def mixedfromstr(string):
try:
return nb.Mixed(int(string))
except:
try:
return nb.Mixed(float(string))
except:
try:
return nb.Mixed(fr.Fraction(string))
except ValueError:
try:
return nb.Mixed(uc.ufloat_fromstr(string))
except ValueError:
raise (Exception(
"The following string looks like a number, "
"but I can't convert it: %s" % (string)))
def centre_of_gravity(liste):
# Calculates the centre of gravity of a list of positions
# of type geo.Pos.
assert isinstance(liste, list), \
"Argument of geo.centre_of_gravity(...) must be of type list."
for item in liste:
assert isinstance(item, Pos), \
"Argument of geo.centre_of_gravity(...) must be a list " \
"of objects of type geo.Pos."
summe = Dif(nb.Matrix([[0], [0], [0], [0]]))
for item in liste:
summe += item - origin
return origin + Dif((summe.value * (1 / nb.Mixed(len(liste)))))
def __init__(self, a, b, c, alpha, beta, gamma):
for number in [a, b, c, alpha, beta, gamma]:
assert isinstance(number, nb.Mixed) \
or isinstance(number, int) \
or isinstance(number, float), \
"Arguments must be of type Mixed, int or float."
self.a = nb.Mixed(a)
self.b = nb.Mixed(b)
self.c = nb.Mixed(c)
self.alpha = nb.Mixed(alpha)
self.beta = nb.Mixed(beta)
self.gamma = nb.Mixed(gamma)
def structurefactor(atomset, metric, q, wavelength):
assert isinstance(atomset, Atomset), \
"atomset must be of type Atomset."
assert isinstance(metric, geo.Metric), \
"metric must be of type geo.Metric."
assert isinstance(q, geo.Rec), \
"q (scattering vector) must be of type geo.Rec."
wavelength = nb.Mixed(wavelength)
assert isinstance(wavelength, nb.Mixed), \
"wavelength must be of type numbers.Mixed or a type " \
"that can be converted to this."
sintl = 0.5 * metric.length(q)
i2pi = np.complex(0, 1) * 2.0 * np.pi
F = 0
for atom in atomset.menge:
F += tables.formfactor(atom.typ, sintl) \
* np.exp(i2pi * float(q * (atom.pos - geo.origin)))
return F
def test_Mixed():
# Create a number of type Mixed with 4 different types.
q = fr.Fraction(2, 3)
e = uc.ufloat(1.2, 0.1)
i = 4
f = 3.5
q1 = fr.Fraction(2, 1)
e1 = uc.ufloat(3.7, 0)
assert isinstance(nb.Mixed(q).value, fr.Fraction)
assert nb.Mixed(q).value == q
assert isinstance(nb.Mixed(e).value, uc.UFloat)
assert (nb.Mixed(e).value).n == e.n
assert (nb.Mixed(e).value).s == e.s
assert isinstance(nb.Mixed(i).value, int)
assert nb.Mixed(i).value == i
assert isinstance(nb.Mixed(f).value, float)
assert nb.Mixed(f).value == f
assert isinstance(nb.Mixed(q1).value, int)
assert nb.Mixed(q1).value == 2
assert isinstance(nb.Mixed(e1).value, uc.UFloat)
assert nb.Mixed(e1).value == uc.ufloat(3.7, 0.0)
# Convert a number of type Mixed to float.
assert isinstance(float(nb.Mixed(q)), float)
assert float(nb.Mixed(q)) == float(2 / 3)
assert isinstance(float(nb.Mixed(e)), float)
assert float(nb.Mixed(e)) == 1.2
assert isinstance(float(nb.Mixed(i)), float)
assert float(nb.Mixed(i)) == 4.0
assert isinstance(float(nb.Mixed(f)), float)
assert float(nb.Mixed(f)) == 3.5
# Print a number of type Mixed as str.
assert isinstance(nb.Mixed(q).__str__(), str)
assert nb.Mixed(q).__str__() == "2/3"
assert isinstance(nb.Mixed(e).__str__(), str)
assert nb.Mixed(e).__str__() == "1.20(10)"
assert isinstance(nb.Mixed(i).__str__(), str)
assert nb.Mixed(i).__str__() == "4"
assert isinstance(nb.Mixed(f).__str__(), str)
assert nb.Mixed(f).__str__() == "3.5"
# Hash
assert isinstance(hash(nb.Mixed(q)), int)
assert isinstance(hash(nb.Mixed(e)), int)
assert isinstance(hash(nb.Mixed(i)), int)
assert isinstance(hash(nb.Mixed(f)), int)
assert hash(nb.Mixed(1.99999999999)) == hash(nb.Mixed(2.00000000000))
assert (hash(nb.Mixed(1.9)) == hash(nb.Mixed(2.0))) == False
e1 = uc.ufloat(1.2, 0.1)
e2 = e1
e3 = uc.ufloat(1.2, 0.1)
me1 = nb.Mixed(e1)
me2 = nb.Mixed(e2)
me3 = nb.Mixed(e3)
assert hash(me1) == hash(me2)
assert (hash(me1) == hash(me3)) == False
# Equal
assert nb.Mixed(q) == nb.Mixed(q)
assert nb.Mixed(e) == nb.Mixed(e)
assert nb.Mixed(i) == nb.Mixed(i)
assert nb.Mixed(f) == nb.Mixed(f)
assert nb.Mixed(fr.Fraction(2, 3)) == nb.Mixed(fr.Fraction(2, 3))
assert (nb.Mixed(fr.Fraction(2, 3)) == nb.Mixed(fr.Fraction(1,
3))) == False
assert (nb.Mixed(uc.ufloat(1.2, 0.1)) == nb.Mixed(uc.ufloat(1.2,
0.1))) == False
assert (nb.Mixed(uc.ufloat(1.2, 0.1)) == nb.Mixed(uc.ufloat(1.2, 0.2))) \
== False
x1 = uc.ufloat(0.5, 0.3)
x2 = uc.ufloat(0.5, 0.4)
x = nb.Mixed(x1) + nb.Mixed(x2)
y = nb.Mixed(x1 + x2)
assert x == y
assert nb.Mixed(fr.Fraction(2, 3)) == nb.Mixed(fr.Fraction(2, 3))
assert (nb.Mixed(fr.Fraction(2, 3)) == nb.Mixed(uc.ufloat(1.2, 0.1))) \
== False
assert (nb.Mixed(fr.Fraction(2, 3)) == nb.Mixed(1)) == False
assert (nb.Mixed(fr.Fraction(2, 3)) == nb.Mixed(0.66)) == False
assert (nb.Mixed(uc.ufloat(1.2, 0.1)) == nb.Mixed(fr.Fraction(2, 3))) \
== False
assert (nb.Mixed(
uc.ufloat(1.2, 0.1) == nb.Mixed(uc.ufloat(1.2, 0.1)))) == False
assert (nb.Mixed(uc.ufloat(1.2, 0.1)) == nb.Mixed(1)) == False
assert (nb.Mixed(uc.ufloat(1.2, 0.1)) == nb.Mixed(0.66)) == False
assert (nb.Mixed(1) == nb.Mixed(fr.Fraction(2, 3))) == False
assert (nb.Mixed(1) == nb.Mixed(uc.ufloat(1.2, 0.1))) == False
assert nb.Mixed(1) == nb.Mixed(1)
assert (nb.Mixed(1) == nb.Mixed(1.0)) == False
assert (nb.Mixed(1.0) == nb.Mixed(fr.Fraction(1, 1))) == False
assert (nb.Mixed(1.0) == nb.Mixed(uc.ufloat(1.0, 0.0))) == False
assert (nb.Mixed(1.0) == nb.Mixed(1)) == False
assert nb.Mixed(1.0) == nb.Mixed(1.0)
assert nb.Mixed(0) == 0
assert (nb.Mixed(0.1) == 0) == False
assert nb.Mixed(fr.Fraction(2, 1)) == 2
# Other relations
# Addition
mq = nb.Mixed(q)
me = nb.Mixed(e)
mi = nb.Mixed(i)
mf = nb.Mixed(f)
mi0 = nb.Mixed(0)
assert isinstance(mq + mq, nb.Mixed)
assert isinstance((mq + mq).value, fr.Fraction)
assert mq + mq == nb.Mixed(fr.Fraction(4, 3))
assert isinstance(mq + q, nb.Mixed)
assert isinstance((mq + q).value, fr.Fraction)
assert mq + q == nb.Mixed(fr.Fraction(4, 3))
assert isinstance(q + mq, nb.Mixed)
assert isinstance((q + mq).value, fr.Fraction)
assert q + mq == nb.Mixed(fr.Fraction(4, 3))
assert isinstance(mq + me, nb.Mixed)
assert isinstance((mq + me).value, uc.UFloat)
assert mq + me == nb.Mixed(e + 2 / 3)
assert isinstance(mq + e, nb.Mixed)
assert isinstance((mq + e).value, uc.UFloat)
assert mq + e == nb.Mixed(e + 2 / 3)
assert isinstance(q + me, nb.Mixed)
assert isinstance((q + me).value, uc.UFloat)
assert q + me == nb.Mixed(e + 2 / 3)
assert isinstance(mq + mi, nb.Mixed)
assert isinstance((mq + mi).value, fr.Fraction)
assert mq + mi == nb.Mixed(fr.Fraction(14, 3))
assert isinstance(mq + i, nb.Mixed)
assert isinstance((mq + i).value, fr.Fraction)
assert mq + i == nb.Mixed(fr.Fraction(14, 3))
assert isinstance(q + mi, nb.Mixed)
assert isinstance((q + mi).value, fr.Fraction)
assert q + mi == nb.Mixed(fr.Fraction(14, 3))
assert isinstance(mq + mf, nb.Mixed)
assert isinstance((mq + mf).value, float)
assert mq + mf == nb.Mixed(3.5 + 2 / 3)
assert isinstance(mq + f, nb.Mixed)
assert isinstance((mq + f).value, float)
assert mq + f == nb.Mixed(3.5 + 2 / 3)
assert isinstance(q + mf, nb.Mixed)
assert isinstance((q + mf).value, float)
assert q + mf == nb.Mixed(3.5 + 2 / 3)
assert isinstance(me + mq, nb.Mixed)
assert isinstance((me + mq).value, uc.UFloat)
assert me + mq == nb.Mixed(e + 2 / 3)
assert isinstance(me + q, nb.Mixed)
assert isinstance((me + q).value, uc.UFloat)
assert me + q == nb.Mixed(e + 2 / 3)
assert isinstance(e + mq, nb.Mixed)
assert isinstance((e + mq).value, uc.UFloat)
assert e + mq == nb.Mixed(e + 2 / 3)
assert isinstance(me + me, nb.Mixed)
assert isinstance((me + me).value, uc.UFloat)
assert me + me == nb.Mixed(e + e)
assert isinstance(me + e, nb.Mixed)
assert isinstance((me + e).value, uc.UFloat)
assert me + e == nb.Mixed(e + e)
assert isinstance(e + me, nb.Mixed)
assert isinstance((e + me).value, uc.UFloat)
assert e + me == nb.Mixed(e + e)
assert isinstance(me + mi, nb.Mixed)
assert isinstance((me + mi).value, uc.UFloat)
assert me + mi == nb.Mixed(e + i)
assert isinstance(me + i, nb.Mixed)
assert isinstance((me + i).value, uc.UFloat)
assert me + i == nb.Mixed(e + i)
assert isinstance(e + mi, nb.Mixed)
assert isinstance((e + mi).value, uc.UFloat)
assert me + i == nb.Mixed(e + i)
assert me + mi0 == nb.Mixed(e)
assert isinstance(me + mf, nb.Mixed)
assert isinstance((me + mf).value, uc.UFloat)
assert me + mf == nb.Mixed(e + f)
assert isinstance(me + f, nb.Mixed)
assert isinstance((me + f).value, uc.UFloat)
assert me + f == nb.Mixed(e + f)
assert isinstance(e + mf, nb.Mixed)
assert isinstance((e + mf).value, uc.UFloat)
assert e + mf == nb.Mixed(e + f)
assert isinstance(mi + mq, nb.Mixed)
assert isinstance((mi + mq).value, fr.Fraction)
assert mi + mq == nb.Mixed(fr.Fraction(14, 3))
assert isinstance(mi + q, nb.Mixed)
assert isinstance((mi + q).value, fr.Fraction)
assert mi + q == nb.Mixed(fr.Fraction(14, 3))
assert isinstance(i + mq, nb.Mixed)
assert isinstance((i + mq).value, fr.Fraction)
assert i + mq == nb.Mixed(fr.Fraction(14, 3))
assert isinstance(mi + me, nb.Mixed)
assert isinstance((mi + me).value, uc.UFloat)
assert mi + me == nb.Mixed(i + e)
assert isinstance(mi + e, nb.Mixed)
assert isinstance((mi + e).value, uc.UFloat)
assert mi + me == nb.Mixed(i + e)
assert isinstance(i + me, nb.Mixed)
assert isinstance((i + me).value, uc.UFloat)
assert i + me == nb.Mixed(i + e)
assert isinstance(mi + mi, nb.Mixed)
assert isinstance((mi + mi).value, int)
assert mi + mi == nb.Mixed(8)
assert isinstance(mi + i, nb.Mixed)
assert isinstance((mi + i).value, int)
assert mi + i == nb.Mixed(8)
assert isinstance(i + mi, nb.Mixed)
assert isinstance((i + mi).value, int)
assert i + mi == nb.Mixed(8)
assert isinstance(mi + mf, nb.Mixed)
assert isinstance((mi + mf).value, float)
assert mi + mf == nb.Mixed(7.5)
assert isinstance(mi + f, nb.Mixed)
assert isinstance((mi + f).value, float)
assert mi + f == nb.Mixed(7.5)
assert isinstance(i + mf, nb.Mixed)
assert isinstance((i + mf).value, float)
assert i + mf == nb.Mixed(7.5)
assert isinstance(mf + mq, nb.Mixed)
assert isinstance((mf + mq).value, float)
assert mf + mq == nb.Mixed(3.5 + 2 / 3)
assert isinstance(mf + q, nb.Mixed)
assert isinstance((mf + q).value, float)
assert mf + q == nb.Mixed(3.5 + 2 / 3)
assert isinstance(f + mq, nb.Mixed)
assert isinstance((f + mq).value, float)
assert f + mq == nb.Mixed(3.5 + 2 / 3)
assert isinstance(mf + me, nb.Mixed)
assert isinstance((mf + me).value, uc.UFloat)
assert mf + me == nb.Mixed(f + e)
assert isinstance(mf + e, nb.Mixed)
assert isinstance((mf + e).value, uc.UFloat)
assert mf + e == nb.Mixed(f + e)
assert isinstance(f + me, nb.Mixed)
assert isinstance((f + me).value, uc.UFloat)
assert f + me == nb.Mixed(f + e)
# Subtraction
q1 = fr.Fraction(1, 2)
q2 = fr.Fraction(1, 4)
e1 = uc.ufloat(1.2, 0.3)
e2 = uc.ufloat(0.2, 0.4)
i1 = 4
i2 = 3
f1 = 3.5
f2 = 3.4
mq1 = nb.Mixed(q1)
mq2 = nb.Mixed(q2)
me1 = nb.Mixed(e1)
me2 = nb.Mixed(e2)
mi1 = nb.Mixed(i1)
mi2 = nb.Mixed(i2)
mf1 = nb.Mixed(f1)
mf2 = nb.Mixed(f2)
assert isinstance(mq1 - mq2, nb.Mixed)
assert isinstance((mq1 - mq2).value, fr.Fraction)
assert mq1 - mq2 == nb.Mixed(fr.Fraction(1, 4))
assert isinstance(mq1 - q2, nb.Mixed)
assert isinstance((mq1 - q2).value, fr.Fraction)
assert mq1 - q2 == nb.Mixed(fr.Fraction(1, 4))
assert isinstance(q1 - mq2, nb.Mixed)
assert isinstance((q1 - mq2).value, fr.Fraction)
assert q1 - mq2 == nb.Mixed(fr.Fraction(1, 4))
assert isinstance(mq1 - me1, nb.Mixed)
assert isinstance((mq1 - me1).value, uc.UFloat)
assert mq1 - me1 == nb.Mixed(float(q1) - e1)
assert isinstance(mq1 - e1, nb.Mixed)
assert isinstance((mq1 - e1).value, uc.UFloat)
assert mq1 - e1 == nb.Mixed(float(q1) - e1)
assert isinstance(q1 - me1, nb.Mixed)
assert isinstance((q1 - me1).value, uc.UFloat)
assert q1 - me1 == nb.Mixed(float(q1) - e1)
assert isinstance(mq1 - mi1, nb.Mixed)
