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<\h2>
Is there a way to substitute functions that are not 𝚜𝚊𝚐𝚎.𝚜𝚢𝚖𝚋𝚘𝚕𝚒𝚌.𝚎𝚡𝚙𝚛𝚎𝚜𝚜𝚒𝚘𝚗.𝙴𝚡𝚙𝚛𝚎𝚜𝚜𝚒𝚘𝚗 but ChartFunctionRing_with_category.element_class?
