what do these mean?



 

> -----Original Message-----
> From: maxima-bounces at math.utexas.edu 
> [mailto:maxima-bounces at math.utexas.edu] On Behalf Of sen1 at math.msu.edu
> Sent: Tuesday, June 12, 2007 8:43 AM
> To: Robert Dodier
> Cc: maxima at math.utexas.edu
> Subject: Re: [Maxima] what do these mean?
> 
> I guess one of my questions is:
> 
> What kind of object is actually produced by
> 
> (%i5) linearinterpol([[2,1], [3,2], [4,3]]);
> 
> Is this a function, boolean expression, list of characters, etc?

Internally it is a symbolic expression, represented in the computer as a
"tree" or in lisp as a list.
If you are viewing it on a display screen it could also be thought of as a
rectangular region of light and dark spots, but that's probably not what you
mean.   

> 
> Logically speaking, if I write
> 
> f(x):= x^2 + 2*x,
> 
> I assume that I am defining a set of ordered pairs of real numbers.

At some level of abstraction, perhaps this is a good way of thinking about
it,  but x need not be a real number.
A more realistic view is that you have defined a symbolic expression
associated with the function property of the symbol "f".   

> In
> a computer, this cannot be stored, so one only gets stored values
> which can have operations on them when one attempts to evaluate the
> function.

No, what you have stored can also be used in other ways.

I hope this, and the previous note, help.
RJF


> 
> So, I am somewhat confused about the differences between
> 
> (%i10) f(x):= linearinterpol([[2,1],[3,2], [4,3]]);
> (%o10)    (x - 1) charfun2(x, minf, 3) + (x - 1) charfun2(x, 3, inf)
> 
> and
> 
> (%i11) f(x):= x^2 + 2*x;
>                                          2
> (%o11)                         f(x) := x  + 2 x
> 
> In the second case the ':=' appears, while in the first case it
> doesn't.
> 
> What exactly are the differences?
> 
> 
> TIA,
>   -sen
> 
> On Tue, 12 Jun 2007, Robert Dodier wrote:
> 
> > On 6/11/07, sen1 at math.msu.edu <sen1 at math.msu.edu> wrote:
> >
> >> (%o4) f(x) := (0.3 x - 0.02) charfun2(x, minf, 0.2)
> >>   + (1.9 x - .8999999999999999) charfun2(x, 0.9, inf)
> >>   + (1.7 x - .7199999999999995) charfun2(x, 0.8, 0.9)
> >>   + (1.5 x - .5600000000000003) charfun2(x, .7000000000000001, 0.8)
> >>   + (1.3 x - .4200000000000002) charfun2(x, .6000000000000001,
> >> .7000000000000001) + (1.1 x - 0.3) charfun2(x, 0.5, 
> .6000000000000001)
> >>   + (.8999999999999998 x - .1999999999999999) charfun2(x, 0.4, 0.5)
> >>   + (.7000000000000002 x - .1200000000000001) charfun2(x, 0.3, 0.4)
> >>   + (0.5 x - 0.06) charfun2(x, 0.2, 0.3)
> >> (%i5) f(2);
> >> (%o5)                                 2.9
> >> (%i6) plot2d('(f(x)),[x,0,1]);
> >> 
> >> Why does one need the apostrophe and the parentheses in 
> the expression
> >> in (%i6), and what does it mean?
> >
> > In Maxima 5.11 and earlier, a Boolean expression could only
> > evaluate to true or false, otherwise it would trigger an error.
> > e.g. when x is not yet assigned a value, if x > 0 then foo else bar
> > triggered an error.
> >
> > The quote mark around f(x) is probably intended to prevent 
> that error.
> > It doesn't appear to be needed in Maxima 5.12.0.
> >> From what I can tell, plot2d(f(x), ...) works OK.
> > (So does plot2d(f, ...), which also works in some, maybe all,
> > pre-5.12 versions.)
> >
> > I guess the documentation can be updated to cut out the quote mark.
> >
> > HTH
> > Robert
> >
> 
> -- 
>   
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> sen1 at math.msu.edu           |
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