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))

then

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

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

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

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

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

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

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.

Daniel

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Comments

Could someone answer this?

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