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from hypothesis import given
from hypothesis import strategies as st
from sympy.abc import x
from sympy.polys.polytools import Poly
def polys(*, nonzero=False, domain="ZZ"):
# This is a simple strategy, but sufficient the tests below
elems = {"ZZ": st.integers(), "QQ": st.fractions()}
coeff_st = st.lists(elems[domain])
if nonzero:
coeff_st = coeff_st.filter(any)
return st.builds(Poly, coeff_st, st.just(x), domain=st.just(domain))
@given(f=polys(), g=polys(), r=polys())
def test_gcd_hypothesis(f, g, r):
gcd_1 = f.gcd(g)
gcd_2 = g.gcd(f)
assert gcd_1 == gcd_2
# multiply by r
gcd_3 = g.gcd(f + r * g)
assert gcd_1 == gcd_3
@given(f_z=polys(), g_z=polys(nonzero=True))
def test_poly_hypothesis_integers(f_z, g_z):
remainder_z = f_z.rem(g_z)
assert g_z.degree() >= remainder_z.degree() or remainder_z.degree() == 0
@given(f_q=polys(domain="QQ"), g_q=polys(nonzero=True, domain="QQ"))
def test_poly_hypothesis_rationals(f_q, g_q):
remainder_q = f_q.rem(g_q)
assert g_q.degree() >= remainder_q.degree() or remainder_q.degree() == 0
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