551 lines
13 KiB
Python
551 lines
13 KiB
Python
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"""Tests for OO layer of several polynomial representations. """
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from sympy.functions.elementary.miscellaneous import sqrt
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from sympy.polys.domains import ZZ, QQ
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from sympy.polys.polyclasses import DMP, DMF, ANP
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from sympy.polys.polyerrors import (CoercionFailed, ExactQuotientFailed,
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NotInvertible)
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from sympy.polys.specialpolys import f_polys
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from sympy.testing.pytest import raises
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f_0, f_1, f_2, f_3, f_4, f_5, f_6 = [ f.to_dense() for f in f_polys() ]
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def test_DMP___init__():
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f = DMP([[0], [], [0, 1, 2], [3]], ZZ)
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assert f.rep == [[1, 2], [3]]
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assert f.dom == ZZ
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assert f.lev == 1
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f = DMP([[1, 2], [3]], ZZ, 1)
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assert f.rep == [[1, 2], [3]]
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assert f.dom == ZZ
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assert f.lev == 1
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f = DMP({(1, 1): 1, (0, 0): 2}, ZZ, 1)
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assert f.rep == [[1, 0], [2]]
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assert f.dom == ZZ
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assert f.lev == 1
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def test_DMP___eq__():
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assert DMP([[ZZ(1), ZZ(2)], [ZZ(3)]], ZZ) == \
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DMP([[ZZ(1), ZZ(2)], [ZZ(3)]], ZZ)
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assert DMP([[ZZ(1), ZZ(2)], [ZZ(3)]], ZZ) == \
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DMP([[QQ(1), QQ(2)], [QQ(3)]], QQ)
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assert DMP([[QQ(1), QQ(2)], [QQ(3)]], QQ) == \
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DMP([[ZZ(1), ZZ(2)], [ZZ(3)]], ZZ)
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assert DMP([[[ZZ(1)]]], ZZ) != DMP([[ZZ(1)]], ZZ)
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assert DMP([[ZZ(1)]], ZZ) != DMP([[[ZZ(1)]]], ZZ)
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def test_DMP___bool__():
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assert bool(DMP([[]], ZZ)) is False
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assert bool(DMP([[1]], ZZ)) is True
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def test_DMP_to_dict():
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f = DMP([[3], [], [2], [], [8]], ZZ)
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assert f.to_dict() == \
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{(4, 0): 3, (2, 0): 2, (0, 0): 8}
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assert f.to_sympy_dict() == \
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{(4, 0): ZZ.to_sympy(3), (2, 0): ZZ.to_sympy(2), (0, 0):
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ZZ.to_sympy(8)}
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def test_DMP_properties():
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assert DMP([[]], ZZ).is_zero is True
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assert DMP([[1]], ZZ).is_zero is False
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assert DMP([[1]], ZZ).is_one is True
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assert DMP([[2]], ZZ).is_one is False
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assert DMP([[1]], ZZ).is_ground is True
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assert DMP([[1], [2], [1]], ZZ).is_ground is False
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assert DMP([[1], [2, 0], [1, 0]], ZZ).is_sqf is True
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assert DMP([[1], [2, 0], [1, 0, 0]], ZZ).is_sqf is False
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assert DMP([[1, 2], [3]], ZZ).is_monic is True
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assert DMP([[2, 2], [3]], ZZ).is_monic is False
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assert DMP([[1, 2], [3]], ZZ).is_primitive is True
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assert DMP([[2, 4], [6]], ZZ).is_primitive is False
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def test_DMP_arithmetics():
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f = DMP([[2], [2, 0]], ZZ)
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assert f.mul_ground(2) == DMP([[4], [4, 0]], ZZ)
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assert f.quo_ground(2) == DMP([[1], [1, 0]], ZZ)
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raises(ExactQuotientFailed, lambda: f.exquo_ground(3))
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f = DMP([[-5]], ZZ)
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g = DMP([[5]], ZZ)
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assert f.abs() == g
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assert abs(f) == g
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assert g.neg() == f
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assert -g == f
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h = DMP([[]], ZZ)
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assert f.add(g) == h
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assert f + g == h
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assert g + f == h
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assert f + 5 == h
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assert 5 + f == h
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h = DMP([[-10]], ZZ)
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assert f.sub(g) == h
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assert f - g == h
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assert g - f == -h
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assert f - 5 == h
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assert 5 - f == -h
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h = DMP([[-25]], ZZ)
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assert f.mul(g) == h
