本文整理汇总了Python中sympy.sec函数的典型用法代码示例。如果您正苦于以下问题：Python sec函数的具体用法？Python sec怎么用？Python sec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sec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_hyper_as_trig
def test_hyper_as_trig():
from sympy.simplify.fu import _osborne as o, _osbornei as i, TR12
eq = sinh(x)**2 + cosh(x)**2
t, f = hyper_as_trig(eq)
assert f(fu(t)) == cosh(2*x)
e, f = hyper_as_trig(tanh(x + y))
assert f(TR12(e)) == (tanh(x) + tanh(y))/(tanh(x)*tanh(y) + 1)
d = Dummy()
assert o(sinh(x), d) == I*sin(x*d)
assert o(tanh(x), d) == I*tan(x*d)
assert o(coth(x), d) == cot(x*d)/I
assert o(cosh(x), d) == cos(x*d)
assert o(sech(x), d) == sec(x*d)
assert o(csch(x), d) == csc(x*d)/I
for func in (sinh, cosh, tanh, coth, sech, csch):
h = func(pi)
assert i(o(h, d), d) == h
# /!\ the _osborne functions are not meant to work
# in the o(i(trig, d), d) direction so we just check
# that they work as they are supposed to work
assert i(cos(x*y + z), y) == cosh(x + z*I)
assert i(sin(x*y + z), y) == sinh(x + z*I)/I
assert i(tan(x*y + z), y) == tanh(x + z*I)/I
assert i(cot(x*y + z), y) == coth(x + z*I)*I
assert i(sec(x*y + z), y) == sech(x + z*I)
assert i(csc(x*y + z), y) == csch(x + z*I)*I
开发者ID:baoqchau，项目名称:sympy，代码行数:28，代码来源:test_fu.py
示例2: trig_substitution_rule
def trig_substitution_rule(integral):
integrand, symbol = integral
A = sympy.Wild('a', exclude=[0, symbol])
B = sympy.Wild('b', exclude=[0, symbol])
theta = sympy.Dummy("theta")
target_pattern = A + B*symbol**2
matches = integrand.find(target_pattern)
for expr in matches:
match = expr.match(target_pattern)
a = match.get(A, ZERO)
b = match.get(B, ZERO)
a_positive = ((a.is_number and a > 0) or a.is_positive)
b_positive = ((b.is_number and b > 0) or b.is_positive)
a_negative = ((a.is_number and a < 0) or a.is_negative)
b_negative = ((b.is_number and b < 0) or b.is_negative)
x_func = None
if a_positive and b_positive:
# a**2 + b*x**2. Assume sec(theta) > 0, -pi/2 < theta < pi/2
x_func = (sympy.sqrt(a)/sympy.sqrt(b)) * sympy.tan(theta)
# Do not restrict the domain: tan(theta) takes on any real
# value on the interval -pi/2 < theta < pi/2 so x takes on
# any value
restriction = True
elif a_positive and b_negative:
# a**2 - b*x**2. Assume cos(theta) > 0, -pi/2 < theta < pi/2
constant = sympy.sqrt(a)/sympy.sqrt(-b)
x_func = constant * sympy.sin(theta)
restriction = sympy.And(symbol > -constant, symbol < constant)
elif a_negative and b_positive:
# b*x**2 - a**2. Assume sin(theta) > 0, 0 < theta < pi
constant = sympy.sqrt(-a)/sympy.sqrt(b)
x_func = constant * sympy.sec(theta)
restriction = sympy.And(symbol > -constant, symbol < constant)
if x_func:
# Manually simplify sqrt(trig(theta)**2) to trig(theta)
# Valid due to assumed domain restriction
substitutions = {}
for f in [sympy.sin, sympy.cos, sympy.tan,
