On Saturday, September 13, 2014 11:18:49 PM UTC+2, Chris Maness wrote:
>
> Is it possible for sage to use an undefined function such that:
>
> diff(f(x(t),y(t)),t) yields the definition of the total derivative?
>
>
I'm not sure about Sage itself, but since SymPy is technically part of
Sage, this should count:
import sympy as sy
t = sy.Symbol("t")
f = sy.Function("f")
x = sy.Function("x")
y = sy.Function("y")
y_dot = f(x(t), y(t)).diff(t)
sy.pprint(y_dot, use_unicode=True)
d ⎛ ∂ ⎞│ d ⎛ ∂ ⎞│
──(x(t))⋅⎜───(f(ξ₁, y(t)))⎟│ + ──(y(t))⋅⎜───(f(x(t), ξ₂))⎟│
dt ⎝∂ξ₁ ⎠│ξ₁=x(t) dt ⎝∂ξ₂ ⎠│ξ₂=y(t)
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