def test_Float():
# NOTE dps is the whole number of decimal digits
assert str(Float('1.23', dps=1 + 2)) == '1.23'
assert str(Float('1.23456789', dps=1 + 8)) == '1.23456789'
assert str(
Float('1.234567890123456789', dps=1 + 18)) == '1.234567890123456789'
assert str(pi.evalf(1 + 2)) == '3.14'
assert str(pi.evalf(1 + 14)) == '3.14159265358979'
assert str(pi.evalf(1 + 64)) == ('3.141592653589793238462643383279'
'5028841971693993751058209749445923')
assert str(pi.round(-1)) == '0.0'
assert str((pi**400 - (pi**400).round(1)).n(2)) == '-0.e+88'
assert sstr(Float("100"), full_prec=False, min=-2, max=2) == '1.0e+2'
assert sstr(Float("100"), full_prec=False, min=-2, max=3) == '100.0'
assert sstr(Float("0.1"), full_prec=False, min=-2, max=3) == '0.1'
assert sstr(Float("0.099"), min=-2, max=3) == '9.90000000000000e-2'
def test_angle_between():
a = Point(1, 2, 3, 4)
b = a.orthogonal_direction
o = a.origin
assert feq(
Line.angle_between(Line(Point(0, 0), Point(1, 1)),
Line(Point(0, 0), Point(5, 0))).evalf(),
pi.evalf() / 4)
assert Line(a, o).angle_between(Line(b, o)) == pi / 2
assert Line3D.angle_between(Line3D(Point3D(0, 0, 0), Point3D(1, 1, 1)),
Line3D(Point3D(0, 0, 0),
Point3D(5, 0, 0))) == acos(sqrt(3) / 3)
def test_fcode_NumberSymbol():
prec = 17
p = FCodePrinter()
assert fcode(
Catalan
) == ' parameter (Catalan = %sd0)\n Catalan' % Catalan.evalf(
prec)
assert fcode(
EulerGamma
) == ' parameter (EulerGamma = %sd0)\n EulerGamma' % EulerGamma.evalf(
prec)
assert fcode(E) == ' parameter (E = %sd0)\n E' % E.evalf(prec)
assert fcode(
GoldenRatio
) == ' parameter (GoldenRatio = %sd0)\n GoldenRatio' % GoldenRatio.evalf(
prec)
assert fcode(
pi) == ' parameter (pi = %sd0)\n pi' % pi.evalf(prec)
assert fcode(
pi,
precision=5) == ' parameter (pi = %sd0)\n pi' % pi.evalf(5)
assert fcode(Catalan,
human=False) == ({(Catalan, p._print(Catalan.evalf(prec)))},
set(), ' Catalan')
assert fcode(EulerGamma, human=False) == ({
(EulerGamma, p._print(EulerGamma.evalf(prec)))
}, set(), ' EulerGamma')
assert fcode(E, human=False) == ({(E, p._print(E.evalf(prec)))}, set(),
' E')
assert fcode(GoldenRatio, human=False) == ({
(GoldenRatio, p._print(GoldenRatio.evalf(prec)))
}, set(), ' GoldenRatio')
assert fcode(pi, human=False) == ({(pi, p._print(pi.evalf(prec)))}, set(),
' pi')
assert fcode(pi,
precision=5, human=False) == ({(pi, p._print(pi.evalf(5)))},
set(), ' pi')
def test_inline_function():
x = symbols('x')
g = implemented_function('g', Lambda(x, 2 * x))
assert fcode(g(x)) == " 2*x"
g = implemented_function('g', Lambda(x, 2 * pi / x))
assert fcode(g(x)) == (" parameter (pi = %sd0)\n"
" 2*pi/x") % pi.evalf(17)
A = IndexedBase('A')
i = Idx('i', symbols('n', integer=True))
g = implemented_function('g', Lambda(x, x * (1 + x) * (2 + x)))
assert fcode(
g(A[i]),
