def test_PolynomialRing_from_FractionField():
x = DMF(([1, 0, 1], [1, 1]), ZZ)
y = DMF(([1, 0, 1], [1]), ZZ)
assert ZZ['x'].from_FractionField(x, ZZ['x']) is None
assert ZZ['x'].from_FractionField(y, ZZ['x']) == DMP(
[ZZ(1), ZZ(0), ZZ(1)], ZZ)
def test_DMF_properties():
assert DMF([[]], ZZ).is_zero == True
assert DMF([[]], ZZ).is_one == False
assert DMF([[1]], ZZ).is_zero == False
assert DMF([[1]], ZZ).is_one == True
assert DMF(([[1]], [[2]]), ZZ).is_one == False
def test___hash__():
# Issue 2472
# Make sure int vs. long doesn't affect hashing with Python ground types
assert DMP([[1, 2], [3]], ZZ) == DMP([[1l, 2l], [3l]], ZZ)
assert hash(DMP([[1, 2], [3]], ZZ)) == hash(DMP([[1l, 2l], [3l]], ZZ))
assert DMF(([[1, 2], [3]], [[1]]), ZZ) == DMF(([[1L, 2L], [3L]], [[1L]]), ZZ)
assert hash(DMF(([[1, 2], [3]], [[1]]), ZZ)) == hash(DMF(([[1L, 2L], [3L]], [[1L]]), ZZ))
assert ANP([1, 1], [1, 0, 1], ZZ) == ANP([1l, 1l], [1l, 0l, 1l], ZZ)
assert hash(ANP([1, 1], [1, 0, 1], ZZ)) == hash(ANP([1l, 1l], [1l, 0l, 1l], ZZ))
def test___hash__():
# issue 5571
# Make sure int vs. long doesn't affect hashing with Python ground types
assert DMP([[1, 2], [3]], ZZ) == DMP([[long(1), long(2)], [long(3)]], ZZ)
assert hash(DMP([[1, 2], [3]], ZZ)) == hash(DMP([[long(1), long(2)], [long(3)]], ZZ))
assert DMF(
([[1, 2], [3]], [[1]]), ZZ) == DMF(([[long(1), long(2)], [long(3)]], [[long(1)]]), ZZ)
assert hash(DMF(([[1, 2], [3]], [[1]]), ZZ)) == hash(DMF(([[long(1),
long(2)], [long(3)]], [[long(1)]]), ZZ))
assert ANP([1, 1], [1, 0, 1], ZZ) == ANP([long(1), long(1)], [long(1), long(0), long(1)], ZZ)
assert hash(
ANP([1, 1], [1, 0, 1], ZZ)) == hash(ANP([long(1), long(1)], [long(1), long(0), long(1)], ZZ))
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_pickling_polys_polyclasses():
from sympy.polys.polyclasses import DMP, DMF, ANP
for c in (DMP, DMP([[ZZ(1)], [ZZ(2)], [ZZ(3)]], 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)
def test_polys():
x = Symbol("x")
ZZ = PythonIntegerRing()
QQ = SymPyRationalField()
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 (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 (PythonIntegerRing, PythonIntegerRing()):
check(c)
for c in (SymPyIntegerRing, SymPyIntegerRing()):
check(c)
for c in (SymPyRationalField, SymPyRationalField()):
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)
from sympy.polys.domains import HAS_FRACTION, HAS_GMPY
if HAS_FRACTION:
from sympy.polys.domains import PythonRationalField
for c in (PythonRationalField, PythonRationalField()):
check(c)
if HAS_GMPY:
from sympy.polys.domains import GMPYIntegerRing, GMPYRationalField
for c in (GMPYIntegerRing, GMPYIntegerRing()):
check(c)
for c in (GMPYRationalField, GMPYRationalField()):
check(c)
f = x**3 + x + 3
g = lambda x: x
