def _richcmp_(self, other, op):
"""
Compare this polynomial with other.
Polynomials are first compared by degree, then in dictionary order
starting with the coefficient of largest degree.
EXAMPLES::
sage: R.<x> = PolynomialRing(ZZ, sparse=True)
sage: 3*x^100 - 12 > 12*x + 5
True
sage: 3*x^100 - 12 > 3*x^100 - x^50 + 5
True
sage: 3*x^100 - 12 < 3*x^100 - x^50 + 5
False
sage: x^100 + x^10 - 1 < x^100 + x^10
True
sage: x^100 < x^100 - x^10
False
TESTS::
sage: R.<x> = PolynomialRing(QQ, sparse=True)
sage: 2*x^2^500 > x^2^500
True
sage: Rd = PolynomialRing(ZZ, 'x', sparse=False)
sage: Rs = PolynomialRing(ZZ, 'x', sparse=True)
sage: for _ in range(100):
....: pd = Rd.random_element()
....: qd = Rd.random_element()
....: assert bool(pd < qd) == bool(Rs(pd) < Rs(qd))
"""
d1 = self.degree()
d2 = other.degree()
# Special case constant polynomials
if d1 <= 0 and d2 <= 0:
return richcmp(self[0], other[0], op)
# For different degrees, compare the degree
if d1 != d2:
return rich_to_bool_sgn(op, d1 - d2)
degs = set(self.__coeffs) | set(other.__coeffs)
for i in sorted(degs, reverse=True):
x = self[i]
y = other[i]
res = richcmp_item(x, y, op)
if res is not NotImplemented:
return res
return rich_to_bool(op, 0)
def _richcmp_(self, other, op):
"""
Compare this polynomial with other.
Polynomials are first compared by degree, then in dictionary order
starting with the coefficient of largest degree.
EXAMPLES::
sage: R.<x> = PolynomialRing(ZZ, sparse=True)
sage: 3*x^100 - 12 > 12*x + 5
True
sage: 3*x^100 - 12 > 3*x^100 - x^50 + 5
True
sage: 3*x^100 - 12 < 3*x^100 - x^50 + 5
False
sage: x^100 + x^10 - 1 < x^100 + x^10
True
sage: x^100 < x^100 - x^10
False
TESTS::
sage: R.<x> = PolynomialRing(QQ, sparse=True)
sage: 2*x^2^500 > x^2^500
True
sage: Rd = PolynomialRing(ZZ, 'x', sparse=False)
sage: Rs = PolynomialRing(ZZ, 'x', sparse=True)
sage: for _ in range(100):
....: pd = Rd.random_element()
....: qd = Rd.random_element()
....: assert bool(pd < qd) == bool(Rs(pd) < Rs(qd))
"""
d1 = self.degree()
d2 = other.degree()
# Special case constant polynomials
if d1 <= 0 and d2 <= 0:
return richcmp(self[0], other[0], op)
# For different degrees, compare the degree
if d1 != d2:
return rich_to_bool_sgn(op, d1 - d2)
degs = set(self.__coeffs) | set(other.__coeffs)
for i in sorted(degs, reverse=True):
x = self[i]
y = other[i]
res = richcmp_item(x, y, op)
if res is not NotImplemented:
return res
return rich_to_bool(op, 0)