assign_to=A[i]) == (" do i = 1, n\n"
" A(i) = (A(i) + 1)*(A(i) + 2)*A(i)\n"
" end do")
def test_nsolve():
# onedimensional
x = Symbol('x')
assert nsolve(sin(x), 2) - pi.evalf() < 1e-15
assert nsolve(Eq(2 * x, 2), x, -10) == nsolve(2 * x - 2, -10)
# Testing checks on number of inputs
raises(TypeError, lambda: nsolve(Eq(2 * x, 2)))
raises(TypeError, lambda: nsolve(Eq(2 * x, 2), x, 1, 2))
# multidimensional
x1 = Symbol('x1')
x2 = Symbol('x2')
f1 = 3 * x1**2 - 2 * x2**2 - 1
f2 = x1**2 - 2 * x1 + x2**2 + 2 * x2 - 8
f = Matrix((f1, f2)).T
F = lambdify((x1, x2), f.T, modules='mpmath')
for x0 in [(-1, 1), (1, -2), (4, 4), (-4, -4)]:
x = nsolve(f, (x1, x2), x0, tol=1.e-8)
assert mnorm(F(*x), 1) <= 1.e-10
# The Chinese mathematician Zhu Shijie was the very first to solve this
# nonlinear system 700 years ago (z was added to make it 3-dimensional)
x = Symbol('x')
y = Symbol('y')
z = Symbol('z')
f1 = -x + 2 * y
f2 = (x**2 + x * (y**2 - 2) - 4 * y) / (x + 4)
f3 = sqrt(x**2 + y**2) * z
f = Matrix((f1, f2, f3)).T
F = lambdify((x, y, z), f.T, modules='mpmath')
def getroot(x0):
root = nsolve(f, (x, y, z), x0)
assert mnorm(F(*root), 1) <= 1.e-8
return root
assert list(map(round, getroot((1, 1, 1)))) == [2.0, 1.0, 0.0]
assert nsolve([Eq(f1, 0), Eq(f2, 0), Eq(f3, 0)], [x, y, z],
(1, 1, 1)) # just see that it works
a = Symbol('a')
assert abs(
nsolve(1 / (0.001 + a)**3 - 6 /
(0.9 - a)**3, a, 0.3) - mpf('0.31883011387318591')) < 1e-15
def test_issue_8821_highprec_from_str():
s = str(pi.evalf(128))
p = sympify(s)
assert Abs(sin(p)) < 1e-127
def test_mpmath_precision():
mpmath.mp.dps = 100
assert str(lambdify((), pi.evalf(100), 'mpmath')()) == str(pi.evalf(100))
def test_issue_8821_highprec_from_str():
s = str(pi.evalf(128))
p = N(s)
assert Abs(sin(p)) < 1e-15
p = N(s, 64)
assert Abs(sin(p)) < 1e-64
def test_evalf_arguments():
raises(TypeError, lambda: pi.evalf(method="garbage"))
def test_evalf_bugs():
assert NS(sin(1) + exp(-10**10), 10) == NS(sin(1), 10)
assert NS(exp(10**10) + sin(1), 10) == NS(exp(10**10), 10)
assert NS('expand_log(log(1+1/10**50))', 20) == '1.0000000000000000000e-50'
assert NS('log(10**100,10)', 10) == '100.0000000'
assert NS('log(2)', 10) == '0.6931471806'
assert NS('(sin(x)-x)/x**3', 15, subs={x:
'1/10**50'}) == '-0.166666666666667'
assert NS(sin(1) + Rational(1, 10**100) * I,
15) == '0.841470984807897 + 1.00000000000000e-100*I'
assert x.evalf() == x
assert NS((1 + I)**2 * I, 6) == '-2.00000'
d = {
n: (-1)**Rational(6, 7),
y: (-1)**Rational(4, 7),
x: (-1)**Rational(2, 7)
}
assert NS((x * (1 + y * (1 + n))).subs(d).evalf(),
6) == '0.346011 + 0.433884*I'
assert NS(((-I - sqrt(2) * I)**2).evalf()) == '-5.82842712474619'
assert NS((1 + I)**2 * I, 15) == '-2.00000000000000'
# issue 4758 (1/2):
assert NS(pi.evalf(69) - pi) == '-4.43863937855894e-71'
