def test_real_coeffs(self):
i = complex(imaginary=1)
z = complex()
r = complex(real=1)
rt2 = pow(2,0.5)
rt3 = pow(3,0.5)
c_x3_m_1 = cubic(1,0,0,-1)
self.check_vector(c_x3_m_1.coeffs(),(1,0,0,-1))
self.check_vector(c_x3_m_1.find_real_roots(),[1])
c = cubic(1,0,0,1)
self.check_vector(c.find_real_roots(),[-1])
c = cubic(1,3,3,1)
self.check_vector(c.find_real_roots(),[-1, -1, -1])
c = cubic(1,-3,3,-1)
self.check_vector(c.find_real_roots(),[1, 1, 1])
c = cubic(1,-6,11,-6)
self.check_vector(c.find_real_roots(),[3,1,2])
c = cubic(1,0,0,1)
self.check_vector(c.find_all_roots(),[-r, r/2-i*rt3/2, r/2+i*rt3/2])
c = cubic(1,-6,11,-6)
self.check_vector(c.find_all_roots(),[r*3,r*1,r*2])
pass
def test_real_coeffs(self):
i = complex(imaginary=1)
z = complex()
r = complex(real=1)
rt2 = pow(2, 0.5)
rt3 = pow(3, 0.5)
c_x3_m_1 = cubic(1, 0, 0, -1)
self.check_vector(c_x3_m_1.coeffs(), (1, 0, 0, -1))
self.check_vector(c_x3_m_1.find_real_roots(), [1])
c = cubic(1, 0, 0, 1)
self.check_vector(c.find_real_roots(), [-1])
c = cubic(1, 3, 3, 1)
self.check_vector(c.find_real_roots(), [-1, -1, -1])
c = cubic(1, -3, 3, -1)
self.check_vector(c.find_real_roots(), [1, 1, 1])
c = cubic(1, -6, 11, -6)
self.check_vector(c.find_real_roots(), [3, 1, 2])
c = cubic(1, 0, 0, 1)
self.check_vector(c.find_all_roots(),
[-r, r / 2 - i * rt3 / 2, r / 2 + i * rt3 / 2])
c = cubic(1, -6, 11, -6)
self.check_vector(c.find_all_roots(), [r * 3, r * 1, r * 2])
pass
def test_complex_coeffs(self):
i = complex(imaginary=1)
z = complex()
r = complex(real=1)
rt2 = pow(2, 0.5)
rt3 = pow(3, 0.5)
for c in [
cubic(r, z, r, r),
cubic(r, z, r, r),
cubic(i * 16, r * 4 + i * 2, i * 3, r),
cubic(1, 0, 1, 1),
cubic(1, -6, 11, -6),
]:
coeffs = c.coeffs()
for r in c.find_all_roots():
f = r * r * r * coeffs[0]
f += r * r * coeffs[1]
f += r * coeffs[2]
f += coeffs[3]
#print f,coeffs,r
self.check_vector([f], [z])
pass
pass
pass
def test_math2(self):
e = complex(real=math.exp(1))
d=pow(e,complex(imaginary=math.pi))
self.check_scalar(d.real(),-1)
self.check_scalar(d.imaginary(),0)
d=pow(e,complex(imaginary=math.pi/2))
self.check_scalar(d.real(),0)
self.check_scalar(d.imaginary(),1)
d=pow(e,complex(real=1,imaginary=math.pi/2))
self.check_scalar(d.real(),0)
self.check_scalar(d.imaginary(),math.exp(1))
pass
def test_real_coeffs(self):
q_xsq_m_1 = quadratic(1,0,-1)
q_xsq_p_1 = quadratic(1,0,1)
self.check_vector(q_xsq_m_1.coeffs(),(1,0,-1))
r = q_xsq_m_1.find_real_roots()
self.check_vector(r,(1,-1))
r = q_xsq_p_1.find_real_roots()
self.check_vector(r,[])
q = quadratic(1,-2,1)
self.check_vector(q.find_real_roots(),(1,1))
