def test_exptrigsimp():
def valid(a, b):
from diofant.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_exptrigsimp():
def valid(a, b):
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_sympyissue_2827_trigsimp_methods():
def measure1(expr):
return len(str(expr))
def measure2(expr):
return -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_sympyissue_2827_trigsimp_methods():
def measure1(expr):
return len(str(expr))
def measure2(expr):
return -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