for c in (RootOf, RootOf(f, 0), RootSum, RootSum(f, g)):
check(c)
def test_polys():
x = Symbol("X")
ZZ = PythonIntegerRing()
QQ = PythonRationalField()
for c in (Poly, Poly(x, x)):
check(c)
for c in (DMP, DMP([[ZZ(1)], [ZZ(2)], [ZZ(3)]], 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 (PythonIntegerRing, PythonIntegerRing()):
check(c)
for c in (PythonRationalField, PythonRationalField()):
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)
from sympy.core.compatibility import HAS_GMPY
if HAS_GMPY:
from sympy.polys.domains import GMPYIntegerRing, GMPYRationalField
for c in (GMPYIntegerRing, GMPYIntegerRing()):
check(c)
for c in (GMPYRationalField, GMPYRationalField()):
check(c)
f = x**3 + x + 3
g = exp
for c in (RootOf, RootOf(f, 0), RootSum, RootSum(f, g)):
check(c)
def test_DMF_arithmetics():
f = DMF([[7],[-9]], ZZ)
g = DMF([[-7],[9]], ZZ)
assert f.neg() == -f == g
f = DMF(([[1]], [[1],[]]), ZZ)
g = DMF(([[1]], [[1,0]]), ZZ)
h = DMF(([[1],[1,0]], [[1,0],[]]), ZZ)
assert f.add(g) == f + g == h
assert g.add(f) == g + f == h
h = DMF(([[-1],[1,0]], [[1,0],[]]), ZZ)
assert f.sub(g) == f - g == h
h = DMF(([[1]], [[1,0],[]]), ZZ)
assert f.mul(g) == f*g == h
assert g.mul(f) == g*f == h
h = DMF(([[1,0]], [[1],[]]), ZZ)
assert f.quo(g) == f/g == h
h = DMF(([[1]], [[1],[],[],[]]), ZZ)
assert f.pow(3) == f**3 == h
h = DMF(([[1]], [[1,0,0,0]]), ZZ)
assert g.pow(3) == g**3 == h
def test_PolynomialRing__from_FractionField():
f = DMF(([1, 0, 1], [1, 1]), ZZ)
g = DMF(([1, 0, 1], [1]), ZZ)
assert ZZ[x].from_FractionField(f, ZZ[x]) is None
assert ZZ[x].from_FractionField(g, ZZ[x]) == DMP([ZZ(1), ZZ(0), ZZ(1)], ZZ)
def test_DMF_arithmetics():
f = DMF([[7],[-9]], ZZ)
g = DMF([[-7],[9]], ZZ)
assert f.neg() == -f == g
f = DMF(([[1]], [[1],[]]), ZZ)
g = DMF(([[1]], [[1,0]]), ZZ)
h = DMF(([[1],[1,0]], [[1,0],[]]), ZZ)
assert f.add(g) == f + g == h
assert g.add(f) == g + f == h
h = DMF(([[-1],[1,0]], [[1,0],[]]), ZZ)
assert f.sub(g) == f - g == h
h = DMF(([[1]], [[1,0],[]]), ZZ)
assert f.mul(g) == f*g == h
assert g.mul(f) == g*f == h
h = DMF(([[1,0]], [[1],[]]), ZZ)
assert f.quo(g) == f/g == h
h = DMF(([[1]], [[1],[],[],[]]), ZZ)
assert f.pow(3) == f**3 == h
h = DMF(([[1]], [[1,0,0,0]]), ZZ)
assert g.pow(3) == g**3 == h
def test_DMF__bool__():
assert bool(DMF([[]], ZZ)) == False
assert bool(DMF([[1]], ZZ)) == True
def test_DMF__init__():
f = DMF(([[0],[],[0,1,2],[3]], [[1,2,3]]), ZZ)
assert f.num == [[1,2],[3]]
assert f.den == [[1,2,3]]
assert f.lev == 1
assert f.dom == ZZ
f = DMF(([[1,2],[3]], [[1,2,3]]), ZZ, 1)
assert f.num == [[1,2],[3]]
assert f.den == [[1,2,3]]
assert f.lev == 1
assert f.dom == ZZ
f = DMF(([[-1],[-2]],[[3],[-4]]), ZZ)
assert f.num == [[-1],[-2]]
assert f.den == [[3],[-4]]
assert f.lev == 1
assert f.dom == ZZ
