def PSC(F, G, x):
"""PSC(F, G, x) returns a set with the non-zero principal subresultant
coefficients (psc) of the two polynomials F and G with respect to the
variable x.
If the degree of the polynomial F is strictly less than the degree of
the polynomial G, then F and G are interchanged.
Extended psc beyond the n-th are not considered, where n is the minimum
of the degrees of F and G with respect to x.
>>> PSC(0, 0, var('x'))
set()
>>> PSC(poly('2*x'), poly('3*y'), var('x'))
{3*y}
>>> PSC(poly('2*x'), poly('3*y + 5*x**2'), var('x')) == {12*var('y'), 2}
True
>>> PSC(poly('x**3'), poly('x**3 + x'), var('x'))
{1}
"""
subs = subresultants(F, G, x)
s = set()
i = len(subs) - 1
if i < 0:
return s
currDeg = degree(subs[i], x)
while i > 0:
nextDeg = degree(subs[i - 1], x)
s.add(LC(subs[i], x)**(nextDeg - currDeg))
currDeg = nextDeg
i -= 1
return s
def test_subresultants_vv_2():
x = var('x')
p = x**8 + x**6 - 3*x**4 - 3*x**3 + 8*x**2 + 2*x - 5
q = 3*x**6 + 5*x**4 - 4*x**2 - 9*x + 21
assert subresultants_vv_2(p, q, x) == subresultants(p, q, x)
assert subresultants_vv_2(p, q, x)[-1] == sylvester(p, q, x).det()
assert subresultants_vv_2(p, q, x) != euclid_amv(p, q, x)
amv_factors = [1, 1, -1, 1, -1, 1]
assert subresultants_vv_2(p, q, x) == [i*j for i, j in zip(amv_factors, modified_subresultants_amv(p, q, x))]
p = x**3 - 7*x + 7
q = 3*x**2 - 7
assert subresultants_vv_2(p, q, x) == euclid_amv(p, q, x)
def test_subresultants_bezout():
x = var('x')
p = x**8 + x**6 - 3*x**4 - 3*x**3 + 8*x**2 + 2*x - 5
q = 3*x**6 + 5*x**4 - 4*x**2 - 9*x + 21
assert subresultants_bezout(p, q, x) == subresultants(p, q, x)
assert subresultants_bezout(p, q, x)[-1] == sylvester(p, q, x).det()
assert subresultants_bezout(p, q, x) != euclid_amv(p, q, x)
amv_factors = [1, 1, -1, 1, -1, 1]
assert subresultants_bezout(p, q, x) == [i*j for i, j in zip(amv_factors, modified_subresultants_amv(p, q, x))]
p = x**3 - 7*x + 7
q = 3*x**2 - 7
assert subresultants_bezout(p, q, x) == euclid_amv(p, q, x)
