本文整理汇总了Python中sympy.conjugate函数的典型用法代码示例。如果您正苦于以下问题：Python conjugate函数的具体用法？Python conjugate怎么用？Python conjugate使用的例子？那么恭喜您, 这里精选的函数代码示例或许可以为您提供帮助。
在下文中一共展示了conjugate函数的20个代码示例，这些例子默认根据受欢迎程度排序。您可以为喜欢或者感觉有用的代码点赞，您的评价将有助于我们的系统推荐出更棒的Python代码示例。
示例1: test_assoc_laguerre
def test_assoc_laguerre():
n = Symbol("n")
m = Symbol("m")
alpha = Symbol("alpha")
# generalized Laguerre polynomials:
assert assoc_laguerre(0, alpha, x) == 1
assert assoc_laguerre(1, alpha, x) == -x + alpha + 1
assert assoc_laguerre(2, alpha, x).expand() == \
(x**2/2 - (alpha + 2)*x + (alpha + 2)*(alpha + 1)/2).expand()
assert assoc_laguerre(3, alpha, x).expand() == \
(-x**3/6 + (alpha + 3)*x**2/2 - (alpha + 2)*(alpha + 3)*x/2 +
(alpha + 1)*(alpha + 2)*(alpha + 3)/6).expand()
# Test the lowest 10 polynomials with laguerre_poly, to make sure it works:
for i in range(10):
assert assoc_laguerre(i, 0, x).expand() == laguerre_poly(i, x)
X = assoc_laguerre(n, m, x)
assert isinstance(X, assoc_laguerre)
assert assoc_laguerre(n, 0, x) == laguerre(n, x)
assert assoc_laguerre(n, alpha, 0) == binomial(alpha + n, alpha)
assert diff(assoc_laguerre(n, alpha, x), x) == \
-assoc_laguerre(n - 1, alpha + 1, x)
assert conjugate(assoc_laguerre(n, alpha, x)) == \
assoc_laguerre(n, conjugate(alpha), conjugate(x))
raises(ValueError, lambda: assoc_laguerre(-2.1, alpha, x))
开发者ID:abhi98khandelwal，项目名称:sympy，代码行数:31，代码来源:test_spec_polynomials.py
示例2: test_pretty_functions
def test_pretty_functions():
f = Function('f')
# Simple
assert pretty( (2*x + exp(x)) ) in [' x \ne + 2*x', ' x\n2*x + e ']
assert pretty(abs(x)) == '|x|'
assert pretty(abs(x/(x**2+1))) in [
'| x |\n|------|\n| 2|\n|1 + x |',
'| x |\n|------|\n| 2 |\n|x + 1|']
assert pretty(conjugate(x)) == '_\nx'
assert pretty(conjugate(f(x+1))) in [
'________\nf(1 + x)',
'________\nf(x + 1)']
# Univariate/Multivariate functions
assert pretty(f(x)) == 'f(x)'
assert pretty(f(x, y)) == 'f(x, y)'
assert pretty(f(x/(y+1), y)) in [
' / x \\\nf|-----, y|\n \\1 + y /',
' / x \\\nf|-----, y|\n \\y + 1 /',
]
# Nesting of square roots
assert pretty( sqrt((sqrt(x+1))+1) ) in [
' _______________\n / _______ \n\\/ 1 + \\/ 1 + x ',
' _______________\n / _______ \n\\/ \\/ x + 1 + 1 ']
# Function powers
assert pretty( sin(x)**2 ) == ' 2 \nsin (x)'
# Conjugates
a,b = map(Symbol, 'ab')
开发者ID:fperez，项目名称:sympy，代码行数:31，代码来源:test_pretty.py
示例3: test_issue_11518
def test_issue_11518():
x = Symbol("x", real=True)
y = Symbol("y", real=True)
r = sqrt(x**2 + y**2)
assert conjugate(r) == r
s = abs(x + I * y)
assert conjugate(s) == r
开发者ID:KonstantinTogoi，项目名称:sympy，代码行数:7，代码来源:test_complex.py
示例4: pinv
def pinv(A_expr):
a_wild_expr = sympy.Wild("a_wild")
assert A_expr == A_expr.replace(sympy.conjugate(a_wild_expr),a_wild_expr)
A_pinv_expr = A_expr.pinv()
A_pinv_expr = A_pinv_expr.replace(sympy.conjugate(a_wild_expr),a_wild_expr)
return A_pinv_expr
开发者ID:mikeroberts3000，项目名称:flashlight，代码行数:7，代码来源:sympy_utils.py