q = quadratic(1,2,1)
self.check_vector(q.find_real_roots(),(-1,-1))
q = quadratic(4,4,1)
self.check_vector(q.find_real_roots(),(-0.5,-0.5))
r = q_xsq_p_1.find_all_roots()
self.check_vector(r,[complex(imaginary=1),complex(imaginary=-1)])
def test_bugs(self):
a = complex(real=1)
a.to_polar()
b = -a
self.check_scalar(b.cartesian()[0],-1)
self.check_scalar(b.cartesian()[1],0)
b = complex()
self.check_scalar(b.cartesian()[0],0)
self.check_scalar(b.cartesian()[1],0)
c = b * complex(real=1) * complex(imaginary=1)
self.check_scalar(c.cartesian()[0],0)
self.check_scalar(c.cartesian()[1],0)
c = pow(b,1)
self.check_scalar(c.cartesian()[0],0)
self.check_scalar(c.cartesian()[1],0)
pass
def test_real_coeffs(self):
q_xsq_m_1 = quadratic(1, 0, -1)
q_xsq_p_1 = quadratic(1, 0, 1)
self.check_vector(q_xsq_m_1.coeffs(), (1, 0, -1))
r = q_xsq_m_1.find_real_roots()
self.check_vector(r, (1, -1))
r = q_xsq_p_1.find_real_roots()
self.check_vector(r, [])
q = quadratic(1, -2, 1)
self.check_vector(q.find_real_roots(), (1, 1))
q = quadratic(1, 2, 1)
self.check_vector(q.find_real_roots(), (-1, -1))
q = quadratic(4, 4, 1)
self.check_vector(q.find_real_roots(), (-0.5, -0.5))
r = q_xsq_p_1.find_all_roots()
self.check_vector(r, [complex(imaginary=1), complex(imaginary=-1)])
def test_make(self):
for (r,i) in [(1,0),(0,1),(1,1),(2,3),(4,5),(3,-1),(0,0)]:
c = complex(cartesian=(r,i))
self.check_scalar(c.cartesian()[0],r)
self.check_scalar(c.cartesian()[1],i)
self.check_scalar(c.polar()[0],math.sqrt(i*i+r*r))
if (r==0) and (i==0):
self.assertFalse(bool(c), 'Zero is apparently nonzero')
else:
self.assertTrue(bool(c), 'Nonzero is apparently zero')
d = c.copy()
c += complex(cartesian=(1,1))
self.check_scalar(d.cartesian()[0],r)
self.check_scalar(d.cartesian()[1],i)
self.check_scalar(d.polar()[0],math.sqrt(i*i+r*r))
self.check_scalar(c.cartesian()[0],r+1)
self.check_scalar(c.cartesian()[1],i+1)
pass
pass
def test_complex_coeffs(self):
i = complex(imaginary=1)
z = complex()
r = complex(real=1)
rt2 = pow(2,0.5)
rt3 = pow(3,0.5)
for c in [cubic(r,z,r,r),
cubic(r,z,r,r),
cubic(i*16,r*4+i*2,i*3,r),
cubic(1,0,1,1),
cubic(1,-6,11,-6),
]:
coeffs = c.coeffs()
for r in c.find_all_roots():
f = r*r*r*coeffs[0]
f += r*r*coeffs[1]
f += r*coeffs[2]
f += coeffs[3]
#print f,coeffs,r
self.check_vector([f],[z])
pass
pass
pass
def test_math(self):
for (r,i) in [(1,0),(0,1),(1,1),(2,3),(4,5),(3,-1)]:
c = complex(cartesian=(r,i))
d = c.conjugate()
self.check_scalar(c.cartesian()[0],r)
self.check_scalar(c.cartesian()[1],i)
self.check_scalar(d.cartesian()[0],r)
self.check_scalar(d.cartesian()[1],-i)
