def test_DUP_to_dict():
f = DUP([3,0,0,2,0,0,0,0,8], ZZ)
assert f.to_dict() == \
{8: 3, 5: 2, 0: 8}
assert f.to_sympy_dict() == \
{8: ZZ.to_sympy(3), 5: ZZ.to_sympy(2), 0: ZZ.to_sympy(8)}
def test_DUP_to_dict():
f = DUP([3,0,0,2,0,0,0,0,8], ZZ)
assert f.to_dict() == \
{8: 3, 5: 2, 0: 8}
assert f.to_sympy_dict() == \
{8: ZZ.to_sympy(3), 5: ZZ.to_sympy(2), 0: ZZ.to_sympy(8)}
def test_DUP___eq__():
assert DUP([ZZ(1),ZZ(2),ZZ(3)], ZZ) == \
DUP([ZZ(1),ZZ(2),ZZ(3)], ZZ)
assert DUP([QQ(1),QQ(2),QQ(3)], QQ) == \
DUP([ZZ(1),ZZ(2),ZZ(3)], ZZ)
assert DUP([ZZ(1),ZZ(2),ZZ(3)], ZZ) == \
DUP([QQ(1),QQ(2),QQ(3)], QQ)
assert DUP([ZZ(1),ZZ(2),ZZ(4)], ZZ) != \
DUP([ZZ(1),ZZ(2),ZZ(3)], ZZ)
assert DUP([QQ(1),QQ(2),QQ(4)], QQ) != \
DUP([ZZ(1),ZZ(2),ZZ(3)], ZZ)
def test_DUP___init__():
f = DUP([0,0,1,2,3], ZZ)
assert f.rep == [1,2,3]
assert f.dom == ZZ
f = DUP({2: QQ(1), 0: QQ(1)}, QQ)
assert f.rep == [QQ(1),QQ(0),QQ(1)]
assert f.dom == QQ
f = DUP(1, QQ)
assert f.rep == [QQ(1)]
assert f.dom == QQ
def test_polys():
x = Symbol("x")
f = Poly(x, x)
g = lambda x: x
ZZ = ZZ_python()
QQ = QQ_sympy()
for c in (Poly, Poly(x, x)):
check(c)
for c in (GFP, GFP([ZZ(1), ZZ(2), ZZ(3)], ZZ(7), ZZ)):
check(c)
for c in (DUP, DUP([ZZ(1), ZZ(2), ZZ(3)], ZZ(7), ZZ)):
check(c)
for c in (DMP, DMP([ZZ(1), ZZ(2), ZZ(3)], 0, ZZ)):
check(c)
for c in (DMF, DMF(([ZZ(1), ZZ(2)], [ZZ(1), ZZ(3)], ZZ))):
check(c)
for c in (ANP, ANP([QQ(1), QQ(2)], [QQ(1), QQ(2), QQ(3)], QQ)):
check(c)
for c in (ZZ_python, ZZ_python()):
check(c)
for c in (ZZ_sympy, ZZ_sympy()):
check(c)
for c in (QQ_sympy, QQ_sympy()):
check(c)
for c in (PolynomialRing, PolynomialRing(ZZ, 'x', 'y')):
check(c)
for c in (FractionField, FractionField(ZZ, 'x', 'y')):
check(c)
for c in (ExpressionDomain, ExpressionDomain()):
check(c)
try:
from sympy.polys.algebratools import QQ_python
for c in (QQ_python, QQ_python()):
check(c)
except ImportError:
pass
try:
from sympy.polys.algebratools import QQ_python
for c in (ZZ_gmpy, ZZ_gmpy()):
check(c)
for c in (QQ_gmpy, QQ_gmpy()):
check(c)
except ImportError:
pass
for c in (RootOf, RootOf(f,
0), RootsOf, RootsOf(x,
x), RootSum, RootSum(g, f)):
check(c)
def test_DMP_properties():
assert DMP([[]], ZZ).is_zero == True
assert DMP([[1]], ZZ).is_zero == False
assert DMP([[1]], ZZ).is_one == True
assert DMP([[2]], ZZ).is_one == False
assert DUP([[1]], ZZ).is_ground == True
assert DUP([[1],[2],[1]], ZZ).is_ground == False
assert DMP([[1],[2,0],[1,0]], ZZ).is_sqf == True
assert DMP([[1],[2,0],[1,0,0]], ZZ).is_sqf == False
assert DMP([[1,2],[3]], ZZ).is_monic == True
assert DMP([[2,2],[3]], ZZ).is_monic == False
assert DMP([[1,2],[3]], ZZ).is_primitive == True
assert DMP([[2,4],[6]], ZZ).is_primitive == False
def test_DUP_arithmetics():
f = DUP([1,1,1], ZZ)
assert f.add_term(2, 1) == DUP([1,3,1], ZZ)
assert f.sub_term(2, 1) == DUP([1,-1,1], ZZ)
assert f.mul_term(2, 1) == DUP([2,2,2,0], ZZ)
raises(TypeError, "f.add_term(2, 'x')")
raises(TypeError, "f.sub_term(2, 'x')")
raises(TypeError, "f.mul_term(2, 'x')")
g = DUP([3,3,3], ZZ)
