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Subtitute functions - in a differential equation - Sagemanifold

asked 2018-12-03 11:33:37 -0600

Dox gravatar image

updated 2018-12-04 01:48:01 -0600

Dear community,

I have a differential equation that depends on a function $\xi(t)$, but is a component of a tensor (calculated with sagemanifold)

M = Manifold(4, 'M', latex_name=r"\mathcal{M}")
U.<t,r,th,ph> = M.chart(r't r:(0,+oo) th:(0,pi):\theta ph:(0,2*pi):\phi')
xi = function('xi')(t)
f = function('f')(t)
h = function('h')(t)
g = function('g')(t)
Ric = M.tensor_field(0,2, 'Ric')
Ric[0,0] = 3/2*f*h - 3/4*h^2 + 3/2*f*xi + 3/4*xi^2 - 3/2*diff(h, t) - 3/2*diff(xi, t)
Ric.display()

I'd like to define the restriction to $\xi = 0$, and assign it to a new tensor

Ric0 = M.tensor_field(0,2, 'Ric0')
Ric0[0,0] = Ric[0,0].substitute_expression({xi:0, diff(xi, t):0})
Ric0.display()

but I get an AttributeError because the

AttributeError: 'ChartFunctionRing_with_category.element_class' object has no attribute 'substitute_expression'

I know that it works for functions

var('t')
xi = function('xi')(t)
f = function('f')(t)
h = function('h')(t)
ode = 3/2*f*h - 3/4*h^2 + 3/2*f*xi + 3/4*xi^2 - 3/2*diff(h, t) - 3/2*diff(xi, t)
ode0 = ode.substitute_expression({xi:0, diff(xi, t):0})

Question

Is there a way to substitute functions that are not ๐šœ๐šŠ๐š๐šŽ.๐šœ๐šข๐š–๐š‹๐š˜๐š•๐š’๐šŒ.๐šŽ๐šก๐š™๐š›๐šŽ๐šœ๐šœ๐š’๐š˜๐š—.๐™ด๐šก๐š™๐š›๐šŽ๐šœ๐šœ๐š’๐š˜๐š— but ChartFunctionRing_with_category.element_class?

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answered 2018-12-03 11:49:32 -0600

It works the same way as last time, by using .expr():

Ric[0,0].expr().substitute({xi:0, diff(xi, t):0})
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Comments

1

hehehehe... Thank you again! I almost got it... but I tried .expression().

Dox gravatar imageDox ( 2018-12-03 12:20:48 -0600 )edit

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Asked: 2018-12-03 11:33:37 -0600

Seen: 33 times

Last updated: Dec 04