示例5: test_erf
def test_erf():
assert erf(nan) == nan
assert erf(oo) == 1
assert erf(-oo) == -1
assert erf(0) == 0
assert erf(I*oo) == oo*I
assert erf(-I*oo) == -oo*I
assert erf(-2) == -erf(2)
assert erf(-x*y) == -erf(x*y)
assert erf(-x - y) == -erf(x + y)
assert erf(I).is_real == False
assert erf(0).is_real == True
assert conjugate(erf(z)) == erf(conjugate(z))
assert erf(x).as_leading_term(x) == x
assert erf(1/x).as_leading_term(x) == erf(1/x)
assert erf(z).rewrite('uppergamma') == sqrt(z**2)*erf(sqrt(z**2))/z
assert limit(exp(x)*exp(x**2)*(erf(x+1/exp(x))-erf(x)), x, oo) == 2/sqrt(pi)
assert limit((1-erf(z))*exp(z**2)*z, z, oo) == 1/sqrt(pi)
assert limit((1-erf(x))*exp(x**2)*sqrt(pi)*x, x, oo) == 1
assert limit(((1-erf(x))*exp(x**2)*sqrt(pi)*x-1)*2*x**2, x, oo) == -1
raises(ArgumentIndexError, 'erf(x).fdiff(2)')
开发者ID:abhishek070193，项目名称:sympy，代码行数:31，代码来源:test_error_functions.py
示例6: test_gegenbauer
def test_gegenbauer():
n = Symbol("n")
a = Symbol("a")
assert gegenbauer(0, a, x) == 1
assert gegenbauer(1, a, x) == 2*a*x
assert gegenbauer(2, a, x) == -a + x**2*(2*a**2 + 2*a)
assert gegenbauer(3, a, x) == \
x**3*(4*a**3/3 + 4*a**2 + 8*a/3) + x*(-2*a**2 - 2*a)
assert gegenbauer(-1, a, x) == 0
assert gegenbauer(n, S(1)/2, x) == legendre(n, x)
assert gegenbauer(n, 1, x) == chebyshevu(n, x)
assert gegenbauer(n, -1, x) == 0
X = gegenbauer(n, a, x)
assert isinstance(X, gegenbauer)
assert gegenbauer(n, a, -x) == (-1)**n*gegenbauer(n, a, x)
assert gegenbauer(n, a, 0) == 2**n*sqrt(pi) * \
gamma(a + n/2)/(gamma(a)*gamma(-n/2 + S(1)/2)*gamma(n + 1))
assert gegenbauer(n, a, 1) == gamma(2*a + n)/(gamma(2*a)*gamma(n + 1))
assert gegenbauer(n, Rational(3, 4), -1) == zoo
m = Symbol("m", positive=True)
assert gegenbauer(m, a, oo) == oo*RisingFactorial(a, m)
assert conjugate(gegenbauer(n, a, x)) == gegenbauer(n, conjugate(a), conjugate(x))
assert diff(gegenbauer(n, a, x), n) == Derivative(gegenbauer(n, a, x), n)
assert diff(gegenbauer(n, a, x), x) == 2*a*gegenbauer(n - 1, a + 1, x)
开发者ID:abhi98khandelwal，项目名称:sympy，代码行数:32，代码来源:test_spec_polynomials.py
示例7: test_DiracDelta
def test_DiracDelta():
assert DiracDelta(1) == 0
assert DiracDelta(5.1) == 0
assert DiracDelta(-pi) == 0
assert DiracDelta(5, 7) == 0
assert DiracDelta(0) == oo
assert DiracDelta(0, 5) == oo
assert DiracDelta(nan) == nan
assert DiracDelta(x).func == DiracDelta
assert conjugate(DiracDelta(x)) == DiracDelta(x)
assert conjugate(DiracDelta(x - y)) == DiracDelta(x - y)
assert DiracDelta(x).diff(x) == DiracDelta(x, 1)
assert DiracDelta(x, 1).diff(x) == DiracDelta(x, 2)
assert DiracDelta(x).is_simple(x) == True
assert DiracDelta(3 * x).is_simple(x) == True
assert DiracDelta(x ** 2).is_simple(x) == False
assert DiracDelta(sqrt(x)).is_simple(x) == False
assert DiracDelta(x).is_simple(y) == False
assert DiracDelta(x * y).simplify(x) == DiracDelta(x) / abs(y)
