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Mini Shell
Mini Shell
"""Tests for OO layer of several polynomial representations. """
from sympy.polys.domains import ZZ, QQ
from sympy.polys.polyclasses import DMP, DMF, ANP
from sympy.polys.polyerrors import ExactQuotientFailed, NotInvertible
from sympy.polys.specialpolys import f_polys
from sympy.testing.pytest import raises
f_0, f_1, f_2, f_3, f_4, f_5, f_6 = [ f.to_dense() for f in f_polys() ]
def test_DMP___init__():
f = DMP([[0], [], [0, 1, 2], [3]], ZZ)
assert f.rep == [[1, 2], [3]]
assert f.dom == ZZ
assert f.lev == 1
f = DMP([[1, 2], [3]], ZZ, 1)
assert f.rep == [[1, 2], [3]]
assert f.dom == ZZ
assert f.lev == 1
f = DMP({(1, 1): 1, (0, 0): 2}, ZZ, 1)
assert f.rep == [[1, 0], [2]]
assert f.dom == ZZ
assert f.lev == 1
def test_DMP___eq__():
assert DMP([[ZZ(1), ZZ(2)], [ZZ(3)]], ZZ) == \
DMP([[ZZ(1), ZZ(2)], [ZZ(3)]], ZZ)
assert DMP([[ZZ(1), ZZ(2)], [ZZ(3)]], ZZ) == \
DMP([[QQ(1), QQ(2)], [QQ(3)]], QQ)
assert DMP([[QQ(1), QQ(2)], [QQ(3)]], QQ) == \
DMP([[ZZ(1), ZZ(2)], [ZZ(3)]], ZZ)
assert DMP([[[ZZ(1)]]], ZZ) != DMP([[ZZ(1)]], ZZ)
assert DMP([[ZZ(1)]], ZZ) != DMP([[[ZZ(1)]]], ZZ)
def test_DMP___bool__():
assert bool(DMP([[]], ZZ)) is False
assert bool(DMP([[1]], ZZ)) is True
def test_DMP_to_dict():
f = DMP([[3], [], [2], [], [8]], ZZ)
assert f.to_dict() == \
{(4, 0): 3, (2, 0): 2, (0, 0): 8}
assert f.to_sympy_dict() == \
{(4, 0): ZZ.to_sympy(3), (2, 0): ZZ.to_sympy(2), (0, 0):
ZZ.to_sympy(8)}
def test_DMP_properties():
assert DMP([[]], ZZ).is_zero is True
assert DMP([[1]], ZZ).is_zero is False
assert DMP([[1]], ZZ).is_one is True
assert DMP([[2]], ZZ).is_one is False
assert DMP([[1]], ZZ).is_ground is True
assert DMP([[1], [2], [1]], ZZ).is_ground is False
assert DMP([[1], [2, 0], [1, 0]], ZZ).is_sqf is True
assert DMP([[1], [2, 0], [1, 0, 0]], ZZ).is_sqf is False
assert DMP([[1, 2], [3]], ZZ).is_monic is True
assert DMP([[2, 2], [3]], ZZ).is_monic is False
assert DMP([[1, 2], [3]], ZZ).is_primitive is True
assert DMP([[2, 4], [6]], ZZ).is_primitive is False
def test_DMP_arithmetics():
f = DMP([[2], [2, 0]], ZZ)
assert f.mul_ground(2) == DMP([[4], [4, 0]], ZZ)
assert f.quo_ground(2) == DMP([[1], [1, 0]], ZZ)
raises(ExactQuotientFailed, lambda: f.exquo_ground(3))
f = DMP([[-5]], ZZ)
g = DMP([[5]], ZZ)
assert f.abs() == g
assert abs(f) == g
assert g.neg() == f
assert -g == f
h = DMP([[]], ZZ)
assert f.add(g) == h
assert f + g == h
assert g + f == h
assert f + 5 == h
assert 5 + f == h
h = DMP([[-10]], ZZ)
assert f.sub(g) == h
assert f - g == h
assert g - f == -h
assert f - 5 == h
assert 5 - f == -h
h = DMP([[-25]], ZZ)
assert f.mul(g) == h
assert f * g == h
assert g * f == h
assert f * 5 == h
assert 5 * f == h
h = DMP([[25]], ZZ)
assert f.sqr() == h
assert f.pow(2) == h
assert f**2 == h
raises(TypeError, lambda: f.pow('x'))
f = DMP([[1], [], [1, 0, 0]], ZZ)
g = DMP([[2], [-2, 0]], ZZ)
q = DMP([[2], [2, 0]], ZZ)
r = DMP([[8, 0, 0]], ZZ)
assert f.pdiv(g) == (q, r)
assert f.pquo(g) == q
assert f.prem(g) == r
raises(ExactQuotientFailed, lambda: f.pexquo(g))
