def test_diop_general_sum_of_squares_quick(): for i in range(3, 10): assert check_solutions(sum(i**2 for i in symbols(':%i' % i)) - i) raises(ValueError, lambda: _diop_general_sum_of_squares((x, y), 2)) assert _diop_general_sum_of_squares((x, y, z), -2) == set() eq = x**2 + y**2 + z**2 - (1 + 4 + 9) assert diop_general_sum_of_squares(eq) == \ set([(1, 2, 3)]) eq = u**2 + v**2 + x**2 + y**2 + z**2 - 1313 assert len(diop_general_sum_of_squares(eq, 3)) == 3 # issue 11016 var = symbols(':5') + (symbols('6', negative=True), ) eq = Add(*[i**2 for i in var]) - 112 base_soln = set([(0, 1, 1, 5, 6, -7), (1, 1, 1, 3, 6, -8), (2, 3, 3, 4, 5, -7), (0, 1, 1, 1, 3, -10), (0, 0, 4, 4, 4, -8), (1, 2, 3, 3, 5, -8), (0, 1, 2, 3, 7, -7), (2, 2, 4, 4, 6, -6), (1, 1, 3, 4, 6, -7), (0, 2, 3, 3, 3, -9), (0, 0, 2, 2, 2, -10), (1, 1, 2, 3, 4, -9), (0, 1, 1, 2, 5, -9), (0, 0, 2, 6, 6, -6), (1, 3, 4, 5, 5, -6), (0, 2, 2, 2, 6, -8), (0, 3, 3, 3, 6, -7), (0, 2, 3, 5, 5, -7), (0, 1, 5, 5, 5, -6)]) assert diophantine(eq) == base_soln assert len(diophantine(eq, permute=True)) == 196800 # handle negated squares with signsimp assert diophantine(12 - x**2 - y**2 - z**2) == set([(2, 2, 2)]) # diophantine handles simplification, so classify_diop should # not have to look for additional patterns that are removed # by diophantine eq = a**2 + b**2 + c**2 + d**2 - 4 raises(NotImplementedError, lambda: classify_diop(-eq))
def test_diop_general_sum_of_squares_quick(): for i in range(3, 10): assert check_solutions(sum(i**2 for i in symbols(':%i' % i)) - i) raises(ValueError, lambda: _diop_general_sum_of_squares((x, y), 2)) assert _diop_general_sum_of_squares((x, y, z), -2) == set() eq = x**2 + y**2 + z**2 - (1 + 4 + 9) assert diop_general_sum_of_squares(eq) == \ set([(1, 2, 3)]) eq = u**2 + v**2 + x**2 + y**2 + z**2 - 1313 assert len(diop_general_sum_of_squares(eq, 3)) == 3 # issue 11016 var = symbols(':5') + (symbols('6', negative=True),) eq = Add(*[i**2 for i in var]) - 112 assert diophantine(eq) == set( [(0, 1, 1, 5, 6, -7), (1, 1, 1, 3, 6, -8), (2, 3, 3, 4, 5, -7), (0, 1, 1, 1, 3, -10), (0, 0, 4, 4, 4, -8), (1, 2, 3, 3, 5, -8), (0, 1, 2, 3, 7, -7), (2, 2, 4, 4, 6, -6), (1, 1, 3, 4, 6, -7), (0, 2, 3, 3, 3, -9), (0, 0, 2, 2, 2, -10), (1, 1, 2, 3, 4, -9), (0, 1, 1, 2, 5, -9), (0, 0, 2, 6, 6, -6), (1, 3, 4, 5, 5, -6), (0, 2, 2, 2, 6, -8), (0, 3, 3, 3, 6, -7), (0, 2, 3, 5, 5, -7), (0, 1, 5, 5, 5, -6)]) # handle negated squares with signsimp assert diophantine(12 - x**2 - y**2 - z**2) == set([(2, 2, 2)]) # diophantine handles simplification, so classify_diop should # not have to look for additional patterns that are removed # by diophantine eq = a**2 + b**2 + c**2 + d**2 - 4 raises(NotImplementedError, lambda: classify_diop(-eq))
