a', 'b', 'c', x]
assert sstr(e) == "[a, b, c, x]"
assert sstrrepr(e) == "['a', 'b', 'c', x]"
def test_tuple():
assert sstr((x,)) == "(x,)"
assert str((x,)) == "(Symbol('x'),)"
assert sstr((x + y, 1 + x)) == "(x + y, x + 1)"
assert str((x + y, 1 + x)) == "(Add(Symbol('x'), Symbol('y')), Add(Symbol('x'), Integer(1)))"
assert sstr((x + y, (1 + x, x**2))) == "(x + y, (x + 1, x**2))"
assert str((x + y, (1 + x, x**2))) == "(Add(Symbol('x'), Symbol('y')), (Add(Symbol('x'), Integer(1)), Pow(Symbol('x'), Integer(2))))"
def test_list():
assert sstr([x]) == "[x]"
assert str([x]) == "[Symbol('x')]"
assert sstr([x**2, x*y + 1]) == "[x**2, x*y + 1]"
assert str([x**2, x*y + 1]) == "[Pow(Symbol('x'), Integer(2)), Add(Mul(Symbol('x'), Symbol('y')), Integer(1))]"
assert sstr([x**2, [y + x]]) == "[x**2, [x + y]]"
assert str([x**2, [y + x]]) == "[Pow(Symbol('x'), Integer(2)), [Add(Symbol('x'), Symbol('y'))]]"
def test_Differential():
tp = TensorProduct(R2.dx, R2.dy)
assert sstr(LieDerivative(R2.e_x, tp)) == 'LieDerivative(e_x, TensorProduct(dx, dy))'
g = Function('g')
s_field = g(R2.x, R2.y)
assert sstr(Differential(s_field)) == 'd(g(x, y))'
def test_tuple():
assert sstr((x,)) == "(x,)"
assert str((x,)) == "(Symbol('x'),)"
assert sstr((x + y, 1 + x)) == "(x + y, x + 1)"
assert str((x + y, 1 + x)) == "(Add(Symbol('x'), Symbol('y')), Add(Symbol('x'), Integer(1)))"
assert sstr((x + y, (1 + x, x**2))) == "(x + y, (x + 1, x**2))"
assert str((x + y, (1 + x, x**2))) == "(Add(Symbol('x'), Symbol('y')), (Add(Symbol('x'), Integer(1)), Pow(Symbol('x'), Integer(2))))"
def test_noncommutative():
A, B, C = symbols('A,B,C', commutative=False)
assert sstr(A*B*C**-1) == "A*B*C**(-1)"
assert sstr(C**-1*A*B) == "C**(-1)*A*B"
assert sstr(A*C**-1*B) == "A*C**(-1)*B"
assert sstr(sqrt(A)) == "sqrt(A)"
assert sstr(1/sqrt(A)) == "A**(-1/2)"
def test_set():
assert sstr(set()) == 'set()'
assert sstr(frozenset()) == 'frozenset()'
assert sstr({1, 2, 3}) == '{1, 2, 3}'
assert sstr(frozenset({1, 2, 3})) == 'frozenset({1, 2, 3})'
assert sstr(
{1, x, x**2, x**3, x**4}) == '{1, x, x**2, x**3, x**4}'
def test_noncommutative():
A, B, C = symbols('A,B,C', commutative=False)
assert sstr(A * B * C**-1) == "A*B*C**(-1)"
assert sstr(C**-1 * A * B) == "C**(-1)*A*B"
assert sstr(A * C**-1 * B) == "A*C**(-1)*B"
assert sstr(sqrt(A)) == "sqrt(A)"
assert sstr(1 / sqrt(A)) == "A**(-1/2)"
def test_intcurve_diffequ():
start_point = R2_r.point([1, 0])
vector_field = -R2.y*R2.e_x + R2.x*R2.e_y
equations, init_cond = intcurve_diffequ(vector_field, t, start_point)
assert sstr(equations) == '[f_1(t) + Derivative(f_0(t), t), -f_0(t) + Derivative(f_1(t), t)]'
assert sstr(init_cond) == '[f_0(0) - 1, f_1(0)]'
equations, init_cond = intcurve_diffequ(vector_field, t, start_point, R2_p)
assert sstr(
equations) == '[Derivative(f_0(t), t), Derivative(f_1(t), t) - 1]'
assert sstr(init_cond) == '[f_0(0) - 1, f_1(0)]'
def test_printmethod():
class R(Abs):
def _diofantstr(self, printer):
return "foo(%s)" % printer._print(self.args[0])