assert isinstance((mq1 - mi1).value, fr.Fraction)
assert mq1 - mi1 == nb.Mixed(q1 - i1)
assert isinstance(mq1 - i1, nb.Mixed)
assert isinstance((mq1 - i1).value, fr.Fraction)
assert mq1 - i1 == nb.Mixed(q1 - i1)
assert isinstance(q1 - mi1, nb.Mixed)
assert isinstance((q1 - mi1).value, fr.Fraction)
assert q1 - mi1 == nb.Mixed(q1 - i1)
assert isinstance(mq1 - mf1, nb.Mixed)
assert isinstance((mq1 - mf1).value, float)
assert mq1 - mf1 == nb.Mixed(-3.0)
assert isinstance(mq1 - f1, nb.Mixed)
assert isinstance((mq1 - f1).value, float)
assert mq1 - f1 == nb.Mixed(-3.0)
assert isinstance(q1 - mf1, nb.Mixed)
assert isinstance((q1 - mf1).value, float)
assert q1 - mf1 == nb.Mixed(-3.0)
assert isinstance(me1 - mq1, nb.Mixed)
assert isinstance((me1 - mq1).value, uc.UFloat)
assert me1 - mq1 == nb.Mixed(e1 - float(q1))
assert isinstance(me1 - q1, nb.Mixed)
assert isinstance((me1 - q1).value, uc.UFloat)
assert me1 - q1 == nb.Mixed(e1 - float(q1))
assert isinstance(e1 - mq1, nb.Mixed)
assert isinstance((e1 - mq1).value, uc.UFloat)
assert e1 - mq1 == nb.Mixed(e1 - float(q1))
assert isinstance(me1 - me2, nb.Mixed)
assert isinstance((me1 - me2).value, uc.UFloat)
assert me1 - me2 == nb.Mixed(e1 - e2)
assert isinstance(me1 - e2, nb.Mixed)
assert isinstance((me1 - e2).value, uc.UFloat)
assert me1 - e2 == nb.Mixed(e1 - e2)
assert isinstance(e1 - me2, nb.Mixed)
assert isinstance((e1 - me2).value, uc.UFloat)
assert e1 - me2 == nb.Mixed(e1 - e2)
assert isinstance(me1 - mi1, nb.Mixed)
assert isinstance((me1 - mi1).value, uc.UFloat)
assert me1 - mi1 == nb.Mixed(e1 - i1)
assert isinstance(me1 - i1, nb.Mixed)
assert isinstance((me1 - i1).value, uc.UFloat)
assert me1 - i1 == nb.Mixed(e1 - i1)
assert isinstance(e1 - mi1, nb.Mixed)
assert isinstance((e1 - mi1).value, uc.UFloat)
assert e1 - mi1 == nb.Mixed(e1 - i1)
assert isinstance(me1 - mf1, nb.Mixed)
assert isinstance((me1 - mf1).value, uc.UFloat)
assert me1 - mf1 == nb.Mixed(e1 - f1)
assert isinstance(me1 - f1, nb.Mixed)
assert isinstance((me1 - f1).value, uc.UFloat)
assert me1 - f1 == nb.Mixed(e1 - f1)
assert isinstance(e1 - mf1, nb.Mixed)
assert isinstance((e1 - mf1).value, uc.UFloat)
assert e1 - mf1 == nb.Mixed(e1 - f1)
assert isinstance(mi1 - mq1, nb.Mixed)
assert isinstance((mi1 - mq1).value, fr.Fraction)
assert mi1 - mq1 == nb.Mixed(fr.Fraction(7, 2))
assert isinstance(mi1 - q1, nb.Mixed)
assert isinstance((mi1 - q1).value, fr.Fraction)
assert mi1 - q1 == nb.Mixed(fr.Fraction(7, 2))
assert isinstance(i1 - mq1, nb.Mixed)
assert isinstance((i1 - mq1).value, fr.Fraction)
assert i1 - mq1 == nb.Mixed(fr.Fraction(7, 2))
assert isinstance(mi1 - me1, nb.Mixed)
assert isinstance((mi1 - me1).value, uc.UFloat)
assert mi1 - me1 == nb.Mixed(i1 - e1)
assert isinstance(mi1 - e1, nb.Mixed)
assert isinstance((mi1 - e1).value, uc.UFloat)
assert mi1 - e1 == nb.Mixed(i1 - e1)
assert isinstance(i1 - me1, nb.Mixed)
assert isinstance((i1 - me1).value, uc.UFloat)
assert i1 - me1 == nb.Mixed(i1 - e1)
assert isinstance(mi1 - mi2, nb.Mixed)
assert isinstance((mi1 - mi2).value, int)
assert mi1 - mi2 == nb.Mixed(1)
assert isinstance(mi1 - i2, nb.Mixed)
assert isinstance((mi1 - i2).value, int)
assert mi1 - i2 == nb.Mixed(1)
assert isinstance(i1 - mi2, nb.Mixed)
assert isinstance((i1 - mi2).value, int)
assert i1 - mi2 == nb.Mixed(1)
assert isinstance(mi1 - mf1, nb.Mixed)
assert isinstance((mi1 - mf1).value, float)
assert mi1 - mf1 == nb.Mixed(0.5)
assert isinstance(mi1 - f1, nb.Mixed)
assert isinstance((mi1 - f1).value, float)
assert mi1 - f1 == nb.Mixed(0.5)
assert isinstance(i1 - mf1, nb.Mixed)
assert isinstance((i1 - mf1).value, float)
assert i1 - mf1 == nb.Mixed(0.5)
assert isinstance(mf1 - mq1, nb.Mixed)
assert isinstance((mf1 - mq1).value, float)
assert mf1 - mq1 == nb.Mixed(3.0)
assert isinstance(mf1 - q1, nb.Mixed)
assert isinstance((mf1 - q1).value, float)
assert mf1 - q1 == nb.Mixed(3.0)
assert isinstance(f1 - mq1, nb.Mixed)
assert isinstance((f1 - mq1).value, float)
assert f1 - mq1 == nb.Mixed(3.0)
assert isinstance(mf1 - me1, nb.Mixed)
assert isinstance((mf1 - me1).value, uc.UFloat)
assert mf1 - me1 == nb.Mixed(f1 - e1)
assert isinstance(mf1 - e1, nb.Mixed)
assert isinstance((mf1 - e1).value, uc.UFloat)
assert mf1 - e1 == nb.Mixed(f1 - e1)
assert isinstance(f1 - me1, nb.Mixed)
assert isinstance((f1 - me1).value, uc.UFloat)
assert f1 - me1 == nb.Mixed(f1 - e1)
assert isinstance(mf1 - mi1, nb.Mixed)
assert isinstance((mf1 - mi1).value, float)
assert mf1 - mi1 == nb.Mixed(-0.5)
assert isinstance(mf1 - i1, nb.Mixed)
assert isinstance((mf1 - i1).value, float)
assert mf1 - i1 == nb.Mixed(-0.5)
assert isinstance(f1 - mi1, nb.Mixed)
assert isinstance((f1 - mi1).value, float)
assert f1 - mi1 == nb.Mixed(-0.5)
assert isinstance(mf1 - mf2, nb.Mixed)
assert isinstance((mf1 - mf2).value, float)
assert mf1 - mf2 == nb.Mixed(3.5 - 3.4)
assert isinstance(mf1 - f2, nb.Mixed)
assert isinstance((mf1 - f2).value, float)
assert mf1 - f2 == nb.Mixed(3.5 - 3.4)
assert isinstance(f1 - mf2, nb.Mixed)
assert isinstance((f1 - mf2).value, float)
assert f1 - mf2 == nb.Mixed(3.5 - 3.4)
# Multiplication
q1 = fr.Fraction(1, 2)
q2 = fr.Fraction(1, 4)
e1 = uc.ufloat(1.2, 0.3)
e2 = uc.ufloat(0.2, 0.4)
i1 = 4
i2 = 3
f1 = 3.5
f2 = 3.4
mq1 = nb.Mixed(q1)
mq2 = nb.Mixed(q2)
me1 = nb.Mixed(e1)
me2 = nb.Mixed(e2)
mi1 = nb.Mixed(i1)
mi2 = nb.Mixed(i2)
mf1 = nb.Mixed(f1)
mf2 = nb.Mixed(f2)
assert isinstance(mq1 * mq2, nb.Mixed)
assert isinstance((mq1 * mq2).value, fr.Fraction)
assert mq1 * mq2 == nb.Mixed(fr.Fraction(1, 8))
assert isinstance(mq1 * q2, nb.Mixed)
assert isinstance((mq1 * q2).value, fr.Fraction)
assert mq1 * q2 == nb.Mixed(fr.Fraction(1, 8))
assert isinstance(q1 * mq2, nb.Mixed)
assert isinstance((q1 * mq2).value, fr.Fraction)
assert q1 * mq2 == nb.Mixed(fr.Fraction(1, 8))
assert isinstance(mq1 * me1, nb.Mixed)
assert isinstance((mq1 * me1).value, uc.UFloat)
assert mq1 * me1 == nb.Mixed(float(q1) * e1)
assert isinstance(mq1 * e1, nb.Mixed)
assert isinstance((mq1 * e1).value, uc.UFloat)
assert mq1 * e1 == nb.Mixed(float(q1) * e1)
assert isinstance(q1 * me1, nb.Mixed)
assert isinstance((q1 * me1).value, uc.UFloat)
assert q1 * me1 == nb.Mixed(float(q1) * e1)
assert isinstance(mq1 * mi2, nb.Mixed)
assert isinstance((mq1 * mi2).value, fr.Fraction)
assert mq1 * mi2 == nb.Mixed(fr.Fraction(3, 2))
assert isinstance(mq1 * i2, nb.Mixed)
assert isinstance((mq1 * i2).value, fr.Fraction)
assert mq1 * i2 == nb.Mixed(fr.Fraction(3, 2))
assert isinstance(q1 * mi2, nb.Mixed)
assert isinstance((q1 * mi2).value, fr.Fraction)
assert q1 * mi2 == nb.Mixed(fr.Fraction(3, 2))
assert isinstance(mq1 * mf1, nb.Mixed)
assert isinstance((mq1 * mf1).value, float)
assert mq1 * mf1 == nb.Mixed(1.75)
assert isinstance(mq1 * f1, nb.Mixed)
assert isinstance((mq1 * f1).value, float)
assert mq1 * f1 == nb.Mixed(1.75)
assert isinstance(q1 * mf1, nb.Mixed)
assert isinstance((q1 * mf1).value, float)
assert q1 * mf1 == nb.Mixed(1.75)
assert isinstance(me1 * mq1, nb.Mixed)
assert isinstance((me1 * mq1).value, uc.UFloat)
assert me1 * mq1 == nb.Mixed(e1 * float(q1))
assert isinstance(me1 * q1, nb.Mixed)
assert isinstance((me1 * q1).value, uc.UFloat)
assert me1 * q1 == nb.Mixed(e1 * float(q1))
assert isinstance(e1 * mq1, nb.Mixed)
assert isinstance((e1 * mq1).value, uc.UFloat)
assert e1 * mq1 == nb.Mixed(e1 * float(q1))
assert isinstance(me1 * me2, nb.Mixed)
assert isinstance((me1 * me2).value, uc.UFloat)
assert me1 * me2 == nb.Mixed(e1 * e2)
assert isinstance(me1 * e2, nb.Mixed)
assert isinstance((me1 * e2).value, uc.UFloat)
assert me1 * e2 == nb.Mixed(e1 * e2)
assert isinstance(e1 * me2, nb.Mixed)
assert isinstance((e1 * me2).value, uc.UFloat)
assert e1 * me2 == nb.Mixed(e1 * e2)
assert isinstance(me1 * mi1, nb.Mixed)
assert isinstance((me1 * mi1).value, uc.UFloat)
assert me1 * mi1 == nb.Mixed(e1 * i1)
assert isinstance(me1 * i1, nb.Mixed)
assert isinstance((me1 * i1).value, uc.UFloat)
assert me1 * i1 == nb.Mixed(e1 * i1)
assert isinstance(e1 * mi1, nb.Mixed)
assert isinstance((e1 * mi1).value, uc.UFloat)
assert e1 * mi1 == nb.Mixed(e1 * i1)
assert isinstance(me1 * mf1, nb.Mixed)
assert isinstance((me1 * mf1).value, uc.UFloat)
assert me1 * mf1 == nb.Mixed(e1 * f1)
assert isinstance(me1 * f1, nb.Mixed)
assert isinstance((me1 * f1).value, uc.UFloat)
assert me1 * f1 == nb.Mixed(e1 * f1)
assert isinstance(e1 * mf1, nb.Mixed)
assert isinstance((e1 * mf1).value, uc.UFloat)
assert e1 * mf1 == nb.Mixed(e1 * f1)
assert isinstance(nb.Mixed(3) * mq1, nb.Mixed)
assert isinstance((nb.Mixed(3) * mq1).value, fr.Fraction)
assert nb.Mixed(3) * mq1 == nb.Mixed(fr.Fraction(3, 2))
assert isinstance(nb.Mixed(3) * q1, nb.Mixed)
assert isinstance((nb.Mixed(3) * q1).value, fr.Fraction)
assert nb.Mixed(3) * q1 == nb.Mixed(fr.Fraction(3, 2))
assert isinstance(3 * mq1, nb.Mixed)
assert isinstance((3 * mq1).value, fr.Fraction)
assert 3 * mq1 == nb.Mixed(fr.Fraction(3, 2))
assert isinstance(mi1 * me1, nb.Mixed)
assert isinstance((mi1 * me1).value, uc.UFloat)
assert mi1 * me1 == nb.Mixed(i1 * e1)
assert isinstance(mi1 * e1, nb.Mixed)
assert isinstance((mi1 * e1).value, uc.UFloat)
assert mi1 * e1 == nb.Mixed(i1 * e1)
assert isinstance(i1 * me1, nb.Mixed)
assert isinstance((i1 * me1).value, uc.UFloat)
assert i1 * me1 == nb.Mixed(i1 * e1)
assert isinstance(mi1 * mi2, nb.Mixed)
assert isinstance((mi1 * mi2).value, int)
assert mi1 * mi2 == nb.Mixed(12)
assert isinstance(mi1 * i2, nb.Mixed)
assert isinstance((mi1 * i2).value, int)
assert mi1 * i2 == nb.Mixed(12)
assert isinstance(i1 * mi2, nb.Mixed)
assert isinstance((i1 * mi2).value, int)
assert i1 * mi2 == nb.Mixed(12)
assert isinstance(mi1 * mf1, nb.Mixed)
assert isinstance((mi1 * mf1).value, float)
assert mi1 * mf1 == nb.Mixed(14.0)
assert isinstance(mi1 * f1, nb.Mixed)
assert isinstance((mi1 * f1).value, float)
assert mi1 * f1 == nb.Mixed(14.0)
assert isinstance(i1 * mf1, nb.Mixed)
assert isinstance((i1 * mf1).value, float)
assert i1 * mf1 == nb.Mixed(14.0)
assert isinstance(mf1 * mq1, nb.Mixed)
assert isinstance((mf1 * mq1).value, float)
assert mf1 * mq1 == nb.Mixed(1.75)
assert isinstance(mf1 * q1, nb.Mixed)
assert isinstance((mf1 * q1).value, float)
assert mf1 * q1 == nb.Mixed(1.75)
assert isinstance(f1 * mq1, nb.Mixed)
assert isinstance((f1 * mq1).value, float)
assert f1 * mq1 == nb.Mixed(1.75)
assert isinstance(mf1 * me1, nb.Mixed)
assert isinstance((mf1 * me1).value, uc.UFloat)
assert mf1 * me1 == nb.Mixed(f1 * e1)
assert isinstance(mf1 * e1, nb.Mixed)
assert isinstance((mf1 * e1).value, uc.UFloat)
assert mf1 * e1 == nb.Mixed(f1 * e1)
assert isinstance(f1 * me1, nb.Mixed)
assert isinstance((f1 * me1).value, uc.UFloat)
assert f1 * me1 == nb.Mixed(f1 * e1)
assert isinstance(mf1 * mi1, nb.Mixed)
assert isinstance((mf1 * mi1).value, float)
assert mf1 * mi1 == nb.Mixed(14.0)
assert isinstance(mf1 * i1, nb.Mixed)
assert isinstance((mf1 * i1).value, float)
assert mf1 * i1 == nb.Mixed(14.0)
assert isinstance(f1 * mi1, nb.Mixed)
assert isinstance((f1 * mi1).value, float)
assert f1 * mi1 == nb.Mixed(14.0)
assert isinstance(mf1 * mf2, nb.Mixed)
assert isinstance((mf1 * mf2).value, float)
assert mf1 * mf2 == nb.Mixed(11.9)
assert isinstance(mf1 * f2, nb.Mixed)
assert isinstance((mf1 * f2).value, float)
assert mf1 * f2 == nb.Mixed(11.9)
assert isinstance(f1 * mf2, nb.Mixed)
assert isinstance((f1 * mf2).value, float)
assert f1 * mf2 == nb.Mixed(11.9)
# Multiplication with integer 0
q = fr.Fraction(2, 3)
e = uc.ufloat(1.2, 0.1)
i = 4
f = 3.5
mq = nb.Mixed(q)
me = nb.Mixed(e)
mi = nb.Mixed(i)
mf = nb.Mixed(f)
m0 = nb.Mixed(0)
for m in [mq, me, mi, mf]:
assert m * m0 == m0
assert m * 0 == m0
assert m0 * m == m0
assert 0 * m == m0
for z in [q, e, i, f]:
assert z * m0 == m0
assert m0 * z == m0
# Division
q1 = fr.Fraction(2, 3)
q2 = fr.Fraction(3, 4)
e1 = uc.ufloat(0.5, 0.3)
