#17445: Missing documentation of derivative operator/notation
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Reporter: schymans | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.5
Component: symbolics | Resolution:
Keywords: | Merged in:
Authors: schymans | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Old description:
> Taking the derivative of a symbolic function returns the D-notation:
> sage: var('x y z')
> sage: f(x) = function('f',x,y,z);
> sage: f(x).diff(x,y)
> D[0, 1](f)(x, y, z)
>
> Unfortunately, the meaning of this notation is not documented anywhere,
> neither in diff(), nor in derivative() nor in function(). There is a ton
> of tickets about improving ambiguities and malfunctions related to this
> notation, but it would be very helpful to at least document how it is
> supposed to work and what it means if a user sees output as above.
>
> See here for related tickets:
> * #6344
> * #6480
> * #6756
> * #12796
>
> and this discussion:
> https://groups.google.com/forum/#!topic/sage-devel/_xD5lymnTuo
New description:
Taking the derivative of a symbolic function returns the D-notation:
sage: var('x y z')
sage: f(x) = function('f',x,y,z);
sage: f(x).diff(x,y)
D[0, 1](f)(x, y, z)
Unfortunately, the meaning of this notation is not documented anywhere,
neither in diff(), nor in derivative() nor in function(). There is a ton
of tickets about improving ambiguities and malfunctions related to this
notation, but it would be very helpful to at least document how it is
supposed to work and what it means if a user sees output as above.
See here for related tickets:
* #6344
* #6480
* #6756
* #12796
* #7401 (similar topic, not same issue)
and this discussion:
https://groups.google.com/forum/#!topic/sage-devel/_xD5lymnTuo
--
Comment (by kcrisman):
Can you comment on some of the chain-rule type issues in #6480, then? I
have to say that in particular the stuff at
http://ask.sagemath.org/question/9932/how-to-substitute-a-function-within-
derivatives/ and #6480 is massively confusing. Heck, let's add #7401
while we're at it.
I don't even know whether ''any'' of those things are "really" right or
wrong at this point. I suppose you shouldn't be allowed to substitute in
a function that "isn't there" in 6 and 7, but then why does 8 "work"? In
any case, shouldn't there be an error raised if one attempts something
like this when it's not "legitimate"?
{{{
# 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)"
}}}
These are ''very'' subtle differences to anyone who is not in symbolic
algebra/expressions, and part of the issue is the difference between
expressions and functions, no doubt. So comment:1 is a good start, but
definitely only a start.
--
Ticket URL: <http://trac.sagemath.org/ticket/17445#comment:4>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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