def test_dup_count_real_roots():
assert dup_count_real_roots([], ZZ) == 0
assert dup_count_real_roots([7], ZZ) == 0
assert dup_count_real_roots([1, -1], ZZ) == 1
assert dup_count_real_roots([1, -1], ZZ, inf=1) == 1
assert dup_count_real_roots([1, -1], ZZ, sup=0) == 0
assert dup_count_real_roots([1, -1], ZZ, sup=1) == 1
assert dup_count_real_roots([1, -1], ZZ, inf=0, sup=1) == 1
assert dup_count_real_roots([1, -1], ZZ, inf=0, sup=2) == 1
assert dup_count_real_roots([1, -1], ZZ, inf=1, sup=2) == 1
assert dup_count_real_roots([1, 0, -2], ZZ) == 2
assert dup_count_real_roots([1, 0, -2], ZZ, sup=0) == 1
assert dup_count_real_roots([1, 0, -2], ZZ, inf=-1, sup=1) == 0
def test_dup_count_real_roots():
assert dup_count_real_roots([], ZZ) == 0
assert dup_count_real_roots([7], ZZ) == 0
assert dup_count_real_roots([1,-1], ZZ) == 1
assert dup_count_real_roots([1,-1], ZZ, inf=1) == 1
assert dup_count_real_roots([1,-1], ZZ, sup=0) == 0
assert dup_count_real_roots([1,-1], ZZ, sup=1) == 1
assert dup_count_real_roots([1,-1], ZZ, inf=0, sup=1) == 1
assert dup_count_real_roots([1,-1], ZZ, inf=0, sup=2) == 1
assert dup_count_real_roots([1,-1], ZZ, inf=1, sup=2) == 1
assert dup_count_real_roots([1,0,-2], ZZ) == 2
assert dup_count_real_roots([1,0,-2], ZZ, sup=0) == 1
assert dup_count_real_roots([1,0,-2], ZZ, inf=-1, sup=1) == 0
def count_real_roots(f, inf=None, sup=None):
"""Return the number of real roots of ``f`` in ``[inf, sup]``. """
return dup_count_real_roots(f.rep, f.dom, inf=inf, sup=sup)
def count_real_roots(f, inf=None, sup=None):
"""Return the number of real roots of ``f`` in ``[inf, sup]``. """
return dup_count_real_roots(f.rep, f.dom, inf=inf, sup=sup)