assert DiracDelta(x * y).simplify(y) == DiracDelta(y) / abs(x)
assert DiracDelta(x ** 2 * y).simplify(x) == DiracDelta(x ** 2 * y)
assert DiracDelta(y).simplify(x) == DiracDelta(y)
raises(ArgumentIndexError, lambda: DiracDelta(x).fdiff(2))
raises(ValueError, lambda: DiracDelta(x, -1))
开发者ID:hector1618，项目名称:sympy，代码行数:28，代码来源:test_delta_functions.py
示例8: test_im
def test_im():
x, y = symbols('x,y')
a, b = symbols('a,b', real=True)
r = Symbol('r', real=True)
i = Symbol('i', imaginary=True)
assert im(nan) == nan
assert im(oo*I) == oo
assert im(-oo*I) == -oo
assert im(0) == 0
assert im(1) == 0
assert im(-1) == 0
assert im(E*I) == E
assert im(-E*I) == -E
assert im(x) == im(x)
assert im(x*I) == re(x)
assert im(r*I) == r
assert im(r) == 0
assert im(i*I) == 0
assert im(i) == -I * i
assert im(x + y) == im(x + y)
assert im(x + r) == im(x)
assert im(x + r*I) == im(x) + r
assert im(im(x)*I) == im(x)
assert im(2 + I) == 1
assert im(x + I) == im(x) + 1
assert im(x + y*I) == im(x) + re(y)
assert im(x + r*I) == im(x) + r
assert im(log(2*I)) == pi/2
assert im((2 + I)**2).expand(complex=True) == 4
assert im(conjugate(x)) == -im(x)
assert conjugate(im(x)) == im(x)
assert im(x).as_real_imag() == (im(x), 0)
assert im(i*r*x).diff(r) == im(i*x)
assert im(i*r*x).diff(i) == -I * re(r*x)
assert im(
sqrt(a + b*I)) == (a**2 + b**2)**Rational(1, 4)*sin(atan2(b, a)/2)
assert im(a * (2 + b*I)) == a*b
assert im((1 + sqrt(a + b*I))/2) == \
(a**2 + b**2)**Rational(1, 4)*sin(atan2(b, a)/2)/2
assert im(x).rewrite(re) == x - re(x)
assert (x + im(y)).rewrite(im, re) == x + y - re(y)
开发者ID:AdrianPotter，项目名称:sympy，代码行数:60，代码来源:test_complexes.py
示例9: test_heaviside
def test_heaviside():
assert Heaviside(0).func == Heaviside
assert Heaviside(-5) == 0
assert Heaviside(1) == 1
assert Heaviside(nan) == nan
assert Heaviside(0, x) == x
assert Heaviside(0, nan) == nan
assert Heaviside(x, None) == Heaviside(x)
assert Heaviside(0, None) == Heaviside(0)
# we do not want None in the args:
assert None not in Heaviside(x, None).args
assert adjoint(Heaviside(x)) == Heaviside(x)
assert adjoint(Heaviside(x - y)) == Heaviside(x - y)
assert conjugate(Heaviside(x)) == Heaviside(x)
assert conjugate(Heaviside(x - y)) == Heaviside(x - y)
assert transpose(Heaviside(x)) == Heaviside(x)
assert transpose(Heaviside(x - y)) == Heaviside(x - y)
assert Heaviside(x).diff(x) == DiracDelta(x)
assert Heaviside(x + I).is_Function is True
assert Heaviside(I*x).is_Function is True
raises(ArgumentIndexError, lambda: Heaviside(x).fdiff(2))
raises(ValueError, lambda: Heaviside(I))
raises(ValueError, lambda: Heaviside(2 + 3*I))
开发者ID:abhi98khandelwal，项目名称:sympy，代码行数:27，代码来源:test_delta_functions.py
示例10: test_DiracDelta
def test_DiracDelta():
assert DiracDelta(1) == 0
assert DiracDelta(5.1) == 0
assert DiracDelta(-pi) == 0
assert DiracDelta(5, 7) == 0
assert DiracDelta(nan) == nan
assert DiracDelta(0).func is DiracDelta
assert DiracDelta(x).func is DiracDelta