e2 = uc.ufloat(0.75, 0.4)
i1 = 4
i2 = 3
f1 = 1.5
f2 = 1.6
mq1 = nb.Mixed(q1)
mq2 = nb.Mixed(q2)
me1 = nb.Mixed(e1)
me2 = nb.Mixed(e2)
mi1 = nb.Mixed(i1)
mi2 = nb.Mixed(i2)
mf1 = nb.Mixed(f1)
mf2 = nb.Mixed(f2)
assert isinstance(mq1 / mq2, nb.Mixed)
assert isinstance((mq1 / mq2).value, fr.Fraction)
assert mq1 / mq2 == nb.Mixed(fr.Fraction(8, 9))
assert isinstance(mq1 / q2, nb.Mixed)
assert isinstance((mq1 / q2).value, fr.Fraction)
assert mq1 / q2 == nb.Mixed(fr.Fraction(8, 9))
assert isinstance(q1 / mq2, nb.Mixed)
assert isinstance((q1 / mq2).value, fr.Fraction)
assert q1 / mq2 == nb.Mixed(fr.Fraction(8, 9))
assert isinstance(mq1 / me1, nb.Mixed)
assert isinstance((mq1 / me1).value, uc.UFloat)
assert mq1 / me1 == nb.Mixed(float(q1) / e1)
assert isinstance(mq1 / e1, nb.Mixed)
assert isinstance((mq1 / e1).value, uc.UFloat)
assert mq1 / e1 == nb.Mixed(float(q1) / e1)
assert isinstance(q1 / me1, nb.Mixed)
assert isinstance((q1 / me1).value, uc.UFloat)
assert q1 / me1 == nb.Mixed(float(q1) / e1)
assert isinstance(mq1 / mi1, nb.Mixed)
assert isinstance((mq1 / mi1).value, fr.Fraction)
assert mq1 / mi1 == nb.Mixed(fr.Fraction(1, 6))
assert isinstance(mq1 / i1, nb.Mixed)
assert isinstance((mq1 / i1).value, fr.Fraction)
assert mq1 / i1 == nb.Mixed(fr.Fraction(1, 6))
assert isinstance(q1 / mi1, nb.Mixed)
assert isinstance((q1 / mi1).value, fr.Fraction)
assert q1 / mi1 == nb.Mixed(fr.Fraction(1, 6))
assert isinstance(mq1 / mf1, nb.Mixed)
assert isinstance((mq1 / mf1).value, float)
assert mq1 / mf1 == nb.Mixed(4.0 / 9.0)
assert isinstance(mq1 / f1, nb.Mixed)
assert isinstance((mq1 / f1).value, float)
assert mq1 / f1 == nb.Mixed(4.0 / 9.0)
assert isinstance(q1 / mf1, nb.Mixed)
assert isinstance((q1 / mf1).value, float)
assert q1 / mf1 == nb.Mixed(4.0 / 9.0)
assert isinstance(me1 / mq1, nb.Mixed)
assert isinstance((me1 / mq1).value, uc.UFloat)
assert me1 / mq1 == nb.Mixed(e1 / float(q1))
assert isinstance(me1 / q1, nb.Mixed)
assert isinstance((me1 / q1).value, uc.UFloat)
assert me1 / q1 == nb.Mixed(e1 / float(q1))
assert isinstance(e1 / mq1, nb.Mixed)
assert isinstance((e1 / mq1).value, uc.UFloat)
assert e1 / mq1 == nb.Mixed(e1 / float(q1))
assert isinstance(me1 / me2, nb.Mixed)
assert isinstance((me1 / me2).value, uc.UFloat)
assert me1 / me2 == nb.Mixed(e1 / e2)
assert isinstance(me1 / e2, nb.Mixed)
assert isinstance((me1 / e2).value, uc.UFloat)
assert me1 / e2 == nb.Mixed(e1 / e2)
assert isinstance(e1 / me2, nb.Mixed)
assert isinstance((e1 / me2).value, uc.UFloat)
assert e1 / me2 == nb.Mixed(e1 / e2)
assert isinstance(me1 / mi1, nb.Mixed)
assert isinstance((me1 / mi1).value, uc.UFloat)
assert me1 / mi1 == nb.Mixed(e1 / i1)
assert isinstance(me1 / i1, nb.Mixed)
assert isinstance((me1 / i1).value, uc.UFloat)
assert me1 / i1 == nb.Mixed(e1 / i1)
assert isinstance(e1 / mi1, nb.Mixed)
assert isinstance((e1 / mi1).value, uc.UFloat)
assert e1 / mi1 == nb.Mixed(e1 / i1)
assert isinstance(me1 / mf1, nb.Mixed)
assert isinstance((me1 / mf1).value, uc.UFloat)
assert me1 / mf1 == nb.Mixed(e1 / f1)
assert isinstance(me1 / f1, nb.Mixed)
assert isinstance((me1 / f1).value, uc.UFloat)
assert me1 / f1 == nb.Mixed(e1 / f1)
assert isinstance(e1 / mf1, nb.Mixed)
assert isinstance((e1 / mf1).value, uc.UFloat)
assert e1 / mf1 == nb.Mixed(e1 / f1)
assert isinstance(mi1 / mq2, nb.Mixed)
assert isinstance((mi1 / mq2).value, fr.Fraction)
assert mi1 / mq2 == nb.Mixed(fr.Fraction(16, 3))
assert isinstance(mi1 / q2, nb.Mixed)
assert isinstance((mi1 / q2).value, fr.Fraction)
assert mi1 / q2 == nb.Mixed(fr.Fraction(16, 3))
assert isinstance(i1 / mq2, nb.Mixed)
assert isinstance((i1 / mq2).value, fr.Fraction)
assert i1 / mq2 == nb.Mixed(fr.Fraction(16, 3))
assert isinstance(mi1 / me1, nb.Mixed)
assert isinstance((mi1 / me1).value, uc.UFloat)
assert mi1 / me1 == nb.Mixed(i1 / e1)
assert isinstance(mi1 / e1, nb.Mixed)
assert isinstance((mi1 / e1).value, uc.UFloat)
assert mi1 / e1 == nb.Mixed(i1 / e1)
assert isinstance(i1 / me1, nb.Mixed)
assert isinstance((i1 / me1).value, uc.UFloat)
assert i1 / me1 == nb.Mixed(i1 / e1)
assert isinstance(mi1 / mi2, nb.Mixed)
assert isinstance((mi1 / mi2).value, fr.Fraction)
assert mi1 / mi2 == nb.Mixed(fr.Fraction(4, 3))
assert isinstance(mi1 / i2, nb.Mixed)
assert isinstance((mi1 / i2).value, fr.Fraction)
assert mi1 / i2 == nb.Mixed(fr.Fraction(4, 3))
assert isinstance(i1 / mi2, nb.Mixed)
assert isinstance((i1 / mi2).value, fr.Fraction)
assert i1 / mi2 == nb.Mixed(fr.Fraction(4, 3))
assert isinstance(mi1 / mf1, nb.Mixed)
assert isinstance((mi1 / mf1).value, float)
assert mi1 / mf1 == nb.Mixed(4.0 / 1.5)
assert isinstance(mi1 / f1, nb.Mixed)
assert isinstance((mi1 / f1).value, float)
assert mi1 / f1 == nb.Mixed(4.0 / 1.5)
assert isinstance(i1 / mf1, nb.Mixed)
assert isinstance((i1 / mf1).value, float)
assert i1 / mf1 == nb.Mixed(4.0 / 1.5)
assert isinstance(mf1 / mq1, nb.Mixed)
assert isinstance((mf1 / mq1).value, float)
assert mf1 / mq1 == nb.Mixed(2.25)
assert isinstance(mf1 / q1, nb.Mixed)
assert isinstance((mf1 / q1).value, float)
assert mf1 / q1 == nb.Mixed(2.25)
assert isinstance(f1 / mq1, nb.Mixed)
assert isinstance((f1 / mq1).value, float)
assert f1 / mq1 == nb.Mixed(2.25)
assert isinstance(mf1 / me1, nb.Mixed)
assert isinstance((mf1 / me1).value, uc.UFloat)
assert mf1 / me1 == nb.Mixed(f1 / e1)
assert isinstance(mf1 / e1, nb.Mixed)
assert isinstance((mf1 / e1).value, uc.UFloat)
assert mf1 / e1 == nb.Mixed(f1 / e1)
assert isinstance(f1 / me1, nb.Mixed)
assert isinstance((f1 / me1).value, uc.UFloat)
assert f1 / me1 == nb.Mixed(f1 / e1)
assert isinstance(mf1 / mi1, nb.Mixed)
assert isinstance((mf1 / mi1).value, float)
assert mf1 / mi1 == nb.Mixed(0.375)
assert isinstance(mf1 / i1, nb.Mixed)
assert isinstance((mf1 / i1).value, float)
assert mf1 / i1 == nb.Mixed(0.375)
assert isinstance(f1 / mi1, nb.Mixed)
assert isinstance((f1 / mi1).value, float)
assert f1 / mi1 == nb.Mixed(0.375)
assert isinstance(mf1 / mf2, nb.Mixed)
assert isinstance((mf1 / mf2).value, float)
assert mf1 / mf2 == nb.Mixed(0.9375)
assert isinstance(mf1 / f2, nb.Mixed)
assert isinstance((mf1 / f2).value, float)
assert mf1 / f2 == nb.Mixed(0.9375)
assert isinstance(f1 / mf2, nb.Mixed)
assert isinstance((f1 / mf2).value, float)
assert f1 / mf2 == nb.Mixed(0.9375)
# Dividing integer 0
q = fr.Fraction(2, 3)
e = uc.ufloat(1.2, 0.1)
i = 4
f = 3.5
mq = nb.Mixed(q)
me = nb.Mixed(e)
mi = nb.Mixed(i)
mf = nb.Mixed(f)
m0 = nb.Mixed(0)
for m in [mq, me, mi, mf]:
assert m0 / m == m0
assert 0 / m == m0
for z in [q, e, i, f]:
assert m0 / z == m0
# negative
q = fr.Fraction(3, 2)
e = uc.ufloat(1.2, 0.1)
i = 4
f = 3.5
mq = nb.Mixed(q)
me = nb.Mixed(e)
mi = nb.Mixed(i)
mf = nb.Mixed(f)
assert isinstance(-mq, nb.Mixed)
assert isinstance((-mq).value, fr.Fraction)
assert -mq == nb.Mixed(fr.Fraction(-3, 2))
assert isinstance(-me, nb.Mixed)
assert isinstance((-me).value, uc.UFloat)
assert -me == nb.Mixed(-e)
assert isinstance(-mi, nb.Mixed)
assert isinstance((-mi).value, int)
assert -mi == nb.Mixed(-4)
assert isinstance(-mf, nb.Mixed)
assert isinstance((-mf).value, float)
assert -mf == nb.Mixed(-3.5)
# Modulo
q = fr.Fraction(5, 2)
e = uc.ufloat(3.2, 0.1)
i = 3
f = 3.5
mq = nb.Mixed(q)
me = nb.Mixed(e)
mi = nb.Mixed(i)
mf = nb.Mixed(f)
assert isinstance(mq % 2, nb.Mixed)
assert isinstance((mq % 2).value, fr.Fraction)
assert mq % 2 == nb.Mixed(fr.Fraction(1, 2))
assert isinstance(me % 2, nb.Mixed)
assert isinstance((me % 2).value, uc.UFloat)
assert approx((me % 2).value.n, 1.2)
assert approx((me % 2).value.s, 0.1)
assert isinstance(mi % 2, nb.Mixed)
assert isinstance((mi % 2).value, int)
assert mi % 2 == nb.Mixed(1)
assert isinstance(mf % 2, nb.Mixed)
assert isinstance((mf % 2).value, float)
assert approx((mf % 2).value, 1.5)
# Constants
assert isinstance(nb.pi, nb.Mixed)
assert isinstance((nb.pi).value, float)
assert (nb.pi).value == 3.141592653589793
# Square-Root
a = nb.sqrt(nb.Mixed(fr.Fraction(2, 3)))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.816496580)
a = nb.sqrt(fr.Fraction(2, 3))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.816496580)
a = nb.sqrt(nb.Mixed(fr.Fraction(1, 2)))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.70710678118)
a = nb.sqrt(fr.Fraction(1, 2))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.70710678118)
a = nb.sqrt(nb.Mixed(fr.Fraction(2, 1)))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 1.41421356237)
a = nb.sqrt(fr.Fraction(2, 1))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 1.41421356237)
a = nb.sqrt(nb.Mixed(fr.Fraction(4, 9)))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, fr.Fraction)
assert a == nb.Mixed(fr.Fraction(2, 3))
a = nb.sqrt(fr.Fraction(4, 9))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, fr.Fraction)
assert a == nb.Mixed(fr.Fraction(2, 3))
a = nb.sqrt(nb.Mixed(uc.ufloat(0.3, 0.1)))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, uc.UFloat)
assert approx(a.value.n, 0.54772255750)
assert approx(a.value.s, 0.09128709291)
a = nb.sqrt(uc.ufloat(0.3, 0.1))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, uc.UFloat)
assert approx(a.value.n, 0.54772255750)
assert approx(a.value.s, 0.09128709291)
a = nb.sqrt(nb.Mixed(3))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 1.7320508075688)
a = nb.sqrt(3)
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 1.7320508075688)
a = nb.sqrt(nb.Mixed(4))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, int)
assert a.value == 2
a = nb.sqrt(4)
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, int)
assert a.value == 2
a = nb.sqrt(nb.Mixed(0.5))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.7071067811)
a = nb.sqrt(0.5)
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.7071067811)
# Trigonometric Functions:
a = nb.deg2rad(nb.Mixed(fr.Fraction(180, 1)))
assert approx(a.value, 3.1415926535)
a = nb.deg2rad(fr.Fraction(180, 1))
assert approx(a.value, 3.1415926535)
a = nb.deg2rad(nb.Mixed(uc.ufloat(180.0, 10.0)))
assert approx(a.value.n, 3.1415926535)
assert approx(a.value.s, 0.174532925199)
a = nb.deg2rad(uc.ufloat(180.0, 10.0))
assert approx(a.value.n, 3.1415926535)
assert approx(a.value.s, 0.174532925199)
a = nb.deg2rad(nb.Mixed(180))
assert approx(a.value, 3.1415926535)
a = nb.deg2rad(180)
assert approx(a.value, 3.1415926535)
a = nb.deg2rad(nb.Mixed(180.0))
assert approx(a.value, 3.1415926535)
a = nb.deg2rad(180.0)
assert approx(a.value, 3.1415926535)
a = nb.rad2deg(nb.Mixed(fr.Fraction(1, 2)))
assert approx(a.value, 28.647889756)
a = nb.rad2deg(fr.Fraction(1, 2))
assert approx(a.value, 28.647889756)
a = nb.rad2deg(nb.Mixed(uc.ufloat(3.1415926535897931,
0.17453292519943295)))
assert approx(a.value.n, 180.0)
assert approx(a.value.s, 10.0)
a = nb.rad2deg(uc.ufloat(3.1415926535897931, 0.17453292519943295))
assert approx(a.value.n, 180.0)
assert approx(a.value.s, 10.0)
a = nb.rad2deg(nb.Mixed(1))
assert approx(a.value, 57.295779513082323)
a = nb.rad2deg(1)
assert approx(a.value, 57.295779513082323)
a = nb.rad2deg(nb.Mixed(3.1415926535897931))
assert approx(a.value, 180.0)
a = nb.rad2deg(3.1415926535897931)
assert approx(a.value, 180.0)
a = nb.sin(nb.Mixed(fr.Fraction(1, 2)))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.47942553860420301)
a = nb.sin(fr.Fraction(1, 2))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.479425538604203)
a = nb.sin(nb.Mixed(uc.ufloat(0.5, 0.1)))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, uc.UFloat)
assert approx(a.value.n, 0.479425538604203)
assert approx(a.value.s, 0.08775825618903728)
a = nb.sin(uc.ufloat(0.5, 0.1))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, uc.UFloat)
assert approx(a.value.n, 0.479425538604203)
assert approx(a.value.s, 0.08775825618903728)
a = nb.sin(nb.Mixed(1))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.8414709848078965)