sympy.sec, sympy.csc, sympy.cot]:
substitutions[sympy.sqrt(f(theta)**2)] = f(theta)
substitutions[sympy.sqrt(f(theta)**(-2))] = 1/f(theta)
replaced = integrand.subs(symbol, x_func).trigsimp()
replaced = replaced.subs(substitutions)
if not replaced.has(symbol):
replaced *= manual_diff(x_func, theta)
replaced = replaced.trigsimp()
secants = replaced.find(1/sympy.cos(theta))
if secants:
replaced = replaced.xreplace({
1/sympy.cos(theta): sympy.sec(theta)
})
substep = integral_steps(replaced, theta)
if not contains_dont_know(substep):
return TrigSubstitutionRule(
theta, x_func, replaced, substep, restriction,
integrand, symbol)
开发者ID:mayank1729，项目名称:sympy，代码行数:60，代码来源:manualintegrate.py
示例3: test_periodicity
def test_periodicity():
x = Symbol('x')
y = Symbol('y')
assert periodicity(sin(2*x), x) == pi
assert periodicity((-2)*tan(4*x), x) == pi/4
assert periodicity(sin(x)**2, x) == 2*pi
assert periodicity(3**tan(3*x), x) == pi/3
assert periodicity(tan(x)*cos(x), x) == 2*pi
assert periodicity(sin(x)**(tan(x)), x) == 2*pi
assert periodicity(tan(x)*sec(x), x) == 2*pi
assert periodicity(sin(2*x)*cos(2*x) - y, x) == pi/2
assert periodicity(tan(x) + cot(x), x) == pi
assert periodicity(sin(x) - cos(2*x), x) == 2*pi
assert periodicity(sin(x) - 1, x) == 2*pi
assert periodicity(sin(4*x) + sin(x)*cos(x), x) == pi
assert periodicity(exp(sin(x)), x) == 2*pi
assert periodicity(log(cot(2*x)) - sin(cos(2*x)), x) == pi
assert periodicity(sin(2*x)*exp(tan(x) - csc(2*x)), x) == pi
assert periodicity(cos(sec(x) - csc(2*x)), x) == 2*pi
assert periodicity(tan(sin(2*x)), x) == pi
assert periodicity(2*tan(x)**2, x) == pi
assert periodicity(sin(x)**2 + cos(x)**2, x) == S.Zero
assert periodicity(tan(x), y) == S.Zero
assert periodicity(exp(x), x) is None
assert periodicity(log(x), x) is None
assert periodicity(exp(x)**sin(x), x) is None
assert periodicity(sin(x)**y, y) is None
开发者ID:Salmista-94，项目名称:sympy，代码行数:30，代码来源:test_util.py
示例4: trig_rule
def trig_rule(integral):
integrand, symbol = integral
if isinstance(integrand, sympy.sin) or isinstance(integrand, sympy.cos):
arg = integrand.args[0]
if not isinstance(arg, sympy.Symbol):
return # perhaps a substitution can deal with it
if isinstance(integrand, sympy.sin):
func = "sin"
else:
func = "cos"
return TrigRule(func, arg, integrand, symbol)
if integrand == sympy.sec(symbol) ** 2:
return TrigRule("sec**2", symbol, integrand, symbol)
elif integrand == sympy.csc(symbol) ** 2:
return TrigRule("csc**2", symbol, integrand, symbol)
if isinstance(integrand, sympy.tan):
rewritten = sympy.sin(*integrand.args) / sympy.cos(*integrand.args)
elif isinstance(integrand, sympy.cot):
rewritten = sympy.cos(*integrand.args) / sympy.sin(*integrand.args)
elif isinstance(integrand, sympy.sec):
arg = integrand.args[0]
