def test_normalize_theta_set(): # Interval assert normalize_theta_set(Interval(9 * pi / 2, 5 * pi)) == Interval(pi / 2, pi) assert normalize_theta_set(Interval(-3*pi/2, pi/2)) == \ Interval(0, 2*pi, False, True) assert normalize_theta_set(Interval(-pi/2, pi/2)) == \ Union(Interval(0, pi/2), Interval(3*pi/2, 2*pi, False, True)) assert normalize_theta_set(Interval(-4*pi, 3*pi)) == \ Interval(0, 2*pi, False, True) assert normalize_theta_set(Interval(-3*pi/2, -pi/2)) == \ Interval(pi/2, 3*pi/2) # FiniteSet assert normalize_theta_set(FiniteSet(0, pi, 3 * pi)) == FiniteSet(0, pi) assert normalize_theta_set(FiniteSet(0, pi/2, pi, 2*pi)) == \ FiniteSet(0, pi/2, pi) assert normalize_theta_set(FiniteSet(0, -pi/2, -pi, -2*pi)) == \ FiniteSet(0, pi, 3*pi/2) assert normalize_theta_set(FiniteSet(-3*pi/2, pi/2)) == \ FiniteSet(pi/2) # ValueError for non-real sets raises(ValueError, lambda: normalize_theta_set(S.Complexes))
def test_normalize_theta_set(): # Interval assert normalize_theta_set(Interval(9*pi/2, 5*pi)) == Interval(pi/2, pi) assert normalize_theta_set(Interval(-3*pi/2, pi/2)) == \ Interval(0, 2*pi, False, True) assert normalize_theta_set(Interval(-pi/2, pi/2)) == \ Union(Interval(0, pi/2), Interval(3*pi/2, 2*pi, False, True)) assert normalize_theta_set(Interval(-4*pi, 3*pi)) == \ Interval(0, 2*pi, False, True) assert normalize_theta_set(Interval(-3*pi/2, -pi/2)) == \ Interval(pi/2, 3*pi/2) # FiniteSet assert normalize_theta_set(FiniteSet(0, pi, 3*pi)) == FiniteSet(0, pi) assert normalize_theta_set(FiniteSet(0, pi/2, pi, 2*pi)) == \ FiniteSet(0, pi/2, pi) assert normalize_theta_set(FiniteSet(0, -pi/2, -pi, -2*pi)) == \ FiniteSet(0, pi, 3*pi/2) assert normalize_theta_set(FiniteSet(-3*pi/2, pi/2)) == \ FiniteSet(pi/2) # ValueError for non-real sets raises(ValueError, lambda: normalize_theta_set(S.Complex))
def test_normalize_theta_set(): # Interval assert normalize_theta_set(Interval(pi, 2*pi)) == \ Union(FiniteSet(0), Interval.Ropen(pi, 2*pi)) assert normalize_theta_set(Interval(9 * pi / 2, 5 * pi)) == Interval(pi / 2, pi) assert normalize_theta_set(Interval(-3 * pi / 2, pi / 2)) == Interval.Ropen(0, 2 * pi) assert normalize_theta_set(Interval.open(-3*pi/2, pi/2)) == \ Union(Interval.Ropen(0, pi/2), Interval.open(pi/2, 2*pi)) assert normalize_theta_set(Interval.open(-7*pi/2, -3*pi/2)) == \ Union(Interval.Ropen(0, pi/2), Interval.open(pi/2, 2*pi)) assert normalize_theta_set(Interval(-pi/2, pi/2)) == \ Union(Interval(0, pi/2), Interval.Ropen(3*pi/2, 2*pi)) assert normalize_theta_set(Interval.open(-pi/2, pi/2)) == \ Union(Interval.Ropen(0, pi/2), Interval.open(3*pi/2, 2*pi)) assert normalize_theta_set(Interval(-4 * pi, 3 * pi)) == Interval.Ropen(0, 2 * pi) assert normalize_theta_set(Interval(-3 * pi / 2, -pi / 2)) == Interval( pi / 2, 3 * pi / 2) assert normalize_theta_set(Interval.open(0, 2 * pi)) == Interval.open( 0, 2 * pi) assert normalize_theta_set(Interval.Ropen(-pi/2, pi/2)) == \ Union(Interval.Ropen(0, pi/2), Interval.Ropen(3*pi/2, 2*pi)) assert normalize_theta_set(Interval.Lopen(-pi/2, pi/2)) == \ Union(Interval(0, pi/2), Interval.open(3*pi/2, 2*pi)) assert normalize_theta_set(Interval(-pi/2, pi/2)) == \ Union(Interval(0, pi/2), Interval.Ropen(3*pi/2, 2*pi)) assert normalize_theta_set(Interval.open(4 * pi, 9 * pi / 