a = nb.sin(1)
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.8414709848078965)
a = nb.sin(nb.Mixed(0.5))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.479425538604203)
a = nb.sin(0.5)
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.479425538604203)
a = nb.cos(nb.Mixed(fr.Fraction(1, 2)))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.8775825618903)
a = nb.cos(fr.Fraction(1, 2))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.8775825618903)
a = nb.cos(nb.Mixed(uc.ufloat(0.5, 0.1)))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, uc.UFloat)
assert approx(a.value.n, 0.8775825619803)
assert approx(a.value.s, 0.0479425538604)
a = nb.cos(uc.ufloat(0.5, 0.1))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, uc.UFloat)
assert approx(a.value.n, 0.8775825619803)
assert approx(a.value.s, 0.0479425538604)
a = nb.cos(nb.Mixed(1))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.54030230586)
a = nb.cos(1)
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.54030230586)
a = nb.cos(nb.Mixed(0.5))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.8775825618903)
a = nb.cos(0.5)
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.8775825618903)
a = nb.arcsin(nb.Mixed(fr.Fraction(1, 2)))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.52359877559829)
a = nb.arcsin(fr.Fraction(1, 2))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.52359877559829)
a = nb.arcsin(nb.Mixed(uc.ufloat(0.5, 0.1)))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, uc.UFloat)
assert approx(a.value.n, 0.52359877559829)
assert approx(a.value.s, 0.11547005383)
a = nb.arcsin(uc.ufloat(0.5, 0.1))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, uc.UFloat)
assert approx(a.value.n, 0.52359877559829)
assert approx(a.value.s, 0.11547005383)
a = nb.arcsin(nb.Mixed(1))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 1.57079632679)
a = nb.arcsin(1)
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 1.57079632679)
a = nb.arcsin(nb.Mixed(0.5))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.52359877559829)
a = nb.arcsin(0.5)
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.52359877559829)
a = nb.arccos(nb.Mixed(fr.Fraction(1, 2)))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 1.04719755119)
a = nb.arccos(fr.Fraction(1, 2))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 1.04719755119)
a = nb.arccos(nb.Mixed(uc.ufloat(0.5, 0.1)))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, uc.UFloat)
assert approx(a.value.n, 1.04719755119)
assert approx(a.value.s, 0.11547005383)
a = nb.arccos(uc.ufloat(0.5, 0.1))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, uc.UFloat)
assert approx(a.value.n, 1.04719755119)
assert approx(a.value.s, 0.11547005383)
a = nb.arccos(nb.Mixed(1))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.0)
a = nb.arccos(1)
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.0)
a = nb.arccos(nb.Mixed(0.5))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 1.04719755119)
a = nb.arccos(0.5)
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 1.04719755119)
a = nb.dsin(fr.Fraction(1, 2))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.00872653549)
a = nb.dsin(fr.Fraction(1, 2))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.00872653549)
a = nb.dsin(nb.Mixed(uc.ufloat(0.5, 0.1)))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, uc.UFloat)
assert approx(a.value.n, 0.00872653549)
assert approx(a.value.s, 0.00174526279)
a = nb.dsin(uc.ufloat(0.5, 0.1))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, uc.UFloat)
assert approx(a.value.n, 0.00872653549)
assert approx(a.value.s, 0.00174526279)
a = nb.dsin(nb.Mixed(1))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.017452406437)
a = nb.dsin(1)
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.017452406437)
a = nb.dsin(nb.Mixed(0.5))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.00872653549)
a = nb.dsin(0.5)
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.00872653549)
z = nb.Mixed(0)
o = nb.Mixed(1)
h = nb.Mixed(fr.Fraction(1, 2))
xs = [0, 30, 90, 150, 180, 210, 270, 330]
ys = [z, h, o, h, z, -h, -o, -h]
for i in range(len(xs)):
x = xs[i]
y = ys[i]
a = nb.dsin(x)
assert a == y
a = nb.dsin(fr.Fraction(x, 1))
assert a == y
a = nb.dsin(nb.Mixed(x))
assert a == y
a = nb.dsin(nb.Mixed(fr.Fraction(x, 1)))
assert a == y
a = nb.dcos(fr.Fraction(1, 2))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.999961923064)
a = nb.dcos(fr.Fraction(1, 2))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.999961923064)
a = nb.dcos(nb.Mixed(uc.ufloat(0.5, 0.1)))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, uc.UFloat)
assert approx(a.value.n, 0.999961923064)
assert approx(a.value.s, 1.5230677e-5)
a = nb.dcos(uc.ufloat(0.5, 0.1))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, uc.UFloat)
assert approx(a.value.n, 0.999961923064)
assert approx(a.value.s, 1.5230677e-5)
a = nb.dcos(nb.Mixed(1))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.9998476951)
a = nb.dcos(1)
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.9998476951)
a = nb.dcos(nb.Mixed(0.5))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.999961923064)
a = nb.dcos(0.5)
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.999961923064)
z = nb.Mixed(0)
o = nb.Mixed(1)
h = nb.Mixed(fr.Fraction(1, 2))
xs = [0, 60, 90, 120, 180, 240, 270, 300]
ys = [o, h, z, -h, -o, -h, -z, h]
for i in range(len(xs)):
x = xs[i]
y = ys[i]
a = nb.dcos(x)
assert a == y
a = nb.dcos(fr.Fraction(x, 1))
assert a == y
a = nb.dcos(nb.Mixed(x))
assert a == y
a = nb.dcos(nb.Mixed(fr.Fraction(x, 1)))
assert a == y
a = nb.darcsin(nb.Mixed(fr.Fraction(1, 3)))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 19.47122063449)
a = nb.darcsin(fr.Fraction(1, 3))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 19.47122063449)
a = nb.darcsin(nb.Mixed(uc.ufloat(0.5, 0.1)))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, uc.UFloat)
assert approx(a.value.n, 30.0)
assert approx(a.value.s, 6.615946745061)
a = nb.darcsin(uc.ufloat(0.5, 0.1))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, uc.UFloat)
assert approx(a.value.n, 30.0)
assert approx(a.value.s, 6.615946745061)
a = nb.darcsin(nb.Mixed(0.5))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 30.0)
a = nb.darcsin(0.5)
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 30.0)
xs = [
-fr.Fraction(1, 1), -fr.Fraction(1, 2),
fr.Fraction(0, 1),
fr.Fraction(1, 2),
fr.Fraction(1, 1)
]
ys = [-90, -30, 0, 30, 90]
for i in range(len(xs)):
x = xs[i]
y = ys[i]
assert isinstance(nb.darcsin(x), nb.Mixed)
assert isinstance(nb.darcsin(x).value, int)
assert nb.darcsin(x) == y
assert isinstance(nb.darcsin(nb.Mixed(x)), nb.Mixed)
assert isinstance(nb.darcsin(nb.Mixed(x)).value, int)
assert nb.darcsin(nb.Mixed(x)) == y
xs = [-1, 0, 1]
ys = [-90, 0, 90]
for i in range(len(xs)):
x = xs[i]
y = ys[i]
assert isinstance(nb.darcsin(x), nb.Mixed)
assert isinstance(nb.darcsin(x).value, int)
assert nb.darcsin(x) == y
assert isinstance(nb.darcsin(nb.Mixed(x)), nb.Mixed)
assert isinstance(nb.darcsin(nb.Mixed(x)).value, int)
assert nb.darcsin(nb.Mixed(x)) == y
a = nb.darccos(nb.Mixed(fr.Fraction(1, 3)))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 70.5287793655)
a = nb.darccos(fr.Fraction(1, 3))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 70.5287793655)
a = nb.darccos(nb.Mixed(uc.ufloat(0.5, 0.1)))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, uc.UFloat)
assert approx(a.value.n, 60.0)
assert approx(a.value.s, 6.615946745061)
a = nb.darccos(uc.ufloat(0.5, 0.1))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, uc.UFloat)
assert approx(a.value.n, 60.0)
assert approx(a.value.s, 6.615946745061)
a = nb.darccos(nb.Mixed(0.5))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 60.0)
a = nb.darccos(0.5)
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 60.0)
xs = [
-fr.Fraction(1, 1), -fr.Fraction(1, 2),
fr.Fraction(0, 1),
fr.Fraction(1, 2),
fr.Fraction(1, 1)
]
ys = [180, 120, 90, 60, 0]
for i in range(len(xs)):
x = xs[i]
y = ys[i]
assert isinstance(nb.darccos(x), nb.Mixed)
assert isinstance(nb.darccos(x).value, int)
assert nb.darccos(x) == y
assert isinstance(nb.darccos(nb.Mixed(x)), nb.Mixed)
assert isinstance(nb.darccos(nb.Mixed(x)).value, int)
assert nb.darccos(nb.Mixed(x)) == y
xs = [-1, 0, 1]
ys = [180, 90, 0]
for i in range(len(xs)):
x = xs[i]
y = ys[i]
assert isinstance(nb.darccos(x), nb.Mixed)
assert isinstance(nb.darccos(x).value, int)
assert nb.darccos(x) == y
assert isinstance(nb.darccos(nb.Mixed(x)), nb.Mixed)
assert isinstance(nb.darccos(nb.Mixed(x)).value, int)
assert nb.darccos(nb.Mixed(x)) == y
def test_Transformation():
t1 = geo.Transformation(nb.Matrix([[0, 1, 0, 0],
[1, 0, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]]))
assert t1.__str__() == "Transformation O -> (0, 0, 0)\n" \
" then\n" \
" a' = b\n" \
" b' = a\n" \
" c' = c"
t2 = geo.Transformation(nb.Matrix([[1, 0, 0, fr.Fraction(1, 2)],
[0, 1, 0, fr.Fraction(1, 4)],
[0, 0, 1, fr.Fraction(1, 3)],
[0, 0, 0, 1]]))
assert t2.__str__() == "Transformation O -> (-1/2, -1/4, -1/3)\n" \
" then\n" \
" a' = a\n" \
" b' = b\n" \
" c' = c"
assert isinstance(t2.inv(), geo.Transformation)
assert t2 * t2.inv() == geo.Transformation(nb.Matrix.onematrix(4))
t3 = geo.Transformation(nb.Matrix([[1.0, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]]))
print(t3.value)
assert t3.__str__() == "Transformation O -> (0, 0, 0)\n" \
" then\n" \
" a' = 1.0a\n" \
" b' = b\n" \
" c' = c"
q1 = geo.Rec(nb.Matrix([[1, 0, 0, 0]]))
t = geo.Transformation(nb.Matrix([[0, 1, 0, 0],
[0, 0, 1, 0],
[1, 0, 0, 0],
[0, 0, 0, 1]]))
assert isinstance(t ** q1, geo.Rec)
assert (t ** q1) == geo.Rec(nb.Matrix([[0, 0, 1, 0]]))
q1 = geo.Rec(nb.Matrix([[1, 0, 0, 0]]))
t = geo.Transformation(nb.Matrix([[0, 1, 0, 0.3],
[0, 0, 1, 0.7],
[1, 0, 0, 100],
[0, 0, 0, 1]]))
assert isinstance(t ** q1, geo.Rec)
assert (t ** q1) == geo.Rec(nb.Matrix([[0, 0, 1, 0]]))
q1 = geo.Rec(nb.Matrix([[0, 0, 1, 0]]))
t = geo.Transformation(nb.Matrix([[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 2, 0],
[0, 0, 0, 1]]))
assert t.__str__() == "Transformation O -> (0, 0, 0)\n" \
" then\n" \
" a' = a\n" \
" b' = b\n" \
" c' = 1/2c"
assert isinstance(t ** q1, geo.Rec)
assert (t ** q1) == \
geo.Rec(nb.Matrix([[0, 0, nb.Mixed(fr.Fraction(1, 2)), 0]]))
q1 = geo.Rec(nb.Matrix([[0, 0, 1, 0]]))
t = geo.Transformation(nb.Matrix([[1, 0, 0, 0],
[0, 0, 2, 0],
[0, -1, 0, 0],
[0, 0, 0, 1]]))
assert t.__str__() == "Transformation O -> (0, 0, 0)\n" \
" then\n" \
" a' = a\n" \
" b' = 1/2c\n" \
" c' = -b"
assert isinstance(t ** q1, geo.Rec)
print(t)
assert (t ** q1) == \
geo.Rec(nb.Matrix([[0, nb.Mixed(fr.Fraction(1, 2)), 0, 0]]))
def test_Mixed():
# Create a number of type Mixed with 4 different types.
q = fr.Fraction(2, 3)
e = uc.ufloat(1.2, 0.1)
i = 4
f = 3.5
q1 = fr.Fraction(2, 1)
e1 = uc.ufloat(3.7, 0)
assert isinstance(nb.Mixed(q).value, fr.Fraction)
assert nb.Mixed(q).value == q
assert isinstance(nb.Mixed(e).value, uc.UFloat)
assert (nb.Mixed(e).value).n == e.n
assert (nb.Mixed(e).value).s == e.s
assert isinstance(nb.Mixed(i).value, int)
assert nb.Mixed(i).value == i
assert isinstance(nb.Mixed(f).value, float)
assert nb.Mixed(f).value == f
assert isinstance(nb.Mixed(q1).value, int)
assert nb.Mixed(q1).value == 2
assert isinstance(nb.Mixed(e1).value, uc.UFloat)
assert nb.Mixed(e1).value == uc.ufloat(3.7, 0.0)
# Convert a number of type Mixed to float.
assert isinstance(float(nb.Mixed(q)), float)
assert float(nb.Mixed(q)) == float(2 / 3)
assert isinstance(float(nb.Mixed(e)), float)
assert float(nb.Mixed(e)) == 1.2
assert isinstance(float(nb.Mixed(i)), float)
assert float(nb.Mixed(i)) == 4.0
assert isinstance(float(nb.Mixed(f)), float)
