using an app command in cas. (area)

[Angus]

hello,

recently there was some confusion about how to use and move data between different modes of the calculator. I, too, have still problems with that topic. I don't got trained on the prime at school nor do I use it on a daily basis, though. Maybe that is part of the problem.

What I was trying to to:

define a funtion inside the function app, say F1(X)=X^2-1.

switching to cas I can do something like F1' or diff(F1) which is what F1' is translated to. However say I need the area under the curve.
area(F1,0,1) gives 0 area(F1(x),0,1) gives 0 area(F1(X),0,1) gives 0.
AREA(F1,0,1) gives a result -0.66666(..)

There are some questions coming up from that. I understand that the area command has to be capitalized. How come that an "undefined" command area() gives a numerical result? e.g. foo(F1,0,1) does not behave like that - gives foo(X->(sq(X)-1),0,1). That makes sense to me since foo() cannot be resolved....

In the help screen it is said that AREA() "Finds the area under the function Fn or below Fn....." Where the Example is: AREA(-X,X^2,-2,1). My question is: As far as I think I understood functions and expressions I would call Fn and Fm an expression. Not a function. But AREA does also work with F1(X).

Maybe someone can explain the points and clear things up a bit more.

What do you people at HP think about data handling in general and the typing related issues (AREA is a pain to type in cas!). Do you see the problems many users have with understanding the interaction of parts inside the calculator and do you see some annoyance of different typings of variables, arguments and function names? Would you improve something if the managment let you?

[parisse]

area (lowercase) is a CAS command used for geometry, it handles geometric objects (area(circle(0,1)) or area(1,2,i) for a polygon with vertices of affixes 1, 2 and i). It will also returns the area under a curve if you provide the following arguments: expression, variable=lower..upper like area(sin(x),x=1..2).
In your example, your arguments are interpreted as affixes of 3 vertices of a triangle, all on the x axis, therefore the polygon has area 0.

[Angus]

Thank you! Is there a larger group of commands missing in the cataloge?

One more thing: area (lowercase) seems to require a functional notation of F1 if used in the original example. area(F1(x), x=0..1) works nicely. area(F1, x=0..1) and area(F1,X=0..1) fail. Is there a rule or explanation on when I have to type F1(x) and when F1 is sufficiant? In the example they show AREA(x^2-1,0,1) where the formula is clearly an expression and no function.... :-(

I can imagine that the area command, when called like area(F1(x),x=0..1) inserts 'x' into the function and therefore is valid under cas. Uppercase single 'X' is treated numerically (its home-value) which is why they are always forbidden under cas (if not used for a numerical value)? Well, is there any benefit from splitting the nomenclature but on the other hand blur their difference? I can type in F1(foo) and get foo^2-1. Which I am pleased with, but in the Function app F1 was defined as F1(X); so I am surprised that the capital X can be treated symbolically after all and replace X with foo.....

edit: I think I see the flaw in my thoughts... ANY function can insert anything as its argument, but if the inserted argument is a capitalized single letter variable like 'X' is has to be treated as a numerical value? ;-) Then only the question remains, why the apps use X wich seems to make things more complicated when it comes to cas interaction?

[parisse]

In the CAS, there is a strict distinction between a function and an expression. For example if you do f(x):=sin(x^2), f is a function (it maps x to sin(x^2)) whereas f(x) is an expression. HOME does not really distinguish between function and expression, and in addition HOME variables like X are assigned (but if you enter F1(X)=SIN(X^2) in the Function App, X is not replaced by the value). This probably make things a little easier for the user if you are doing something standard (in the Apps), but if you want to do something more elaborate, you must understand the distinction.