assert adjoint(DiracDelta(x)) == DiracDelta(x)
assert adjoint(DiracDelta(x - y)) == DiracDelta(x - y)
assert conjugate(DiracDelta(x)) == DiracDelta(x)
assert conjugate(DiracDelta(x - y)) == DiracDelta(x - y)
assert transpose(DiracDelta(x)) == DiracDelta(x)
assert transpose(DiracDelta(x - y)) == DiracDelta(x - y)
assert DiracDelta(x).diff(x) == DiracDelta(x, 1)
assert DiracDelta(x, 1).diff(x) == DiracDelta(x, 2)
assert DiracDelta(x).is_simple(x) is True
assert DiracDelta(3*x).is_simple(x) is True
assert DiracDelta(x**2).is_simple(x) is False
assert DiracDelta(sqrt(x)).is_simple(x) is False
assert DiracDelta(x).is_simple(y) is False
assert DiracDelta(x*y).simplify(x) == DiracDelta(x)/abs(y)
assert DiracDelta(x*y).simplify(y) == DiracDelta(y)/abs(x)
assert DiracDelta(x**2*y).simplify(x) == DiracDelta(x**2*y)
assert DiracDelta(y).simplify(x) == DiracDelta(y)
assert DiracDelta((x - 1)*(x - 2)*(x - 3)).simplify(x) == \
DiracDelta(x - 3)/2 + DiracDelta(x - 2) + DiracDelta(x - 1)/2
raises(ArgumentIndexError, lambda: DiracDelta(x).fdiff(2))
raises(ValueError, lambda: DiracDelta(x, -1))
开发者ID:A-turing-machine，项目名称:sympy，代码行数:34，代码来源:test_delta_functions.py
示例11: test_conjugates
def test_conjugates(self):
"""com1 is real and com4 is imaginary."""
for scalar in (x, z):
self.assertEqual((conjugate(com1(scalar))
- com1(conjugate(scalar))).expand(), 0)
self.assertEqual((conjugate(com4(scalar))
+ com4(conjugate(scalar))).expand(), 0)
开发者ID:PreludeAndFugue，项目名称:newmanpenrose，代码行数:7，代码来源:test_equations.py
示例12: test_pretty_functions
def test_pretty_functions():
f = Function("f")
# Simple
assert pretty((2 * x + exp(x))) in [" x \ne + 2*x", " x\n2*x + e "]
assert pretty(abs(x)) == "|x|"
assert pretty(abs(x / (x ** 2 + 1))) in [
"| x |\n|------|\n| 2|\n|1 + x |",
"| x |\n|------|\n| 2 |\n|x + 1|",
]
assert pretty(conjugate(x)) == "_\nx"
assert pretty(conjugate(f(x + 1))) in ["________\nf(1 + x)", "________\nf(x + 1)"]
# Univariate/Multivariate functions
assert pretty(f(x)) == "f(x)"
assert pretty(f(x, y)) == "f(x, y)"
assert pretty(f(x / (y + 1), y)) in [
" / x \\\nf|-----, y|\n \\1 + y /",
" / x \\\nf|-----, y|\n \\y + 1 /",
]
# Nesting of square roots
assert pretty(sqrt((sqrt(x + 1)) + 1)) in [
" _______________\n / _______ \n\\/ 1 + \\/ 1 + x ",
" _______________\n / _______ \n\\/ \\/ x + 1 + 1 ",
]
# Function powers
assert pretty(sin(x) ** 2) == " 2 \nsin (x)"
# Conjugates
a, b = map(Symbol, "ab")
开发者ID:Praveen-Ramanujam，项目名称:MobRAVE，代码行数:31，代码来源:test_pretty.py
示例13: test_erf2
def test_erf2():
assert erf2(0, 0) == S.Zero
assert erf2(x, x) == S.Zero
assert erf2(nan, 0) == nan
assert erf2(-oo, y) == erf(y) + 1
assert erf2( oo, y) == erf(y) - 1
assert erf2( x, oo) == 1 - erf(x)
assert erf2( x,-oo) == -1 - erf(x)
assert erf2(x, erf2inv(x, y)) == y
assert erf2(-x, -y) == -erf2(x,y)
assert erf2(-x, y) == erf(y) + erf(x)
assert erf2( x, -y) == -erf(y) - erf(x)