2)) == Interval.open( 0, pi / 2) assert normalize_theta_set(Interval.Lopen(4 * pi, 9 * pi / 2)) == Interval.Lopen( 0, pi / 2) assert normalize_theta_set(Interval.Ropen(4 * pi, 9 * pi / 2)) == Interval.Ropen( 0, pi / 2) assert normalize_theta_set(Interval.open(3*pi, 5*pi)) == \ Union(Interval.Ropen(0, pi), Interval.open(pi, 2*pi)) # FiniteSet assert normalize_theta_set(FiniteSet(0, pi, 3 * pi)) == FiniteSet(0, pi) assert normalize_theta_set(FiniteSet(0, pi / 2, pi, 2 * pi)) == FiniteSet(0, pi / 2, pi) assert normalize_theta_set(FiniteSet(0, -pi / 2, -pi, -2 * pi)) == FiniteSet( 0, pi, 3 * pi / 2) assert normalize_theta_set(FiniteSet(-3*pi/2, pi/2)) == \ FiniteSet(pi/2) assert normalize_theta_set(FiniteSet(2 * pi)) == FiniteSet(0) # Unions assert normalize_theta_set(Union(Interval(0, pi/3), Interval(pi/2, pi))) == \ Union(Interval(0, pi/3), Interval(pi/2, pi)) assert normalize_theta_set(Union(Interval(0, pi), Interval(2*pi, 7*pi/3))) == \ Interval(0, pi) # ValueError for non-real sets raises(ValueError, lambda: normalize_theta_set(S.Complexes))
def test_normalize_theta_set(): # Interval assert normalize_theta_set(Interval(pi, 2*pi)) == \ Union(FiniteSet(0), Interval.Ropen(pi, 2*pi)) assert normalize_theta_set(Interval(9*pi/2, 5*pi)) == Interval(pi/2, pi) assert normalize_theta_set(Interval(-3*pi/2, pi/2)) == Interval.Ropen(0, 2*pi) assert normalize_theta_set(Interval.open(-3*pi/2, pi/2)) == \ Union(Interval.Ropen(0, pi/2), Interval.open(pi/2, 2*pi)) assert normalize_theta_set(Interval.open(-7*pi/2, -3*pi/2)) == \ Union(Interval.Ropen(0, pi/2), Interval.open(pi/2, 2*pi)) assert normalize_theta_set(Interval(-pi/2, pi/2)) == \ Union(Interval(0, pi/2), Interval.Ropen(3*pi/2, 2*pi)) assert normalize_theta_set(Interval.open(-pi/2, pi/2)) == \ Union(Interval.Ropen(0, pi/2), Interval.open(3*pi/2, 2*pi)) assert normalize_theta_set(Interval(-4*pi, 3*pi)) == Interval.Ropen(0, 2*pi) assert normalize_theta_set(Interval(-3*pi/2, -pi/2)) == Interval(pi/2, 3*pi/2) assert normalize_theta_set(Interval.open(0, 2*pi)) == Interval.open(0, 2*pi) assert normalize_theta_set(Interval.Ropen(-pi/2, pi/2)) == \ Union(Interval.Ropen(0, pi/2), Interval.Ropen(3*pi/2, 2*pi)) assert normalize_theta_set(Interval.Lopen(-pi/2, pi/2)) == \ Union(Interval(0, pi/2), Interval.open(3*pi/2, 2*pi)) assert normalize_theta_set(Interval(-pi/2, pi/2)) == \ Union(Interval(0, pi/2), Interval.Ropen(3*pi/2, 2*pi)) assert normalize_theta_set(Interval.open(4*pi, 9*pi/2)) == Interval.open(0, pi/2) assert normalize_theta_set(Interval.Lopen(4*pi, 9*pi/2)) == Interval.Lopen(0, pi/2) assert normalize_theta_set(Interval.Ropen(4*pi, 9*pi/2)) == Interval.Ropen(0, pi/2) assert normalize_theta_set(Interval.open(3*pi, 5*pi)) == \ Union(Interval.Ropen(0, pi), Interval.open(pi, 2*pi)) # FiniteSet assert normalize_theta_set(FiniteSet(0, pi, 3*pi)) == FiniteSet(0, pi) assert normalize_theta_set(FiniteSet(0, pi/2, pi, 2*pi)) == FiniteSet(0, pi/2, pi) assert normalize_theta_set(FiniteSet(0, -pi/2, -pi, -2*pi)) == FiniteSet(0, pi, 3*pi/2) assert normalize_theta_set(FiniteSet(-3*pi/2, pi/2)) == \ FiniteSet(pi/2) assert normalize_theta_set(FiniteSet(2*pi)) == FiniteSet(0) # Unions assert normalize_theta_set(Union(Interval(0, pi/3), Interval(pi/2, pi))) == \ Union(Interval(0, pi/3), Interval(pi/2, pi)) assert normalize_theta_set(Union(Interval(0, pi), Interval(2*pi, 7*pi/3))) == \ Interval(0, pi) # ValueError for non-real sets raises(ValueError, lambda: normalize_theta_set(S.Complexes))