assert sstr(R(x)) == "foo(x)"
class R(Abs):
def _diofantstr(self, printer):
return "foo"
assert sstr(R(x)) == "foo"
def test_dict():
assert sstr({1: 1 + x}) == "{1: x + 1}"
assert str({1: 1 + x}) == "{1: Add(Symbol('x'), Integer(1))}"
assert str({
1: x**2,
2: y * x
}) in (
"{1: Pow(Symbol('x'), Integer(2)), 2: Mul(Symbol('x'), Symbol('y'))}",
"{1: Mul(Symbol('x'), Symbol('y')), 2: Pow(Symbol('x'), Integer(2))}")
assert sstr({1: x**2, 2: y * x}) == "{1: x**2, 2: x*y}"
def test_printmethod():
class R(Abs):
def _diofantstr(self, printer):
return "foo(%s)" % printer._print(self.args[0])
assert sstr(R(x)) == "foo(x)"
class R(Abs):
def _diofantstr(self, printer):
return "foo"
assert sstr(R(x)) == "foo"
def test_Matrix_str():
M = Matrix([[x**+1, 1], [y, x + y]])
assert str(M) == "Matrix([\n[x, 1],\n[y, x + y]])"
assert sstr(M) == "Matrix([\n[x, 1],\n[y, x + y]])"
M = Matrix([[1]])
assert str(M) == sstr(M) == "Matrix([[1]])"
M = Matrix([[1, 2]])
assert str(M) == sstr(M) == "Matrix([[1, 2]])"
M = Matrix()
assert str(M) == sstr(M) == "Matrix(0, 0, [])"
M = Matrix(0, 1, lambda i, j: 0)
assert str(M) == sstr(M) == "Matrix(0, 1, [])"
def test_Matrix_str():
M = Matrix([[x**+1, 1], [y, x + y]])
assert str(M) == "Matrix([\n[x, 1],\n[y, x + y]])"
assert sstr(M) == "Matrix([\n[x, 1],\n[y, x + y]])"
M = Matrix([[1]])
assert str(M) == sstr(M) == "Matrix([[1]])"
M = Matrix([[1, 2]])
assert str(M) == sstr(M) == "Matrix([[1, 2]])"
M = Matrix()
assert str(M) == sstr(M) == "Matrix(0, 0, [])"
M = Matrix(0, 1, lambda i, j: 0)
assert str(M) == sstr(M) == "Matrix(0, 1, [])"
def test_intcurve_diffequ():
start_point = R2_r.point([1, 0])
vector_field = -R2.y*R2.e_x + R2.x*R2.e_y
equations, init_cond = intcurve_diffequ(vector_field, t, start_point)
assert sstr(equations) == '[f_1(t) + Derivative(f_0(t), t), -f_0(t) + Derivative(f_1(t), t)]'
assert sstr(init_cond) == '[f_0(0) - 1, f_1(0)]'
equations, init_cond = intcurve_diffequ(vector_field, t, start_point, R2_p)
assert sstr(
equations) == '[Derivative(f_0(t), t), Derivative(f_1(t), t) - 1]'
assert sstr(init_cond) == '[f_0(0) - 1, f_1(0)]'
start_point = R2_r.point([x, y])
vector_field = R2_r.e_x
assert intcurve_series(vector_field, t, start_point,
n=3) == Matrix([[t + x], [y]])
def __repr__(self):
lines = sstr(self._diofant_matrix()).split('\n')
t = " : %s -> %s" % (self.domain, self.codomain)
s = ' ' * len(t)
n = len(lines)
for i in range(n // 2):
lines[i] += s
lines[n // 2] += t
for i in range(n // 2 + 1, n):
lines[i] += s
return '\n'.join(lines)
def test_full_prec():
assert sstr(Float(0.3), full_prec=True) == "0.300000000000000"
assert sstr(Float(0.3), full_prec="auto") == "0.300000000000000"
assert sstr(Float(0.3), full_prec=False) == "0.3"
assert sstr(Float(0.3) * x, full_prec=True) in [
"0.300000000000000*x", "x*0.300000000000000"
]
assert sstr(Float(0.3) * x, full_prec="auto") in ["0.3*x", "x*0.3"]
assert sstr(Float(0.3) * x, full_prec=False) in ["0.3*x", "x*0.3"]
def test_Permutation_Cycle():