def test_classify_diop(): raises(TypeError, lambda: classify_diop(x**2/3 - 1)) raises(ValueError, lambda: classify_diop(1)) raises(NotImplementedError, lambda: classify_diop(w*x*y*z - 1)) assert classify_diop(14*x**2 + 15*x - 42) == ( [x], {1: -42, x: 15, x**2: 14}, 'univariate') assert classify_diop(x*y + z) == ( [x, y, z], {x*y: 1, z: 1}, 'inhomogeneous_ternary_quadratic') assert classify_diop(x*y + z + w + x**2) == ( [w, x, y, z], {x*y: 1, w: 1, x**2: 1, z: 1}, 'inhomogeneous_general_quadratic') assert classify_diop(x*y + x*z + x**2 + 1) == ( [x, y, z], {x*y: 1, x*z: 1, x**2: 1, 1: 1}, 'inhomogeneous_general_quadratic') assert classify_diop(x*y + z + w + 42) == ( [w, x, y, z], {x*y: 1, w: 1, 1: 42, z: 1}, 'inhomogeneous_general_quadratic') assert classify_diop(x*y + z*w) == ( [w, x, y, z], {x*y: 1, w*z: 1}, 'homogeneous_general_quadratic') assert classify_diop(x*y**2 + 1) == ( [x, y], {x*y**2: 1, 1: 1}, 'cubic_thue')
def test_classify_diop(): raises(TypeError, lambda: classify_diop(x**2 / 3 - 1)) raises(ValueError, lambda: classify_diop(1)) raises(NotImplementedError, lambda: classify_diop(w * x * y * z - 1)) assert classify_diop(14 * x**2 + 15 * x - 42) == ([x], { 1: -42, x: 15, x**2: 14 }, 'univariate') assert classify_diop(x * y + z) == ([x, y, z], { x * y: 1, z: 1 }, 'inhomogeneous_ternary_quadratic') assert classify_diop(x * y + z + w + x**2) == ([w, x, y, z], { x * y: 1, w: 1, x**2: 1, z: 1 }, 'inhomogeneous_general_quadratic') assert classify_diop(x * y + x * z + x**2 + 1) == ([x, y, z], { x * y: 1, x * z: 1, x**2: 1, 1: 1 }, 'inhomogeneous_general_quadratic') assert classify_diop(x * y + z + w + 42) == ([w, x, y, z], { x * y: 1, w: 1, 1: 42, z: 1 }, 'inhomogeneous_general_quadratic') assert classify_diop(x * y + z * w) == ([w, x, y, z], { x * y: 1, w * z: 1 }, 'homogeneous_general_quadratic') assert classify_diop(x * y**2 + 1) == ([x, y], { x * y**2: 1, 1: 1 }, 'cubic_thue')
def test_classify_diop(): raises(TypeError, lambda: classify_diop(x ** 2 / 3 - 1)) raises(ValueError, lambda: classify_diop(1)) raises(NotImplementedError, lambda: classify_diop(w * x * y * z - 1)) raises(NotImplementedError, lambda: classify_diop(x ** 3 + y ** 3 + z ** 4 - 90)) assert classify_diop(14 * x ** 2 + 15 * x - 42) == ([x], {1: -42, x: 15, x ** 2: 14}, "univariate") assert classify_diop(x * y + z) == ([x, y, z], {x * y: 1, z: 1}, "inhomogeneous_ternary_quadratic") assert classify_diop(x * y + z + w + x ** 2) == ( [w, x, y, z], {x * y: 1, w: 1, x ** 2: 1, z: 1}, "inhomogeneous_general_quadratic", ) assert classify_diop(x * y + x * z + x ** 2 + 1) == ( [x, y, z], {x * y: 1, x * z: 1, x ** 2: 1, 1: 1}, "inhomogeneous_general_quadratic", ) assert classify_diop(x * y + z + w + 42) == ( [w, x, y, z], {x * y: 1, w: 1, 1: 42, z: 1}, "inhomogeneous_general_quadratic", ) assert classify_diop(x * y + z * w) == ([w, x, y, z], {x * y: 1, w * z: 1}, "homogeneous_general_quadratic") assert classify_diop(x * y ** 2 + 1) == ([x, y], {x * y ** 2: 1, 1: 1}, "cubic_thue") assert classify_diop(x ** 4 + y ** 4 + z ** 4 - (1 + 16 + 81)) == ( [x, y, z], {1: -98, x ** 4: 1, z ** 4: 1, y ** 4: 1}, "general_sum_of_even_powers", )