f = DMP([[1], [], [1, 0, 0]], ZZ)
g = DMP([[1], [-1, 0]], ZZ)
q = DMP([[1], [1, 0]], ZZ)
r = DMP([[2, 0, 0]], ZZ)
assert f.div(g) == (q, r)
assert f.quo(g) == q
assert f.rem(g) == r
assert divmod(f, g) == (q, r)
assert f // g == q
assert f % g == r
raises(ExactQuotientFailed, lambda: f.exquo(g))
def test_DMP_functionality():
f = DMP([[1], [2, 0], [1, 0, 0]], ZZ)
g = DMP([[1], [1, 0]], ZZ)
h = DMP([[1]], ZZ)
assert f.degree() == 2
assert f.degree_list() == (2, 2)
assert f.total_degree() == 2
assert f.LC() == ZZ(1)
assert f.TC() == ZZ(0)
assert f.nth(1, 1) == ZZ(2)
raises(TypeError, lambda: f.nth(0, 'x'))
assert f.max_norm() == 2
assert f.l1_norm() == 4
u = DMP([[2], [2, 0]], ZZ)
assert f.diff(m=1, j=0) == u
assert f.diff(m=1, j=1) == u
raises(TypeError, lambda: f.diff(m='x', j=0))
u = DMP([1, 2, 1], ZZ)
v = DMP([1, 2, 1], ZZ)
assert f.eval(a=1, j=0) == u
assert f.eval(a=1, j=1) == v
assert f.eval(1).eval(1) == ZZ(4)
assert f.cofactors(g) == (g, g, h)
assert f.gcd(g) == g
assert f.lcm(g) == f
u = DMP([[QQ(45), QQ(30), QQ(5)]], QQ)
v = DMP([[QQ(1), QQ(2, 3), QQ(1, 9)]], QQ)
assert u.monic() == v
assert (4*f).content() == ZZ(4)
assert (4*f).primitive() == (ZZ(4), f)
f = DMP([[1], [2], [3], [4], [5], [6]], ZZ)
assert f.trunc(3) == DMP([[1], [-1], [], [1], [-1], []], ZZ)
f = DMP(f_4, ZZ)
assert f.sqf_part() == -f
assert f.sqf_list() == (ZZ(-1), [(-f, 1)])
f = DMP([[-1], [], [], [5]], ZZ)
g = DMP([[3, 1], [], []], ZZ)
h = DMP([[45, 30, 5]], ZZ)
r = DMP([675, 675, 225, 25], ZZ)
assert f.subresultants(g) == [f, g, h]
assert f.resultant(g) == r
f = DMP([1, 3, 9, -13], ZZ)
assert f.discriminant() == -11664
f = DMP([QQ(2), QQ(0)], QQ)
g = DMP([QQ(1), QQ(0), QQ(-16)], QQ)
s = DMP([QQ(1, 32), QQ(0)], QQ)
t = DMP([QQ(-1, 16)], QQ)
h = DMP([QQ(1)], QQ)
assert f.half_gcdex(g) == (s, h)
assert f.gcdex(g) == (s, t, h)
assert f.invert(g) == s
f = DMP([[1], [2], [3]], QQ)
raises(ValueError, lambda: f.half_gcdex(f))
raises(ValueError, lambda: f.gcdex(f))
raises(ValueError, lambda: f.invert(f))
f = DMP([1, 0, 20, 0, 150, 0, 500, 0, 625, -2, 0, -10, 9], ZZ)
g = DMP([1, 0, 0, -2, 9], ZZ)
h = DMP([1, 0, 5, 0], ZZ)
assert g.compose(h) == f
assert f.decompose() == [g, h]
f = DMP([[1], [2], [3]], QQ)
raises(ValueError, lambda: f.decompose())
raises(ValueError, lambda: f.sturm())
def test_DMP_exclude():
f = [[[[[[[[[[[[[[[[[[[[[[[[[[1]], [[]]]]]]]]]]]]]]]]]]]]]]]]]]
J = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,
18, 19, 20, 21, 22, 24, 25]
assert DMP(f, ZZ).exclude() == (J, DMP([1, 0], ZZ))
assert DMP([[1], [1, 0]], ZZ).exclude() == ([], DMP([[1], [1, 0]], 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 test_DMF__bool__():
assert bool(DMF([[]], ZZ)) is False
assert bool(DMF([[1]], ZZ)) is True
def test_DMF_properties():
assert DMF([[]], ZZ).is_zero is True
assert DMF([[]], ZZ).is_one is False
assert DMF([[1]], ZZ).is_zero is False
assert DMF([[1]], ZZ).is_one is True
assert DMF(([[1]], [[2]]), ZZ).is_one is False
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
h = DMF(([[1, 0]], [[1]]), ZZ)
assert g.pow(-1) == g**-1 == h
def test_ANP___init__():