# issue 4758 (2/2): With the bug present, this still only fails if the
# terms are in the order given here. This is not generally the case,
# because the order depends on the hashes of the terms.
assert NS(20 - 5008329267844 * n**25 - 477638700 * n**37 - 19 * n,
subs={n: .01}) == '19.8100000000000'
assert NS(
((x - 1) * (1 - x)**
1000).n()) == '(1.00000000000000 - x)**1000*(x - 1.00000000000000)'
assert NS((-x).n()) == '-x'
assert NS((-2 * x).n()) == '-2.00000000000000*x'
assert NS((-2 * x * y).n()) == '-2.00000000000000*x*y'
assert cos(x).n(subs={x: 1 + I}) == cos(x).subs(x, 1 + I).n()
# issue 6660. Also NaN != mpmath.nan
# In this order:
# 0*nan, 0/nan, 0*inf, 0/inf
# 0+nan, 0-nan, 0+inf, 0-inf
# >>> n = Some Number
# n*nan, n/nan, n*inf, n/inf
# n+nan, n-nan, n+inf, n-inf
assert (0 * E**(oo)).n() is S.NaN
assert (0 / E**(oo)).n() is S.Zero
assert (0 + E**(oo)).n() is S.Infinity
assert (0 - E**(oo)).n() is S.NegativeInfinity
assert (5 * E**(oo)).n() is S.Infinity
assert (5 / E**(oo)).n() is S.Zero
assert (5 + E**(oo)).n() is S.Infinity
assert (5 - E**(oo)).n() is S.NegativeInfinity
#issue 7416
assert as_mpmath(0.0, 10, {'chop': True}) == 0
#issue 5412
assert ((oo * I).n() == S.Infinity * I)
assert ((oo + oo * I).n() == S.Infinity + S.Infinity * I)
#issue 11518
assert NS(2 * x**2.5, 5) == '2.0000*x**2.5000'
#issue 13076
assert NS(Mul(Max(0, y), x, evaluate=False).evalf()) == 'x*Max(0, y)'
#issue 18516
assert NS(
log(
S(3273390607896141870013189696827599152216642046043064789483291368096133796404674554883270092325904157150886684127560071009217256545885393053328527589376
) /
36360291795869936842385267079543319118023385026001623040346035832580600191583895484198508262979388783308179702534403855752855931517013066142992430916562025780021771247847643450125342836565813209972590371590152578728008385990139795377610001
).evalf(15, chop=True)) == '-oo'
def test_polygon():
x = Symbol('x', real=True)
y = Symbol('y', real=True)
q = Symbol('q', real=True)
u = Symbol('u', real=True)
v = Symbol('v', real=True)
w = Symbol('w', real=True)
x1 = Symbol('x1', real=True)
half = S.Half
a, b, c = Point(0, 0), Point(2, 0), Point(3, 3)
t = Triangle(a, b, c)
assert Polygon(Point(0, 0)) == Point(0, 0)
assert Polygon(a, Point(1, 0), b, c) == t
assert Polygon(Point(1, 0), b, c, a) == t
assert Polygon(b, c, a, Point(1, 0)) == t
# 2 "remove folded" tests
assert Polygon(a, Point(3, 0), b, c) == t
assert Polygon(a, b, Point(3, -1), b, c) == t
# remove multiple collinear points
assert Polygon(Point(-4, 15), Point(-11, 15), Point(-15, 15),
Point(-15, 33/5), Point(-15, -87/10), Point(-15, -15),
Point(-42/5, -15), Point(-2, -15), Point(7, -15), Point(15, -15),
Point(15, -3), Point(15, 10), Point(15, 15)) == \
Polygon(Point(-15, -15), Point(15, -15), Point(15, 15), Point(-15, 15))
p1 = Polygon(Point(0, 0), Point(3, -1), Point(6, 0), Point(4, 5),
Point(2, 3), Point(0, 3))
p2 = Polygon(Point(6, 0), Point(3, -1), Point(0, 0), Point(0, 3),
Point(2, 3), Point(4, 5))
p3 = Polygon(Point(0, 0), Point(3, 0), Point(5, 2), Point(4, 4))
p4 = Polygon(Point(0, 0), Point(4, 4), Point(5, 2), Point(3, 0))
p5 = Polygon(Point(0, 0), Point(4, 4), Point(0, 4))