rewritten = (sympy.sec(arg) ** 2 + sympy.tan(arg) * sympy.sec(arg)) / (sympy.sec(arg) + sympy.tan(arg))
elif isinstance(integrand, sympy.csc):
arg = integrand.args[0]
rewritten = (sympy.csc(arg) ** 2 + sympy.cot(arg) * sympy.csc(arg)) / (sympy.csc(arg) + sympy.cot(arg))
else:
return
return RewriteRule(rewritten, integral_steps(rewritten, symbol), integrand, symbol)
开发者ID:latot，项目名称:sympy，代码行数:34，代码来源:manualintegrate.py
示例5: test_periodicity_check
def test_periodicity_check():
x = Symbol('x')
y = Symbol('y')
assert periodicity(tan(x), x, check=True) == pi
assert periodicity(sin(x) + cos(x), x, check=True) == 2*pi
assert periodicity(sec(x), x) == 2*pi
assert periodicity(sin(x*y), x) == 2*pi/abs(y)
assert periodicity(Abs(sec(sec(x))), x) == pi
开发者ID:baoqchau，项目名称:sympy，代码行数:9，代码来源:test_util.py
示例6: test_manualintegrate_trigonometry
def test_manualintegrate_trigonometry():
assert manualintegrate(sin(x), x) == -cos(x)
assert manualintegrate(tan(x), x) == -log(cos(x))
assert manualintegrate(sec(x), x) == log(sec(x) + tan(x))
assert manualintegrate(csc(x), x) == -log(csc(x) + cot(x))
assert manualintegrate(sin(x) * cos(x), x) in [sin(x) ** 2 / 2, -cos(x)**2 / 2]
assert manualintegrate(-sec(x) * tan(x), x) == -sec(x)
assert manualintegrate(csc(x) * cot(x), x) == -csc(x)
开发者ID:cstrobach83，项目名称:sympy，代码行数:10，代码来源:test_manual.py
示例7: test_trigintegrate_mixed
def test_trigintegrate_mixed():
assert trigintegrate(sin(x)*sec(x), x) == -log(sin(x)**2 - 1)/2
assert trigintegrate(sin(x)*csc(x), x) == x
assert trigintegrate(sin(x)*cot(x), x) == sin(x)
assert trigintegrate(cos(x)*sec(x), x) == x
assert trigintegrate(cos(x)*csc(x), x) == log(cos(x)**2 - 1)/2
assert trigintegrate(cos(x)*tan(x), x) == -cos(x)
assert trigintegrate(cos(x)*cot(x), x) == log(cos(x) - 1)/2 \
- log(cos(x) + 1)/2 + cos(x)
开发者ID:FireJade，项目名称:sympy，代码行数:10，代码来源:test_trigonometry.py
示例8: test_sech
def test_sech():
x, y = symbols('x, y')
k = Symbol('k', integer=True)
n = Symbol('n', positive=True)
assert sech(nan) == nan
assert sech(zoo) == nan
assert sech(oo) == 0
assert sech(-oo) == 0
assert sech(0) == 1
assert sech(-1) == sech(1)
assert sech(-x) == sech(x)
assert sech(pi*I) == sec(pi)
assert sech(-pi*I) == sec(pi)
assert sech(-2**1024 * E) == sech(2**1024 * E)
assert sech(pi*I/2) == zoo
assert sech(-pi*I/2) == zoo
assert sech((-3*10**73 + 1)*pi*I/2) == zoo
assert sech((7*10**103 + 1)*pi*I/2) == zoo
assert sech(pi*I) == -1
assert sech(-pi*I) == -1
assert sech(5*pi*I) == -1
assert sech(8*pi*I) == 1
assert sech(pi*I/3) == 2
assert sech(-2*pi*I/3) == -2
assert sech(pi*I/4) == sqrt(2)
assert sech(-pi*I/4) == sqrt(2)
assert sech(5*pi*I/4) == -sqrt(2)
assert sech(-5*pi*I/4) == -sqrt(2)
assert sech(pi*I/6) == 2/sqrt(3)
assert sech(-pi*I/6) == 2/sqrt(3)
assert sech(7*pi*I/6) == -2/sqrt(3)