assert erf2(x, y).rewrite('fresnels') == erf(y).rewrite(fresnels)-erf(x).rewrite(fresnels)
assert erf2(x, y).rewrite('fresnelc') == erf(y).rewrite(fresnelc)-erf(x).rewrite(fresnelc)
assert erf2(x, y).rewrite('hyper') == erf(y).rewrite(hyper)-erf(x).rewrite(hyper)
assert erf2(x, y).rewrite('meijerg') == erf(y).rewrite(meijerg)-erf(x).rewrite(meijerg)
assert erf2(x, y).rewrite('uppergamma') == erf(y).rewrite(uppergamma) - erf(x).rewrite(uppergamma)
assert erf2(x, y).rewrite('expint') == erf(y).rewrite(expint)-erf(x).rewrite(expint)
assert erf2(I, 0).is_real is False
assert erf2(0, 0).is_real is True
assert expand_func(erf(x) + erf2(x, y)) == erf(y)
assert conjugate(erf2(x, y)) == erf2(conjugate(x), conjugate(y))
assert erf2(x, y).rewrite('erf') == erf(y) - erf(x)
assert erf2(x, y).rewrite('erfc') == erfc(x) - erfc(y)
assert erf2(x, y).rewrite('erfi') == I*(erfi(I*x) - erfi(I*y))
raises(ArgumentIndexError, lambda: erfi(x).fdiff(3))
开发者ID:KonstantinTogoi，项目名称:sympy，代码行数:34，代码来源:test_error_functions.py
示例14: test_jacobi
def test_jacobi():
n = Symbol("n")
a = Symbol("a")
b = Symbol("b")
assert jacobi(0, a, b, x) == 1
assert jacobi(1, a, b, x) == a/2 - b/2 + x*(a/2 + b/2 + 1)
assert jacobi(n, a, a, x) == RisingFactorial(a + 1, n)*gegenbauer(n, a + S(1)/2, x)/RisingFactorial(2*a + 1, n)
assert jacobi(n, a, -a, x) == ((-1)**a*(-x + 1)**(-a/2)*(x + 1)**(a/2)*assoc_legendre(n, a, x)*
factorial(-a + n)*gamma(a + n + 1)/(factorial(a + n)*gamma(n + 1)))
assert jacobi(n, -b, b, x) == ((-x + 1)**(b/2)*(x + 1)**(-b/2)*assoc_legendre(n, b, x)*
gamma(-b + n + 1)/gamma(n + 1))
assert jacobi(n, 0, 0, x) == legendre(n, x)
assert jacobi(n, S.Half, S.Half, x) == RisingFactorial(S(3)/2, n)*chebyshevu(n, x)/factorial(n + 1)
assert jacobi(n, -S.Half, -S.Half, x) == RisingFactorial(S(1)/2, n)*chebyshevt(n, x)/factorial(n)
X = jacobi(n, a, b, x)
assert isinstance(X, jacobi)
assert jacobi(n, a, b, -x) == (-1)**n*jacobi(n, b, a, x)
assert jacobi(n, a, b, 0) == 2**(-n)*gamma(a + n + 1)*hyper((-b - n, -n), (a + 1,), -1)/(factorial(n)*gamma(a + 1))
assert jacobi(n, a, b, 1) == RisingFactorial(a + 1, n)/factorial(n)
m = Symbol("m", positive=True)
assert jacobi(m, a, b, oo) == oo*RisingFactorial(a + b + m + 1, m)
assert conjugate(jacobi(m, a, b, x)) == jacobi(m, conjugate(a), conjugate(b), conjugate(x))
assert diff(jacobi(n,a,b,x), n) == Derivative(jacobi(n, a, b, x), n)
assert diff(jacobi(n,a,b,x), x) == (a/2 + b/2 + n/2 + S(1)/2)*jacobi(n - 1, a + 1, b + 1, x)
开发者ID:StefenYin，项目名称:sympy，代码行数:31，代码来源:test_spec_polynomials.py
示例15: test_gamma
def test_gamma():
assert gamma(nan) == nan
assert gamma(oo) == oo
assert gamma(-100) == zoo
assert gamma(0) == zoo
assert gamma(1) == 1
assert gamma(2) == 1
assert gamma(3) == 2
assert gamma(102) == factorial(101)
assert gamma(Rational(1, 2)) == sqrt(pi)
assert gamma(Rational(3, 2)) == Rational(1, 2)*sqrt(pi)