rep = [QQ(1), QQ(1)]
mod = [QQ(1), QQ(0), QQ(1)]
f = ANP(rep, mod, QQ)
assert f.rep == [QQ(1), QQ(1)]
assert f.mod == [QQ(1), QQ(0), QQ(1)]
assert f.dom == QQ
rep = {1: QQ(1), 0: QQ(1)}
mod = {2: QQ(1), 0: QQ(1)}
f = ANP(rep, mod, QQ)
assert f.rep == [QQ(1), QQ(1)]
assert f.mod == [QQ(1), QQ(0), QQ(1)]
assert f.dom == QQ
f = ANP(1, mod, QQ)
assert f.rep == [QQ(1)]
assert f.mod == [QQ(1), QQ(0), QQ(1)]
assert f.dom == QQ
def test_ANP___eq__():
a = ANP([QQ(1), QQ(1)], [QQ(1), QQ(0), QQ(1)], QQ)
b = ANP([QQ(1), QQ(1)], [QQ(1), QQ(0), QQ(2)], QQ)
assert (a == a) is True
assert (a != a) is False
assert (a == b) is False
assert (a != b) is True
b = ANP([QQ(1), QQ(2)], [QQ(1), QQ(0), QQ(1)], QQ)
assert (a == b) is False
assert (a != b) is True
def test_ANP___bool__():
assert bool(ANP([], [QQ(1), QQ(0), QQ(1)], QQ)) is False
assert bool(ANP([QQ(1)], [QQ(1), QQ(0), QQ(1)], QQ)) is True
def test_ANP_properties():
mod = [QQ(1), QQ(0), QQ(1)]
assert ANP([QQ(0)], mod, QQ).is_zero is True
assert ANP([QQ(1)], mod, QQ).is_zero is False
assert ANP([QQ(1)], mod, QQ).is_one is True
assert ANP([QQ(2)], mod, QQ).is_one is False
def test_ANP_arithmetics():
mod = [QQ(1), QQ(0), QQ(0), QQ(-2)]
a = ANP([QQ(2), QQ(-1), QQ(1)], mod, QQ)
b = ANP([QQ(1), QQ(2)], mod, QQ)
c = ANP([QQ(-2), QQ(1), QQ(-1)], mod, QQ)
assert a.neg() == -a == c
c = ANP([QQ(2), QQ(0), QQ(3)], mod, QQ)
assert a.add(b) == a + b == c
assert b.add(a) == b + a == c
c = ANP([QQ(2), QQ(-2), QQ(-1)], mod, QQ)
assert a.sub(b) == a - b == c
c = ANP([QQ(-2), QQ(2), QQ(1)], mod, QQ)
assert b.sub(a) == b - a == c
c = ANP([QQ(3), QQ(-1), QQ(6)], mod, QQ)
assert a.mul(b) == a*b == c
assert b.mul(a) == b*a == c
c = ANP([QQ(-1, 43), QQ(9, 43), QQ(5, 43)], mod, QQ)
assert a.pow(0) == a**(0) == ANP(1, mod, QQ)
assert a.pow(1) == a**(1) == a
assert a.pow(-1) == a**(-1) == c
assert a.quo(a) == a.mul(a.pow(-1)) == a*a**(-1) == ANP(1, mod, QQ)
c = ANP([], [1, 0, 0, -2], QQ)
r1 = a.rem(b)
(q, r2) = a.div(b)
assert r1 == r2 == c == a % b
raises(NotInvertible, lambda: a.div(c))
raises(NotInvertible, lambda: a.rem(c))
# Comparison with "hard-coded" value fails despite looking identical
# from sympy import Rational
# c = ANP([Rational(11, 10), Rational(-1, 5), Rational(-3, 5)], [1, 0, 0, -2], QQ)
assert q == a/b # == c
def test_ANP_unify():
mod = [QQ(1), QQ(0), QQ(-2)]
a = ANP([QQ(1)], mod, QQ)
b = ANP([ZZ(1)], mod, ZZ)
assert a.unify(b)[0] == QQ
assert b.unify(a)[0] == QQ
assert a.unify(a)[0] == QQ
assert b.unify(b)[0] == 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([[int(1), int(2)], [int(3)]], ZZ)
assert hash(DMP([[1, 2], [3]], ZZ)) == hash(DMP([[int(1), int(2)], [int(3)]], ZZ))
assert DMF(
([[1, 2], [3]], [[1]]), ZZ) == DMF(([[int(1), int(2)], [int(3)]], [[int(1)]]), ZZ)
assert hash(DMF(([[1, 2], [3]], [[1]]), ZZ)) == hash(DMF(([[int(1),
int(2)], [int(3)]], [[int(1)]]), ZZ))
assert ANP([1, 1], [1, 0, 1], ZZ) == ANP([int(1), int(1)], [int(1), int(0), int(1)], ZZ)
assert hash(
ANP([1, 1], [1, 0, 1], ZZ)) == hash(ANP([int(1), int(1)], [int(1), int(0), int(1)], ZZ))
Zerion Mini Shell 1.0