assert float(nb.Mixed(f)) == 3.5
# Print a number of type Mixed as str.
assert isinstance(nb.Mixed(q).__str__(), str)
assert nb.Mixed(q).__str__() == "2/3"
assert isinstance(nb.Mixed(e).__str__(), str)
assert nb.Mixed(e).__str__() == "1.20(10)"
assert isinstance(nb.Mixed(i).__str__(), str)
assert nb.Mixed(i).__str__() == "4"
assert isinstance(nb.Mixed(f).__str__(), str)
assert nb.Mixed(f).__str__() == "3.5"
# Hash
assert isinstance(hash(nb.Mixed(q)), int)
assert isinstance(hash(nb.Mixed(e)), int)
assert isinstance(hash(nb.Mixed(i)), int)
assert isinstance(hash(nb.Mixed(f)), int)
# Equal
assert nb.Mixed(q) == nb.Mixed(q)
assert nb.Mixed(e) == nb.Mixed(e)
assert nb.Mixed(i) == nb.Mixed(i)
assert nb.Mixed(f) == nb.Mixed(f)
assert nb.Mixed(fr.Fraction(2, 3)) == nb.Mixed(fr.Fraction(2, 3))
assert (nb.Mixed(fr.Fraction(2, 3)) == nb.Mixed(fr.Fraction(1, 3))) == False
assert nb.Mixed(uc.ufloat(1.2, 0.1)) == nb.Mixed(uc.ufloat(1.2, 0.1))
assert (nb.Mixed(uc.ufloat(1.2, 0.1)) == nb.Mixed(uc.ufloat(1.2, 0.2))) \
== False
x = nb.Mixed(uc.ufloat(0.5, 0.3) + uc.ufloat(0.5, 0.4))
y = nb.Mixed(uc.ufloat(1.0, 0.5))
assert x == y
assert nb.Mixed(fr.Fraction(2, 3)) == nb.Mixed(fr.Fraction(2, 3))
assert (nb.Mixed(fr.Fraction(2, 3)) == nb.Mixed(uc.ufloat(1.2, 0.1))) \
== False
assert (nb.Mixed(fr.Fraction(2, 3)) == nb.Mixed(1)) == False
assert (nb.Mixed(fr.Fraction(2, 3)) == nb.Mixed(0.66)) == False
assert (nb.Mixed(uc.ufloat(1.2, 0.1)) == nb.Mixed(fr.Fraction(2, 3))) \
== False
assert nb.Mixed(uc.ufloat(1.2, 0.1) == nb.Mixed(uc.ufloat(1.2, 0.1)))
assert (nb.Mixed(uc.ufloat(1.2, 0.1)) == nb.Mixed(1)) == False
assert (nb.Mixed(uc.ufloat(1.2, 0.1)) == nb.Mixed(0.66)) == False
assert (nb.Mixed(1) == nb.Mixed(fr.Fraction(2, 3))) == False
assert (nb.Mixed(1) == nb.Mixed(uc.ufloat(1.2, 0.1))) == False
assert nb.Mixed(1) == nb.Mixed(1)
assert (nb.Mixed(1) == nb.Mixed(1.0)) == False
assert (nb.Mixed(1.0) == nb.Mixed(fr.Fraction(1, 1))) == False
assert (nb.Mixed(1.0) == nb.Mixed(uc.ufloat(1.0, 0.0))) == False
assert (nb.Mixed(1.0) == nb.Mixed(1)) == False
assert nb.Mixed(1.0) == nb.Mixed(1.0)
assert nb.Mixed(0) == 0
assert (nb.Mixed(0.1) == 0) == False
assert nb.Mixed(fr.Fraction(2, 1)) == 2
# Other relations
# Addition
mq = nb.Mixed(q)
me = nb.Mixed(e)
mi = nb.Mixed(i)
mf = nb.Mixed(f)
"""for x1 in [q, e, i, f]:
for x2 in [q, e, i, f]:
m1 = nb.Mixed(x1)
m2 = nb.Mixed(x2)
assert isinstance(m1 + m2, nb.Mixed)
assert isinstance((m1 + m2).value
assert isinstance(m1 + x2, nb.Mixed)
assert isinstance(
assert isinstance(m2 + m1, nb.Mixed)"""
assert isinstance(mq + mq, nb.Mixed)
assert isinstance((mq + mq).value, fr.Fraction)
assert mq + mq == nb.Mixed(fr.Fraction(4, 3))
assert isinstance(mq + q, nb.Mixed)
assert isinstance((mq + q).value, fr.Fraction)
assert mq + q == nb.Mixed(fr.Fraction(4, 3))
assert isinstance(q + mq, nb.Mixed)
assert isinstance((q + mq).value, fr.Fraction)
assert q + mq == nb.Mixed(fr.Fraction(4, 3))
assert isinstance(mq + me, nb.Mixed)
assert isinstance((mq + me).value, uc.UFloat)
assert mq + me == nb.Mixed(uc.ufloat(1.2, 0.10) + 2 / 3)
assert isinstance(mq + e, nb.Mixed)
assert isinstance((mq + e).value, uc.UFloat)
assert mq + e == nb.Mixed(uc.ufloat(1.2, 0.10) + 2 / 3)
assert isinstance(q + me, nb.Mixed)
assert isinstance((q + me).value, uc.UFloat)
assert q + me == nb.Mixed(uc.ufloat(1.2, 0.10) + 2 / 3)
assert isinstance(mq + mi, nb.Mixed)
assert isinstance((mq + mi).value, fr.Fraction)
assert mq + mi == nb.Mixed(fr.Fraction(14, 3))
assert isinstance(mq + i, nb.Mixed)
assert isinstance((mq + i).value, fr.Fraction)
assert mq + i == nb.Mixed(fr.Fraction(14, 3))
assert isinstance(q + mi, nb.Mixed)
assert isinstance((q + mi).value, fr.Fraction)
assert q + mi == nb.Mixed(fr.Fraction(14, 3))
assert isinstance(mq + mf, nb.Mixed)
assert isinstance((mq + mf).value, float)
assert mq + mf == nb.Mixed(3.5 + 2 / 3)
assert isinstance(mq + f, nb.Mixed)
assert isinstance((mq + f).value, float)
assert mq + f == nb.Mixed(3.5 + 2 / 3)
assert isinstance(q + mf, nb.Mixed)
assert isinstance((q + mf).value, float)
assert q + mf == nb.Mixed(3.5 + 2 / 3)
assert isinstance(me + mq, nb.Mixed)
assert isinstance((me + mq).value, uc.UFloat)
assert me + mq == nb.Mixed(uc.ufloat(1.2, 0.1) + 2 / 3)
assert isinstance(me + q, nb.Mixed)
assert isinstance((me + q).value, uc.UFloat)
assert me + q == nb.Mixed(uc.ufloat(1.2, 0.1) + 2 / 3)
assert isinstance(e + mq, nb.Mixed)
assert isinstance((e + mq).value, uc.UFloat)
assert e + mq == nb.Mixed(uc.ufloat(1.2, 0.1) + 2 / 3)
assert isinstance(me + me, nb.Mixed)
assert isinstance((me + me).value, uc.UFloat)
assert me + me == nb.Mixed(uc.ufloat(1.2, 0.1) + uc.ufloat(1.2, 0.1))
assert isinstance(me + e, nb.Mixed)
assert isinstance((me + e).value, uc.UFloat)
assert me + e == nb.Mixed(uc.ufloat(1.2, 0.1) + uc.ufloat(1.2, 0.1))
assert isinstance(e + me, nb.Mixed)
assert isinstance((e + me).value, uc.UFloat)
assert e + me == nb.Mixed(uc.ufloat(1.2, 0.1) + uc.ufloat(1.2, 0.1))
assert isinstance(me + mi, nb.Mixed)
assert isinstance((me + mi).value, uc.UFloat)
assert me + mi == nb.Mixed(uc.ufloat(5.2, 0.1))
assert isinstance(me + i, nb.Mixed)
assert isinstance((me + i).value, uc.UFloat)
assert me + i == nb.Mixed(uc.ufloat(5.2, 0.1))
assert isinstance(e + mi, nb.Mixed)
assert isinstance((e + mi).value, uc.UFloat)
assert me + i == nb.Mixed(uc.ufloat(5.2, 0.1))
assert isinstance(me + mf, nb.Mixed)
assert isinstance((me + mf).value, uc.UFloat)
assert me + mf == nb.Mixed(uc.ufloat(4.7, 0.1))
assert isinstance(me + f, nb.Mixed)
assert isinstance((me + f).value, uc.UFloat)
assert me + f == nb.Mixed(uc.ufloat(4.7, 0.1))
assert isinstance(e + mf, nb.Mixed)
assert isinstance((e + mf).value, uc.UFloat)
assert e + mf == nb.Mixed(uc.ufloat(4.7, 0.1))
assert isinstance(mi + mq, nb.Mixed)
assert isinstance((mi + mq).value, fr.Fraction)
assert mi + mq == nb.Mixed(fr.Fraction(14, 3))
assert isinstance(mi + q, nb.Mixed)
assert isinstance((mi + q).value, fr.Fraction)
assert mi + q == nb.Mixed(fr.Fraction(14, 3))
assert isinstance(i + mq, nb.Mixed)
assert isinstance((i + mq).value, fr.Fraction)
assert i + mq == nb.Mixed(fr.Fraction(14, 3))
assert isinstance(mi + me, nb.Mixed)
assert isinstance((mi + me).value, uc.UFloat)
assert mi + me == nb.Mixed(uc.ufloat(5.2, 0.1))
assert isinstance(mi + e, nb.Mixed)
assert isinstance((mi + e).value, uc.UFloat)
assert mi + me == nb.Mixed(uc.ufloat(5.2, 0.1))
assert isinstance(i + me, nb.Mixed)
assert isinstance((i + me).value, uc.UFloat)
assert i + me == nb.Mixed(uc.ufloat(5.2, 0.1))
assert isinstance(mi + mi, nb.Mixed)
assert isinstance((mi + mi).value, int)
assert mi + mi == nb.Mixed(8)
assert isinstance(mi + i, nb.Mixed)
assert isinstance((mi + i).value, int)
assert mi + i == nb.Mixed(8)
assert isinstance(i + mi, nb.Mixed)
assert isinstance((i + mi).value, int)
assert i + mi == nb.Mixed(8)
assert isinstance(mi + mf, nb.Mixed)
assert isinstance((mi + mf).value, float)
assert mi + mf == nb.Mixed(7.5)
assert isinstance(mi + f, nb.Mixed)
assert isinstance((mi + f).value, float)
assert mi + f == nb.Mixed(7.5)
assert isinstance(i + mf, nb.Mixed)
assert isinstance((i + mf).value, float)
assert i + mf == nb.Mixed(7.5)
assert isinstance(mf + mq, nb.Mixed)
assert isinstance((mf + mq).value, float)
assert mf + mq == nb.Mixed(3.5 + 2 / 3)
assert isinstance(mf + q, nb.Mixed)
assert isinstance((mf + q).value, float)
assert mf + q == nb.Mixed(3.5 + 2 / 3)
assert isinstance(f + mq, nb.Mixed)
assert isinstance((f + mq).value, float)
assert f + mq == nb.Mixed(3.5 + 2 / 3)
assert isinstance(mf + me, nb.Mixed)
assert isinstance((mf + me).value, uc.UFloat)
assert mf + me == nb.Mixed(uc.ufloat(4.7, 0.1))
assert isinstance(mf + e, nb.Mixed)
assert isinstance((mf + e).value, uc.UFloat)
assert mf + e == nb.Mixed(uc.ufloat(4.7, 0.1))
assert isinstance(f + me, nb.Mixed)
assert isinstance((f + me).value, uc.UFloat)
assert f + me == nb.Mixed(uc.ufloat(4.7, 0.1))
# Subtraction
q1 = fr.Fraction(1, 2)
q2 = fr.Fraction(1, 4)
e1 = uc.ufloat(1.2, 0.3)
e2 = uc.ufloat(0.2, 0.4)
i1 = 4
i2 = 3
f1 = 3.5
f2 = 3.4
mq1 = nb.Mixed(q1)
mq2 = nb.Mixed(q2)
me1 = nb.Mixed(e1)
me2 = nb.Mixed(e2)
mi1 = nb.Mixed(i1)
mi2 = nb.Mixed(i2)
mf1 = nb.Mixed(f1)
mf2 = nb.Mixed(f2)
assert isinstance(mq1 - mq2, nb.Mixed)
assert isinstance((mq1 - mq2).value, fr.Fraction)
assert mq1 - mq2 == nb.Mixed(fr.Fraction(1, 4))
assert isinstance(mq1 - q2, nb.Mixed)
assert isinstance((mq1 - q2).value, fr.Fraction)
assert mq1 - q2 == nb.Mixed(fr.Fraction(1, 4))
assert isinstance(q1 - mq2, nb.Mixed)
assert isinstance((q1 - mq2).value, fr.Fraction)
assert q1 - mq2 == nb.Mixed(fr.Fraction(1, 4))
assert isinstance(mq1 - me1, nb.Mixed)
assert isinstance((mq1 - me1).value, uc.UFloat)
assert mq1 - me1 == nb.Mixed(uc.ufloat(-0.7, 0.3))
assert isinstance(mq1 - e1, nb.Mixed)
assert isinstance((mq1 - e1).value, uc.UFloat)
assert mq1 - e1 == nb.Mixed(uc.ufloat(-0.7, 0.3))
assert isinstance(q1 - me1, nb.Mixed)
assert isinstance((q1 - me1).value, uc.UFloat)
assert q1 - me1 == nb.Mixed(uc.ufloat(-0.7, 0.3))
assert isinstance(mq1 - mi1, nb.Mixed)
assert isinstance((mq1 - mi1).value, fr.Fraction)
assert mq1 - mi1 == nb.Mixed(fr.Fraction(-7, 2))
assert isinstance(mq1 - i1, nb.Mixed)
assert isinstance((mq1 - i1).value, fr.Fraction)
assert mq1 - i1 == nb.Mixed(fr.Fraction(-7, 2))
assert isinstance(q1 - mi1, nb.Mixed)
assert isinstance((q1 - mi1).value, fr.Fraction)
assert q1 - mi1 == nb.Mixed(fr.Fraction(-7, 2))
assert isinstance(mq1 - mf1, nb.Mixed)
assert isinstance((mq1 - mf1).value, float)
assert mq1 - mf1 == nb.Mixed(-3.0)
assert isinstance(mq1 - f1, nb.Mixed)
assert isinstance((mq1 - f1).value, float)
assert mq1 - f1 == nb.Mixed(-3.0)
assert isinstance(q1 - mf1, nb.Mixed)
assert isinstance((q1 - mf1).value, float)
assert q1 - mf1 == nb.Mixed(-3.0)
assert isinstance(me1 - mq1, nb.Mixed)
assert isinstance((me1 - mq1).value, uc.UFloat)
assert me1 - mq1 == nb.Mixed(uc.ufloat(0.7, 0.3))
assert isinstance(me1 - q1, nb.Mixed)
assert isinstance((me1 - q1).value, uc.UFloat)
assert me1 - q1 == nb.Mixed(uc.ufloat(0.7, 0.3))
assert isinstance(e1 - mq1, nb.Mixed)
assert isinstance((e1 - mq1).value, uc.UFloat)
assert e1 - mq1 == nb.Mixed(uc.ufloat(0.7, 0.3))
assert isinstance(me1 - me2, nb.Mixed)
assert isinstance((me1 - me2).value, uc.UFloat)
assert me1 - me2 == nb.Mixed(uc.ufloat(1.0, 0.5))
assert isinstance(me1 - e2, nb.Mixed)
assert isinstance((me1 - e2).value, uc.UFloat)
assert me1 - e2 == nb.Mixed(uc.ufloat(1.0, 0.5))
assert isinstance(e1 - me2, nb.Mixed)
assert isinstance((e1 - me2).value, uc.UFloat)
assert e1 - me2 == nb.Mixed(uc.ufloat(1.0, 0.5))
assert isinstance(me1 - mi1, nb.Mixed)
assert isinstance((me1 - mi1).value, uc.UFloat)
assert me1 - mi1 == nb.Mixed(uc.ufloat(-2.8, 0.3))
assert isinstance(me1 - i1, nb.Mixed)
assert isinstance((me1 - i1).value, uc.UFloat)
assert me1 - i1 == nb.Mixed(uc.ufloat(-2.8, 0.3))
assert isinstance(e1 - mi1, nb.Mixed)
assert isinstance((e1 - mi1).value, uc.UFloat)
assert e1 - mi1 == nb.Mixed(uc.ufloat(-2.8, 0.3))
assert isinstance(me1 - mf1, nb.Mixed)
assert isinstance((me1 - mf1).value, uc.UFloat)
assert me1 - mf1 == nb.Mixed(uc.ufloat(-2.3, 0.3))
assert isinstance(me1 - f1, nb.Mixed)
assert isinstance((me1 - f1).value, uc.UFloat)
assert me1 - f1 == nb.Mixed(uc.ufloat(-2.3, 0.3))
assert isinstance(e1 - mf1, nb.Mixed)
assert isinstance((e1 - mf1).value, uc.UFloat)
assert e1 - mf1 == nb.Mixed(uc.ufloat(-2.3, 0.3))
assert isinstance(mi1 - mq1, nb.Mixed)
assert isinstance((mi1 - mq1).value, fr.Fraction)
assert mi1 - mq1 == nb.Mixed(fr.Fraction(7, 2))
assert isinstance(mi1 - q1, nb.Mixed)
assert isinstance((mi1 - q1).value, fr.Fraction)
assert mi1 - q1 == nb.Mixed(fr.Fraction(7, 2))
assert isinstance(i1 - mq1, nb.Mixed)
assert isinstance((i1 - mq1).value, fr.Fraction)
assert i1 - mq1 == nb.Mixed(fr.Fraction(7, 2))
assert isinstance(mi1 - me1, nb.Mixed)
assert isinstance((mi1 - me1).value, uc.UFloat)
assert mi1 - me1 == nb.Mixed(uc.ufloat(2.8, 0.3))
assert isinstance(mi1 - e1, nb.Mixed)
assert isinstance((mi1 - e1).value, uc.UFloat)
assert mi1 - e1 == nb.Mixed(uc.ufloat(2.8, 0.3))
assert isinstance(i1 - me1, nb.Mixed)
assert isinstance((i1 - me1).value, uc.UFloat)
assert i1 - me1 == nb.Mixed(uc.ufloat(2.8, 0.3))
assert isinstance(mi1 - mi2, nb.Mixed)
assert isinstance((mi1 - mi2).value, int)
