So it seems there are (at least!) two classes of functions; those
which accept symbolic input, like sin:
m(x)=sin(x/2)
and those which don't, such as mod. I had not realized there was such
a distinction. Thank you all.
-Alasdair
On Jul 2, 5:15 am, William Stein <wst...@gmail.com> wrote:
> On Wed, Jul 1, 2009 at 8:52 PM, Simon King<simon.k...@uni-jena.de> wrote:
>
> > Hi Alasdair,
>
> > On 1 Jul., 13:00, David Joyner <wdjoy...@gmail.com> wrote:
> >> I think the first tries to use Sage's symbolic expression machinery
> >> but the second does not.
>
> > Yes, it seems so.
>
> > Using Sage, one should always be aware that some very handy/fancy
> > syntax is only available due to the Sage preparser.
>
> > E.g., some definitions such as f(x) = sin(x) or R.<x>=QQ[] are not
> > valid Python. But when you do this in Sage, it internally becomes
> > sage: preparse('m(x)=sin(x)')
> > '__tmp__=var("x"); m = symbolic_expression(sin(x)).function(x)'
>
> > In your first approach, you get '__tmp__=var("x"); m =
> > symbolic_expression(mod(x,Integer(10))).function(x)'
>
> > But mod(x,Integer(10)) gives an error, since x is a symbolic variable
> > and not an integer, and since "mod" is not symbolic, in contrast to
> > "sin":
> > sage: type(sin)
> > <class 'sage.functions.trig.Function_sin'>
> > sage: type(mod)
> > <type 'builtin_function_or_method'>
>
> For the record, at some point we may want to make "mod" work with
> symbolic input.
> I.e., I don't see any reason why at some point in the future we could
> make the following make sense:
>
> sage: x = var('x')
> sage: f = mod(x, 3)
> sage: f
> Mod(x, 3)
> sage: f.subs(x=5)
> 2
>
> This is already how Mathematica works:
>
> f := Mod[x,3]; f
> Mod[x, 3]
>
> f /. x -> 5
> 2
>
> William
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