def test_rewrite1():
e = exp(x)
assert rewrite(e, mrv(e, x), x, m) == (1/m, -x)
e = exp(x**2)
assert rewrite(e, mrv(e, x), x, m) == (1/m, -x**2)
e = exp(x+1/x)
assert rewrite(e, mrv(e, x), x, m) == (1/m, -x-1/x)
e = 1/exp(-x+exp(-x))-exp(x)
assert rewrite(e, mrv(e, x), x, m) == (1/(m*exp(m))-1/m, -x)
def test_mrv1():
assert mrv(x, x) == set([x])
assert mrv(x+1/x, x) == set([x])
assert mrv(x**2, x) == set([x])
assert mrv(log(x), x) == set([x])
assert mrv(exp(x), x) == set([exp(x)])
assert mrv(exp(-x), x) == set([exp(-x)])
assert mrv(exp(x**2), x) == set([exp(x**2)])
assert mrv(-exp(1/x), x) == set([x])
assert mrv(exp(x+1/x), x) == set([exp(x+1/x)])
def test_mrv3():
assert mrv(exp(x**2)+x*exp(x)+log(x)**x/x, x) == set([exp(x**2)])
assert mrv(exp(x)*(exp(1/x+exp(-x))-exp(1/x)), x) == set([exp(x), exp(-x)])
assert mrv(log(x**2+2*exp(exp(3*x**3*log(x)))), x) == set([exp(exp(3*x**3*log(x)))])
assert mrv(log(x-log(x))/log(x), x) == set([x])
assert mrv((exp(1/x-exp(-x))-exp(1/x))*exp(x), x) == set([exp(x), exp(-x)])
assert mrv(1/exp(-x+exp(-x))-exp(x), x) == set([exp(x), exp(-x), exp(x-exp(-x))])
assert mrv(log(log(x*exp(x*exp(x))+1)), x) == set([exp(x*exp(x))])
assert mrv(exp(exp(log(log(x)+1/x))), x) == set([x])
def test_mrv2c():
assert mrv(exp(-x+1/x**2)-exp(x+1/x), x) == set([exp(x+1/x), exp(1/x**2-x)])
def test_mrv2b():
assert mrv(exp(x+exp(-x**2)), x) == set([exp(-x**2)])
def test_mrv2a():
assert mrv(exp(x+exp(-exp(x))), x) == set([exp(-exp(x))])
assert mrv(exp(x+exp(-x)), x) == set([exp(x+exp(-x)), exp(-x)])
assert mrv(exp(1/x+exp(-x)), x) == set([exp(-x)])
def test_mrv_leadterm3():
#Gruntz: p56, 3.27
assert mrv(exp(-x+exp(-x)*exp(-x*log(x))), x) == set([exp(-x-x*log(x))])
assert mrv_leadterm(exp(-x+exp(-x)*exp(-x*log(x))), x) == (exp(-x), 0)
def test_rewrite3():
e = exp(-x+1/x**2)-exp(x+1/x)
#both of these are correct and should be equivalent:
assert rewrite(e, mrv(e, x), x, m) in [(-1/m + m*exp(1/x+1/x**2), -x-1/x), (m - 1/m*exp(1/x + x**(-2)), x**(-2) - x)]
def test_rewrite2():
e = exp(x)*log(log(exp(x)))
assert mrv(e, x) == set([exp(x)])
assert rewrite(e, mrv(e, x), x, m) == (1/m*log(x), -x)
def test_mrv4():
ln = log
assert mrv((ln(ln(x)+ln(ln(x)))-ln(ln(x)))/ln(ln(x)+ln(ln(ln(x))))*ln(x),
x) == set([x])
assert mrv(log(log(x*exp(x*exp(x))+1)) - exp(exp(log(log(x)+1/x))), x) == \
set([exp(x*exp(x))])
