Pullback of diff_map does not finish

asked 2018-03-15 14:45:47 -0500

danielvolinski gravatar image

Using SageMath 8.1 on Windows 10 Native with Jupyter Notebook

This is a continuation of Straight line parametrization with diff_map

I have the following code:

R2 = Manifold(2, 'R2', latex_name=r'\mathbb{R}^2')
cartesian2d.<x,y> = R2.chart()
R1 = Manifold(1, 'R1', start_index=1, latex_name=r'\mathbb{R}')
cartesian1d.<t> = R1.chart()
omega = R2.diff_form(1, 'omega', latex_name=r'\omega')
omega[:] = (4*y^2+exp(x^2)*sin(x^3), 6*x*y+log(5+y))


A = R2.point((3,2), name='A')
B = R2.point((-1,2), name='B')
C = R2.point((-2,-1), name='C')
P = R2.point((-1,-4), name='P')
Q = R2.point((3,-4), name='Q')
R = R2.point((5,-1), name='R')

I define the following diff_maps and try to pullback


C1 = R1.diff_map(R2, [t*B.coord()[i] + (1-t)*A.coord()[i] for i in range(2)], latex_name=r'C_1')
Pb1 = C1.pullback(omega)


C2 = R1.diff_map(R2, [t*C.coord()[i] + (1-t)*B.coord()[i] for i in range(2)], latex_name=r'C_2')
Pb2 = C2.pullback(omega)
I2 = numerical_integral(Pb2[1].expr().simplify_full(),0,1); I2


C3 = R1.diff_map(R2, [t*P.coord()[i] + (1-t)*C.coord()[i] for i in range(2)], latex_name=r'C_3')
Pb3 = C3.pullback(omega)
I3 = numerical_integral(Pb3[1].expr().simplify_full(),0,1); I3


C4 = R1.diff_map(R2, [t*Q.coord()[i] + (1-t)*P.coord()[i] for i in range(2)], latex_name=r'C_4')
Pb4 = C4.pullback(omega)


C5 = R1.diff_map(R2, [t*R.coord()[i] + (1-t)*Q.coord()[i] for i in range(2)], latex_name=r'C_5')
Pb5 = C5.pullback(omega)


C6 = R1.diff_map(R2, [t*A.coord()[i] + (1-t)*R.coord()[i] for i in range(2)], latex_name=r'C_6')
Pb6 = C6.pullback(omega)

C2 and C3 work all right but with C1, C4, C5 and C6 the pullback does not end.


edit retag flag offensive close merge delete


Could someone answer this?

danielvolinski gravatar imagedanielvolinski ( 2018-04-18 11:14:39 -0500 )edit