#6480: .subs_expr() method doesn't work for argument of D derivative operator
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Reporter: gmhossain | Owner:
Type: defect | Status: new
Priority: major | Milestone:
Component: symbolics | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: | Stopgaps:
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Old description:
> In computing functional derivative, one needs to vary
> a functional. For example, in sage-3.4 one can do as follows
> {{{
> sage: f(x) = function('f',x)
> sage: df(x) = function('df',x)
> sage: g = f(x).diff(x)
> sage: g
> diff(f(x), x, 1)
> sage: g.subs_expr(f(x)==f(x)+df(x))
> diff(f(x) + df(x), x, 1)
> }}}
>
> In new symbolics, if I do the same I get
>
> {{{
> sage: g
> D[0](f)(x)
> sage: g.subs_expr(f(x)==f(x)+df(x))
> D[0](f)(x)
> }}}
New description:
In computing functional derivative, one needs to vary
a functional. For example, in sage-3.4 one can do as follows
{{{
sage: f(x) = function('f',x)
sage: df(x) = function('df',x)
sage: g = f(x).diff(x)
sage: g
diff(f(x), x, 1)
sage: g.subs_expr(f(x)==f(x)+df(x))
diff(f(x) + df(x), x, 1)
}}}
In new symbolics, if I do the same I get
{{{
sage: g
D[0](f)(x)
sage: g.subs_expr(f(x)==f(x)+df(x))
D[0](f)(x)
}}}
----
From #11842, the list of what does/doesn't work:
{{{
from sage.all import *
# 1. Fails.
x = var('x')
f = function('f', x)
g = function('g', x)
p = f
print p.substitute_function(f, g) # Outputs "f(x)"
# 2. Fails.
x = var('x')
f = function('f')
g = function('g')
p = f(x)
print p.substitute_function(f(x), g(x)) # Outputs "f(x)"
# 3. Works.
x = var('x')
f = function('f')
g = function('g')
p = f(x)
print p.substitute_function(f, g) # Outputs "g(x)"
# 4. Fails.
x = var('x')
f = function('f')
g = function('g')
p = f(1)
print p.substitute_function(f(1), g(1)) # Outputs "f(1)"
# 5. Works.
x = var('x')
f = function('f')
g = function('g')
p = f(1)
print p.substitute_function(f, g) # Outputs "g(1)"
# 6. Fails.
x = var('x')
f = function('f', x)
g = function('g', x)
p = f.diff()
print p.substitute_function(f, g) # Outputs "D[0](f)(x)"
# 7. Fails.
x = var('x')
f = function('f', x)
g = function('g', x)
p = f.diff()
print p.substitute_function(f(x), g(x)) # Outputs "D[0](f)(x)"
# 8. Works.
x = var('x')
f = function('f')
g = function('g')
p = f(x).diff()
print p.substitute_function(f, g) # Outputs "D[0](g)(x)"
# 9. Fails.
x = var('x')
f = function('f')
g = function('g')
p = f(x).diff()(1)
print p.substitute_function(f(x).diff(), g(x).diff()) # Outputs
"D[0](f)(1)"
# 10. Works..
x = var('x')
f = function('f')
g = function('g')
p = f(x).diff()(1)
print p.substitute_function(f, g) # Prints D[0](g)(1).
}}}
--
Comment (by kcrisman):
I feel like if that one is closed, we should have the list here, so I'm
updating the description.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6480#comment:6>
Sage <http://www.sagemath.org>
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