p6 = Polygon(Point(-11, 1), Point(-9, 6.6), Point(-4, -3),
Point(-8.4, -8.7))
p7 = Polygon(Point(x, y), Point(q, u), Point(v, w))
p8 = Polygon(Point(x, y), Point(v, w), Point(q, u))
p9 = Polygon(Point(0, 0), Point(4, 4), Point(3, 0), Point(5, 2))
p10 = Polygon(Point(0, 2), Point(2, 2), Point(0, 0), Point(2, 0))
p11 = Polygon(Point(0, 0), 1, n=3)
p12 = Polygon(Point(0, 0), 1, 0, n=3)
r = Ray(Point(-9, 6.6), Point(-9, 5.5))
#
# General polygon
#
assert p1 == p2
assert len(p1.args) == 6
assert len(p1.sides) == 6
assert p1.perimeter == 5 + 2 * sqrt(10) + sqrt(29) + sqrt(8)
assert p1.area == 22
assert not p1.is_convex()
assert Polygon((-1, 1), (2, -1), (2, 1), (-1, -1),
(3, 0)).is_convex() is False
# ensure convex for both CW and CCW point specification
assert p3.is_convex()
assert p4.is_convex()
dict5 = p5.angles
assert dict5[Point(0, 0)] == pi / 4
assert dict5[Point(0, 4)] == pi / 2
assert p5.encloses_point(Point(x, y)) is None
assert p5.encloses_point(Point(1, 3))
assert p5.encloses_point(Point(0, 0)) is False
assert p5.encloses_point(Point(4, 0)) is False
assert p1.encloses(Circle(Point(2.5, 2.5), 5)) is False
assert p1.encloses(Ellipse(Point(2.5, 2), 5, 6)) is False
assert p5.plot_interval('x') == [x, 0, 1]
assert p5.distance(Polygon(Point(10, 10), Point(14, 14),
Point(10, 14))) == 6 * sqrt(2)
assert p5.distance(
Polygon(Point(1, 8), Point(5, 8), Point(8, 12), Point(1, 12))) == 4
with warns(UserWarning, \
match="Polygons may intersect producing erroneous output"):
Polygon(Point(0, 0), Point(1, 0), Point(1, 1)).distance(
Polygon(Point(0, 0), Point(0, 1), Point(1, 1)))
assert hash(p5) == hash(Polygon(Point(0, 0), Point(4, 4), Point(0, 4)))
assert hash(p1) == hash(p2)
assert hash(p7) == hash(p8)
assert hash(p3) != hash(p9)
assert p5 == Polygon(Point(4, 4), Point(0, 4), Point(0, 0))
assert Polygon(Point(4, 4), Point(0, 4), Point(0, 0)) in p5
assert p5 != Point(0, 4)
assert Point(0, 1) in p5
assert p5.arbitrary_point('t').subs(Symbol('t', real=True), 0) == \
Point(0, 0)
raises(
ValueError, lambda: Polygon(Point(x, 0), Point(0, y), Point(x, y)).
arbitrary_point('x'))
assert p6.intersection(r) == [
Point(-9, Rational(-84, 13)),
Point(-9, Rational(33, 5))
]
assert p10.area == 0
assert p11 == RegularPolygon(Point(0, 0), 1, 3, 0)
assert p11 == p12
assert p11.vertices[0] == Point(1, 0)
assert p11.args[0] == Point(0, 0)
p11.spin(pi / 2)
assert p11.vertices[0] == Point(0, 1)
#
# Regular polygon
#
p1 = RegularPolygon(Point(0, 0), 10, 5)
p2 = RegularPolygon(Point(0, 0), 5, 5)
raises(GeometryError,
lambda: RegularPolygon(Point(0, 0), Point(0, 1), Point(1, 1)))
raises(GeometryError, lambda: RegularPolygon(Point(0, 0), 1, 2))
raises(ValueError, lambda: RegularPolygon(Point(0, 0), 1, 2.5))
assert p1 != p2
assert p1.interior_angle == pi * Rational(3, 5)
assert p1.exterior_angle == pi * Rational(2, 5)
assert p2.apothem == 5 * cos(pi / 5)
assert p2.circumcenter == p1.circumcenter == Point(0, 0)
assert p1.circumradius == p1.radius == 10
assert p2.circumcircle == Circle(Point(0, 0), 5)
assert p2.incircle == Circle(Point(0, 0), p2.apothem)
assert p2.inradius == p2.apothem == (5 * (1 + sqrt(5)) / 4)
p2.spin(pi / 10)
dict1 = p2.angles
assert dict1[Point(0, 5)] == 3 * pi / 5
