On 9/12/07, Robert Bradshaw <[EMAIL PROTECTED]> wrote:
> Letting x + sin == x + sin(x) was my way of justifying (x + sin)(5)
> == 5 + sin(5). I was thinking "sin" was a function of exactly one
> variable, it just doesn't know/have a name for that variable yet.
Personally, I think you're applying some of the very structured coercion
model thinking in this situation, which is I think the wrong approach
for symbol pushing and symbolic calculus.
> Perhaps this was a bad idea, but then it is unclear what (x+sin) is.
> For callable symbolic expressions I think it may be a bit clearer.
Currently it is the formal sum of a symbolic variable and an
unevaluated function. This is meaningful in the world of
symbolic manipulation.
> sage: f(x) = x^2
> sage: f + sin
> x^2 + sin(x) # because f.parent()(sin) = sin(x) ??
That's very reasonable and should be fixed:
sage: f(x) = x^2
sage: f + sin
x |--> sin(x) + x^2
Right now one gets the following, which is very lame (if you
agree, please add this to the trac ticket):
sage: f(x) = x^2
sage: f + sin
x |--> sin + x^2
sage: f(10)
100
> Also, what should (x+y+sin)(5) be? An error? 5+y+sin?
If
( x + sin)(5) is 5 + sin(5),
then the above should be 5 + y + sin(5). The expression
x + y + sin is evaluated at 1 input, so since the variables
are (x,y), this is turned into (x+y+sin)(x=5). Next, this
is evaluated term by term and the result is added.
x(x=5) is 5
y(x=5) is y
sin (x=5) is sin(5), *if* we have the rule that calling
an unevaluated function with a named variable evaluates
the unevaluated function at the value of that variable.
> What should
> sin.variables() return?
What it does now:
sage: sin.variables()
()
> I think it should be a tuple with one
> element, as it takes one argument...
> Or something special?
It has no variables right now, so why should it return any? It's
an unevaluate function.
William
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