# general principle: economically, canonically show all moved elements
# and the size of the permutation.
for p, s in [
(Cycle(), 'Cycle()'),
(Cycle(2), 'Cycle(2)'),
(Cycle(2, 1), 'Cycle(1, 2)'),
(Cycle(1, 2)(5)(6, 7)(10), 'Cycle(1, 2)(6, 7)(10)'),
(Cycle(3, 4)(1, 2)(3, 4), 'Cycle(1, 2)(4)'),
]:
assert str(p) == s
Permutation.print_cyclic = False
for p, s in [
(Permutation([]), 'Permutation([])'),
(Permutation([], size=1), 'Permutation([0])'),
(Permutation([], size=2), 'Permutation([0, 1])'),
(Permutation([], size=10), 'Permutation([], size=10)'),
(Permutation([1, 0, 2]), 'Permutation([1, 0, 2])'),
(Permutation([1, 0, 2, 3, 4, 5]), 'Permutation([1, 0], size=6)'),
(Permutation([1, 0, 2, 3, 4, 5],
size=10), 'Permutation([1, 0], size=10)'),
]:
assert str(p) == s
Permutation.print_cyclic = True
for p, s in [
(Permutation([]), 'Permutation()'),
(Permutation([], size=1), 'Permutation(0)'),
(Permutation([], size=2), 'Permutation(1)'),
(Permutation([], size=10), 'Permutation(9)'),
(Permutation([1, 0, 2]), 'Permutation(2)(0, 1)'),
(Permutation([1, 0, 2, 3, 4, 5]), 'Permutation(5)(0, 1)'),
(Permutation([1, 0, 2, 3, 4, 5], size=10), 'Permutation(9)(0, 1)'),
(Permutation([0, 1, 3, 2, 4, 5], size=10), 'Permutation(9)(2, 3)'),
]:
assert str(p) == s
assert str(AbelianGroup(3, 4)) == ("PermutationGroup([\n "
"Permutation(6)(0, 1, 2),\n"
" Permutation(3, 4, 5, 6)])")
assert sstr(Cycle(1, 2)) == repr(Cycle(1, 2))
def test_full_prec():
assert sstr(Float(0.3), full_prec=True) == "0.300000000000000"
assert sstr(Float(0.3), full_prec="auto") == "0.300000000000000"
assert sstr(Float(0.3), full_prec=False) == "0.3"
assert sstr(Float(0.3)*x, full_prec=True) in [
"0.300000000000000*x",
"x*0.300000000000000"
]
assert sstr(Float(0.3)*x, full_prec="auto") in [
"0.3*x",
"x*0.3"
]
assert sstr(Float(0.3)*x, full_prec=False) in [
"0.3*x",
"x*0.3"
]
def test_PrettyPoly():
F = QQ.frac_field(x, y)
R = QQ.poly_ring(x, y)
assert sstr(F.convert(x / (x + y))) == sstr(x / (x + y))
assert sstr(R.convert(x + y)) == sstr(x + y)
def test_infinity():
assert sstr(oo * I) == "oo*I"
def test_SparseMatrix():
M = SparseMatrix([[x**+1, 1], [y, x + y]])
assert str(M) == "Matrix([\n[x, 1],\n[y, x + y]])"
assert sstr(M) == "Matrix([\n[x, 1],\n[y, x + y]])"
def test_SparseMatrix():
M = SparseMatrix([[x**+1, 1], [y, x + y]])
assert str(M) == "Matrix([\n[x, 1],\n[y, x + y]])"
assert sstr(M) == "Matrix([\n[x, 1],\n[y, x + y]])"
def test_infinity():
assert sstr(oo*I) == "oo*I"
def test_DMP():
assert sstr(DMP([[0], [], [0, 1, 2], [3]], ZZ)) == 'DMP([[1, 2], [3]], ZZ)'
def test_Geometry():
assert sstr(Point(0, 0)) == 'Point2D(0, 0)'
assert sstr(Circle(Point(0, 0), 3)) == 'Circle(Point2D(0, 0), 3)'
def test_PrettyPoly():
from diofant.polys.domains import QQ
F = QQ.frac_field(x, y)
R = QQ[x, y]
assert sstr(F.convert(x / (x + y))) == sstr(x / (x + y))
assert sstr(R.convert(x + y)) == sstr(x + y)
def test_Permutation_Cycle():
