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Description
substitute_function expects two function objects as argument not expressions (f(x)). This leads to the (to some users) unexpected:
sage: f = function('f')(x)
....: g = function('g')(x)
....: df = f(x).diff(x)
sage: f.substitute_function(f,g)
f(x)
sage: f(1).substitute_function(f,g)
f(1)
sage: df.substitute_function(f,g)
diff(f(x), x)
sage: df(1).substitute_function(f,g)
D[0](f)(1)
(same with f(x)=function...)
The problem is that f and g are not function objects like sin. Taking this into account:
sage: f.substitute_function(f.operator(), g.operator())
g(x)
sage: f(1).substitute_function(f.operator(), g.operator())
g(1)
sage: df.substitute_function(f.operator(), g.operator())
diff(g(x), x)
sage: df(1).substitute_function(f.operator(), g.operator())
D[0](g)(1)
The ticket should make substitute_function raise an exception with a hint. Note that the mess results from function('f') returning a function object but function('f')(x) returning f(x) and users assigning this to f or f(x) instead of just doing
sage: f=function('f')
sage: f(1).substitute_function(f,g)
g(1)
Documentation of substitute_function could be made more explicit as well.
Component: symbolics
Issue created by migration from https://trac.sagemath.org/ticket/22401