# Subtitute functions - in a differential equation - Sagemanifold

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๐๐๐.๐๐ข๐๐๐๐๐๐.๐๐ก๐๐๐๐๐๐๐๐.๐ด๐ก๐๐๐๐๐๐๐๐ but ChartFunctionRing_with_category.element_class?

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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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1

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

( 2018-12-03 19:20:48 +0200 )edit