f = DMF(([[1],[2]],[[-3],[4]]), ZZ)
assert f.num == [[-1],[-2]]
assert f.den == [[3],[-4]]
assert f.lev == 1
assert f.dom == ZZ
f = DMF(([[1],[2]],[[-3],[4]]), ZZ)
assert f.num == [[-1],[-2]]
assert f.den == [[3],[-4]]
assert f.lev == 1
assert f.dom == ZZ
f = DMF(([[]],[[-3],[4]]), ZZ)
assert f.num == [[]]
assert f.den == [[1]]
assert f.lev == 1
assert f.dom == ZZ
f = DMF(17, ZZ, 1)
assert f.num == [[17]]
assert f.den == [[1]]
assert f.lev == 1
assert f.dom == ZZ
f = DMF(([[1],[2]]), ZZ)
assert f.num == [[1],[2]]
assert f.den == [[1]]
assert f.lev == 1
assert f.dom == ZZ
f = DMF([[0],[],[0,1,2],[3]], ZZ)
assert f.num == [[1,2],[3]]
assert f.den == [[1]]
assert f.lev == 1
assert f.dom == ZZ
f = DMF({(1,1): 1, (0,0): 2}, ZZ, 1)
assert f.num == [[1,0],[2]]
assert f.den == [[1]]
assert f.lev == 1
assert f.dom == ZZ
raises(ValueError, "DMF(([1], [[1]]), ZZ)")
raises(ZeroDivisionError, "DMF(([1], []), ZZ)")
def test_DMF__init__():
f = DMF(([[0], [], [0, 1, 2], [3]], [[1, 2, 3]]), ZZ)
assert f.num == [[1, 2], [3]]
assert f.den == [[1, 2, 3]]
assert f.lev == 1
assert f.dom == ZZ
f = DMF(([[1, 2], [3]], [[1, 2, 3]]), ZZ, 1)
assert f.num == [[1, 2], [3]]
assert f.den == [[1, 2, 3]]
assert f.lev == 1
assert f.dom == ZZ
f = DMF(([[-1], [-2]], [[3], [-4]]), ZZ)
assert f.num == [[-1], [-2]]
assert f.den == [[3], [-4]]
assert f.lev == 1
assert f.dom == ZZ
f = DMF(([[1], [2]], [[-3], [4]]), ZZ)
assert f.num == [[-1], [-2]]
assert f.den == [[3], [-4]]
assert f.lev == 1
assert f.dom == ZZ
f = DMF(([[1], [2]], [[-3], [4]]), ZZ)
assert f.num == [[-1], [-2]]
assert f.den == [[3], [-4]]
assert f.lev == 1
assert f.dom == ZZ
f = DMF(([[]], [[-3], [4]]), ZZ)
assert f.num == [[]]
assert f.den == [[1]]
assert f.lev == 1
assert f.dom == ZZ
f = DMF(17, ZZ, 1)
assert f.num == [[17]]
assert f.den == [[1]]
assert f.lev == 1
assert f.dom == ZZ
f = DMF(([[1], [2]]), ZZ)
assert f.num == [[1], [2]]
assert f.den == [[1]]
assert f.lev == 1
assert f.dom == ZZ
f = DMF([[0], [], [0, 1, 2], [3]], ZZ)
assert f.num == [[1, 2], [3]]
assert f.den == [[1]]
assert f.lev == 1
assert f.dom == ZZ
f = DMF({(1, 1): 1, (0, 0): 2}, ZZ, 1)
assert f.num == [[1, 0], [2]]
assert f.den == [[1]]
assert f.lev == 1
assert f.dom == ZZ
f = DMF(([[QQ(1)], [QQ(2)]], [[-QQ(3)], [QQ(4)]]), QQ)
assert f.num == [[-QQ(1)], [-QQ(2)]]
assert f.den == [[QQ(3)], [-QQ(4)]]
assert f.lev == 1
assert f.dom == QQ
f = DMF(([[QQ(1, 5)], [QQ(2, 5)]], [[-QQ(3, 7)], [QQ(4, 7)]]), QQ)
assert f.num == [[-QQ(7)], [-QQ(14)]]
assert f.den == [[QQ(15)], [-QQ(20)]]
assert f.lev == 1
assert f.dom == QQ
raises(ValueError, lambda: DMF(([1], [[1]]), ZZ))
raises(ZeroDivisionError, lambda: DMF(([1], []), ZZ))
def __call__(self, a):
"""Construct an element of `self` domain from `a`. """
return DMF(a, self.dom, len(self.gens)-1, ring=self)