assert p1.is_convex()
assert p1.rotation == 0
assert p1.encloses_point(Point(0, 0))
assert p1.encloses_point(Point(11, 0)) is False
assert p2.encloses_point(Point(0, 4.9))
p1.spin(pi / 3)
assert p1.rotation == pi / 3
assert p1.vertices[0] == Point(5, 5 * sqrt(3))
for var in p1.args:
if isinstance(var, Point):
assert var == Point(0, 0)
else:
assert var in (5, 10, pi / 3)
assert p1 != Point(0, 0)
assert p1 != p5
# while spin works in place (notice that rotation is 2pi/3 below)
# rotate returns a new object
p1_old = p1
assert p1.rotate(pi / 3) == RegularPolygon(Point(0, 0), 10, 5,
pi * Rational(2, 3))
assert p1 == p1_old
assert p1.area == (-250 * sqrt(5) + 1250) / (4 * tan(pi / 5))
assert p1.length == 20 * sqrt(-sqrt(5) / 8 + Rational(5, 8))
assert p1.scale(2, 2) == \
RegularPolygon(p1.center, p1.radius*2, p1._n, p1.rotation)
assert RegularPolygon((0, 0), 1, 4).scale(2, 3) == \
Polygon(Point(2, 0), Point(0, 3), Point(-2, 0), Point(0, -3))
assert repr(p1) == str(p1)
#
# Angles
#
angles = p4.angles
assert feq(angles[Point(0, 0)].evalf(), Float("0.7853981633974483"))
assert feq(angles[Point(4, 4)].evalf(), Float("1.2490457723982544"))
assert feq(angles[Point(5, 2)].evalf(), Float("1.8925468811915388"))
assert feq(angles[Point(3, 0)].evalf(), Float("2.3561944901923449"))
angles = p3.angles
assert feq(angles[Point(0, 0)].evalf(), Float("0.7853981633974483"))
assert feq(angles[Point(4, 4)].evalf(), Float("1.2490457723982544"))
assert feq(angles[Point(5, 2)].evalf(), Float("1.8925468811915388"))
assert feq(angles[Point(3, 0)].evalf(), Float("2.3561944901923449"))
#
# Triangle
#
p1 = Point(0, 0)
p2 = Point(5, 0)
p3 = Point(0, 5)
t1 = Triangle(p1, p2, p3)
t2 = Triangle(p1, p2, Point(Rational(5, 2), sqrt(Rational(75, 4))))
t3 = Triangle(p1, Point(x1, 0), Point(0, x1))
s1 = t1.sides
assert Triangle(p1, p2, p1) == Polygon(p1, p2, p1) == Segment(p1, p2)
raises(GeometryError, lambda: Triangle(Point(0, 0)))
# Basic stuff
assert Triangle(p1, p1, p1) == p1
assert Triangle(p2, p2 * 2, p2 * 3) == Segment(p2, p2 * 3)
assert t1.area == Rational(25, 2)
assert t1.is_right()
assert t2.is_right() is False
assert t3.is_right()
assert p1 in t1
assert t1.sides[0] in t1
assert Segment((0, 0), (1, 0)) in t1
assert Point(5, 5) not in t2
assert t1.is_convex()
assert feq(t1.angles[p1].evalf(), pi.evalf() / 2)
assert t1.is_equilateral() is False
assert t2.is_equilateral()
assert t3.is_equilateral() is False
assert are_similar(t1, t2) is False
assert are_similar(t1, t3)
assert are_similar(t2, t3) is False
assert t1.is_similar(Point(0, 0)) is False
assert t1.is_similar(t2) is False
# Bisectors
bisectors = t1.bisectors()
assert bisectors[p1] == Segment(p1, Point(Rational(5, 2), Rational(5, 2)))
assert t2.bisectors()[p2] == Segment(
Point(5, 0), Point(Rational(5, 4), 5 * sqrt(3) / 4))
p4 = Point(0, x1)
assert t3.bisectors()[p4] == Segment(p4, Point(x1 * (sqrt(2) - 1), 0))
ic = (250 - 125 * sqrt(2)) / 50
assert t1.incenter == Point(ic, ic)
# Inradius
assert t1.inradius == t1.incircle.radius == 5 - 5 * sqrt(2) / 2
assert t2.inradius == t2.incircle.radius == 5 * sqrt(3) / 6
assert t3.inradius == t3.incircle.radius == x1**2 / (
(2 + sqrt(2)) * Abs(x1))