e = c*d
m = c.modulus()
self.check_scalar(e.cartesian()[0],m*m)
self.check_scalar(e.cartesian()[1],0)
self.check_scalar(abs(c),m)
ci = c.reciprocal()
f = ci*c
self.check_scalar(f.cartesian()[0],1)
self.check_scalar(f.cartesian()[1],0)
f = c*c/c
self.check_scalar(f.cartesian()[0],r)
self.check_scalar(f.cartesian()[1],i)
f = (c+c)/2
self.check_scalar(f.cartesian()[0],r)
self.check_scalar(f.cartesian()[1],i)
f = (c+c)/c
self.check_scalar(f.cartesian()[0],2)
self.check_scalar(f.cartesian()[1],0)
f = (c-c)
self.check_scalar(f.cartesian()[0],0)
self.check_scalar(f.cartesian()[1],0)
f = ((c*2)*c-(c*c))/c
self.check_scalar(f.cartesian()[0],r)
self.check_scalar(f.cartesian()[1],i)
f = c.sqrt()
g = f*f
self.check_scalar(g.cartesian()[0],c.cartesian()[0])
self.check_scalar(g.cartesian()[1],c.cartesian()[1])
self.check_scalar(g.cartesian()[0],r)
self.check_scalar(g.cartesian()[1],i)
f = c.pow(0.25)
g = f*f
g = g*g
self.check_scalar(g.cartesian()[0],c.cartesian()[0])
self.check_scalar(g.cartesian()[1],c.cartesian()[1])
self.check_scalar(g.cartesian()[0],r)
self.check_scalar(g.cartesian()[1],i)
pass
pass
def test_complex_coeffs(self):
i = complex(imaginary=1)
z = complex()
r = complex(real=1)
rt2 = pow(2,0.5)
q_xsq_m_i = quadratic(r,z,i)
self.check_vector(q_xsq_m_i.coeffs(),(r,z,i))
self.check_vector(q_xsq_m_i.find_all_roots(),(complex(1/rt2,-1/rt2),
complex(-1/rt2,1/rt2)))
q_ixsq_m_1 = quadratic(i,z,r)
self.check_vector(q_ixsq_m_1.coeffs(),(i,z,r))
self.check_vector(q_ixsq_m_1.find_all_roots(),(complex(1/rt2,1/rt2),
complex(-1/rt2,-1/rt2)))
q = quadratic(1,2,1)
self.check_vector(q.find_all_roots(),(complex(-1),complex(-1)))
q = quadratic(i,i*2,i)
self.check_vector(q.find_all_roots(),(complex(-1),complex(-1)))
q = quadratic(r,i*2,r)
self.check_vector(q.find_all_roots(),(i*(rt2-1),-i*(rt2+1)))
def test_complex_coeffs(self):
i = complex(imaginary=1)
z = complex()
r = complex(real=1)
rt2 = pow(2, 0.5)
q_xsq_m_i = quadratic(r, z, i)
self.check_vector(q_xsq_m_i.coeffs(), (r, z, i))
self.check_vector(
q_xsq_m_i.find_all_roots(),
(complex(1 / rt2, -1 / rt2), complex(-1 / rt2, 1 / rt2)))
q_ixsq_m_1 = quadratic(i, z, r)
self.check_vector(q_ixsq_m_1.coeffs(), (i, z, r))
self.check_vector(
q_ixsq_m_1.find_all_roots(),
(complex(1 / rt2, 1 / rt2), complex(-1 / rt2, -1 / rt2)))
q = quadratic(1, 2, 1)
self.check_vector(q.find_all_roots(), (complex(-1), complex(-1)))
q = quadratic(i, i * 2, i)
self.check_vector(q.find_all_roots(), (complex(-1), complex(-1)))
q = quadratic(r, i * 2, r)
self.check_vector(q.find_all_roots(), (i * (rt2 - 1), -i * (rt2 + 1)))