assert f.mul_ground(3) == g
assert g.exquo_ground(3) == f
raises(ExactQuotientFailed, "f.quo_ground(4)")
f = DUP([1,-2,3,-4], ZZ)
g = DUP([1,2,3,4], ZZ)
h = DUP([-1,2,-3,4], ZZ)
assert f.abs() == g
assert abs(f) == g
assert f.neg() == h
assert -f == h
h = DUP([2,0,6,0], ZZ)
assert f.add(g) == h
assert f + g == h
assert g + f == h
h = DUP([1,-2,3,1], ZZ)
assert f + 5 == h
assert 5 + f == h
h = DUP([-4,0,-8], ZZ)
assert f.sub(g) == h
assert f - g == h
assert g - f == -h
h = DUP([1,-2,3,-9], ZZ)
assert f - 5 == h
assert 5 - f == -h
g = DUP([2], ZZ)
h = DUP([2,-4,6,-8], ZZ)
assert f.mul(g) == h
assert f * g == h
assert g * f == h
assert f * 2 == h
assert 2 * f == h
h = DUP([4], ZZ)
assert g.sqr() == h
assert g.pow(2) == h
assert g**2 == h
raises(TypeError, "f.pow('x')")
f = DUP([3,1,1,5], ZZ)
g = DUP([5,-3,1], ZZ)
q = DUP([15, 14], ZZ)
r = DUP([52, 111], ZZ)
assert f.pdiv(g) == (q, r)
assert f.pexquo(g) == q
assert f.prem(g) == r
raises(ExactQuotientFailed, 'f.pquo(g)')
q, r = DUP([], ZZ), f
assert f.div(g) == (q, r)
assert f.exquo(g) == q
assert f.rem(g) == r
raises(ExactQuotientFailed, 'f.quo(g)')
def test_DUP_functionality():
f = DUP([1,2,3,4], ZZ)
g = DUP([3,4,3], ZZ)
assert f.degree() == 3
assert f.LC() == ZZ(1)
assert f.TC() == ZZ(4)
assert f.nth(1) == ZZ(3)
raises(TypeError, "f.nth('x')")
assert f.max_norm() == ZZ(4)
assert f.l1_norm() == ZZ(10)
assert f.diff(1) == g
assert f.eval(1) == ZZ(10)
raises(TypeError, "f.diff('x')")
f = DUP([QQ(2),QQ(0)], QQ)
g = DUP([QQ(1),QQ(0),QQ(-16)], QQ)
s = DUP([QQ(1,32),QQ(0)], QQ)
t = DUP([QQ(-1,16)], QQ)
h = DUP([QQ(1)], QQ)
assert f.half_gcdex(g) == (s, h)
assert f.gcdex(g) == (s, t, h)
assert f.invert(g) == s
f = DUP([1,-2,1], ZZ)
g = DUP([1,0,-1], ZZ)
a = DUP([2,-2], ZZ)
assert f.subresultants(g) == [f, g, a]
assert f.resultant(g) == 0
f = DUP([1,3,9,-13], ZZ)
assert f.discriminant() == -11664
f = DUP([1,2,1], ZZ)
g = DUP([1,1], ZZ)
h = DUP([1], ZZ)
assert f.cofactors(g) == (g, g, h)
assert f.gcd(g) == g
assert f.lcm(g) == f
assert f.sqf_part() == g
assert f.sqf_list() == (ZZ(1), [(g, 2)])
f = DUP([1,2,3,4,5,6], ZZ)
assert f.trunc(3) == DUP([1,-1,0,1,-1,0], ZZ)
f = DUP([QQ(3),QQ(-6)], QQ)
g = DUP([QQ(1),QQ(-2)], QQ)
assert f.monic() == g
f = DUP([3,-6], ZZ)
g = DUP([1,-2], ZZ)
assert f.content() == ZZ(3)
assert f.primitive() == (ZZ(3), g)
f = DUP([1,0,20,0,150,0,500,0,625,-2,0,-10,9], ZZ)
g = DUP([1,0,0,-2,9], ZZ)
h = DUP([1,0,5,0], ZZ)
assert g.compose(h) == f
assert f.decompose() == [g, h]
f = DUP([QQ(1),QQ(0)], QQ)
assert f.sturm() == [f, DUP([QQ(1)], QQ)]
def test_DUP_arithmetics():
f = DUP([1,1,1], ZZ)
assert f.add_term(2, 1) == DUP([1,3,1], ZZ)
assert f.sub_term(2, 1) == DUP([1,-1,1], ZZ)
assert f.mul_term(2, 1) == DUP([2,2,2,0], ZZ)
raises(TypeError, "f.add_term(2, 'x')")
raises(TypeError, "f.sub_term(2, 'x')")
raises(TypeError, "f.mul_term(2, 'x')")
g = DUP([3,3,3], ZZ)
assert f.mul_ground(3) == g
assert g.exquo_ground(3) == f
raises(ExactQuotientFailed, "f.quo_ground(4)")
f = DUP([1,-2,3,-4], ZZ)
g = DUP([1,2,3,4], ZZ)