assert gamma(Rational(5, 2)) == Rational(3, 4)*sqrt(pi)
assert gamma(Rational(7, 2)) == Rational(15, 8)*sqrt(pi)
assert gamma(Rational(-1, 2)) == -2*sqrt(pi)
assert gamma(Rational(-3, 2)) == Rational(4, 3)*sqrt(pi)
assert gamma(Rational(-5, 2)) == -Rational(8, 15)*sqrt(pi)
assert gamma(Rational(-15, 2)) == Rational(256, 2027025)*sqrt(pi)
assert gamma(Rational(
-11, 8)).expand(func=True) == Rational(64, 33)*gamma(Rational(5, 8))
assert gamma(Rational(
-10, 3)).expand(func=True) == Rational(81, 280)*gamma(Rational(2, 3))
assert gamma(Rational(
14, 3)).expand(func=True) == Rational(880, 81)*gamma(Rational(2, 3))
assert gamma(Rational(
17, 7)).expand(func=True) == Rational(30, 49)*gamma(Rational(3, 7))
assert gamma(Rational(
19, 8)).expand(func=True) == Rational(33, 64)*gamma(Rational(3, 8))
assert gamma(x).diff(x) == gamma(x)*polygamma(0, x)
assert gamma(x - 1).expand(func=True) == gamma(x)/(x - 1)
assert gamma(x + 2).expand(func=True, mul=False) == x*(x + 1)*gamma(x)
assert conjugate(gamma(x)) == gamma(conjugate(x))
assert expand_func(gamma(x + Rational(3, 2))) == \
(x + Rational(1, 2))*gamma(x + Rational(1, 2))
assert expand_func(gamma(x - Rational(1, 2))) == \
gamma(Rational(1, 2) + x)/(x - Rational(1, 2))
# Test a bug:
assert expand_func(gamma(x + Rational(3, 4))) == gamma(x + Rational(3, 4))
assert gamma(3*exp_polar(I*pi)/4).is_nonnegative is False
assert gamma(3*exp_polar(I*pi)/4).is_nonpositive is True
# Issue 8526
k = Symbol('k', integer=True, nonnegative=True)
assert isinstance(gamma(k), gamma)
assert gamma(-k) == zoo
开发者ID:A-turing-machine，项目名称:sympy，代码行数:59，代码来源:test_gamma_functions.py
示例16: test_re
def test_re():
x, y = symbols('x,y')
a, b = symbols('a,b', real=True)
r = Symbol('r', real=True)
i = Symbol('i', imaginary=True)
assert re(nan) == nan
assert re(oo) == oo
assert re(-oo) == -oo
assert re(0) == 0
assert re(1) == 1
assert re(-1) == -1
assert re(E) == E
assert re(-E) == -E
assert re(x) == re(x)
assert re(x*I) == -im(x)
assert re(r*I) == 0
assert re(r) == r
assert re(i*I) == I * i
assert re(i) == 0
assert re(x + y) == re(x + y)
assert re(x + r) == re(x) + r
assert re(re(x)) == re(x)
assert re(2 + I) == 2
assert re(x + I) == re(x)
assert re(x + y*I) == re(x) - im(y)
assert re(x + r*I) == re(x)
assert re(log(2*I)) == log(2)
assert re((2 + I)**2).expand(complex=True) == 3
assert re(conjugate(x)) == re(x)
assert conjugate(re(x)) == re(x)
assert re(x).as_real_imag() == (re(x), 0)
assert re(i*r*x).diff(r) == re(i*x)
assert re(i*r*x).diff(i) == I*r*im(x)
assert re(
sqrt(a + b*I)) == (a**2 + b**2)**Rational(1, 4)*cos(atan2(b, a)/2)
assert re(a * (2 + b*I)) == 2*a
assert re((1 + sqrt(a + b*I))/2) == \
(a**2 + b**2)**Rational(1, 4)*cos(atan2(b, a)/2)/2 + Rational(1, 2)
assert re(x).rewrite(im) == x - im(x)
assert (x + re(y)).rewrite(re, im) == x + y - im(y)
开发者ID:AdrianPotter，项目名称:sympy，代码行数:59，代码来源:test_complexes.py
示例17: test_DiracDelta
def test_DiracDelta():