# general principle: economically, canonically show all moved elements
# and the size of the permutation.
for p, s in [
(Cycle(),
'Cycle()'),
(Cycle(2),
'Cycle(2)'),
(Cycle(2, 1),
'Cycle(1, 2)'),
(Cycle(1, 2)(5)(6, 7)(10),
'Cycle(1, 2)(6, 7)(10)'),
(Cycle(3, 4)(1, 2)(3, 4),
'Cycle(1, 2)(4)'),
]:
assert str(p) == s
Permutation.print_cyclic = False
for p, s in [
(Permutation([]),
'Permutation([])'),
(Permutation([], size=1),
'Permutation([0])'),
(Permutation([], size=2),
'Permutation([0, 1])'),
(Permutation([], size=10),
'Permutation([], size=10)'),
(Permutation([1, 0, 2]),
'Permutation([1, 0, 2])'),
(Permutation([1, 0, 2, 3, 4, 5]),
'Permutation([1, 0], size=6)'),
(Permutation([1, 0, 2, 3, 4, 5], size=10),
'Permutation([1, 0], size=10)'),
]:
assert str(p) == s
Permutation.print_cyclic = True
for p, s in [
(Permutation([]),
'Permutation()'),
(Permutation([], size=1),
'Permutation(0)'),
(Permutation([], size=2),
'Permutation(1)'),
(Permutation([], size=10),
'Permutation(9)'),
(Permutation([1, 0, 2]),
'Permutation(2)(0, 1)'),
(Permutation([1, 0, 2, 3, 4, 5]),
'Permutation(5)(0, 1)'),
(Permutation([1, 0, 2, 3, 4, 5], size=10),
'Permutation(9)(0, 1)'),
(Permutation([0, 1, 3, 2, 4, 5], size=10),
'Permutation(9)(2, 3)'),
]:
assert str(p) == s
assert str(AbelianGroup(3, 4)) == ("PermutationGroup([\n "
"Permutation(6)(0, 1, 2),\n"
" Permutation(3, 4, 5, 6)])")
assert sstr(Cycle(1, 2)) == repr(Cycle(1, 2))
def test_settings():
pytest.raises(TypeError, lambda: sstr(Integer(4), method="garbage"))
def test_Dict():
assert str(Dict({1: 1 + x})) == sstr({1: 1 + x}) == "{1: x + 1}"
assert str(Dict({1: x**2, 2: y*x})) in (
"{1: x**2, 2: x*y}", "{2: x*y, 1: x**2}")
assert sstr(Dict({1: x**2, 2: y*x})) == "{1: x**2, 2: x*y}"
def test_dict():
assert sstr({1: 1 + x}) == "{1: x + 1}"
assert str({1: 1 + x}) == "{1: Add(Symbol('x'), Integer(1))}"
assert str({1: x**2, 2: y*x}) in ("{1: Pow(Symbol('x'), Integer(2)), 2: Mul(Symbol('x'), Symbol('y'))}", "{1: Mul(Symbol('x'), Symbol('y')), 2: Pow(Symbol('x'), Integer(2))}")
assert sstr({1: x**2, 2: y*x}) == "{1: x**2, 2: x*y}"
def test_PrettyPoly():
F = QQ.frac_field(x, y)
R = QQ.poly_ring(x, y)
assert sstr(F.convert(x/(x + y))) == sstr(x/(x + y))
assert sstr(R.convert(x + y)) == sstr(x + y)
def __str__(self):
"""String representation of a GeometryEntity."""
from diofant.printing import sstr
return type(self).__name__ + sstr(self.args)
def test_settings():
pytest.raises(TypeError, lambda: sstr(Integer(4), method="garbage"))
def test_ImmutableDenseNDimArray():
m = [2 * i + j for i in range(2) for j in range(2)]
assert sstr(ImmutableDenseNDimArray(m, (2, 2))) == '[[0, 1], [2, 3]]'
def test_true_false():
assert str(true) == repr(true) == sstr(true) == "true"
assert str(false) == repr(false) == sstr(false) == "false"
def test_Geometry():
assert sstr(Point(0, 0)) == 'Point2D(0, 0)'
assert sstr(Circle(Point(0, 0), 3)) == 'Circle(Point2D(0, 0), 3)'
def test_ImmutableDenseNDimArray():
m = [2*i + j for i in range(2) for j in range(2)]
assert sstr(ImmutableDenseNDimArray(m, (2, 2))) == '[[0, 1], [2, 3]]'
def test_true_false():
assert str(true) == repr(true) == sstr(true) == "true"
assert str(false) == repr(false) == sstr(false) == "false"