def test_exptrigsimp():
def valid(a, b):
from sympy.testing.randtest import verify_numerically as tn
if not (tn(a, b) and a == b):
return False
return True
assert exptrigsimp(exp(x) + exp(-x)) == 2 * cosh(x)
assert exptrigsimp(exp(x) - exp(-x)) == 2 * sinh(x)
assert exptrigsimp(
(2 * exp(x) - 2 * exp(-x)) / (exp(x) + exp(-x))) == 2 * tanh(x)
assert exptrigsimp((2 * exp(2 * x) - 2) / (exp(2 * x) + 1)) == 2 * tanh(x)
e = [
cos(x) + I * sin(x),
cos(x) - I * sin(x),
cosh(x) - sinh(x),
cosh(x) + sinh(x)
]
ok = [exp(I * x), exp(-I * x), exp(-x), exp(x)]
assert all(valid(i, j) for i, j in zip([exptrigsimp(ei) for ei in e], ok))
ue = [
cos(x) + sin(x),
cos(x) - sin(x),
cosh(x) + I * sinh(x),
cosh(x) - I * sinh(x),
]
assert [exptrigsimp(ei) == ei for ei in ue]
res = []
ok = [
y * tanh(1),
1 / (y * tanh(1)),
I * y * tan(1),
-I / (y * tan(1)),
y * tanh(x),
1 / (y * tanh(x)),
I * y * tan(x),
-I / (y * tan(x)),
y * tanh(1 + I),
1 / (y * tanh(1 + I)),
]
for a in (1, I, x, I * x, 1 + I):
w = exp(a)
eq = y * (w - 1 / w) / (w + 1 / w)
res.append(simplify(eq))
res.append(simplify(1 / eq))
assert all(valid(i, j) for i, j in zip(res, ok))
for a in range(1, 3):
w = exp(a)
e = w + 1 / w
s = simplify(e)
assert s == exptrigsimp(e)
assert valid(s, 2 * cosh(a))
e = w - 1 / w
s = simplify(e)
assert s == exptrigsimp(e)
assert valid(s, 2 * sinh(a))
def test_exptrigsimp():
def valid(a, b):
from sympy.utilities.randtest import verify_numerically as tn
if not (tn(a, b) and a == b):
return False
return True
assert exptrigsimp(exp(x) + exp(-x)) == 2*cosh(x)
assert exptrigsimp(exp(x) - exp(-x)) == 2*sinh(x)
e = [cos(x) + I*sin(x), cos(x) - I*sin(x),
cosh(x) - sinh(x), cosh(x) + sinh(x)]
ok = [exp(I*x), exp(-I*x), exp(-x), exp(x)]
assert all(valid(i, j) for i, j in zip(
[exptrigsimp(ei) for ei in e], ok))
ue = [cos(x) + sin(x), cos(x) - sin(x),
cosh(x) + I*sinh(x), cosh(x) - I*sinh(x)]
assert [exptrigsimp(ei) == ei for ei in ue]
res = []
ok = [y*tanh(1), 1/(y*tanh(1)), I*y*tan(1), -I/(y*tan(1)),
y*tanh(x), 1/(y*tanh(x)), I*y*tan(x), -I/(y*tan(x)),
y*tanh(1 + I), 1/(y*tanh(1 + I))]
for a in (1, I, x, I*x, 1 + I):
w = exp(a)
eq = y*(w - 1/w)/(w + 1/w)
s = simplify(eq)
assert s == exptrigsimp(eq)
res.append(s)
sinv = simplify(1/eq)
assert sinv == exptrigsimp(1/eq)
res.append(sinv)
assert all(valid(i, j) for i, j in zip(res, ok))
for a in range(1, 3):
w = exp(a)
e = w + 1/w
s = simplify(e)
assert s == exptrigsimp(e)
assert valid(s, 2*cosh(a))
e = w - 1/w
s = simplify(e)
assert s == exptrigsimp(e)
assert valid(s, 2*sinh(a))
def test_issue_2827_trigsimp_methods():
measure1 = lambda expr: len(str(expr))
measure2 = lambda expr: -count_ops(expr)
# Return the most complicated result
expr = (x + 1) / (x + sin(x)**2 + cos(x)**2)
ans = Matrix([1])
M = Matrix([expr])
assert trigsimp(M, method='fu', measure=measure1) == ans
assert trigsimp(M, method='fu', measure=measure2) != ans
# all methods should work with Basic expressions even if they
# aren't Expr
M = Matrix.eye(1)
assert all(
trigsimp(M, method=m) == M for m in 'fu matching groebner old'.split())
# watch for E in exptrigsimp, not only exp()
eq = 1 / sqrt(E) + E
assert exptrigsimp(eq) == eq
def test_issue_2827_trigsimp_methods():
measure1 = lambda expr: len(str(expr))
measure2 = lambda expr: -count_ops(expr)
# Return the most complicated result
expr = (x + 1)/(x + sin(x)**2 + cos(x)**2)
ans = Matrix([1])
M = Matrix([expr])
assert trigsimp(M, method='fu', measure=measure1) == ans
assert trigsimp(M, method='fu', measure=measure2) != ans
# all methods should work with Basic expressions even if they
# aren't Expr
M = Matrix.eye(1)
assert all(trigsimp(M, method=m) == M for m in
'fu matching groebner old'.split())
# watch for E in exptrigsimp, not only exp()
eq = 1/sqrt(E) + E
assert exptrigsimp(eq) == eq
def _is_ac(self, expr):
# Convert exp(-j*x*t) + exp(j*x*t) into 2 * cos(x) etc.
expr = sym.exptrigsimp(expr.rewrite(cos))
terms = expr.as_ordered_terms()
if len(terms) > 1:
return self._is_sum_ac(terms)
factors = expr.as_ordered_factors()
self.amp = 1
for factor in factors:
if factor.is_Function:
if factor.func not in (cos, sin, exp):
return False
if not self._find_freq_phase(factor):
return False
elif is_dc(factor, self.var):
self.amp *= factor
else:
return False
return True
def test_exptrigsimp_noncommutative():
a, b = symbols('a b', commutative=False)
x = Symbol('x', commutative=True)
assert exp(a + x) == exptrigsimp(exp(a) * exp(x))
p = exp(a) * exp(b) - exp(b) * exp(a)
assert p == exptrigsimp(p) != 0
def test_exptrigsimp_noncommutative():
a,b = symbols('a b', commutative=False)
x = Symbol('x', commutative=True)
assert exp(a + x) == exptrigsimp(exp(a)*exp(x))
p = exp(a)*exp(b) - exp(b)*exp(a)
assert p == exptrigsimp(p) != 0