> > sage: f(u) = u^2
> > sage: f(4)
> > 16
> > sage: integrate(sin(u),u,2,11)
> > cos(2) - cos(11)
> > sage: diff(u*y,u)
> > y
> > sage: def g(n):
> > ....: return n*n
> > ....:
> > sage: g(9)
> > 81
> f(u) = u^2 implicitly declares a variable. More precisely, this is
> what happens:
>
> sage: preparse('f(u) = u^2')
> '_ = var("u"); f = symbolic_expression(u**Integer(2)).function(u)'
Incidentally, that is a good argument for always declaring your
functions as callable; it relieves one of this tedious var business.
I will make a mental note of it for intro material in Sage.
Yes, I realize I realize this shoots some of my earlier arguments
about calling symbolic expressions in the foot :)
>
> > When must you absolutely need to declare vars? My examples above give
> > the impression you can avoid declaring them for a good long time.
>
Did this question get answered? Apparently the answer is, "only when
you want to manipulate symbolic expressions that are not callable".
At least that's how I understand it. E.g.
sage: integrate(z^2,z)
yields an error about z if you don't define z. Incidentally, so does
sage: diff(z*x^2,x)
where I assume I already defined x to be a variable, so you must have
already had y defined above. But
sage: z=3
sage: diff(z*x^2,x)
6*x
so if you assign a value to a variable then you don't have to declare
it either (though of course it ceases to be a variable in the
mathematical sense).
- kcrisman
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