h = DUP([-1,2,-3,4], ZZ)
assert f.abs() == g
assert abs(f) == g
assert f.neg() == h
assert -f == h
h = DUP([2,0,6,0], ZZ)
assert f.add(g) == h
assert f + g == h
assert g + f == h
h = DUP([1,-2,3,1], ZZ)
assert f + 5 == h
assert 5 + f == h
h = DUP([-4,0,-8], ZZ)
assert f.sub(g) == h
assert f - g == h
assert g - f == -h
h = DUP([1,-2,3,-9], ZZ)
assert f - 5 == h
assert 5 - f == -h
g = DUP([2], ZZ)
h = DUP([2,-4,6,-8], ZZ)
assert f.mul(g) == h
assert f * g == h
assert g * f == h
assert f * 2 == h
assert 2 * f == h
h = DUP([4], ZZ)
assert g.sqr() == h
assert g.pow(2) == h
assert g**2 == h
raises(TypeError, "f.pow('x')")
f = DUP([3,1,1,5], ZZ)
g = DUP([5,-3,1], ZZ)
q = DUP([15, 14], ZZ)
r = DUP([52, 111], ZZ)
assert f.pdiv(g) == (q, r)
assert f.pexquo(g) == q
assert f.prem(g) == r
raises(ExactQuotientFailed, 'f.pquo(g)')
q, r = DUP([], ZZ), f
assert f.div(g) == (q, r)
assert f.exquo(g) == q
assert f.rem(g) == r
raises(ExactQuotientFailed, 'f.quo(g)')
def test_DUP_properties():
assert DUP([QQ(0)], QQ).is_zero == True
assert DUP([QQ(1)], QQ).is_zero == False
assert DUP([QQ(1)], QQ).is_one == True
assert DUP([QQ(2)], QQ).is_one == False
assert DUP([1], ZZ).is_ground == True
assert DUP([1,2,1], ZZ).is_ground == False
assert DUP([1,2,2], ZZ).is_sqf == True
assert DUP([1,2,1], ZZ).is_sqf == False
assert DUP([1,2,3], ZZ).is_monic == True
assert DUP([2,2,3], ZZ).is_monic == False
assert DUP([1,2,3], ZZ).is_primitive == True
assert DUP([2,4,6], ZZ).is_primitive == False
def test_DUP___bool__():
assert bool(DUP([], ZZ)) == False
assert bool(DUP([1], ZZ)) == True
def test_DUP_functionality():
f = DUP([1,2,3,4], ZZ)
g = DUP([3,4,3], ZZ)
assert f.degree() == 3
assert f.LC() == ZZ(1)
assert f.TC() == ZZ(4)
assert f.nth(1) == ZZ(3)
raises(TypeError, "f.nth('x')")
assert f.max_norm() == ZZ(4)
assert f.l1_norm() == ZZ(10)
assert f.diff(1) == g
assert f.eval(1) == ZZ(10)
raises(TypeError, "f.diff('x')")
f = DUP([QQ(2),QQ(0)], QQ)
g = DUP([QQ(1),QQ(0),QQ(-16)], QQ)
s = DUP([QQ(1,32),QQ(0)], QQ)
t = DUP([QQ(-1,16)], QQ)
h = DUP([QQ(1)], QQ)
assert f.half_gcdex(g) == (s, h)
assert f.gcdex(g) == (s, t, h)
assert f.invert(g) == s
f = DUP([1,-2,1], ZZ)
g = DUP([1,0,-1], ZZ)
a = DUP([2,-2], ZZ)
assert f.subresultants(g) == [f, g, a]
assert f.resultant(g) == 0
f = DUP([1,3,9,-13], ZZ)
assert f.discriminant() == -11664
f = DUP([1,2,1], ZZ)
g = DUP([1,1], ZZ)
h = DUP([1], ZZ)
assert f.cofactors(g) == (g, g, h)
assert f.gcd(g) == g
assert f.lcm(g) == f
assert f.sqf_part() == g
assert f.sqf_list() == (ZZ(1), [(g, 2)])
f = DUP([1,2,3,4,5,6], ZZ)
assert f.trunc(3) == DUP([1,-1,0,1,-1,0], ZZ)
f = DUP([QQ(3),QQ(-6)], QQ)
g = DUP([QQ(1),QQ(-2)], QQ)
assert f.monic() == g
f = DUP([3,-6], ZZ)
g = DUP([1,-2], ZZ)
assert f.content() == ZZ(3)
assert f.primitive() == (ZZ(3), g)
f = DUP([1,0,20,0,150,0,500,0,625,-2,0,-10,9], ZZ)
g = DUP([1,0,0,-2,9], ZZ)
h = DUP([1,0,5,0], ZZ)
assert g.compose(h) == f
assert f.decompose() == [g, h]
f = DUP([QQ(1),QQ(0)], QQ)
assert f.sturm() == [f, DUP([QQ(1)], QQ)]