# Exradius
assert t1.exradii[t1.sides[2]] == 5 * sqrt(2) / 2
# Excenters
assert t1.excenters[t1.sides[2]] == Point2D(25 * sqrt(2), -5 * sqrt(2) / 2)
# Circumcircle
assert t1.circumcircle.center == Point(2.5, 2.5)
# Medians + Centroid
m = t1.medians
assert t1.centroid == Point(Rational(5, 3), Rational(5, 3))
assert m[p1] == Segment(p1, Point(Rational(5, 2), Rational(5, 2)))
assert t3.medians[p1] == Segment(p1, Point(x1 / 2, x1 / 2))
assert intersection(m[p1], m[p2], m[p3]) == [t1.centroid]
assert t1.medial == Triangle(Point(2.5, 0), Point(0, 2.5), Point(2.5, 2.5))
# Nine-point circle
assert t1.nine_point_circle == Circle(Point(2.5, 0), Point(0, 2.5),
Point(2.5, 2.5))
assert t1.nine_point_circle == Circle(Point(0, 0), Point(0, 2.5),
Point(2.5, 2.5))
# Perpendicular
altitudes = t1.altitudes
assert altitudes[p1] == Segment(p1, Point(Rational(5, 2), Rational(5, 2)))
assert altitudes[p2].equals(s1[0])
assert altitudes[p3] == s1[2]
assert t1.orthocenter == p1
t = S('''Triangle(
Point(100080156402737/5000000000000, 79782624633431/500000000000),
Point(39223884078253/2000000000000, 156345163124289/1000000000000),
Point(31241359188437/1250000000000, 338338270939941/1000000000000000))''')
assert t.orthocenter == S(
'''Point(-780660869050599840216997'''
'''79471538701955848721853/80368430960602242240789074233100000000000000,'''
'''20151573611150265741278060334545897615974257/16073686192120448448157'''
'''8148466200000000000)''')
# Ensure
assert len(intersection(*bisectors.values())) == 1
assert len(intersection(*altitudes.values())) == 1
assert len(intersection(*m.values())) == 1
# Distance
p1 = Polygon(Point(0, 0), Point(1, 0), Point(1, 1), Point(0, 1))
p2 = Polygon(Point(0,
Rational(5) / 4), Point(1,
Rational(5) / 4),
Point(1,
Rational(9) / 4), Point(0,
Rational(9) / 4))
p3 = Polygon(Point(1, 2), Point(2, 2), Point(2, 1))
p4 = Polygon(Point(1, 1), Point(Rational(6) / 5, 1),
Point(1,
Rational(6) / 5))
pt1 = Point(half, half)
pt2 = Point(1, 1)
'''Polygon to Point'''
assert p1.distance(pt1) == half
assert p1.distance(pt2) == 0
assert p2.distance(pt1) == Rational(3) / 4
assert p3.distance(pt2) == sqrt(2) / 2
'''Polygon to Polygon'''
# p1.distance(p2) emits a warning
with warns(UserWarning, \
match="Polygons may intersect producing erroneous output"):
assert p1.distance(p2) == half / 2
assert p1.distance(p3) == sqrt(2) / 2
# p3.distance(p4) emits a warning
with warns(UserWarning, \
match="Polygons may intersect producing erroneous output"):
assert p3.distance(p4) == (sqrt(2) / 2 - sqrt(Rational(2) / 25) / 2)
def test_construct_domain():
assert construct_domain([1, 2, 3]) == (ZZ, [ZZ(1), ZZ(2), ZZ(3)])
assert construct_domain([1, 2, 3],
field=True) == (QQ, [QQ(1), QQ(2),
QQ(3)])
assert construct_domain([S.One, S(2), S(3)]) == (ZZ, [ZZ(1), ZZ(2), ZZ(3)])
assert construct_domain([S.One, S(2), S(3)],
field=True) == (QQ, [QQ(1), QQ(2),
QQ(3)])
assert construct_domain([S.Half, S(2)]) == (QQ, [QQ(1, 2), QQ(2)])
result = construct_domain([3.14, 1, S.Half])
assert isinstance(result[0], RealField)
assert result[1] == [RR(3.14), RR(1.0), RR(0.5)]
result = construct_domain([3.14, I, S.Half])
assert isinstance(result[0], ComplexField)
assert result[1] == [CC(3.14), CC(1.0j), CC(0.5)]