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assert f * g == h
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assert g * f == h
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assert f * 5 == h
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assert 5 * f == h
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h = DMP([[25]], ZZ)
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assert f.sqr() == h
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assert f.pow(2) == h
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assert f**2 == h
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raises(TypeError, lambda: f.pow('x'))
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f = DMP([[1], [], [1, 0, 0]], ZZ)
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g = DMP([[2], [-2, 0]], ZZ)
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q = DMP([[2], [2, 0]], ZZ)
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r = DMP([[8, 0, 0]], ZZ)
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assert f.pdiv(g) == (q, r)
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assert f.pquo(g) == q
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assert f.prem(g) == r
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raises(ExactQuotientFailed, lambda: f.pexquo(g))
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f = DMP([[1], [], [1, 0, 0]], ZZ)
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g = DMP([[1], [-1, 0]], ZZ)
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q = DMP([[1], [1, 0]], ZZ)
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r = DMP([[2, 0, 0]], ZZ)
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assert f.div(g) == (q, r)
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assert f.quo(g) == q
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assert f.rem(g) == r
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assert divmod(f, g) == (q, r)
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assert f // g == q
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assert f % g == r
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raises(ExactQuotientFailed, lambda: f.exquo(g))
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def test_DMP_functionality():
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f = DMP([[1], [2, 0], [1, 0, 0]], ZZ)
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g = DMP([[1], [1, 0]], ZZ)
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h = DMP([[1]], ZZ)
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assert f.degree() == 2
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assert f.degree_list() == (2, 2)
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assert f.total_degree() == 2
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assert f.LC() == ZZ(1)
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assert f.TC() == ZZ(0)
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assert f.nth(1, 1) == ZZ(2)
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raises(TypeError, lambda: f.nth(0, 'x'))
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assert f.max_norm() == 2
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assert f.l1_norm() == 4
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u = DMP([[2], [2, 0]], ZZ)
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assert f.diff(m=1, j=0) == u
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assert f.diff(m=1, j=1) == u
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raises(TypeError, lambda: f.diff(m='x', j=0))
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u = DMP([1, 2, 1], ZZ)
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v = DMP([1, 2, 1], ZZ)
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assert f.eval(a=1, j=0) == u
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assert f.eval(a=1, j=1) == v
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assert f.eval(1).eval(1) == ZZ(4)
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assert f.cofactors(g) == (g, g, h)
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assert f.gcd(g) == g
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assert f.lcm(g) == f
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u = DMP([[QQ(45), QQ(30), QQ(5)]], QQ)
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v = DMP([[QQ(1), QQ(2, 3), QQ(1, 9)]], QQ)
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assert u.monic() == v
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assert (4*f).content() == ZZ(4)
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assert (4*f).primitive() == (ZZ(4), f)
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f = DMP([[1], [2], [3], [4], [5], [6]], ZZ)
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assert f.trunc(3) == DMP([[1], [-1], [], [1], [-1], []], ZZ)
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f = DMP(f_4, ZZ)
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assert f.sqf_part() == -f
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assert f.sqf_list() == (ZZ(-1), [(-f, 1)])
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f = DMP([[-1], [], [], [5]], ZZ)
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g = DMP([[3, 1], [], []], ZZ)
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h = DMP([[45, 30, 5]], ZZ)
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r = DMP([675, 675, 225, 25], ZZ)
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assert f.subresultants(g) == [f, g, h]
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assert f.resultant(g) == r
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f = DMP([1, 3, 9, -13], ZZ)
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assert f.discriminant() == -11664
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f = DMP([QQ(2), QQ(0)], QQ)
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g = DMP([QQ(1), QQ(0), QQ(-16)], QQ)
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s = DMP([QQ(1, 32), QQ(0)], QQ)
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t = DMP([QQ(-1, 16)], QQ)
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h = DMP([QQ(1)], QQ)
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assert f.half_gcdex(g) == (s, h)
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assert f.gcdex(g) == (s, t, h)
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assert f.invert(g) == s
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f = DMP([[1], [2], [3]], QQ)
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raises(ValueError, lambda: f.half_gcdex(f))
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raises(ValueError, lambda: f.gcdex(f))
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raises(ValueError, lambda: f.invert(f))