assert mi1 - mi2 == nb.Mixed(1)
assert isinstance(mi1 - i2, nb.Mixed)
assert isinstance((mi1 - i2).value, int)
assert mi1 - i2 == nb.Mixed(1)
assert isinstance(i1 - mi2, nb.Mixed)
assert isinstance((i1 - mi2).value, int)
assert i1 - mi2 == nb.Mixed(1)
assert isinstance(mi1 - mf1, nb.Mixed)
assert isinstance((mi1 - mf1).value, float)
assert mi1 - mf1 == nb.Mixed(0.5)
assert isinstance(mi1 - f1, nb.Mixed)
assert isinstance((mi1 - f1).value, float)
assert mi1 - f1 == nb.Mixed(0.5)
assert isinstance(i1 - mf1, nb.Mixed)
assert isinstance((i1 - mf1).value, float)
assert i1 - mf1 == nb.Mixed(0.5)
assert isinstance(mf1 - mq1, nb.Mixed)
assert isinstance((mf1 - mq1).value, float)
assert mf1 - mq1 == nb.Mixed(3.0)
assert isinstance(mf1 - q1, nb.Mixed)
assert isinstance((mf1 - q1).value, float)
assert mf1 - q1 == nb.Mixed(3.0)
assert isinstance(f1 - mq1, nb.Mixed)
assert isinstance((f1 - mq1).value, float)
assert f1 - mq1 == nb.Mixed(3.0)
assert isinstance(mf1 - me1, nb.Mixed)
assert isinstance((mf1 - me1).value, uc.UFloat)
assert mf1 - me1 == nb.Mixed(uc.ufloat(2.3, 0.3))
assert isinstance(mf1 - e1, nb.Mixed)
assert isinstance((mf1 - e1).value, uc.UFloat)
assert mf1 - e1 == nb.Mixed(uc.ufloat(2.3, 0.3))
assert isinstance(f1 - me1, nb.Mixed)
assert isinstance((f1 - me1).value, uc.UFloat)
assert f1 - me1 == nb.Mixed(uc.ufloat(2.3, 0.3))
assert isinstance(mf1 - mi1, nb.Mixed)
assert isinstance((mf1 - mi1).value, float)
assert mf1 - mi1 == nb.Mixed(-0.5)
assert isinstance(mf1 - i1, nb.Mixed)
assert isinstance((mf1 - i1).value, float)
assert mf1 - i1 == nb.Mixed(-0.5)
assert isinstance(f1 - mi1, nb.Mixed)
assert isinstance((f1 - mi1).value, float)
assert f1 - mi1 == nb.Mixed(-0.5)
assert isinstance(mf1 - mf2, nb.Mixed)
assert isinstance((mf1 - mf2).value, float)
assert mf1 - mf2 == nb.Mixed(3.5 - 3.4)
assert isinstance(mf1 - f2, nb.Mixed)
assert isinstance((mf1 - f2).value, float)
assert mf1 - f2 == nb.Mixed(3.5 - 3.4)
assert isinstance(f1 - mf2, nb.Mixed)
assert isinstance((f1 - mf2).value, float)
assert f1 - mf2 == nb.Mixed(3.5 - 3.4)
# Multiplication
q1 = fr.Fraction(1, 2)
q2 = fr.Fraction(1, 4)
e1 = uc.ufloat(1.2, 0.3)
e2 = uc.ufloat(0.2, 0.4)
i1 = 4
i2 = 3
f1 = 3.5
f2 = 3.4
mq1 = nb.Mixed(q1)
mq2 = nb.Mixed(q2)
me1 = nb.Mixed(e1)
me2 = nb.Mixed(e2)
mi1 = nb.Mixed(i1)
mi2 = nb.Mixed(i2)
mf1 = nb.Mixed(f1)
mf2 = nb.Mixed(f2)
assert isinstance(mq1 * mq2, nb.Mixed)
assert isinstance((mq1 * mq2).value, fr.Fraction)
assert mq1 * mq2 == nb.Mixed(fr.Fraction(1, 8))
assert isinstance(mq1 * q2, nb.Mixed)
assert isinstance((mq1 * q2).value, fr.Fraction)
assert mq1 * q2 == nb.Mixed(fr.Fraction(1, 8))
assert isinstance(q1 * mq2, nb.Mixed)
assert isinstance((q1 * mq2).value, fr.Fraction)
assert q1 * mq2 == nb.Mixed(fr.Fraction(1, 8))
assert isinstance(mq1 * me1, nb.Mixed)
assert isinstance((mq1 * me1).value, uc.UFloat)
assert mq1 * me1 == nb.Mixed(uc.ufloat(0.6, 0.15))
assert isinstance(mq1 * e1, nb.Mixed)
assert isinstance((mq1 * e1).value, uc.UFloat)
assert mq1 * e1 == nb.Mixed(uc.ufloat(0.6, 0.15))
assert isinstance(q1 * me1, nb.Mixed)
assert isinstance((q1 * me1).value, uc.UFloat)
assert q1 * me1 == nb.Mixed(uc.ufloat(0.6, 0.15))
assert isinstance(mq1 * mi2, nb.Mixed)
assert isinstance((mq1 * mi2).value, fr.Fraction)
assert mq1 * mi2 == nb.Mixed(fr.Fraction(3, 2))
assert isinstance(mq1 * i2, nb.Mixed)
assert isinstance((mq1 * i2).value, fr.Fraction)
assert mq1 * i2 == nb.Mixed(fr.Fraction(3, 2))
assert isinstance(q1 * mi2, nb.Mixed)
assert isinstance((q1 * mi2).value, fr.Fraction)
assert q1 * mi2 == nb.Mixed(fr.Fraction(3, 2))
assert isinstance(mq1 * mf1, nb.Mixed)
assert isinstance((mq1 * mf1).value, float)
assert mq1 * mf1 == nb.Mixed(1.75)
assert isinstance(mq1 * f1, nb.Mixed)
assert isinstance((mq1 * f1).value, float)
assert mq1 * f1 == nb.Mixed(1.75)
assert isinstance(q1 * mf1, nb.Mixed)
assert isinstance((q1 * mf1).value, float)
assert q1 * mf1 == nb.Mixed(1.75)
assert isinstance(me1 * mq1, nb.Mixed)
assert isinstance((me1 * mq1).value, uc.UFloat)
assert me1 * mq1 == nb.Mixed(uc.ufloat(0.6, 0.15))
assert isinstance(me1 * q1, nb.Mixed)
assert isinstance((me1 * q1).value, uc.UFloat)
assert me1 * q1 == nb.Mixed(uc.ufloat(0.6, 0.15))
assert isinstance(e1 * mq1, nb.Mixed)
assert isinstance((e1 * mq1).value, uc.UFloat)
assert e1 * mq1 == nb.Mixed(uc.ufloat(0.6, 0.15))
assert isinstance(me1 * me2, nb.Mixed)
assert isinstance((me1 * me2).value, uc.UFloat)
assert me1 * me2 == nb.Mixed(uc.ufloat(1.2, 0.3) * uc.ufloat(0.2, 0.4))
assert isinstance(me1 * e2, nb.Mixed)
assert isinstance((me1 * e2).value, uc.UFloat)
assert me1 * e2 == nb.Mixed(uc.ufloat(1.2, 0.3) * uc.ufloat(0.2, 0.4))
assert isinstance(e1 * me2, nb.Mixed)
assert isinstance((e1 * me2).value, uc.UFloat)
assert e1 * me2 == nb.Mixed(uc.ufloat(1.2, 0.3) * uc.ufloat(0.2, 0.4))
assert isinstance(me1 * mi1, nb.Mixed)
assert isinstance((me1 * mi1).value, uc.UFloat)
assert me1 * mi1 == nb.Mixed(uc.ufloat(4.8, 1.2))
assert isinstance(me1 * i1, nb.Mixed)
assert isinstance((me1 * i1).value, uc.UFloat)
assert me1 * i1 == nb.Mixed(uc.ufloat(4.8, 1.2))
assert isinstance(e1 * mi1, nb.Mixed)
assert isinstance((e1 * mi1).value, uc.UFloat)
assert e1 * mi1 == nb.Mixed(uc.ufloat(4.8, 1.2))
assert isinstance(me1 * mf1, nb.Mixed)
assert isinstance((me1 * mf1).value, uc.UFloat)
assert me1 * mf1 == nb.Mixed(uc.ufloat(4.2, 1.05))
assert isinstance(me1 * f1, nb.Mixed)
assert isinstance((me1 * f1).value, uc.UFloat)
assert me1 * f1 == nb.Mixed(uc.ufloat(4.2, 1.05))
assert isinstance(e1 * mf1, nb.Mixed)
assert isinstance((e1 * mf1).value, uc.UFloat)
assert e1 * mf1 == nb.Mixed(uc.ufloat(4.2, 1.05))
assert isinstance(nb.Mixed(3) * mq1, nb.Mixed)
assert isinstance((nb.Mixed(3) * mq1).value, fr.Fraction)
assert nb.Mixed(3) * mq1 == nb.Mixed(fr.Fraction(3, 2))
assert isinstance(nb.Mixed(3) * q1, nb.Mixed)
assert isinstance((nb.Mixed(3) * q1).value, fr.Fraction)
assert nb.Mixed(3) * q1 == nb.Mixed(fr.Fraction(3, 2))
assert isinstance(3 * mq1, nb.Mixed)
assert isinstance((3 * mq1).value, fr.Fraction)
assert 3 * mq1 == nb.Mixed(fr.Fraction(3, 2))
assert isinstance(mi1 * me1, nb.Mixed)
assert isinstance((mi1 * me1).value, uc.UFloat)
assert mi1 * me1 == nb.Mixed(uc.ufloat(4.8, 1.2))
assert isinstance(mi1 * e1, nb.Mixed)
assert isinstance((mi1 * e1).value, uc.UFloat)
assert mi1 * e1 == nb.Mixed(uc.ufloat(4.8, 1.2))
assert isinstance(i1 * me1, nb.Mixed)
assert isinstance((i1 * me1).value, uc.UFloat)
assert i1 * me1 == nb.Mixed(uc.ufloat(4.8, 1.2))
assert isinstance(mi1 * mi2, nb.Mixed)
assert isinstance((mi1 * mi2).value, int)
assert mi1 * mi2 == nb.Mixed(12)
assert isinstance(mi1 * i2, nb.Mixed)
assert isinstance((mi1 * i2).value, int)
assert mi1 * i2 == nb.Mixed(12)
assert isinstance(i1 * mi2, nb.Mixed)
assert isinstance((i1 * mi2).value, int)
assert i1 * mi2 == nb.Mixed(12)
assert isinstance(mi1 * mf1, nb.Mixed)
assert isinstance((mi1 * mf1).value, float)
assert mi1 * mf1 == nb.Mixed(14.0)
assert isinstance(mi1 * f1, nb.Mixed)
assert isinstance((mi1 * f1).value, float)
assert mi1 * f1 == nb.Mixed(14.0)
assert isinstance(i1 * mf1, nb.Mixed)
assert isinstance((i1 * mf1).value, float)
assert i1 * mf1 == nb.Mixed(14.0)
assert isinstance(mf1 * mq1, nb.Mixed)
assert isinstance((mf1 * mq1).value, float)
assert mf1 * mq1 == nb.Mixed(1.75)
assert isinstance(mf1 * q1, nb.Mixed)
assert isinstance((mf1 * q1).value, float)
assert mf1 * q1 == nb.Mixed(1.75)
assert isinstance(f1 * mq1, nb.Mixed)
assert isinstance((f1 * mq1).value, float)
assert f1 * mq1 == nb.Mixed(1.75)
assert isinstance(mf1 * me1, nb.Mixed)
assert isinstance((mf1 * me1).value, uc.UFloat)
assert mf1 * me1 == nb.Mixed(uc.ufloat(4.2, 1.05))
assert isinstance(mf1 * e1, nb.Mixed)
assert isinstance((mf1 * e1).value, uc.UFloat)
assert mf1 * e1 == nb.Mixed(uc.ufloat(4.2, 1.05))
assert isinstance(f1 * me1, nb.Mixed)
assert isinstance((f1 * me1).value, uc.UFloat)
assert f1 * me1 == nb.Mixed(uc.ufloat(4.2, 1.05))
assert isinstance(mf1 * mi1, nb.Mixed)
assert isinstance((mf1 * mi1).value, float)
assert mf1 * mi1 == nb.Mixed(14.0)
assert isinstance(mf1 * i1, nb.Mixed)
assert isinstance((mf1 * i1).value, float)
assert mf1 * i1 == nb.Mixed(14.0)
assert isinstance(f1 * mi1, nb.Mixed)
assert isinstance((f1 * mi1).value, float)
assert f1 * mi1 == nb.Mixed(14.0)
assert isinstance(mf1 * mf2, nb.Mixed)
assert isinstance((mf1 * mf2).value, float)
assert mf1 * mf2 == nb.Mixed(11.9)
assert isinstance(mf1 * f2, nb.Mixed)
assert isinstance((mf1 * f2).value, float)
assert mf1 * f2 == nb.Mixed(11.9)
assert isinstance(f1 * mf2, nb.Mixed)
assert isinstance((f1 * mf2).value, float)
assert f1 * mf2 == nb.Mixed(11.9)
# Multiplication with integer 0
q = fr.Fraction(2, 3)
e = uc.ufloat(1.2, 0.1)
i = 4
f = 3.5
mq = nb.Mixed(q)
me = nb.Mixed(e)
mi = nb.Mixed(i)
mf = nb.Mixed(f)
m0 = nb.Mixed(0)
for m in [mq, me, mi, mf]:
assert m * m0 == m0
assert m * 0 == m0
assert m0 * m == m0
assert 0 * m == m0
for z in [q, e, i, f]:
assert z * m0 == m0
assert m0 * z == m0
# Division
q1 = fr.Fraction(2, 3)
q2 = fr.Fraction(3, 4)
e1 = uc.ufloat(0.5, 0.3)
e2 = uc.ufloat(0.75, 0.4)
i1 = 4
i2 = 3
f1 = 1.5
f2 = 1.6
mq1 = nb.Mixed(q1)
mq2 = nb.Mixed(q2)
me1 = nb.Mixed(e1)
me2 = nb.Mixed(e2)
mi1 = nb.Mixed(i1)
mi2 = nb.Mixed(i2)
mf1 = nb.Mixed(f1)
mf2 = nb.Mixed(f2)
assert isinstance(mq1 / mq2, nb.Mixed)
assert isinstance((mq1 / mq2).value, fr.Fraction)
assert mq1 / mq2 == nb.Mixed(fr.Fraction(8, 9))
assert isinstance(mq1 / q2, nb.Mixed)
assert isinstance((mq1 / q2).value, fr.Fraction)
assert mq1 / q2 == nb.Mixed(fr.Fraction(8, 9))
assert isinstance(q1 / mq2, nb.Mixed)
assert isinstance((q1 / mq2).value, fr.Fraction)
assert q1 / mq2 == nb.Mixed(fr.Fraction(8, 9))
assert isinstance(mq1 / me1, nb.Mixed)
assert isinstance((mq1 / me1).value, uc.UFloat)
assert mq1 / me1 == nb.Mixed(uc.ufloat(4 / 3, 0.3 * 2 / 3 / (1 / 2) ** 2))
assert isinstance(mq1 / e1, nb.Mixed)
assert isinstance((mq1 / e1).value, uc.UFloat)
assert mq1 / e1 == nb.Mixed(uc.ufloat(4 / 3, 0.3 * 2 / 3 / (1 / 2) ** 2))
assert isinstance(q1 / me1, nb.Mixed)
assert isinstance((q1 / me1).value, uc.UFloat)
assert q1 / me1 == nb.Mixed(uc.ufloat(4 / 3, 0.3 * 2 / 3 / (1 / 2) ** 2))
assert isinstance(mq1 / mi1, nb.Mixed)
assert isinstance((mq1 / mi1).value, fr.Fraction)
assert mq1 / mi1 == nb.Mixed(fr.Fraction(1, 6))
assert isinstance(mq1 / i1, nb.Mixed)
assert isinstance((mq1 / i1).value, fr.Fraction)
assert mq1 / i1 == nb.Mixed(fr.Fraction(1, 6))
assert isinstance(q1 / mi1, nb.Mixed)
assert isinstance((q1 / mi1).value, fr.Fraction)
assert q1 / mi1 == nb.Mixed(fr.Fraction(1, 6))
assert isinstance(mq1 / mf1, nb.Mixed)
assert isinstance((mq1 / mf1).value, float)
assert mq1 / mf1 == nb.Mixed(4.0 / 9.0)
assert isinstance(mq1 / f1, nb.Mixed)
assert isinstance((mq1 / f1).value, float)
assert mq1 / f1 == nb.Mixed(4.0 / 9.0)
assert isinstance(q1 / mf1, nb.Mixed)
assert isinstance((q1 / mf1).value, float)
assert q1 / mf1 == nb.Mixed(4.0 / 9.0)
assert isinstance(me1 / mq1, nb.Mixed)
assert isinstance((me1 / mq1).value, uc.UFloat)
assert me1 / mq1 == nb.Mixed(uc.ufloat(0.5, 0.3) / (2 / 3))
assert isinstance(me1 / q1, nb.Mixed)
assert isinstance((me1 / q1).value, uc.UFloat)
assert me1 / q1 == nb.Mixed(uc.ufloat(0.5, 0.3) / (2 / 3))
assert isinstance(e1 / mq1, nb.Mixed)
assert isinstance((e1 / mq1).value, uc.UFloat)
assert e1 / mq1 == nb.Mixed(uc.ufloat(0.5, 0.3) / (2 / 3))
assert isinstance(me1 / me2, nb.Mixed)
assert isinstance((me1 / me2).value, uc.UFloat)
assert me1 / me2 == nb.Mixed(uc.ufloat(0.5, 0.3) / uc.ufloat(0.75, 0.4))
assert isinstance(me1 / e2, nb.Mixed)
assert isinstance((me1 / e2).value, uc.UFloat)
assert me1 / e2 == nb.Mixed(uc.ufloat(0.5, 0.3) / uc.ufloat(0.75, 0.4))
assert isinstance(e1 / me2, nb.Mixed)
assert isinstance((e1 / me2).value, uc.UFloat)
assert e1 / me2 == nb.Mixed(uc.ufloat(0.5, 0.3) / uc.ufloat(0.75, 0.4))
assert isinstance(me1 / mi1, nb.Mixed)
assert isinstance((me1 / mi1).value, uc.UFloat)
assert me1 / mi1 == nb.Mixed(uc.ufloat(0.125, 0.075))
assert isinstance(me1 / i1, nb.Mixed)
assert isinstance((me1 / i1).value, uc.UFloat)
assert me1 / i1 == nb.Mixed(uc.ufloat(0.125, 0.075))
assert isinstance(e1 / mi1, nb.Mixed)
assert isinstance((e1 / mi1).value, uc.UFloat)
assert e1 / mi1 == nb.Mixed(uc.ufloat(0.125, 0.075))
assert isinstance(me1 / mf1, nb.Mixed)