def test_normalize_theta_set(): # Interval assert normalize_theta_set(Interval(pi, 2*pi)) == \ Union(FiniteSet(0), Interval.Ropen(pi, 2*pi)) assert normalize_theta_set(Interval(pi * Rational(9, 2), 5 * pi)) == Interval(pi / 2, pi) assert normalize_theta_set(Interval(pi * Rational(-3, 2), pi / 2)) == Interval.Ropen(0, 2 * pi) assert normalize_theta_set(Interval.open(pi*Rational(-3, 2), pi/2)) == \ Union(Interval.Ropen(0, pi/2), Interval.open(pi/2, 2*pi)) assert normalize_theta_set(Interval.open(pi*Rational(-7, 2), pi*Rational(-3, 2))) == \ Union(Interval.Ropen(0, pi/2), Interval.open(pi/2, 2*pi)) assert normalize_theta_set(Interval(-pi/2, pi/2)) == \ Union(Interval(0, pi/2), Interval.Ropen(pi*Rational(3, 2), 2*pi)) assert normalize_theta_set(Interval.open(-pi/2, pi/2)) == \ Union(Interval.Ropen(0, pi/2), Interval.open(pi*Rational(3, 2), 2*pi)) assert normalize_theta_set(Interval(-4 * pi, 3 * pi)) == Interval.Ropen(0, 2 * pi) assert normalize_theta_set(Interval(pi * Rational(-3, 2), -pi / 2)) == Interval( pi / 2, pi * Rational(3, 2)) assert normalize_theta_set(Interval.open(0, 2 * pi)) == Interval.open( 0, 2 * pi) assert normalize_theta_set(Interval.Ropen(-pi/2, pi/2)) == \ Union(Interval.Ropen(0, pi/2), Interval.Ropen(pi*Rational(3, 2), 2*pi)) assert normalize_theta_set(Interval.Lopen(-pi/2, pi/2)) == \ Union(Interval(0, pi/2), Interval.open(pi*Rational(3, 2), 2*pi)) assert normalize_theta_set(Interval(-pi/2, pi/2)) == \ Union(Interval(0, pi/2), Interval.Ropen(pi*Rational(3, 2), 2*pi)) assert normalize_theta_set(Interval.open( 4 * pi, pi * Rational(9, 2))) == Interval.open(0, pi / 2) assert normalize_theta_set(Interval.Lopen( 4 * pi, pi * Rational(9, 2))) == Interval.Lopen(0, pi / 2) assert normalize_theta_set(Interval.Ropen( 4 * pi, pi * Rational(9, 2))) == Interval.Ropen(0, pi / 2) assert normalize_theta_set(Interval.open(3*pi, 5*pi)) == \ Union(Interval.Ropen(0, pi), Interval.open(pi, 2*pi)) # FiniteSet assert normalize_theta_set(FiniteSet(0, pi, 3 * pi)) == FiniteSet(0, pi) assert normalize_theta_set(FiniteSet(0, pi / 2, pi, 2 * pi)) == FiniteSet(0, pi / 2, pi) assert normalize_theta_set(FiniteSet(0, -pi / 2, -pi, -2 * pi)) == FiniteSet( 0, pi, pi * Rational(3, 2)) assert normalize_theta_set(FiniteSet(pi*Rational(-3, 2), pi/2)) == \ FiniteSet(pi/2) assert normalize_theta_set(FiniteSet(2 * pi)) == FiniteSet(0) # Unions assert normalize_theta_set(Union(Interval(0, pi/3), Interval(pi/2, pi))) == \ Union(Interval(0, pi/3), Interval(pi/2, pi)) assert normalize_theta_set(Union(Interval(0, pi), Interval(2*pi, pi*Rational(7, 3)))) == \ Interval(0, pi) # ValueError for non-real sets raises(ValueError, lambda: normalize_theta_set(S.Complexes)) # NotImplementedError for subset of reals raises(NotImplementedError, lambda: normalize_theta_set(Interval(0, 1))) # NotImplementedError without pi as coefficient raises(NotImplementedError, lambda: normalize_theta_set(Interval(1, 2 * pi))) raises(NotImplementedError, lambda: normalize_theta_set(Interval(2 * pi, 10))) raises(NotImplementedError, lambda: normalize_theta_set(FiniteSet(0, 3, 3 * pi)))