Opened 12 years ago
Last modified 5 years ago
#6480 new defect
Failure with diff(f(x),x).subs(f(x) == g(x))
Reported by: | gmhossain | Owned by: | |
---|---|---|---|
Priority: | major | Milestone: | sage-8.0 |
Component: | symbolics | Keywords: | |
Cc: | kcrisman, mjo, eviatarbach, jakobkroeker | Merged in: | |
Authors: | Reviewers: | ||
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: | wrongAnswerMarker |
Description (last modified by )
Subject says it all.
Previous (no longer up-to-date) description was:
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).
Change History (18)
comment:1 Changed 11 years ago by
- Cc kcrisman added
- Report Upstream set to N/A
comment:2 Changed 10 years ago by
- Cc mjo added
comment:3 Changed 8 years ago by
- Cc eviatarbach added
comment:4 Changed 8 years ago by
.substitute_function
seems to work: http://ask.sagemath.org/question/2380/how-to-substitute-a-function-within-derivatives
comment:5 Changed 8 years ago by
One of the cases in #11842 that used to crash now works, but a lot of them still don't. I updated the list.
comment:6 Changed 8 years ago by
- Description modified (diff)
I feel like if that one is closed, we should have the list here, so I'm updating the description.
comment:7 Changed 6 years ago by
- Stopgaps set to todo
comment:8 Changed 5 years ago by
I think these are different issues because substitute_function
handles a narrowly defined set of cases, and it expects two functions (f, g, sin
) not expressions (f(x), diff(f(x),x)
) as function arguments. Cases above that are in the former category:
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)
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)
I opened #22401 for this.
comment:9 Changed 5 years ago by
Also, even if subs
is fixed there is no way atm to get and use diff(f(x)+g(x),x)
:
sage: diff(f(x)+g(x),x) diff(f(x), x) + diff(g(x), x) sage: diff(f(x)+g(x),x,hold=True) TypeError: derivative() got an unexpected keyword argument 'hold'
diff
is not a function, although it could well be theoretically:
sage: diff(f(x),x) diff(f(x), x) sage: _._dbgprinttree() fderivative f @0x34a8c00, hash=0x1023d75fb40091, flags=0xb, nops=1, params=0 x (symbol) @0x2895f10, serial=7, hash=0xe3706ef, flags=0xf, domain=0, iflags=0000000000000000 ===== sage: diff(f(x),x) diff(f(x), x) sage: _.operator() D[0](f) sage: type(_) <class 'sage.symbolic.operators.FDerivativeOperator'>
I cannot see why diff(f(x)+g(x),x,hold=True)
should be supported so I'm not opening a ticket. Just don't expect that as output from a fixed subs
.
comment:10 Changed 5 years ago by
So, what should work is
sage: f = function('f') sage: g = function('g') sage: f(x).subs(f(x) == g(x)) g(x) sage: f(x).subs(f == g) g(x) sage: f(x).subs({f : g}) g(x) sage: df = f(x).diff(x); df diff(f(x), x) sage: df.subs(f(x) == g(x)) diff(g(x), x) sage: df.subs(f == g) diff(g(x), x) sage: df.subs(f(x) == f(x) + g(x)) diff(f(x), x) + diff(g(x), x) sage: df.subs(f == f + g) diff(f(x), x) + diff(g(x), x)
but it mostly doesn't:
Failed example: f(x).subs(f == g) Exception raised: Traceback (most recent call last): File "/home/ralf/sage/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 498, in _run self.compile_and_execute(example, compiler, test.globs) File "/home/ralf/sage/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 861, in compile_and_execute exec(compiled, globs) File "<doctest sage.symbolic.expression.Expression.substitute[67]>", line 1, in <module> f(x).subs(f == g) File "sage/symbolic/expression.pyx", line 4961, in sage.symbolic.expression.Expression.substitute (build/cythonized/sage/symbolic/expression.cpp:29715) g(x) File "sage/symbolic/expression.pyx", line 348, in sage.symbolic.expression._subs_make_dict (build/cythonized/sage/symbolic/expression.cpp:5364) raise TypeError(msg.format(s)) TypeError: not able to determine a substitution from False ********************************************************************** Failed example: f(x).subs({f : g}) Exception raised: Traceback (most recent call last): File "/home/ralf/sage/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 498, in _run self.compile_and_execute(example, compiler, test.globs) File "/home/ralf/sage/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 861, in compile_and_execute exec(compiled, globs) File "<doctest sage.symbolic.expression.Expression.substitute[68]>", line 1, in <module> f(x).subs({f : g}) File "sage/symbolic/expression.pyx", line 4971, in sage.symbolic.expression.Expression.substitute (build/cythonized/sage/symbolic/expression.cpp:30001) diff(f(x), x) + diff(g(x), x) File "sage/symbolic/expression.pyx", line 2885, in sage.symbolic.expression.Expression.coerce_in (build/cythonized/sage/symbolic/expression.cpp:21682) return self._parent._coerce_(z) File "sage/structure/parent_old.pyx", line 241, in sage.structure.parent_old.Parent._coerce_ (build/cythonized/sage/structure/parent_old.c:4949) return self.coerce(x) File "sage/structure/parent.pyx", line 1195, in sage.structure.parent.Parent.coerce (build/cythonized/sage/structure/parent.c:11169) raise TypeError("no canonical coercion from %s to %s" % (parent(x), self)) TypeError: no canonical coercion from <class 'sage.symbolic.function_factory.NewSymbolicFunction'> to Symbolic Ring ********************************************************************** df.subs(f(x) == g(x)) Expected: diff(g(x), x) Got: diff(f(x), x) ********************************************************************** df.subs(f == g) Exception raised: Traceback (most recent call last): File "/home/ralf/sage/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 498, in _run self.compile_and_execute(example, compiler, test.globs) File "/home/ralf/sage/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 861, in compile_and_execute exec(compiled, globs) File "<doctest sage.symbolic.expression.Expression.substitute[71]>", line 1, in <module> df.subs(f == g) File "sage/symbolic/expression.pyx", line 4961, in sage.symbolic.expression.Expression.substitute (build/cythonized/sage/symbolic/expression.cpp:29715) g(x) File "sage/symbolic/expression.pyx", line 348, in sage.symbolic.expression._subs_make_dict (build/cythonized/sage/symbolic/expression.cpp:5364) raise TypeError(msg.format(s)) TypeError: not able to determine a substitution from False ********************************************************************** df.subs(f(x) == f(x) + g(x)) Expected: diff(f(x), x) + diff(g(x), x) Got: diff(f(x), x) ********************************************************************** df.subs(f == f + g) Exception raised: Traceback (most recent call last): File "/home/ralf/sage/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 498, in _run self.compile_and_execute(example, compiler, test.globs) File "/home/ralf/sage/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 861, in compile_and_execute exec(compiled, globs) File "<doctest sage.symbolic.expression.Expression.substitute[73]>", line 1, in <module> df.subs(f == f + g) TypeError: unsupported operand type(s) for +: 'NewSymbolicFunction' and 'NewSymbolicFunction'
comment:11 follow-up: ↓ 16 Changed 5 years ago by
The above consists of three problems. The central one is the failure to f(x).subs(f(x) == g(x))
; the diff
case is probably only a result; it looks like this is a Pynac bug, and when fixed there it should be doctested here.
The second is the failure of f(x).subs({f : g})
. Maybe we can delegate to substitute_function
if the dict key/val pair consists of function objects.
The third is that f+g
already bails out. But SR('f')+SR('g')
does not so this would be a workaround.
comment:12 Changed 5 years ago by
- Milestone set to sage-7.7
- Stopgaps todo deleted
- Summary changed from .subs_expr() method doesn't work for argument of D derivative operator to Failure with f(x).subs(f(x) == g(x))
comment:13 Changed 5 years ago by
- Description modified (diff)
comment:14 Changed 5 years ago by
- Summary changed from Failure with f(x).subs(f(x) == g(x)) to diff(f(x),x).subs(f(x) == g(x))
Nah, it was wrong, only diff(f(x),x).subs(f(x) == g(x))
doesn't work.
comment:15 Changed 5 years ago by
- Summary changed from diff(f(x),x).subs(f(x) == g(x)) to Failure with diff(f(x),x).subs(f(x) == g(x))
comment:16 in reply to: ↑ 11 Changed 5 years ago by
Replying to rws:
The above consists of three problems. The central one is the failure to
f(x).subs(f(x) == g(x))
; thediff
case is probably only a result; it looks like this is a Pynac bug, and when fixed there it should be doctested here.
The special status of fderivative
in Pynac (not a function) may be the reason, see also https://groups.google.com/d/msg/sage-support/lZ4AjbmvvQE/-BJ_xvMlAQAJ
comment:18 Changed 5 years ago by
- Cc jakobkroeker added
- Stopgaps set to wrongAnswerMarker
I duped this in #11842. We might be able to make use of the test cases there when this gets fixed.