203 lines
5.8 KiB
Python
203 lines
5.8 KiB
Python
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"""Tests on algebraic numbers. """
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from sympy.core.containers import Tuple
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from sympy.core.numbers import (AlgebraicNumber, I, Rational)
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from sympy.core.singleton import S
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from sympy.core.symbol import Symbol
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from sympy.functions.elementary.miscellaneous import sqrt
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from sympy.polys.polytools import Poly
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from sympy.polys.numberfields.subfield import to_number_field
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from sympy.polys.polyclasses import DMP
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from sympy.polys.domains import QQ
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from sympy.polys.rootoftools import CRootOf
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from sympy.abc import x, y
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def test_AlgebraicNumber():
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minpoly, root = x**2 - 2, sqrt(2)
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a = AlgebraicNumber(root, gen=x)
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assert a.rep == DMP([QQ(1), QQ(0)], QQ)
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assert a.root == root
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assert a.alias is None
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assert a.minpoly == minpoly
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assert a.is_number
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assert a.is_aliased is False
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assert a.coeffs() == [S.One, S.Zero]
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assert a.native_coeffs() == [QQ(1), QQ(0)]
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a = AlgebraicNumber(root, gen=x, alias='y')
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assert a.rep == DMP([QQ(1), QQ(0)], QQ)
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assert a.root == root
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assert a.alias == Symbol('y')
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assert a.minpoly == minpoly
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assert a.is_number
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assert a.is_aliased is True
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a = AlgebraicNumber(root, gen=x, alias=Symbol('y'))
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assert a.rep == DMP([QQ(1), QQ(0)], QQ)
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assert a.root == root
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assert a.alias == Symbol('y')
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assert a.minpoly == minpoly
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assert a.is_number
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assert a.is_aliased is True
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assert AlgebraicNumber(sqrt(2), []).rep == DMP([], QQ)
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assert AlgebraicNumber(sqrt(2), ()).rep == DMP([], QQ)
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assert AlgebraicNumber(sqrt(2), (0, 0)).rep == DMP([], QQ)
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assert AlgebraicNumber(sqrt(2), [8]).rep == DMP([QQ(8)], QQ)
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assert AlgebraicNumber(sqrt(2), [Rational(8, 3)]).rep == DMP([QQ(8, 3)], QQ)
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assert AlgebraicNumber(sqrt(2), [7, 3]).rep == DMP([QQ(7), QQ(3)], QQ)
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assert AlgebraicNumber(
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sqrt(2), [Rational(7, 9), Rational(3, 2)]).rep == DMP([QQ(7, 9), QQ(3, 2)], QQ)
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assert AlgebraicNumber(sqrt(2), [1, 2, 3]).rep == DMP([QQ(2), QQ(5)], QQ)
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a = AlgebraicNumber(AlgebraicNumber(root, gen=x), [1, 2])
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assert a.rep == DMP([QQ(1), QQ(2)], QQ)
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assert a.root == root
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assert a.alias is None
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assert a.minpoly == minpoly
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assert a.is_number
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assert a.is_aliased is False
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assert a.coeffs() == [S.One, S(2)]
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assert a.native_coeffs() == [QQ(1), QQ(2)]
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a = AlgebraicNumber((minpoly, root), [1, 2])
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assert a.rep == DMP([QQ(1), QQ(2)], QQ)
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assert a.root == root
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assert a.alias is None
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assert a.minpoly == minpoly
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assert a.is_number
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assert a.is_aliased is False
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a = AlgebraicNumber((Poly(minpoly), root), [1, 2])
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assert a.rep == DMP([QQ(1), QQ(2)], QQ)
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assert a.root == root
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assert a.alias is None
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assert a.minpoly == minpoly
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assert a.is_number
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assert a.is_aliased is False
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assert AlgebraicNumber( sqrt(3)).rep == DMP([ QQ(1), QQ(0)], QQ)
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assert AlgebraicNumber(-sqrt(3)).rep == DMP([ QQ(1), QQ(0)], QQ)