assert isinstance((me1 / mf1).value, uc.UFloat)
assert me1 / mf1 == nb.Mixed(uc.ufloat(0.5 / 1.5, 0.3 / 1.5))
assert isinstance(me1 / f1, nb.Mixed)
assert isinstance((me1 / f1).value, uc.UFloat)
assert me1 / f1 == nb.Mixed(uc.ufloat(0.5 / 1.5, 0.3 / 1.5))
assert isinstance(e1 / mf1, nb.Mixed)
assert isinstance((e1 / mf1).value, uc.UFloat)
assert e1 / mf1 == nb.Mixed(uc.ufloat(0.5 / 1.5, 0.3 / 1.5))
assert isinstance(mi1 / mq2, nb.Mixed)
assert isinstance((mi1 / mq2).value, fr.Fraction)
assert mi1 / mq2 == nb.Mixed(fr.Fraction(16, 3))
assert isinstance(mi1 / q2, nb.Mixed)
assert isinstance((mi1 / q2).value, fr.Fraction)
assert mi1 / q2 == nb.Mixed(fr.Fraction(16, 3))
assert isinstance(i1 / mq2, nb.Mixed)
assert isinstance((i1 / mq2).value, fr.Fraction)
assert i1 / mq2 == nb.Mixed(fr.Fraction(16, 3))
assert isinstance(mi1 / me1, nb.Mixed)
assert isinstance((mi1 / me1).value, uc.UFloat)
assert mi1 / me1 == nb.Mixed(uc.ufloat(8.0, 4.8))
assert isinstance(mi1 / e1, nb.Mixed)
assert isinstance((mi1 / e1).value, uc.UFloat)
assert mi1 / e1 == nb.Mixed(uc.ufloat(8.0, 4.8))
assert isinstance(i1 / me1, nb.Mixed)
assert isinstance((i1 / me1).value, uc.UFloat)
assert i1 / me1 == nb.Mixed(uc.ufloat(8.0, 4.8))
assert isinstance(mi1 / mi2, nb.Mixed)
assert isinstance((mi1 / mi2).value, fr.Fraction)
assert mi1 / mi2 == nb.Mixed(fr.Fraction(4, 3))
assert isinstance(mi1 / i2, nb.Mixed)
assert isinstance((mi1 / i2).value, fr.Fraction)
assert mi1 / i2 == nb.Mixed(fr.Fraction(4, 3))
assert isinstance(i1 / mi2, nb.Mixed)
assert isinstance((i1 / mi2).value, fr.Fraction)
assert i1 / mi2 == nb.Mixed(fr.Fraction(4, 3))
assert isinstance(mi1 / mf1, nb.Mixed)
assert isinstance((mi1 / mf1).value, float)
assert mi1 / mf1 == nb.Mixed(4.0 / 1.5)
assert isinstance(mi1 / f1, nb.Mixed)
assert isinstance((mi1 / f1).value, float)
assert mi1 / f1 == nb.Mixed(4.0 / 1.5)
assert isinstance(i1 / mf1, nb.Mixed)
assert isinstance((i1 / mf1).value, float)
assert i1 / mf1 == nb.Mixed(4.0 / 1.5)
assert isinstance(mf1 / mq1, nb.Mixed)
assert isinstance((mf1 / mq1).value, float)
assert mf1 / mq1 == nb.Mixed(2.25)
assert isinstance(mf1 / q1, nb.Mixed)
assert isinstance((mf1 / q1).value, float)
assert mf1 / q1 == nb.Mixed(2.25)
assert isinstance(f1 / mq1, nb.Mixed)
assert isinstance((f1 / mq1).value, float)
assert f1 / mq1 == nb.Mixed(2.25)
assert isinstance(mf1 / me1, nb.Mixed)
assert isinstance((mf1 / me1).value, uc.UFloat)
assert mf1 / me1 == nb.Mixed(uc.ufloat(3.0, 0.3 * 1.5 / 0.5 ** 2))
assert isinstance(mf1 / e1, nb.Mixed)
assert isinstance((mf1 / e1).value, uc.UFloat)
assert mf1 / e1 == nb.Mixed(uc.ufloat(3.0, 0.3 * 1.5 / 0.5 ** 2))
assert isinstance(f1 / me1, nb.Mixed)
assert isinstance((f1 / me1).value, uc.UFloat)
assert f1 / me1 == nb.Mixed(uc.ufloat(3.0, 0.3 * 1.5 / 0.5 ** 2))
assert isinstance(mf1 / mi1, nb.Mixed)
assert isinstance((mf1 / mi1).value, float)
assert mf1 / mi1 == nb.Mixed(0.375)
assert isinstance(mf1 / i1, nb.Mixed)
assert isinstance((mf1 / i1).value, float)
assert mf1 / i1 == nb.Mixed(0.375)
assert isinstance(f1 / mi1, nb.Mixed)
assert isinstance((f1 / mi1).value, float)
assert f1 / mi1 == nb.Mixed(0.375)
assert isinstance(mf1 / mf2, nb.Mixed)
assert isinstance((mf1 / mf2).value, float)
assert mf1 / mf2 == nb.Mixed(0.9375)
assert isinstance(mf1 / f2, nb.Mixed)
assert isinstance((mf1 / f2).value, float)
assert mf1 / f2 == nb.Mixed(0.9375)
assert isinstance(f1 / mf2, nb.Mixed)
assert isinstance((f1 / mf2).value, float)
assert f1 / mf2 == nb.Mixed(0.9375)
# Dividing integer 0
q = fr.Fraction(2, 3)
e = uc.ufloat(1.2, 0.1)
i = 4
f = 3.5
mq = nb.Mixed(q)
me = nb.Mixed(e)
mi = nb.Mixed(i)
mf = nb.Mixed(f)
m0 = nb.Mixed(0)
for m in [mq, me, mi, mf]:
assert m0 / m == m0
assert 0 / m == m0
for z in [q, e, i, f]:
assert m0 / z == m0
# negative
q = fr.Fraction(3, 2)
e = uc.ufloat(1.2, 0.1)
i = 4
f = 3.5
mq = nb.Mixed(q)
me = nb.Mixed(e)
mi = nb.Mixed(i)
mf = nb.Mixed(f)
assert isinstance(-mq, nb.Mixed)
assert isinstance((-mq).value, fr.Fraction)
assert -mq == nb.Mixed(fr.Fraction(-3, 2))
assert isinstance(-me, nb.Mixed)
assert isinstance((-me).value, uc.UFloat)
assert -me == nb.Mixed(uc.ufloat(-1.2, 0.1))
assert isinstance(-mi, nb.Mixed)
assert isinstance((-mi).value, int)
assert -mi == nb.Mixed(-4)
assert isinstance(-mf, nb.Mixed)
assert isinstance((-mf).value, float)
assert -mf == nb.Mixed(-3.5)
# Modulo
q = fr.Fraction(5, 2)
e = uc.ufloat(3.2, 0.1)
i = 3
f = 3.5
mq = nb.Mixed(q)
me = nb.Mixed(e)
mi = nb.Mixed(i)
mf = nb.Mixed(f)
assert isinstance(mq % 2, nb.Mixed)
assert isinstance((mq % 2).value, fr.Fraction)
assert mq % 2 == nb.Mixed(fr.Fraction(1, 2))
assert isinstance(me % 2, nb.Mixed)
assert isinstance((me % 2).value, uc.UFloat)
assert approx((me % 2).value.n, 1.2)
assert approx((me % 2).value.s, 0.1)
assert isinstance(mi % 2, nb.Mixed)
assert isinstance((mi % 2).value, int)
assert mi % 2 == nb.Mixed(1)
assert isinstance(mf % 2, nb.Mixed)
assert isinstance((mf % 2).value, float)
assert approx((mf % 2).value, 1.5)
# Constants
assert isinstance(nb.pi, nb.Mixed)
assert isinstance((nb.pi).value, float)
assert (nb.pi).value == 3.141592653589793
# Square-Root
a = nb.sqrt(nb.Mixed(fr.Fraction(2, 3)))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.816496580)
a = nb.sqrt(fr.Fraction(2, 3))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.816496580)
a = nb.sqrt(nb.Mixed(fr.Fraction(1, 2)))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.70710678118)
a = nb.sqrt(fr.Fraction(1, 2))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.70710678118)
a = nb.sqrt(nb.Mixed(fr.Fraction(2, 1)))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 1.41421356237)
a = nb.sqrt(fr.Fraction(2, 1))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 1.41421356237)
a = nb.sqrt(nb.Mixed(fr.Fraction(4, 9)))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, fr.Fraction)
assert a == nb.Mixed(fr.Fraction(2, 3))
a = nb.sqrt(fr.Fraction(4, 9))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, fr.Fraction)
assert a == nb.Mixed(fr.Fraction(2, 3))
a = nb.sqrt(nb.Mixed(uc.ufloat(0.3, 0.1)))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, uc.UFloat)
assert approx(a.value.n, 0.54772255750)
assert approx(a.value.s, 0.09128709291)
a = nb.sqrt(uc.ufloat(0.3, 0.1))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, uc.UFloat)
assert approx(a.value.n, 0.54772255750)
assert approx(a.value.s, 0.09128709291)
a = nb.sqrt(nb.Mixed(3))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 1.7320508075688)
a = nb.sqrt(3)
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 1.7320508075688)
a = nb.sqrt(nb.Mixed(4))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, int)
assert a.value == 2
a = nb.sqrt(4)
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, int)
assert a.value == 2
a = nb.sqrt(nb.Mixed(0.5))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.7071067811)
a = nb.sqrt(0.5)
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.7071067811)
# Trigonometric Functions:
a = nb.deg2rad(nb.Mixed(fr.Fraction(180, 1)))
assert approx(a.value, 3.1415926535)
a = nb.deg2rad(fr.Fraction(180, 1))
assert approx(a.value, 3.1415926535)
a = nb.deg2rad(nb.Mixed(uc.ufloat(180.0, 10.0)))
assert approx(a.value.n, 3.1415926535)
assert approx(a.value.s, 0.174532925199)
a = nb.deg2rad(uc.ufloat(180.0, 10.0))
assert approx(a.value.n, 3.1415926535)
assert approx(a.value.s, 0.174532925199)
a = nb.deg2rad(nb.Mixed(180))
assert approx(a.value, 3.1415926535)
a = nb.deg2rad(180)
assert approx(a.value, 3.1415926535)
a = nb.deg2rad(nb.Mixed(180.0))
assert approx(a.value, 3.1415926535)
a = nb.deg2rad(180.0)
assert approx(a.value, 3.1415926535)
a = nb.rad2deg(nb.Mixed(fr.Fraction(1, 2)))
assert approx(a.value, 28.647889756)
a = nb.rad2deg(fr.Fraction(1, 2))
assert approx(a.value, 28.647889756)
a = nb.rad2deg(nb.Mixed(uc.ufloat(3.1415926535897931, 0.17453292519943295)))
assert approx(a.value.n, 180.0)
assert approx(a.value.s, 10.0)
a = nb.rad2deg(uc.ufloat(3.1415926535897931, 0.17453292519943295))
assert approx(a.value.n, 180.0)
assert approx(a.value.s, 10.0)
a = nb.rad2deg(nb.Mixed(1))
assert approx(a.value, 57.295779513082323)
a = nb.rad2deg(1)
assert approx(a.value, 57.295779513082323)
a = nb.rad2deg(nb.Mixed(3.1415926535897931))
assert approx(a.value, 180.0)
a = nb.rad2deg(3.1415926535897931)
assert approx(a.value, 180.0)
a = nb.sin(nb.Mixed(fr.Fraction(1, 2)))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.47942553860420301)
a = nb.sin(fr.Fraction(1, 2))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.479425538604203)
a = nb.sin(nb.Mixed(uc.ufloat(0.5, 0.1)))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, uc.UFloat)
assert approx(a.value.n, 0.479425538604203)
assert approx(a.value.s, 0.08775825618903728)
a = nb.sin(uc.ufloat(0.5, 0.1))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, uc.UFloat)
assert approx(a.value.n, 0.479425538604203)
assert approx(a.value.s, 0.08775825618903728)
a = nb.sin(nb.Mixed(1))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.8414709848078965)
a = nb.sin(1)
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.8414709848078965)
a = nb.sin(nb.Mixed(0.5))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.479425538604203)
a = nb.sin(0.5)
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.479425538604203)
a = nb.cos(nb.Mixed(fr.Fraction(1, 2)))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.8775825618903)
a = nb.cos(fr.Fraction(1, 2))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.8775825618903)
a = nb.cos(nb.Mixed(uc.ufloat(0.5, 0.1)))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, uc.UFloat)
assert approx(a.value.n, 0.8775825619803)
assert approx(a.value.s, 0.0479425538604)
a = nb.cos(uc.ufloat(0.5, 0.1))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, uc.UFloat)
assert approx(a.value.n, 0.8775825619803)
assert approx(a.value.s, 0.0479425538604)
a = nb.cos(nb.Mixed(1))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.54030230586)
a = nb.cos(1)
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.54030230586)
a = nb.cos(nb.Mixed(0.5))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.8775825618903)
a = nb.cos(0.5)
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.8775825618903)
a = nb.arccos(nb.Mixed(fr.Fraction(1, 2)))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 1.04719755119)
a = nb.arccos(fr.Fraction(1, 2))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 1.04719755119)
a = nb.arccos(nb.Mixed(uc.ufloat(0.5, 0.1)))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, uc.UFloat)
assert approx(a.value.n, 1.04719755119)
assert approx(a.value.s, 0.11547005383)
a = nb.arccos(uc.ufloat(0.5, 0.1))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, uc.UFloat)
assert approx(a.value.n, 1.04719755119)
assert approx(a.value.s, 0.11547005383)
a = nb.arccos(nb.Mixed(1))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.0)
a = nb.arccos(1)
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 0.0)
a = nb.arccos(nb.Mixed(0.5))
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 1.04719755119)
a = nb.arccos(0.5)
assert isinstance(a, nb.Mixed)
assert isinstance(a.value, float)
assert approx(a.value, 1.04719755119)
def test_Row():
# Create
e = uc.ufloat(1.2, 0.1)
R = nb.Row([nb.Mixed(fr.Fraction(1, 2)),
nb.Mixed(e),
nb.Mixed(1),
nb.Mixed(0.5)])
assert isinstance(R.liste, list)
assert isinstance(R.liste[0], nb.Mixed)
assert isinstance(R.liste[0].value, fr.Fraction)
assert R.liste[0] == nb.Mixed(fr.Fraction(1, 2))
assert isinstance(R.liste[1], nb.Mixed)
assert isinstance(R.liste[1].value, uc.UFloat)
assert R.liste[1] == nb.Mixed(e)
assert isinstance(R.liste[2], nb.Mixed)
assert isinstance(R.liste[2].value, int)
assert R.liste[2] == nb.Mixed(1)
assert isinstance(R.liste[3], nb.Mixed)
assert isinstance(R.liste[3].value, float)
assert approx(R.liste[3].value, 0.5)
R = nb.Row([fr.Fraction(1, 2),
e,
1,
0.5])
assert isinstance(R.liste, list)
assert isinstance(R.liste[0], nb.Mixed)
assert isinstance(R.liste[0].value, fr.Fraction)
assert R.liste[0] == nb.Mixed(fr.Fraction(1, 2))
assert isinstance(R.liste[1], nb.Mixed)
assert isinstance(R.liste[1].value, uc.UFloat)
assert R.liste[1] == nb.Mixed(e)
assert isinstance(R.liste[2], nb.Mixed)
assert isinstance(R.liste[2].value, int)
assert R.liste[2] == nb.Mixed(1)