assert DiracDelta(1) == 0
assert DiracDelta(5.1) == 0
assert DiracDelta(-pi) == 0
assert DiracDelta(5, 7) == 0
assert DiracDelta(i) == 0
assert DiracDelta(j) == 0
assert DiracDelta(k) == 0
assert DiracDelta(nan) == nan
assert DiracDelta(0).func is DiracDelta
assert DiracDelta(x).func is DiracDelta
# FIXME: this is generally undefined @ x=0
# But then limit(Delta(c)*Heaviside(x),x,-oo)
# need's to be implemented.
#assert 0*DiracDelta(x) == 0
assert adjoint(DiracDelta(x)) == DiracDelta(x)
assert adjoint(DiracDelta(x - y)) == DiracDelta(x - y)
assert conjugate(DiracDelta(x)) == DiracDelta(x)
assert conjugate(DiracDelta(x - y)) == DiracDelta(x - y)
assert transpose(DiracDelta(x)) == DiracDelta(x)
assert transpose(DiracDelta(x - y)) == DiracDelta(x - y)
assert DiracDelta(x).diff(x) == DiracDelta(x, 1)
assert DiracDelta(x, 1).diff(x) == DiracDelta(x, 2)
assert DiracDelta(x).is_simple(x) is True
assert DiracDelta(3*x).is_simple(x) is True
assert DiracDelta(x**2).is_simple(x) is False
assert DiracDelta(sqrt(x)).is_simple(x) is False
assert DiracDelta(x).is_simple(y) is False
assert DiracDelta(x*y).expand(diracdelta=True, wrt=x) == DiracDelta(x)/abs(y)
assert DiracDelta(x*y).expand(diracdelta=True, wrt=y) == DiracDelta(y)/abs(x)
assert DiracDelta(x**2*y).expand(diracdelta=True, wrt=x) == DiracDelta(x**2*y)
assert DiracDelta(y).expand(diracdelta=True, wrt=x) == DiracDelta(y)
assert DiracDelta((x - 1)*(x - 2)*(x - 3)).expand(diracdelta=True, wrt=x) == (
DiracDelta(x - 3)/2 + DiracDelta(x - 2) + DiracDelta(x - 1)/2)
assert DiracDelta(2*x) != DiracDelta(x) # scaling property
assert DiracDelta(x) == DiracDelta(-x) # even function
assert DiracDelta(-x, 2) == DiracDelta(x, 2)
assert DiracDelta(-x, 1) == -DiracDelta(x, 1) # odd deriv is odd
assert DiracDelta(-oo*x) == DiracDelta(oo*x)
assert DiracDelta(x - y) != DiracDelta(y - x)
assert signsimp(DiracDelta(x - y) - DiracDelta(y - x)) == 0
with raises(SymPyDeprecationWarning):
assert DiracDelta(x*y).simplify(x) == DiracDelta(x)/abs(y)
assert DiracDelta(x*y).simplify(y) == DiracDelta(y)/abs(x)
assert DiracDelta(x**2*y).simplify(x) == DiracDelta(x**2*y)
assert DiracDelta(y).simplify(x) == DiracDelta(y)
assert DiracDelta((x - 1)*(x - 2)*(x - 3)).simplify(x) == (
DiracDelta(x - 3)/2 + DiracDelta(x - 2) + DiracDelta(x - 1)/2)
raises(ArgumentIndexError, lambda: DiracDelta(x).fdiff(2))
raises(ValueError, lambda: DiracDelta(x, -1))
raises(ValueError, lambda: DiracDelta(I))
raises(ValueError, lambda: DiracDelta(2 + 3*I))
开发者ID:KonstantinTogoi，项目名称:sympy，代码行数:59，代码来源:test_delta_functions.py
示例18: test_conjugate_transpose
def test_conjugate_transpose():
A, B = symbols("A B", commutative=False)
p = Piecewise((A*B**2, x > 0), (A**2*B, True))
assert p.adjoint() == \
Piecewise((adjoint(A*B**2), x > 0), (adjoint(A**2*B), True))
assert p.conjugate() == \
Piecewise((conjugate(A*B**2), x > 0), (conjugate(A**2*B), True))
assert p.transpose() == \
Piecewise((transpose(A*B**2), x > 0), (transpose(A**2*B), True))
开发者ID:HuibinLin，项目名称:sympy，代码行数:9，代码来源:test_piecewise.py
示例19: test_atan2
def test_atan2():
assert atan2.nargs == FiniteSet(2)
assert atan2(0, 0) == S.NaN
assert atan2(0, 1) == 0
assert atan2(1, 1) == pi/4
assert atan2(1, 0) == pi/2
assert atan2(1, -1) == 3*pi/4
assert atan2(0, -1) == pi
assert atan2(-1, -1) == -3*pi/4
assert atan2(-1, 0) == -pi/2
assert atan2(-1, 1) == -pi/4
i = symbols('i', imaginary=True)
