thank you john
On Mar 9, 9:35 am, John H Palmieri <jhpalmier...@gmail.com> wrote:
> On Mar 8, 3:14 pm, compound eye <compound...@gmail.com> wrote:
>
>
>
> > thank you john,
>
> > it's early morning in australia
> > and I just woke up realising
> > i had forgotten that what i am entering into my notebook is python
> > not mysterious sagese configuration script
>
> > I think I need to go do some python tutorials, what you've said makes
> > perfect sense, and is exactly the behaviour I would have expected,
> > except that in the example:
>
> > x = var('x')
> > def splitAgain(n):
>
> > if n < 2:
> > return n
> > else:
> > return 2-n
>
> > plot(splitAgain(x),0,4)
>
> > the evaluation of splitAgain(x) passed to plot(),
> > is neither a reference to splitAgain,
> > or an evaluation of splitAgain(x) for some value of x,
> > but 2-x, as this draws 2-x
>
> > this is a behaviour pattern I haven't encountered before, I am a bit
> > mystified by it and would like to understand it, is this a python
> > feature to do with : x = var('x') , or is something specifically to do
> > with plot()?
>
> Well, again 'x<2' evaluates to false, so the function returns the
> other option, which in this case is 2-x. I think that since 'x' is a
> variable, any expression in it becomes a symbolic expression and is
> evaluated accordingly. If a boolean symbolic expression (like 'x<2')
> is not obviously true, then it returns False. Then the function
> substitutes x for n to get the symbolic expression 2-x. Then this
> gets plotted.
>
> From this:
>
> sage: type(splitAgain)
> <type 'function'>
> sage: type(2-x)
> <class 'sage.calculus.calculus.SymbolicArithmetic'>
> sage: type(splitAgain(x))
> <class 'sage.calculus.calculus.SymbolicArithmetic'>
>
> you can see that symbolic expressions are a Sage thing, not a Python
> thing.
>
> It also doesn't have anything to do with plot(). Well, not much: plot
> can accept a python function like splitAgain as an argument, and it
> can also accept a symbolic expression like splitAgain(x) as an
> argument. In fact you can plot any of these objects, and more:
>
> sage: type(sin(x))
> <class 'sage.calculus.calculus.SymbolicComposition'>
> sage: type(sin)
> <class 'sage.calculus.calculus.Function_sin'>
> sage: def f(y):
> ....: return sin(y)
> sage: type(f)
> <type 'function'>
>
> 'plot(f, 0, 2*pi)', 'plot(sin, 0, 2*pi)', and 'plot(sin(x), 0, 2*pi)'
> all produce the same picture.
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