assert sech(-5*pi*I/6) == -2/sqrt(3)
assert sech(pi*I/105) == 1/cos(pi/105)
assert sech(-pi*I/105) == 1/cos(pi/105)
assert sech(x*I) == 1/cos(x)
assert sech(k*pi*I) == 1/cos(k*pi)
assert sech(17*k*pi*I) == 1/cos(17*k*pi)
assert sech(n).is_real is True
开发者ID:certik，项目名称:sympy，代码行数:54，代码来源:test_hyperbolic.py
示例9: test_periodicity
def test_periodicity():
x = Symbol('x')
y = Symbol('y')
assert periodicity(sin(2*x), x) == pi
assert periodicity((-2)*tan(4*x), x) == pi/4
assert periodicity(sin(x)**2, x) == 2*pi
assert periodicity(3**tan(3*x), x) == pi/3
assert periodicity(tan(x)*cos(x), x) == 2*pi
assert periodicity(sin(x)**(tan(x)), x) == 2*pi
assert periodicity(tan(x)*sec(x), x) == 2*pi
assert periodicity(sin(2*x)*cos(2*x) - y, x) == pi/2
assert periodicity(tan(x) + cot(x), x) == pi
assert periodicity(sin(x) - cos(2*x), x) == 2*pi
assert periodicity(sin(x) - 1, x) == 2*pi
assert periodicity(sin(4*x) + sin(x)*cos(x), x) == pi
assert periodicity(exp(sin(x)), x) == 2*pi
assert periodicity(log(cot(2*x)) - sin(cos(2*x)), x) == pi
assert periodicity(sin(2*x)*exp(tan(x) - csc(2*x)), x) == pi
assert periodicity(cos(sec(x) - csc(2*x)), x) == 2*pi
assert periodicity(tan(sin(2*x)), x) == pi
assert periodicity(2*tan(x)**2, x) == pi
assert periodicity(sin(x%4), x) == 4
assert periodicity(sin(x)%4, x) == 2*pi
assert periodicity(tan((3*x-2)%4), x) == 4/3
assert periodicity((sqrt(2)*(x+1)+x) % 3, x) == 3 / (sqrt(2)+1)
assert periodicity((x**2+1) % x, x) == None
assert periodicity(sin(x)**2 + cos(x)**2, x) == S.Zero
assert periodicity(tan(x), y) == S.Zero
assert periodicity(exp(x), x) is None
assert periodicity(log(x), x) is None
assert periodicity(exp(x)**sin(x), x) is None
assert periodicity(sin(x)**y, y) is None
assert periodicity(Abs(sin(Abs(sin(x)))),x) == pi
assert all(periodicity(Abs(f(x)),x) == pi for f in (
cos, sin, sec, csc, tan, cot))
assert periodicity(Abs(sin(tan(x))), x) == pi
assert periodicity(Abs(sin(sin(x) + tan(x))), x) == 2*pi
assert periodicity(sin(x) > S.Half, x) is 2*pi
assert periodicity(x > 2, x) is None
assert periodicity(x**3 - x**2 + 1, x) is None
assert periodicity(Abs(x), x) is None
assert periodicity(Abs(x**2 - 1), x) is None
assert periodicity((x**2 + 4)%2, x) is None
assert periodicity((E**x)%3, x) is None
开发者ID:baoqchau，项目名称:sympy，代码行数:50，代码来源:test_util.py
示例10: test_manualintegrate_trigpowers
def test_manualintegrate_trigpowers():
assert manualintegrate(sin(x)**2 * cos(x), x) == sin(x)**3 / 3
assert manualintegrate(sin(x)**2 * cos(x) **2, x) == \
x / 8 - sin(4*x) / 32
assert manualintegrate(sin(x) * cos(x)**3, x) == -cos(x)**4 / 4
assert manualintegrate(sin(x)**3 * cos(x)**2, x) == \
cos(x)**5 / 5 - cos(x)**3 / 3
assert manualintegrate(tan(x)**3 * sec(x), x) == sec(x)**3/3 - sec(x)
assert manualintegrate(tan(x) * sec(x) **2, x) == sec(x)**2/2