assert construct_domain([1.0 + I]) == (CC, [CC(1.0, 1.0)])
assert construct_domain([2.0 + 3.0 * I]) == (CC, [CC(2.0, 3.0)])
assert construct_domain([1, I]) == (ZZ_I, [ZZ_I(1, 0), ZZ_I(0, 1)])
assert construct_domain([1,
I / 2]) == (QQ_I, [QQ_I(1, 0),
QQ_I(0, S.Half)])
assert construct_domain([3.14, sqrt(2)],
extension=None) == (EX, [EX(3.14),
EX(sqrt(2))])
assert construct_domain([3.14, sqrt(2)],
extension=True) == (EX, [EX(3.14),
EX(sqrt(2))])
assert construct_domain([1, sqrt(2)],
extension=None) == (EX, [EX(1), EX(sqrt(2))])
assert construct_domain([x, sqrt(x)]) == (EX, [EX(x), EX(sqrt(x))])
assert construct_domain([x, sqrt(x), sqrt(y)
]) == (EX, [EX(x),
EX(sqrt(x)),
EX(sqrt(y))])
alg = QQ.algebraic_field(sqrt(2))
assert construct_domain([7, S.Half, sqrt(2)], extension=True) == \
(alg, [alg.convert(7), alg.convert(S.Half), alg.convert(sqrt(2))])
alg = QQ.algebraic_field(sqrt(2) + sqrt(3))
assert construct_domain([7, sqrt(2), sqrt(3)], extension=True) == \
(alg, [alg.convert(7), alg.convert(sqrt(2)), alg.convert(sqrt(3))])
dom = ZZ[x]
assert construct_domain([2*x, 3]) == \
(dom, [dom.convert(2*x), dom.convert(3)])
dom = ZZ[x, y]
assert construct_domain([2*x, 3*y]) == \
(dom, [dom.convert(2*x), dom.convert(3*y)])
dom = QQ[x]
assert construct_domain([x/2, 3]) == \
(dom, [dom.convert(x/2), dom.convert(3)])
dom = QQ[x, y]
assert construct_domain([x/2, 3*y]) == \
(dom, [dom.convert(x/2), dom.convert(3*y)])
dom = ZZ_I[x]
assert construct_domain([2*x, I]) == \
(dom, [dom.convert(2*x), dom.convert(I)])
dom = ZZ_I[x, y]
assert construct_domain([2*x, I*y]) == \
(dom, [dom.convert(2*x), dom.convert(I*y)])
dom = QQ_I[x]
assert construct_domain([x/2, I]) == \
(dom, [dom.convert(x/2), dom.convert(I)])
dom = QQ_I[x, y]
assert construct_domain([x/2, I*y]) == \
(dom, [dom.convert(x/2), dom.convert(I*y)])
dom = RR[x]
assert construct_domain([x/2, 3.5]) == \
(dom, [dom.convert(x/2), dom.convert(3.5)])
dom = RR[x, y]
assert construct_domain([x/2, 3.5*y]) == \
(dom, [dom.convert(x/2), dom.convert(3.5*y)])
dom = CC[x]
assert construct_domain([I*x/2, 3.5]) == \
(dom, [dom.convert(I*x/2), dom.convert(3.5)])
dom = CC[x, y]
assert construct_domain([I*x/2, 3.5*y]) == \
(dom, [dom.convert(I*x/2), dom.convert(3.5*y)])
dom = CC[x]
assert construct_domain([x/2, I*3.5]) == \
(dom, [dom.convert(x/2), dom.convert(I*3.5)])
dom = CC[x, y]
assert construct_domain([x/2, I*3.5*y]) == \
(dom, [dom.convert(x/2), dom.convert(I*3.5*y)])
dom = ZZ.frac_field(x)
assert construct_domain([2/x, 3]) == \
(dom, [dom.convert(2/x), dom.convert(3)])
dom = ZZ.frac_field(x, y)
assert construct_domain([2/x, 3*y]) == \
(dom, [dom.convert(2/x), dom.convert(3*y)])
dom = RR.frac_field(x)
assert construct_domain([2/x, 3.5]) == \
(dom, [dom.convert(2/x), dom.convert(3.5)])
dom = RR.frac_field(x, y)
assert construct_domain([2/x, 3.5*y]) == \
(dom, [dom.convert(2/x), dom.convert(3.5*y)])
dom = RealField(prec=336)[x]
assert construct_domain([pi.evalf(100)*x]) == \
(dom, [dom.convert(pi.evalf(100)*x)])
assert construct_domain(2) == (ZZ, ZZ(2))
assert construct_domain(S(2) / 3) == (QQ, QQ(2, 3))
assert construct_domain(Rational(2, 3)) == (QQ, QQ(2, 3))
assert construct_domain({}) == (ZZ, {})
