On May 9, 2007, at 3:28 PM, Bobby Moretti wrote:
> On 5/9/07, Justin C. Walker <[EMAIL PROTECTED]> wrote:
>> On May 9, 2007, at 10:51 AM, Timothy Clemans wrote:
>> I'm not sure these are failures, per se. This may be a in issue with
>> the Principal of Least Surprise :-}
> This is definitely the case here. In every one of your examples,
> Timothy,
> the module is doing what it's supposed to. Sorry, the documentation
> is kind
> of lacking in the tutorial. I'm working on it right now. For now
> I'd suggest
> looking at the reference manual and especially the docstring for
> sage.calculus.calculus.
Manual? Read? :-}
> Now, by default, the symbols f, g, and most other single-character
> symbols
> are instances of SymbolicVariable. They are not callable. What you
> really
> are trying to do is make a formal function f, and a formal function
> g, and
> differentiate those. So to do that, you need to use the commands:
>
> sage: f = function('f')
> sage: g = function('g')
> sage: foo = diff(f(x) + g(x))
> diff(g(x), x, 1) + diff(f(x), x, 1)
>
> and then you can do something like
> sage: foo(f=sin, g=x^3)
> cos(x) + 3*x^2
Thanks for this. Now, David's reply makes even more sense :-} I
cobbled up my response by communing with the ether, rather than
actually reading something...
> They are, but not as formal functions. They're defined as
> SymbolicVariables.
This is the part that I didn't really get until now.
The calculus package is a great addition. It seems to 'just work'.
I have a few concerns (cf. the Principal above), since this package
is affected by what you change during a session, but overall, I like it.
Here's an example of what I'm hinting at:
> sage: f=c*x
> sage: diff(f,c)
> x
> sage: diff(f,x)
> c
> sage: c=3
> sage: type(c)
> <type 'sage.rings.integer.Integer'>
> sage: type(f)
> <class 'sage.calculus.calculus.SymbolicArithmetic'>
> sage: diff(f,c)
> .....
> <type 'exceptions.ValueError'>: must supply an explicit variable
> for an expression containing more than one variable
so above, the substitution 'c -> 3' takes place at the call. Below,
> sage: diff(f,x)
> c
> sage:
no substitution happens. On the other hand:
> sage: a=1
> sage: g=a*x
> sage: diff(g,x)
> 1
> sage:
Justin
--
Justin C. Walker, Curmudgeon-At-Large
Director
Institute for the Enhancement of the Director's Income
--------
"Weaseling out of things is what separates us from the animals.
Well, except the weasel."
- Homer J Simpson
--------
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