assert manualintegrate(cot(x)**5 * csc(x), x) == \
-csc(x)**5/5 + 2*csc(x)**3/3 - csc(x)
assert manualintegrate(cot(x)**2 * csc(x)**6, x) == \
-cot(x)**7/7 - 2*cot(x)**5/5 - cot(x)**3/3
开发者ID:gamechanger98，项目名称:sympy，代码行数:15，代码来源:test_manual.py
示例11: test_conv7
def test_conv7():
x = Symbol("x")
y = Symbol("y")
assert sin(x/3) == sin(sympy.Symbol("x") / 3)
assert cos(x/3) == cos(sympy.Symbol("x") / 3)
assert tan(x/3) == tan(sympy.Symbol("x") / 3)
assert cot(x/3) == cot(sympy.Symbol("x") / 3)
assert csc(x/3) == csc(sympy.Symbol("x") / 3)
assert sec(x/3) == sec(sympy.Symbol("x") / 3)
assert asin(x/3) == asin(sympy.Symbol("x") / 3)
assert acos(x/3) == acos(sympy.Symbol("x") / 3)
assert atan(x/3) == atan(sympy.Symbol("x") / 3)
assert acot(x/3) == acot(sympy.Symbol("x") / 3)
assert acsc(x/3) == acsc(sympy.Symbol("x") / 3)
assert asec(x/3) == asec(sympy.Symbol("x") / 3)
assert sin(x/3)._sympy_() == sympy.sin(sympy.Symbol("x") / 3)
assert sin(x/3)._sympy_() != sympy.cos(sympy.Symbol("x") / 3)
assert cos(x/3)._sympy_() == sympy.cos(sympy.Symbol("x") / 3)
assert tan(x/3)._sympy_() == sympy.tan(sympy.Symbol("x") / 3)
assert cot(x/3)._sympy_() == sympy.cot(sympy.Symbol("x") / 3)
assert csc(x/3)._sympy_() == sympy.csc(sympy.Symbol("x") / 3)
assert sec(x/3)._sympy_() == sympy.sec(sympy.Symbol("x") / 3)
assert asin(x/3)._sympy_() == sympy.asin(sympy.Symbol("x") / 3)
assert acos(x/3)._sympy_() == sympy.acos(sympy.Symbol("x") / 3)
assert atan(x/3)._sympy_() == sympy.atan(sympy.Symbol("x") / 3)
assert acot(x/3)._sympy_() == sympy.acot(sympy.Symbol("x") / 3)
assert acsc(x/3)._sympy_() == sympy.acsc(sympy.Symbol("x") / 3)
assert asec(x/3)._sympy_() == sympy.asec(sympy.Symbol("x") / 3)
开发者ID:cbehan，项目名称:symengine.py，代码行数:29，代码来源:test_sympy_conv.py
示例12: test_stationary_points
def test_stationary_points():
x, y = symbols('x y')
assert stationary_points(sin(x), x, Interval(-pi/2, pi/2)
) == {-pi/2, pi/2}
assert stationary_points(sin(x), x, Interval.Ropen(0, pi/4)
) == EmptySet()
assert stationary_points(tan(x), x,
) == EmptySet()
assert stationary_points(sin(x)*cos(x), x, Interval(0, pi)
) == {pi/4, 3*pi/4}
assert stationary_points(sec(x), x, Interval(0, pi)
) == {0, pi}
assert stationary_points((x+3)*(x-2), x
) == FiniteSet(-S.Half)
assert stationary_points((x + 3)/(x - 2), x, Interval(-5, 5)
) == EmptySet()
assert stationary_points((x**2+3)/(x-2), x
) == {2 - sqrt(7), 2 + sqrt(7)}
assert stationary_points((x**2+3)/(x-2), x, Interval(0, 5)
) == {2 + sqrt(7)}
assert stationary_points(x**4 + x**3 - 5*x**2, x, S.Reals
) == FiniteSet(-2, 0, S(5)/4)
assert stationary_points(exp(x), x
) == EmptySet()
assert stationary_points(log(x) - x, x, S.Reals
) == {1}
assert stationary_points(cos(x), x, Union(Interval(0, 5), Interval(-6, -3))
) == {0, -pi, pi}