r = symbols('r', real=True)
eq = atan2(r, i)
ans = -I*log((i + I*r)/sqrt(i**2 + r**2))
reps = ((r, 2), (i, I))
assert eq.subs(reps) == ans.subs(reps)
x = Symbol('x', negative=True)
y = Symbol('y', negative=True)
assert atan2(y, x) == atan(y/x) - pi
y = Symbol('y', nonnegative=True)
assert atan2(y, x) == atan(y/x) + pi
y = Symbol('y')
assert atan2(y, x) == atan2(y, x, evaluate=False)
u = Symbol("u", positive=True)
assert atan2(0, u) == 0
u = Symbol("u", negative=True)
assert atan2(0, u) == pi
assert atan2(y, oo) == 0
assert atan2(y, -oo)== 2*pi*Heaviside(re(y)) - pi
assert atan2(y, x).rewrite(log) == -I*log((x + I*y)/sqrt(x**2 + y**2))
assert atan2(y, x).rewrite(atan) == 2*atan(y/(x + sqrt(x**2 + y**2)))
ex = atan2(y, x) - arg(x + I*y)
assert ex.subs({x:2, y:3}).rewrite(arg) == 0
assert ex.subs({x:2, y:3*I}).rewrite(arg) == -pi - I*log(sqrt(5)*I/5)
assert ex.subs({x:2*I, y:3}).rewrite(arg) == -pi/2 - I*log(sqrt(5)*I)
assert ex.subs({x:2*I, y:3*I}).rewrite(arg) == -pi + atan(2/S(3)) + atan(3/S(2))
i = symbols('i', imaginary=True)
r = symbols('r', real=True)
e = atan2(i, r)
rewrite = e.rewrite(arg)
reps = {i: I, r: -2}
assert rewrite == -I*log(abs(I*i + r)/sqrt(abs(i**2 + r**2))) + arg((I*i + r)/sqrt(i**2 + r**2))
assert (e - rewrite).subs(reps).equals(0)
assert conjugate(atan2(x, y)) == atan2(conjugate(x), conjugate(y))
assert diff(atan2(y, x), x) == -y/(x**2 + y**2)
assert diff(atan2(y, x), y) == x/(x**2 + y**2)
assert simplify(diff(atan2(y, x).rewrite(log), x)) == -y/(x**2 + y**2)
assert simplify(diff(atan2(y, x).rewrite(log), y)) == x/(x**2 + y**2)
开发者ID:AdrianPotter，项目名称:sympy，代码行数:57，代码来源:test_trigonometric.py
示例20: test_sign
def test_sign():
assert sign(1.2) == 1
assert sign(-1.2) == -1
assert sign(3*I) == I
assert sign(-3*I) == -I
assert sign(0) == 0
assert sign(nan) == nan
x = Symbol('x')
assert sign(x).is_zero == None
assert sign(x).doit() == sign(x)
assert sign(1.2*x) == sign(x)
assert sign(2*x) == sign(x)
assert sign(I*x) == I*sign(x)
assert sign(-2*I*x) == -I*sign(x)
assert sign(conjugate(x)) == conjugate(sign(x))
p = Symbol('p', positive = True)
n = Symbol('n', negative = True)
m = Symbol('m', negative = True)
assert sign(2*p*x) == sign(x)
assert sign(n*x) == -sign(x)
assert sign(n*m*x) == sign(x)
x = Symbol('x', imaginary=True)
assert sign(x).is_zero == False
assert sign(x).diff(x) == 2*DiracDelta(-I*x)
assert sign(x).doit() == x / Abs(x)
assert conjugate(sign(x)) == -sign(x)
x = Symbol('x', real=True)
assert sign(x).is_zero == None
assert sign(x).diff(x) == 2*DiracDelta(x)
assert sign(x).doit() == sign(x)
assert conjugate(sign(x)) == sign(x)
x = Symbol('x', nonzero=True)
assert sign(x).is_zero == False
assert sign(x).doit() == x / Abs(x)
assert sign(Abs(x)) == 1
assert Abs(sign(x)) == 1
x = Symbol('x', positive=True)
assert sign(x).is_zero == False
assert sign(x).doit() == x / Abs(x)
assert sign(Abs(x)) == 1
assert Abs(sign(x)) == 1
x = 0
assert sign(x).is_zero == True
assert sign(x).doit() == 0
assert sign(Abs(x)) == 0
assert Abs(sign(x)) == 0
nz = Symbol('nz', nonzero=True, integer=True)
assert sign(nz)**2 == 1
assert (sign(nz)**3).args == (sign(nz), 3)
开发者ID:BDGLunde，项目名称:sympy，代码行数:57，代码来源:test_complexes.py
注：本文中的sympy.conjugate函数示例由纯净天空整理自Github/MSDocs等源码及文档管理平台，相关代码片段筛选自各路编程大神贡献的开源项目，源码版权归原作者所有，传播和使用请参考对应项目的License；未经允许，请勿转载。 |
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