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f = DMP([1, 0, 20, 0, 150, 0, 500, 0, 625, -2, 0, -10, 9], ZZ)
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g = DMP([1, 0, 0, -2, 9], ZZ)
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h = DMP([1, 0, 5, 0], ZZ)
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assert g.compose(h) == f
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assert f.decompose() == [g, h]
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f = DMP([[1], [2], [3]], QQ)
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raises(ValueError, lambda: f.decompose())
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raises(ValueError, lambda: f.sturm())
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def test_DMP_exclude():
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f = [[[[[[[[[[[[[[[[[[[[[[[[[[1]], [[]]]]]]]]]]]]]]]]]]]]]]]]]]
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J = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,
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18, 19, 20, 21, 22, 24, 25]
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assert DMP(f, ZZ).exclude() == (J, DMP([1, 0], ZZ))
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assert DMP([[1], [1, 0]], ZZ).exclude() == ([], DMP([[1], [1, 0]], ZZ))
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def test_DMF__init__():
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f = DMF(([[0], [], [0, 1, 2], [3]], [[1, 2, 3]]), ZZ)
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assert f.num == [[1, 2], [3]]
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assert f.den == [[1, 2, 3]]
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assert f.lev == 1
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assert f.dom == ZZ
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f = DMF(([[1, 2], [3]], [[1, 2, 3]]), ZZ, 1)
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assert f.num == [[1, 2], [3]]
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assert f.den == [[1, 2, 3]]
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assert f.lev == 1
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assert f.dom == ZZ
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f = DMF(([[-1], [-2]], [[3], [-4]]), ZZ)
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assert f.num == [[-1], [-2]]
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assert f.den == [[3], [-4]]
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assert f.lev == 1
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assert f.dom == ZZ
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f = DMF(([[1], [2]], [[-3], [4]]), ZZ)
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assert f.num == [[-1], [-2]]
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assert f.den == [[3], [-4]]
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assert f.lev == 1
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assert f.dom == ZZ
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f = DMF(([[1], [2]], [[-3], [4]]), ZZ)
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assert f.num == [[-1], [-2]]
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assert f.den == [[3], [-4]]
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assert f.lev == 1
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assert f.dom == ZZ
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f = DMF(([[]], [[-3], [4]]), ZZ)
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assert f.num == [[]]
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assert f.den == [[1]]
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assert f.lev == 1
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assert f.dom == ZZ
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f = DMF(17, ZZ, 1)
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assert f.num == [[17]]
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assert f.den == [[1]]
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assert f.lev == 1
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assert f.dom == ZZ
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f = DMF(([[1], [2]]), ZZ)
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assert f.num == [[1], [2]]
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assert f.den == [[1]]
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assert f.lev == 1
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assert f.dom == ZZ
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f = DMF([[0], [], [0, 1, 2], [3]], ZZ)
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assert f.num == [[1, 2], [3]]
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assert f.den == [[1]]
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assert f.lev == 1
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assert f.dom == ZZ
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f = DMF({(1, 1): 1, (0, 0): 2}, ZZ, 1)
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assert f.num == [[1, 0], [2]]
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assert f.den == [[1]]
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assert f.lev == 1
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assert f.dom == ZZ
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f = DMF(([[QQ(1)], [QQ(2)]], [[-QQ(3)], [QQ(4)]]), QQ)
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assert f.num == [[-QQ(1)], [-QQ(2)]]
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assert f.den == [[QQ(3)], [-QQ(4)]]
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assert f.lev == 1
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assert f.dom == QQ
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f = DMF(([[QQ(1, 5)], [QQ(2, 5)]], [[-QQ(3, 7)], [QQ(4, 7)]]), QQ)
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assert f.num == [[-QQ(7)], [-QQ(14)]]
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assert f.den == [[QQ(15)], [-QQ(20)]]
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assert f.lev == 1
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assert f.dom == QQ
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raises(ValueError, lambda: DMF(([1], [[1]]), ZZ))
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raises(ZeroDivisionError, lambda: DMF(([1], []), ZZ))
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def test_DMF__bool__():
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assert bool(DMF([[]], ZZ)) is False
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||
|
|
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
|
||
|
|
|
||
|
|
f = ANP([1, 0.5], mod, QQ)
|
||
|
|
|
||
|
|
assert all(QQ.of_type(a) for a in f.rep)
|
||
|
|
|
||
|
|
raises(CoercionFailed, lambda: ANP([sqrt(2)], mod, 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))
|