assert stationary_points(y, x, S.Reals
) == S.Reals
开发者ID:bjodah，项目名称:sympy，代码行数:31，代码来源:test_util.py
示例13: eval_trigsubstitution
def eval_trigsubstitution(theta, func, rewritten, substep, restriction, integrand, symbol):
func = func.subs(sympy.sec(theta), 1/sympy.cos(theta))
trig_function = list(func.find(TrigonometricFunction))
assert len(trig_function) == 1
trig_function = trig_function[0]
relation = sympy.solve(symbol - func, trig_function)
assert len(relation) == 1
numer, denom = sympy.fraction(relation[0])
if isinstance(trig_function, sympy.sin):
opposite = numer
hypotenuse = denom
adjacent = sympy.sqrt(denom**2 - numer**2)
inverse = sympy.asin(relation[0])
elif isinstance(trig_function, sympy.cos):
adjacent = numer
hypotenuse = denom
opposite = sympy.sqrt(denom**2 - numer**2)
inverse = sympy.acos(relation[0])
elif isinstance(trig_function, sympy.tan):
opposite = numer
adjacent = denom
hypotenuse = sympy.sqrt(denom**2 + numer**2)
inverse = sympy.atan(relation[0])
substitution = [
(sympy.sin(theta), opposite/hypotenuse),
(sympy.cos(theta), adjacent/hypotenuse),
(sympy.tan(theta), opposite/adjacent),
(theta, inverse)
]
return sympy.Piecewise(
(_manualintegrate(substep).subs(substitution).trigsimp(), restriction)
)
开发者ID:DVNSarma，项目名称:sympy，代码行数:35，代码来源:manualintegrate.py
示例14: test_periodicity_check
def test_periodicity_check():
x = Symbol('x')
y = Symbol('y')
assert periodicity(tan(x), x, check=True) == pi
assert periodicity(sin(x) + cos(x), x, check=True) == 2*pi
raises(NotImplementedError, lambda: periodicity(sec(x), x, check=True))
raises(NotImplementedError, lambda: periodicity(sin(x*y), x, check=True))
开发者ID:Salmista-94，项目名称:sympy，代码行数:8，代码来源:test_util.py
示例15: eval_trig
def eval_trig(func, arg, integrand, symbol):
if func == 'sin':
return -sympy.cos(arg)
elif func == 'cos':
return sympy.sin(arg)
elif func == 'sec*tan':
return sympy.sec(arg)
elif func == 'csc*cot':
return sympy.csc(arg)
开发者ID:cstrobach83，项目名称:sympy，代码行数:9，代码来源:manualintegrate.py
示例16: test_inverses
def test_inverses():
raises(AttributeError, lambda: sin(x).inverse())
raises(AttributeError, lambda: cos(x).inverse())
assert tan(x).inverse() == atan
assert cot(x).inverse() == acot
raises(AttributeError, lambda: csc(x).inverse())
raises(AttributeError, lambda: sec(x).inverse())
assert asin(x).inverse() == sin
assert acos(x).inverse() == cos
assert atan(x).inverse() == tan
assert acot(x).inverse() == cot
开发者ID:mattpap，项目名称:sympy，代码行数:11，代码来源:test_trigonometric.py
示例17: manual_diff
def manual_diff(f, symbol):
"""Derivative of f in form expected by find_substitutions
SymPy's derivatives for some trig functions (like cot) aren't in a form
that works well with finding substitutions; this replaces the
derivatives for those particular forms with something that works better.