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a = AlgebraicNumber(sqrt(2))
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b = AlgebraicNumber(sqrt(2))
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assert a == b
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c = AlgebraicNumber(sqrt(2), gen=x)
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assert a == b
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assert a == c
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a = AlgebraicNumber(sqrt(2), [1, 2])
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b = AlgebraicNumber(sqrt(2), [1, 3])
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assert a != b and a != sqrt(2) + 3
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assert (a == x) is False and (a != x) is True
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a = AlgebraicNumber(sqrt(2), [1, 0])
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b = AlgebraicNumber(sqrt(2), [1, 0], alias=y)
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assert a.as_poly(x) == Poly(x, domain='QQ')
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assert b.as_poly() == Poly(y, domain='QQ')
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assert a.as_expr() == sqrt(2)
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assert a.as_expr(x) == x
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assert b.as_expr() == sqrt(2)
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assert b.as_expr(x) == x
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a = AlgebraicNumber(sqrt(2), [2, 3])
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b = AlgebraicNumber(sqrt(2), [2, 3], alias=y)
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p = a.as_poly()
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assert p == Poly(2*p.gen + 3)
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assert a.as_poly(x) == Poly(2*x + 3, domain='QQ')
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assert b.as_poly() == Poly(2*y + 3, domain='QQ')
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assert a.as_expr() == 2*sqrt(2) + 3
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assert a.as_expr(x) == 2*x + 3
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assert b.as_expr() == 2*sqrt(2) + 3
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assert b.as_expr(x) == 2*x + 3
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a = AlgebraicNumber(sqrt(2))
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b = to_number_field(sqrt(2))
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assert a.args == b.args == (sqrt(2), Tuple(1, 0))
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b = AlgebraicNumber(sqrt(2), alias='alpha')
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assert b.args == (sqrt(2), Tuple(1, 0), Symbol('alpha'))
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a = AlgebraicNumber(sqrt(2), [1, 2, 3])
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assert a.args == (sqrt(2), Tuple(1, 2, 3))
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a = AlgebraicNumber(sqrt(2), [1, 2], "alpha")
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b = AlgebraicNumber(a)
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c = AlgebraicNumber(a, alias="gamma")
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assert a == b
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assert c.alias.name == "gamma"
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a = AlgebraicNumber(sqrt(2) + sqrt(3), [S(1)/2, 0, S(-9)/2, 0])
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b = AlgebraicNumber(a, [1, 0, 0])
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assert b.root == a.root
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assert a.to_root() == sqrt(2)
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assert b.to_root() == 2
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a = AlgebraicNumber(2)
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assert a.is_primitive_element is True
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def test_to_algebraic_integer():
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a = AlgebraicNumber(sqrt(3), gen=x).to_algebraic_integer()
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assert a.minpoly == x**2 - 3
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assert a.root == sqrt(3)
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assert a.rep == DMP([QQ(1), QQ(0)], QQ)
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a = AlgebraicNumber(2*sqrt(3), gen=x).to_algebraic_integer()
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assert a.minpoly == x**2 - 12
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assert a.root == 2*sqrt(3)
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assert a.rep == DMP([QQ(1), QQ(0)], QQ)
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a = AlgebraicNumber(sqrt(3)/2, gen=x).to_algebraic_integer()
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assert a.minpoly == x**2 - 12
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assert a.root == 2*sqrt(3)
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assert a.rep == DMP([QQ(1), QQ(0)], QQ)
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a = AlgebraicNumber(sqrt(3)/2, [Rational(7, 19), 3], gen=x).to_algebraic_integer()
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assert a.minpoly == x**2 - 12
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assert a.root == 2*sqrt(3)
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assert a.rep == DMP([QQ(7, 19), QQ(3)], QQ)
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def test_AlgebraicNumber_to_root():
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assert AlgebraicNumber(sqrt(2)).to_root() == sqrt(2)
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zeta5_squared = AlgebraicNumber(CRootOf(x**5 - 1, 4), coeffs=[1, 0, 0])
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assert zeta5_squared.to_root() == CRootOf(x**4 + x**3 + x**2 + x + 1, 1)
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zeta3_squared = AlgebraicNumber(CRootOf(x**3 - 1, 2), coeffs=[1, 0, 0])
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assert zeta3_squared.to_root() == -S(1)/2 - sqrt(3)*I/2
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assert zeta3_squared.to_root(radicals=False) == CRootOf(x**2 + x + 1, 0)
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