On 9/12/07, Soroosh Yazdani <[EMAIL PROTECTED]> wrote:
> Hmm, there seems to be many assumptions that I would like it be clarified.
> Specifically where do all these objects live in.
> For example, sin is a function from K->K.
> same as cos.
What is K? sin is symbolic so the input is anything symbolic. It's formal.
> If that's the case, then sin+cos makes perfect sense.
> Can we make the same assumtion for x? Is it safe to assume x is also
> a function from K->K?
x is a symbolic variable. It also has a call method. Actually,
i don't know what you mean by x in the questions above.
> Can we assume sin(x)=sin?
No, and they aren't equal. That doesn't make sense. One is
an unevaluated function, and the other is evaluated at the point
x. The data types are totally different.
> BTW, I don't think this is a good idea:
> >> sage: x, y=vars('x y')
> >> sage: y + sin
> >> y + sin(y)
> >> sage: x + sin
> >> x + sin(x)
That's definitely not how SAGE works now, and now how
it should work. This is what currently happens:
sage: x,y = var('x y')
sage: y + sin
sin + y
sage: x + sin
sin + x
sage: (x + sin)(5) # this is bad -- it's the trac ticket robert opened
sin + 5 # should be sin(5) + 5.
> If I understand the logic of everything, y is an element of functions
> from K^2 -> K, while sin is a function from K->K.
No, that's not right. There is absolutely no mathematical
difference between x and y at all. They are both formal indeterminates.
Thanks for your questions and comments.
> Soroosh
>
> On Wed, Sep 12, 2007 at 02:29:26PM -0700, Robert Bradshaw wrote:
> > On Sep 12, 2007, at 2:24 PM, William Stein wrote:
> >
> > > On 9/12/07, Robert Bradshaw <[EMAIL PROTECTED]> wrote:
> > >>>> BTW, I think this is a bug:
> > >>>>
> > >>>> sage: f = x+y
> > >>>> sage: f
> > >>>> y + x
> > >>>> sage: f(4)
> > >>>> y + 4
> > >>>>
> > >>>
> > >>> That's not a bug, that's *exactly* how we designed things
> > >>> to work. Calling when the inputs are explicit is done with
> > >>> the variables in dictionary order.
> > >>
> > >> I'll take that back, I didn't know dictionary order was explicitly
> > >> used, and I'm OK with that as there is no ambiguity. Is there any
> > >> reason f(2,3) does not work?
> > >>
> > >
> > > I can't think of any, so *that* must be a bug. Could you open
> > > a trac ticket for it?
> > >
> > > William
> >
> > Done. http://www.sagemath.org:9002/sage_trac/ticket/645
> >
> >
> >
>
> >
>
--
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org
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