"""
if f.args:
arg = f.args[0]
if isinstance(f, sympy.tan):
return arg.diff(symbol) * sympy.sec(arg)**2
elif isinstance(f, sympy.cot):
return -arg.diff(symbol) * sympy.csc(arg)**2
elif isinstance(f, sympy.sec):
return arg.diff(symbol) * sympy.sec(arg) * sympy.tan(arg)
elif isinstance(f, sympy.csc):
return -arg.diff(symbol) * sympy.csc(arg) * sympy.cot(arg)
elif isinstance(f, sympy.Add):
return sum([manual_diff(arg, symbol) for arg in f.args])
return f.diff(symbol)
开发者ID:cstrobach83，项目名称:sympy，代码行数:21，代码来源:manualintegrate.py
示例18: trig_substitution_rule
def trig_substitution_rule(integral):
integrand, symbol = integral
a = sympy.Wild('a', exclude=[0, symbol])
b = sympy.Wild('b', exclude=[0, symbol])
theta = sympy.Dummy("theta")
matches = integrand.find(a + b*symbol**2)
if matches:
for expr in matches:
match = expr.match(a + b*symbol**2)
a = match[a]
b = match[b]
a_positive = ((a.is_number and a > 0) or a.is_positive)
b_positive = ((b.is_number and b > 0) or b.is_positive)
x_func = None
if a_positive and b_positive:
# a**2 + b*x**2
x_func = (sympy.sqrt(a)/sympy.sqrt(b)) * sympy.tan(theta)
elif a_positive and not b_positive:
# a**2 - b*x**2
x_func = (sympy.sqrt(a)/sympy.sqrt(-b)) * sympy.sin(theta)
elif not a_positive and b_positive:
# b*x**2 - a**2
x_func = (sympy.sqrt(-a)/sympy.sqrt(b)) * sympy.sec(theta)
if x_func:
replaced = integrand.subs(symbol, x_func).trigsimp()
if not replaced.has(symbol):
replaced *= manual_diff(x_func, theta)
replaced = replaced.trigsimp()
secants = replaced.find(1/sympy.cos(theta))
if secants:
replaced = replaced.xreplace({
1/sympy.cos(theta): sympy.sec(theta)
})
substep = integral_steps(replaced, theta)
if not contains_dont_know(substep):
return TrigSubstitutionRule(
theta, x_func, replaced, substep, integrand, symbol)
开发者ID:B-Rich，项目名称:sympy，代码行数:40，代码来源:manualintegrate.py
示例19: test_manualintegrate_trigonometry
def test_manualintegrate_trigonometry():
assert manualintegrate(sin(x), x) == -cos(x)
assert manualintegrate(tan(x), x) == -log(cos(x))
assert manualintegrate(sec(x), x) == log(sec(x) + tan(x))
assert manualintegrate(csc(x), x) == -log(csc(x) + cot(x))
assert manualintegrate(sin(x) * cos(x), x) in [sin(x) ** 2 / 2, -cos(x)**2 / 2]
assert manualintegrate(-sec(x) * tan(x), x) == -sec(x)
assert manualintegrate(csc(x) * cot(x), x) == -csc(x)
assert manualintegrate(sec(x)**2, x) == tan(x)
assert manualintegrate(csc(x)**2, x) == -cot(x)
assert manualintegrate(x * sec(x**2), x) == log(tan(x**2) + sec(x**2))/2
assert manualintegrate(cos(x)*csc(sin(x)), x) == -log(cot(sin(x)) + csc(sin(x)))
assert manualintegrate(cos(3*x)*sec(x), x) == -x + sin(2*x)
assert manualintegrate(sin(3*x)*sec(x), x) == \
-3*log(cos(x)) + 2*log(cos(x)**2) - 2*cos(x)**2
开发者ID:gamechanger98，项目名称:sympy，代码行数:18，代码来源:test_manual.py
示例20: eval_trig
def eval_trig(func, arg, integrand, symbol):
if func == "sin":
return -sympy.cos(arg)
elif func == "cos":
return sympy.sin(arg)
elif func == "sec*tan":
return sympy.sec(arg)
elif func == "csc*cot":
return sympy.csc(arg)
elif func == "sec**2":
return sympy.tan(arg)
elif func == "csc**2":
return -sympy.cot(arg)
开发者ID:latot，项目名称:sympy，代码行数:13，代码来源:manualintegrate.py
注：本文中的sympy.sec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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