assert isinstance(R.liste[3], nb.Mixed)
assert isinstance(R.liste[3].value, float)
assert approx(R.liste[3].value, 0.5)
# len
R = nb.Row([fr.Fraction(1, 2),
uc.ufloat(1.2, 0.1),
1,
0.5])
assert len(R) == 4
assert R.__str__() == "( 1/2 1.20(10) 1 0.5 )"
# Equal
e = uc.ufloat(1.2, 0.1)
R1 = nb.Row([fr.Fraction(1, 2),
e,
1,
0.5])
R2 = nb.Row([fr.Fraction(1, 2),
e,
1,
0.5])
R2wrong = nb.Row([fr.Fraction(1, 2),
uc.ufloat(1.2, 0.1),
1,
0.5])
R3 = nb.Row([fr.Fraction(1, 2),
e,
1,
fr.Fraction(1, 2)])
R4 = nb.Row([fr.Fraction(1, 2),
e,
1])
assert R1 == R2
assert (R1 == R2wrong) == False
assert (R1 == R3) == False
assert (R1 == R4) == False
assert (R1 == 5) == False
# Hash
R1 = nb.Row([0, 0, 1.00000000])
R2 = nb.Row([0, 0, 0.99999999])
assert hash(R1) == hash(R2)
e1 = uc.ufloat(1.2, 0.1)
R1 = nb.Row([0, 0, e1])
R2 = nb.Row([0, 0, e1])
R3 = nb.Row([0, 0, uc.ufloat(1.2, 0.1)])
assert hash(R1) == hash(R2)
assert (hash(R1) == hash(R3)) == False
# canonical
assert nb.Row.canonical(5, 3) == nb.Row([0, 0, 0, 1, 0])
# block
R = nb.Row([1, 2, 3, 4])
assert R.block(1, 3) == nb.Row([2, 3])
# Addition
R1 = nb.Row([1, 2, fr.Fraction(1, 2)])
R2 = nb.Row([2, 3, 4])
assert R1 + R2 == nb.Row([3, 5, fr.Fraction(9, 2)])
# Subtraction
R1 = nb.Row([1, 2, fr.Fraction(1, 2)])
R2 = nb.Row([2, 3, 4])
assert R1 - R2 == nb.Row([-1, -1, fr.Fraction(-7, 2)])
# Multiplication
R1 = nb.Row([1, 2, fr.Fraction(1, 2)])
assert R1 * nb.Mixed(2) == nb.Row([2, 4, 1])
assert nb.Mixed(2) * R1 == nb.Row([2, 4, 1])
assert R1 * 2 == nb.Row([2, 4, 1])
assert 2 * R1 == nb.Row([2, 4, 1])
# neg
R1 = nb.Row([1, 2, 3])
assert -R1 == nb.Row([-1, -2, -3])
def test_Matrix():
# create and shape
M1 = nb.Matrix([nb.Row([1, 2, 3]), nb.Row([4, 5, 6])])
M2 = nb.Matrix([[1, 2, 3], [4, 5, 6]])
assert M1.shape() == (2, 3)
assert M2.shape() == (2, 3)
# Equal
M1 = nb.Matrix([nb.Row([1, 2, 3]), nb.Row([4, 5, 6])])
M2 = nb.Matrix([[1, 2, 3], [4, 5, 6]])
M3 = nb.Matrix([[1, 2, 3], [4, 5.1, 6]])
M4 = nb.Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
M5 = nb.Matrix([[1, 2], [4, 5]])
M6 = nb.Matrix([[1, 2, 3], [4, 5.0, 6]])
M7 = nb.Matrix([[1, 2, 3], [4, fr.Fraction(5, 1), 6]])
assert M1 == M2
assert (M1 == M3) == False
assert (M1 == M4) == False
assert (M1 == M5) == False
assert (M1 == M6) == False
assert M1 == M7
M1 = nb.Matrix([nb.Row([1, 2, 3.0]), nb.Row([4, 5, 6])])
M2 = nb.Matrix([nb.Row([1, 2, 2.999999999999]), nb.Row([4, 5, 6])])
print(hash(M1))
print(hash(M2))
assert hash(M1) == hash(M2)
e = uc.ufloat(1.2, 0.1)
M1 = nb.Matrix([nb.Row([1, 2, e]), nb.Row([4, 5, 6])])
M2 = nb.Matrix([nb.Row([1, 2, e]), nb.Row([4, 5, 6])])
M3 = nb.Matrix([nb.Row([1, 2, uc.ufloat(1.2, 0.1)]), nb.Row([4, 5, 6])])
assert M1 == M2
assert (M1 == M3) == False
assert hash(M1) == hash(M2)
assert (hash(M1) == hash(M3)) == False
# print
assert nb.Matrix([[1, 2]]).__str__() == " < 1 2 > "
assert nb.Matrix([[1, 2], [3, 4]]).__str__() == " / 1 2 \ \n" \
" \ 3 4 / "
assert nb.Matrix([[1, 2, 3], [4, 5, 6], [7, 800, 9]]).__str__() == \
" / 1 2 3 \ \n" \
"| 4 5 6 |\n" \
" \ 7 800 9 / "
# Addition
assert nb.Matrix([[1, 2], [3, 4]]) + nb.Matrix([[5, 6], [7, 8]]) == \
nb.Matrix([[6, 8], [10, 12]])
assert nb.Matrix([[1, 2], [3, 4], [5, 6]]) + \
nb.Matrix([[1, 1], [1, 1], [1, 1]]) == \
nb.Matrix([[2, 3], [4, 5], [6, 7]])
# Subtraction
assert nb.Matrix([[1, 2], [3, 4]]) - nb.Matrix([[5, 6], [7, 8]]) == \
nb.Matrix([[-4, -4], [-4, -4]])
assert nb.Matrix([[1, 2], [3, 4], [5, 6]]) - \
nb.Matrix([[1, 1], [1, 1], [1, 1]]) == \
nb.Matrix([[0, 1], [2, 3], [4, 5]])
# neg
M1 = nb.Matrix([[1, 2, 3], [4, 5, 6]])
assert -M1 == nb.Matrix([[-1, -2, -3], [-4, -5, -6]])
# Multiplication "Matrix * Matrix"
M1 = nb.Matrix([[1, 2], [3, 4]])
M2 = nb.Matrix([[5, 6], [7, 8]])
assert isinstance(M1 * M2, nb.Matrix)
assert M1 * M2 == nb.Matrix([[19, 22], [43, 50]])
M1 = nb.Matrix([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
M2 = nb.Matrix([[uc.ufloat(1.2, 0.1)], [1], [2]])
print(M2)
print(M1*M2)
assert (M1 * M2).liste[1].liste[0] == M2.liste[1].liste[0]
assert M1 * M2 == M2
# Multiplication "Scalar * Matrix"
M1 = nb.Matrix([[1, 2], [3, 4]])
assert M1 * nb.Mixed(fr.Fraction(1, 2)) == \
nb.Matrix([[fr.Fraction(1, 2), 1], [fr.Fraction(3, 2), 2]])
assert M1 * fr.Fraction(1, 2) == \
nb.Matrix([[fr.Fraction(1, 2), 1], [fr.Fraction(3, 2), 2]])
assert nb.Mixed(fr.Fraction(1, 2)) * M1 == \
nb.Matrix([[fr.Fraction(1, 2), 1], [fr.Fraction(3, 2), 2]])
assert fr.Fraction(1, 2) * M1 == \
nb.Matrix([[fr.Fraction(1, 2), 1], [fr.Fraction(3, 2), 2]])
M = M1 * nb.Mixed(uc.ufloat(1.2, 0.1))
assert approx(M.liste[0].liste[0].value.n, 1.2)
assert approx(M.liste[0].liste[0].value.s, 0.1)
assert approx(M.liste[0].liste[1].value.n, 2.4)
assert approx(M.liste[0].liste[1].value.s, 0.2)
assert approx(M.liste[1].liste[0].value.n, 3.6)
assert approx(M.liste[1].liste[0].value.s, 0.3)
assert approx(M.liste[1].liste[1].value.n, 4.8)
assert approx(M.liste[1].liste[1].value.s, 0.4)
M = M1 * uc.ufloat(1.2, 0.1)
assert approx(M.liste[0].liste[0].value.n, 1.2)
assert approx(M.liste[0].liste[0].value.s, 0.1)
assert approx(M.liste[0].liste[1].value.n, 2.4)
assert approx(M.liste[0].liste[1].value.s, 0.2)
assert approx(M.liste[1].liste[0].value.n, 3.6)
assert approx(M.liste[1].liste[0].value.s, 0.3)
assert approx(M.liste[1].liste[1].value.n, 4.8)
assert approx(M.liste[1].liste[1].value.s, 0.4)
M = nb.Mixed(uc.ufloat(1.2, 0.1)) * M1
assert approx(M.liste[0].liste[0].value.n, 1.2)
assert approx(M.liste[0].liste[0].value.s, 0.1)
assert approx(M.liste[0].liste[1].value.n, 2.4)
assert approx(M.liste[0].liste[1].value.s, 0.2)
assert approx(M.liste[1].liste[0].value.n, 3.6)
assert approx(M.liste[1].liste[0].value.s, 0.3)
assert approx(M.liste[1].liste[1].value.n, 4.8)
assert approx(M.liste[1].liste[1].value.s, 0.4)
M = uc.ufloat(1.2, 0.1) * M1
assert approx(M.liste[0].liste[0].value.n, 1.2)
assert approx(M.liste[0].liste[0].value.s, 0.1)
assert approx(M.liste[0].liste[1].value.n, 2.4)
assert approx(M.liste[0].liste[1].value.s, 0.2)
assert approx(M.liste[1].liste[0].value.n, 3.6)
assert approx(M.liste[1].liste[0].value.s, 0.3)
assert approx(M.liste[1].liste[1].value.n, 4.8)
assert approx(M.liste[1].liste[1].value.s, 0.4)
assert M1 * nb.Mixed(2) == nb.Matrix([[2, 4], [6, 8]])
assert M1 * 2 == nb.Matrix([[2, 4], [6, 8]])
assert nb.Mixed(2) * M1 == nb.Matrix([[2, 4], [6, 8]])
assert 2 * M1 == nb.Matrix([[2, 4], [6, 8]])
M = M1 * nb.Mixed(2.5)
assert approx(M.liste[0].liste[0].value, 2.5)
assert approx(M.liste[0].liste[1].value, 5.0)
assert approx(M.liste[1].liste[0].value, 7.5)
assert approx(M.liste[1].liste[1].value, 10.0)
M = M1 * 2.5
assert approx(M.liste[0].liste[0].value, 2.5)
assert approx(M.liste[0].liste[1].value, 5.0)
assert approx(M.liste[1].liste[0].value, 7.5)
assert approx(M.liste[1].liste[1].value, 10.0)
M = nb.Mixed(2.5) * M1
assert approx(M.liste[0].liste[0].value, 2.5)
assert approx(M.liste[0].liste[1].value, 5.0)
assert approx(M.liste[1].liste[0].value, 7.5)
assert approx(M.liste[1].liste[1].value, 10.0)
M = 2.5 * M1
assert approx(M.liste[0].liste[0].value, 2.5)
assert approx(M.liste[0].liste[1].value, 5.0)
assert approx(M.liste[1].liste[0].value, 7.5)
assert approx(M.liste[1].liste[1].value, 10.0)
# onematrix
assert nb.Matrix.onematrix(2) == nb.Matrix([[1, 0], [0, 1]])
assert nb.Matrix.onematrix(3) == nb.Matrix([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
# block
M = nb.Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
assert M.block(0, 2, 0, 2) == nb.Matrix([[1, 2], [4, 5]])
assert M.block(1, 2, 0, 3) == nb.Matrix([[4, 5, 6]])
M = nb.Matrix([[1, 2, 3, 4]])
assert M.block(0, 1, 0, 3) == nb.Matrix([[1, 2, 3]])
# swap_rows
M = nb.Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
assert M.swap_rows(0, 1) == nb.Matrix([[4, 5, 6], [1, 2, 3], [7, 8, 9]])
# vglue
M1 = nb.Matrix([[1, 2, 3]])
M2 = nb.Matrix([[4, 5, 6]])
assert nb.Matrix.vglue(M1, M2) == nb.Matrix([[1, 2, 3], [4, 5, 6]])
# subtract_x_times_rowj_from_rowi
M = nb.Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
assert M.subtract_x_times_rowj_from_rowi(2, 2, 0) == \
nb.Matrix([[1, 2, 3], [4, 5, 6], [5, 4, 3]])
# inv
assert nb.Matrix([[2, 3],
[4, 5]]).inv() == \
nb.Matrix([[-fr.Fraction(5, 2), fr.Fraction(3, 2)],
[2, -1]])
assert nb.Matrix([[0, 1, 1],
[1, 0, 0],
[0, 0, -1]]).inv() == \
nb.Matrix([[0, 1, 0],
[1, 0, 1],
[0, 0, -1]])
assert nb.Matrix([[0, 0, 1, 0],
[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 0, 1]]).inv() == \
nb.Matrix([[0, 1, 0, 0],
[0, 0, 1, 0],
[1, 0, 0, 0],
[0, 0, 0, 1]])
# transpose
assert nb.Matrix([[1, 2, 3], [4, 5, 6]]).transpose() == \
nb.Matrix([[1, 4], [2, 5], [3, 6]])
# delete_ith_row_and_first_column
M = nb.Matrix([[1, 2, 3, 4],
[5, 6, 7, 8],
[9, 10, 11, 12]])
assert M.delete_ith_row_and_first_column(1) == nb.Matrix([[2, 3, 4],
[10, 11, 12]])
# det
M = nb.Matrix([[3]])
assert M.det() == 3
M = nb.Matrix([[1, 2],
[3, 4]])
assert M.det() == -2
M = nb.Matrix([[1, 2, 3],
[4, 5, 6],
[7, 8, 9]])
assert M.det() == 0
M = nb.Matrix([[1, 2, 3, 4],
[5, 6, 7, 8],
[9, 8, 11, 12],
[13, 14, 15, 17]])
assert M.det() == -16
# delete_translation
M = nb.Matrix([[1, 2, 3, 4],
[5, 6, 7, 8],
[9, 10, 11, 12],
[0, 0, 0, 1]])
assert M.delete_translation() == nb.Matrix([[1, 2, 3, 0],
[5, 6, 7, 0],
[9, 10, 11, 0],
[0, 0, 0, 1]])
def test_fromstr():
string = "1/2"
assert isinstance(fs(string), nb.Mixed)
assert fs(string) == nb.Mixed(fr.Fraction(1, 2))
string = "1.2+/-0.1"
assert fs(string).value.n == nb.Mixed(uc.ufloat(1.2, 0.1)).value.n
assert fs(string).value.s == nb.Mixed(uc.ufloat(1.2, 0.1)).value.s
string = "1.2(1)"
assert fs(string).value.n == nb.Mixed(uc.ufloat(1.2, 0.1)).value.n
assert fs(string).value.s == nb.Mixed(uc.ufloat(1.2, 0.1)).value.s
string = "4"
assert fs(string) == nb.Mixed(fr.Fraction(4, 1))
string = "4.5"
assert fs(string) == nb.Mixed(4.5)
string = "1 2 3"
assert fromstr.typefromstr(string) == nb.Matrix
assert fs(string) == nb.Matrix([[1, 2, 3]])
string = "/ 1 2 \ \n \ 3 4 /"
assert fs(string) == \
nb.Matrix([nb.Row([nb.Mixed(1), nb.Mixed(2)]),
nb.Row([nb.Mixed(3), nb.Mixed(4)])])
string = "1 2 \n 3 4"
assert fs(string) == \
nb.Matrix([nb.Row([nb.Mixed(1), nb.Mixed(2)]),
nb.Row([nb.Mixed(3), nb.Mixed(4)])])
string = "x+y,y - x +1/3,2z"
g = fs(string)
assert g == geo.Symmetry(
fs("/ 1 1 0 0 \n"
" -1 1 0 1/3 \n"
" 0 0 2 0 \n"
" 0 0 0 1"))
string = "O->(0,0,0)\n" \
"then\n" \
"a' = a-b \n" \
"b' = b+a \n" \
"c' = 2c"
g = fs(string)
assert g == geo.Transformation(
fs(" 1 1 0 0 \n"
"-1 1 0 0 \n"
" 0 0 2 0 \n"
" 0 0 0 1").inv())
string = "O->(0,0,0) \n" \
"then\n" \
"a' = c \n" \
"b' = a \n" \
"c' = b"
g = fs(string)
assert g == geo.Transformation(
fs("0 1 0 0 \n"
"0 0 1 0 \n"
"1 0 0 0 \n"
"0 0 0 1").inv())
string = "O -> (1/2, 0, 0) \n" \
"then\n" \
"a' = a \n" \
"b' = b \n" \
"c' = c"
g = fs(string)
assert g == geo.Transformation(
fs("1 0 0 -1/2 \n"
"0 1 0 0 \n"
"0 0 1 0 \n"
"0 0 0 1"))
string1 = "O -> (1/2, 0, 0) \n" \
"then\n" \
"a' = a \n" \
"b' = b \n" \
"c' = c"
string2 = "O -> (0,0,0) \n" \
"then\n" \
"a' = b\n" \
"b' = a\n" \
"c' = c"
string = "O -> (1/2, 0, 0) \n" \
"then\n"\
"a' = b\n"\
"b' = a\n"\
"c' = c"
g1 = fs(string1)
g2 = fs(string2)
g = fs(string)
assert g == g2 * g1
string = "O -> (1/2, 0, 0) \n" \
"then\n" \
"a' = a + b\n" \
"b' = b\n" \
"c' = c"
print("--------")
g = fs(string)
print(g.value)
assert g**fs("p 1/2 0 0") == fs("p 0 0 0")
assert g**fs("p 1/2 1/3 0") == fs("p 0 1/3 0")
assert g**fs("p 0 0 0") == fs("p -1/2 1/2 0")
assert g * g.inv() == geo.Transformation(nb.Matrix.onematrix(4))
string = "p0 0 0"
p = fs(string)
assert p == geo.Pos(fs("0 \n 0 \n 0 \n 1"))
string = "P0 0 0"
p = fs(string)
assert p == geo.Pos(fs("0 \n 0 \n 0 \n 1"))
string = "r0 0 0"
p = fs(string)
assert p == geo.Pos(fs("0 \n 0 \n 0 \n 1"))
string = "R0 0 0"
p = fs(string)
assert p == geo.Pos(fs("0 \n 0 \n 0 \n 1"))
string = p.__str__()
assert string == "Pos / 0 \ \n" \
" | 0 |\n" \
" \ 0 / "
p1 = fs(string)
assert p == p1
string = "R1/2 1/2 1/2"
p = fs(string)
assert p == geo.Pos(fs("1/2 \n 1/2 \n 1/2 \n 1"))
q = fs("k1 2 3")
assert q == geo.Rec(fs("1 2 3 0"))
q = fs("K 1 2 3")
assert q == geo.Rec(fs("1 2 3 0"))
q = fs("q 1/2 1/2 0")
assert q == geo.Rec(fs("1/2 1/2 0 0"))
q = fs("Q0 0 0")
assert q == geo.Rec(fs("0 0 0 0"))
q = fs("Rec < 1 2 3 > ")
assert q == geo.Rec(fs("1 2 3 0"))