def test_deprecations(self): base = Ga('a b', g=[1, 1], coords=symbols('x, y', real=True)) l = base.lt([[1, 2], [3, 4]]) with pytest.warns(DeprecationWarning): assert l.X == l.Ga.coord_vec with pytest.warns(DeprecationWarning): assert l.coords == l.Ga.coords l = base.lt('L', mode='a') with pytest.warns(DeprecationWarning): assert l.mode == 'a' with pytest.warns(DeprecationWarning): assert not l.fct_flg l = base.lt('L', mode='s', f=True) with pytest.warns(DeprecationWarning): assert l.mode == 's' with pytest.warns(DeprecationWarning): assert l.fct_flg
def test_lt_function(self): """ Test construction from a function """ base = Ga('a b', g=[1, 1], coords=symbols('x, y', real=True)) a, b = base.mv() def not_linear(x): return x * x with pytest.raises(ValueError, match='linear'): base.lt(not_linear) def not_vector(x): return x + S.One with pytest.raises(ValueError, match='vector'): base.lt(not_vector) def ok(x): return (x | b) * a + 2*x f = base.lt(ok) x = base.mv('x', 'vector') y = base.mv('y', 'vector') assert f(x) == ok(x) assert f(x^y) == ok(x)^ok(y) assert f(1 + 2*(x^y)) == 1 + 2*(ok(x)^ok(y))
def main(): # Print_Function() (x, y, z) = xyz = symbols('x,y,z',real=True) (o3d, ex, ey, ez) = Ga.build('e_x e_y e_z', g=[1, 1, 1], coords=xyz) grad = o3d.grad (u, v) = uv = symbols('u,v',real=True) (g2d, eu, ev) = Ga.build('e_u e_v', coords=uv) grad_uv = g2d.grad v_xyz = o3d.mv('v','vector') A_xyz = o3d.mv('A','vector',f=True) A_uv = g2d.mv('A','vector',f=True) print('#3d orthogonal ($A$ is vector function)') print('A =', A_xyz) print('%A^{2} =', A_xyz * A_xyz) print('grad|A =', grad | A_xyz) print('grad*A =', grad * A_xyz) print('v|(grad*A) =',v_xyz|(grad*A_xyz)) print('#2d general ($A$ is vector function)') print('A =', A_uv) print('%A^{2} =', A_uv * A_uv) print('grad|A =', grad_uv | A_uv) print('grad*A =', grad_uv * A_uv) A = o3d.lt('A') print('#3d orthogonal ($A,\\;B$ are linear transformations)') print('A =', A) print(r'\f{mat}{A} =', A.matrix()) print('\\f{\\det}{A} =', A.det()) print('\\overline{A} =', A.adj()) print('\\f{\\Tr}{A} =', A.tr()) print('\\f{A}{e_x^e_y} =', A(ex^ey)) print('\\f{A}{e_x}^\\f{A}{e_y} =', A(ex)^A(ey)) B = o3d.lt('B') print('g =', o3d.g) print('%g^{-1} =', latex(o3d.g_inv)) print('A + B =', A + B) print('AB =', A * B) print('A - B =', A - B) print('General Symmetric Linear Transformation') Asym = o3d.lt('A',mode='s') print('A =', Asym) print('General Antisymmetric Linear Transformation') Aasym = o3d.lt('A',mode='a') print('A =', Aasym) print('#2d general ($A,\\;B$ are linear transformations)') A2d = g2d.lt('A') print('g =', g2d.g) print('%g^{-1} =', latex(g2d.g_inv)) print('%gg^{-1} =', latex(simplify(g2d.g * g2d.g_inv))) print('A =', A2d) print(r'\f{mat}{A} =', A2d.matrix()) print('\\f{\\det}{A} =', A2d.det()) A2d_adj = A2d.adj() print('\\overline{A} =', A2d_adj) print('\\f{mat}{\\overline{A}} =', latex(simplify(A2d_adj.matrix()))) print('\\f{\\Tr}{A} =', A2d.tr()) print('\\f{A}{e_u^e_v} =', A2d(eu^ev)) print('\\f{A}{e_u}^\\f{A}{e_v} =', A2d(eu)^A2d(ev)) B2d = g2d.lt('B') print('B =', B2d) print('A + B =', A2d + B2d) print('A - B =', A2d - B2d) # TODO: add this back when we drop Sympy 1.3. The 64kB of output is far too # printer-dependent if False: print('AB =', A2d * B2d) a = g2d.mv('a','vector') b = g2d.mv('b','vector') print(r'a|\f{\overline{A}}{b}-b|\f{\underline{A}}{a} =',((a|A2d.adj()(b))-(b|A2d(a))).simplify()) m4d = Ga('e_t e_x e_y e_z', g=[1, -1, -1, -1],coords=symbols('t,x,y,z',real=True)) T = m4d.lt('T') print('g =', m4d.g) print(r'\underline{T} =',T) print(r'\overline{T} =',T.adj()) print(r'\f{\det}{\underline{T}} =',T.det()) print(r'\f{\mbox{tr}}{\underline{T}} =',T.tr()) a = m4d.mv('a','vector') b = m4d.mv('b','vector') print(r'a|\f{\overline{T}}{b}-b|\f{\underline{T}}{a} =',((a|T.adj()(b))-(b|T(a))).simplify()) coords = (r, th, phi) = symbols('r,theta,phi', real=True) (sp3d, er, eth, ephi) = Ga.build('e_r e_th e_ph', g=[1, r**2, r**2*sin(th)**2], coords=coords) grad = sp3d.grad sm_coords = (u, v) = symbols('u,v', real=True) smap = [1, u, v] # Coordinate map for sphere of r = 1 sph2d = sp3d.sm(smap,sm_coords,norm=True) (eu, ev) = sph2d.mv() grad_uv = sph2d.grad F = sph2d.mv('F','vector',f=True) f = sph2d.mv('f','scalar',f=True) print('f =',f) print('grad*f =',grad_uv * f) print('F =',F) print('grad*F =',grad_uv * F) tp = (th,phi) = symbols('theta,phi',real=True) smap = [sin(th)*cos(phi),sin(th)*sin(phi),cos(th)] sph2dr = o3d.sm(smap,tp,norm=True) (eth, ephi) = sph2dr.mv() grad_tp = sph2dr.grad F = sph2dr.mv('F','vector',f=True) f = sph2dr.mv('f','scalar',f=True) print('f =',f) print('grad*f =',grad_tp * f) print('F =',F) print('grad*F =',grad_tp * F) return
def test_lt_matrix(self): base = Ga('a b', g=[1, 1], coords=symbols('x, y', real=True)) a, b = base.mv() A = base.lt([a+b, 2*a-b]) assert str(A) == 'Lt(a) = a + b\nLt(b) = 2*a - b' assert str(A.matrix()) == 'Matrix([[1, 2], [1, -1]])'
# A2d.adj().Fmt(4,'\\overline{A}') print('\\f{\\Tr}{A} =', A2d.tr()) print('\\f{A}{e_u^e_v} =', A2d(eu ^ ev)) print('\\f{A}{e_u}^\\f{A}{e_v} =', A2d(eu) ^ A2d(ev)) B2d = g2d.lt('B') print('B =', B2d) print('A + B =', A2d + B2d) print('AB =', A2d * B2d) print('A - B =', A2d - B2d) a = g2d.mv('a', 'vector') b = g2d.mv('b', 'vector') print(r'a|\f{\overline{A}}{b}-b|\f{\underline{A}}{a} =', ((a | A2d.adj()(b)) - (b | A2d(a))).simplify()) print('#4d Minkowski spaqce (Space Time)') m4d = Ga('e_t e_x e_y e_z', g=[1, -1, -1, -1], coords=symbols('t,x,y,z', real=True)) T = m4d.lt('T') print('g =', m4d.g) # FIXME incorrect sign for T and T.adj() print(r'\underline{T} =', T) print(r'\overline{T} =', T.adj()) # m4d.mv(T.det()).Fmt(4,r'\f{\det}{\underline{T}}') print(r'\f{\mbox{tr}}{\underline{T}} =', T.tr()) a = m4d.mv('a', 'vector') b = m4d.mv('b', 'vector') print(r'a|\f{\overline{T}}{b}-b|\f{\underline{T}}{a} =', ((a | T.adj()(b)) - (b | T(a))).simplify()) xpdf(paper=(10, 12), debug=True)